Astronomy

Can a star fall in a super massive black hole without getting destroyed?

Can a star fall in a super massive black hole without getting destroyed?


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This is the first of many similar questions I have to build up to a specific question or scenario that I want to explore and find an answer to.


Yes, it is easily possible, but it depends critically on how massive the black hole is. A simple calculation will suffice.

If we take a Newtonian approximation for the tidal acceleration across a star of radius $R_*$ as it reaches the event horizon $$ a_{ m tidal} sim 2frac{GM_{ m BH}R_*}{r_s^3} ,$$ where $r_s = 2GM_{ m BH}/c^2$ is the Schwarzschild radius.

The gravitational acceleration at the surface of the star, due to its own mass is just $$a_* = frac{GM_*}{R_*^2} .$$

If we take the ratio of the two, we can assume the star will survive being ripped up before it crosses the event horizon if this ratio is less than $sim 1$. i.e. when $$frac{a_{ m tidal}}{a_*}= frac{c^6 R_*^3}{4G^3 M_{ m BH}^2 M_*} <1$$

The tidal acceleration reduces markedly for high mass black holes. We can rearrange this inequality to give us the minimum black hole mass for survival: $$ M_{ m BH} > left(frac{c^6 R_*^3}{4G^3 M_*} ight)^{0.5} = 1.5 imes 10^{8} left(frac{M_*}{M_{odot}} ight)^{-1/2} left(frac{R_*}{R_{odot}} ight)^{3/2} M_{odot}$$

To first order, this is almost independent of the type of star swallowed. It depends on the inverse square root of the average stellar density, which doesn't vary a lot.

This means that a star could fall into a black hole like that in M87 ($M_{ m BH}simeq 6 imes 10^9 M_{odot}$), but would not survive to the event horizon of Sgr A* ($M_{ m BH}simeq 4 imes 10^6 M_{odot}$).

I think in practice this calculation can only be accurate to factors of a few. I have not taken into account shearing forces that would be present for a rotating black hole, or the compression due to tangential tidal forces, or any heating effects from hot gas near the black hole, or interaction with an accretion disk. A full hydrodynamic simulation is needed (and perhaps has been done?).

Also note, this calculation is just for getting past the event horizon. The tidal forces grow as $r^{-3}$, so any normal star will be ripped up shortly after this, even for the most massive black holes we know of.

Please note: This answer is written from the point of view of the falling star. A distant observer will not see the star (or anything else) cross the event horizon.


This is a great question! Simply put, we do not know. However, I would say that the star in question would likely be pulled apart therefore leaving the star structure destroyed but the energy of the star still intact. Imagine a mirror being shattered! The pieces (energy) of that mirror (STAR) are still existent, however the mirror is shattered (destroyed). I hope this makes sense? The energy of the star would likely continue to exist, but the formation of the star would likely be altered.


Thread: Would the EH form first in the center of a star?

From my understanding an EH would first form in the center of a star and actually grow outward to include the rest of star.

As a star collapses at some point the EH is created. It would be created when at some point of the star the gravitational potential energy is great enough so that the EH would be created.
This would first happen at the core as it is the place that has the lowest potential.

Can someone please correct this if it is wrong.

This was a statement that I made on a thread . which was based on another thread where grant described this in detail.

but now there seems to be debate about it again.

Where this is wrong is that you arent even close to using the correct science to figure out how things work in the middle of a type 2 supernova.

A core collapse involves two phase transitions (from electron degenerate to neutron degenerate to collapse), an emission of a rather immense amount of energy, and an extremely turbulent extremely hot environment. The initial event horizon is probably a very chaotic shape based on where matter locally has sufficient density to create one, and then there is an emission of gravitational energy to round it out, all of this taking a very short time, while in the middle of an extremely large exploding star.

The gravitational potential at any point in the core is only one of many factors that goes into the formation of a black hole. Figuring out to any real accuracy what is happening is not really possible right now.

From my understanding an EH would first form in the center of a star and actually grow outward to include the rest of star.

As a star collapses at some point the EH is created. It would be created when at some point of the star the gravitational potential energy is great enough so that the EH would be created.
This would first happen at the core as it is the place that has the lowest potential.

Can someone please correct this if it is wrong.

This was a statement that I made on a thread . which was based on another thread where grant described this in detail.

but now there seems to be debate about it again.

It does form at the center and expands outwards. At least under the assumptions of null pressure, a starting homogeneous mass density and an isotropic collapse.
Solutions that go beyond those assumptions are not generally agreed upon, and are under active research (you'd get naked singularities and other issues).

ETA: this is however not due to the gravitational potential being minimal.

It does form at the center and expands outwards. At least under the assumptions of null pressure, a starting homogeneous mass density and an isotropic collapse.
Solutions that go beyond those assumptions are not generally agreed upon, and are under active research (you'd get naked singularities and other issues).

ETA: this is however not due to the gravitational potential being minimal.

The pressure in a neutron star. is that homogeneous? Its as tightly packed as possible . drop more mass onto the neutron star and the mass density of the core doesn't increase until the neutron degeneracy pressure is over come. just working this out in my head. Isn't the gravitational potential the greatest at or near the surface of the neutron star? I REALLY need to crunch some numbers on this because I don't think the answer is very intuitive. Do you have any links or references that talks about the collapse of an object uniform mass density?

My big issue is that the EH can't form at r = 0 because before the density = ∞ at r = 0 there would be a m/(4/3πrsh 3 ) > .
Am I getting the maths wrong?

Probably correct . but lets just take a simple collapse for a second where there is nothing stopping all of the mass of a star from fully collapsing ( lets forget about all of the things that would stop it for a second ).

During the collapse there would be a point where the gravitational potential energy would be sufficient for an EH to form, since the gravitationa potential energy is greatest at the center, the center would be the first place the EH would appear. It would then very quickly grow otwards as additional mass collapsed towards it.

Energy is a scalar quantity.

Where this is wrong is that you arent even close to using the correct science to figure out how things work in the middle of a type 2 supernova.

A core collapse involves two phase transitions (from electron degenerate to neutron degenerate to collapse), an emission of a rather immense amount of energy, and an extremely turbulent extremely hot environment. The initial event horizon is probably a very chaotic shape based on where matter locally has sufficient density to create one, and then there is an emission of gravitational energy to round it out, all of this taking a very short time, while in the middle of an extremely large exploding star.

The gravitational potential at any point in the core is only one of many factors that goes into the formation of a black hole. Figuring out to any real accuracy what is happening is not really possible right now.

One point to remember is that adding additional mass anywhere will increase the gravitational potential energy at the core. This is partly why the EH extends and grows outwards.

my question was how can a star collapse when time stops once the EH has formed. After a long q & a lesson from grant, thanks grant, he pointed out that although nothing more can fall past the EH . as matter gets close to the EH there is an increase in gravitational potential energy and the EH will expand.

This is similar to when two black holes get close to each other. at the midpoint between the two bhs there is signifigant gravitational potential energy and each holese EH expands in that area even though no additional matter fell into either of the holes.

I'm replying to your OP without having read any posts after it.
I think I read the thread you link to, but that was a year ago.

From my understanding an EH would first form in the center of a
star and actually grow outward to include the rest of star.

As a star collapses at some point the EH is created. It would be
created when at some point of the star the gravitational potential
energy is great enough so that the EH would be created.
This would first happen at the core as it is the place that has the
lowest potential.

The core of a star is a very big thing. The event horizon will be
only a few kilometers in radius after the core has fully collapsed.

The event horizon definitely forms before the star is entirely within
the final Schwarzschild radius, and it definitely grows as matter
from outer parts of the core fall in. So it must start out smaller
than the final size, and grow to that final size. Its size at formation
is what you want to know.

It can't be *very* small, because that would require a density much
greater than the actual density of the collapsing core at that moment.
Assuming that the density of the collapsing core is pretty uniform,
formation of a tiny black hole (say, a centimeter in radius) would
require the density to be such that the entire mass of the core was
*already* compacted into a volume smaller than the Schwarzschild
radius of the core. So it must start out larger than that. With the
assumption that the density of the core is uniform as it collapses,
it should be easy to calculate the density and mass required for an
event horizon to form.

I'll now read the thread and see if anyone has done so yet.

I just said what Wayne said in his first post.

The way I used it in the other thread was a point where Time stopped for the external observer. The reason that was important to that thread was that if time stopped then how could the rest of the star fall in? It was answered nicely by grant in that other thread.

But in any case that is how I am defining the EH.

(Why do you always type above the quote? It's a little odd. Anyway. )

That page links to gravitational energy, which yes, is related to gravitational potential, but isn't the same. You keep writing gravitational potential energy. That's different. ( http://en.wikipedia.org/wiki/Gravita. tential_energy )

However, I'm not looking for a wiki reference, I want to know what you think it means. Because it seems you are using it differently than others, and until you've explained what you mean by it, it's not clear why you think it's greatest at the centre of the star.

It is the field of energy at a point that is produced from gravity. At any point there is a gravitational effect on the stress energy tensor.

(Why do you always type above the quote? It's a little odd. Anyway. )

That page links to gravitational energy, which yes, is related to gravitational potential, but isn't the same. You keep writing gravitational potential energy. That's different. ( http://en.wikipedia.org/wiki/Gravita. tential_energy )

However, I'm not looking for a wiki reference, I want to know what you think it means. Because it seems you are using it differently than others, and until you've explained what you mean by it, it's not clear why you think it's greatest at the centre of the star.

I put some effort into getting these numbers right, but I won't
be surprised if I've bungled them totally.


When a quantity of matter is packed inside its Schwarzschild
radius, an event horizon forms at that radius. The matter will
continue collapsing without known limit.

If the same quantity of matter is packed with uniform density into
a volume larger than its Schwarzschild radius, it won't have the
required density, so no event horizon forms.

A mass of 6.73 x 10^29 kg has a Schwarzschild radius of 1 km.

When that mass is packed into a sphere of 1 km radius, an event
horizon forms at the surface and we have a black hole.

If that mass is packed with uniform density into a volume with
a radius larger than 1 km, it won't have the required density
to form an event horizon.

A mass of 6.73 x 10^24 kg has a Schwarzschild radius of 1 cm.

When that mass is packed into a sphere of 1 cm radius, an event
horizon forms at the surface and we have a black hole.

If that mass is packed with uniform density into a volume with
a radius larger than 1 cm, it won't have the required density
to form an event horizon.

6.73 x 10^29 kg in a volume of 1 km radius has a density of
1.61 x 10^20 kg/m^3.

6.73 x 10^24 kg in a volume of 1 cm radius has a density of
1.61 x 10^29 kg/m^3.

The collapsing core of a star should have roughly uniform density.
As it collapses, the density should increase uniformly throughout.
For simplicity, I'll further assume that matter outside the core
doesn't contribute to the collapse.

The collapsing core of a large star would reach a density of
1.61 x 10^20 kg/m^3 before it would reach a density of
1.61 x 10^29 kg/m^3. So an event horizon 1 km in radius would
form before an event horizon 1 cm in radius could form. The
collapsing core would never have an event horizon less than
1 km in radius.

You're using the equations for a static solution of a black hole to the dynamic situation of the formation of that black hole, thereby getting an incorrect result.
Things turn out to be a lot more difficult than that. An isotropic collapse from a homogeneous density with null pressure will form the event horizon at the center, which will then expand outwards. Using more realistic assumptions gets into a whole range of issues. For example using an initial density gradient that increases towards the center will in some cases not develop an event horizon in the first place, getting you a naked singularity.

See the spacetime diagram i linked to in the other thread, here.

Exactly what do you mean by "the center"?

How big do you think it is when it forms?

I put some effort into getting these numbers right, but I won't
be surprised if I've bungled them totally.


When a quanty of matter is packed inside its Schwarzschild radius,
an event horizon forms at that radius. The matter will continue
collapsing without known limit.

If the same quantity of matter is packed with uniform density into
a volume larger than its Schwarzschild radius, it won't have the
required density, so no event horizon forms.

A mass of 6.73 x 10^29 kg has a Schwarzschild radius of 1 km.

When that mass is packed into a sphere of 1 km radius, an event
horizon forms at the surface and we have a black hole.

If that mass is packed with uniform density into a volume with
a radius larger than 1 km, it won't have the required density
to form an event horizon.

A mass of 6.73 x 10^24 kg has a Schwarzschild radius of 1 cm.

When that mass is packed into a sphere of 1 cm radius, an event
horizon forms at the surface and we have a black hole.

If that mass is packed with uniform density into a volume with
a radius larger than 1 cm, it won't have the required density
to form an event horizon.

6.73 x 10^29 kg in a volume of 1 km radius has a density of
1.61 x 10^20 kg/m^3.

6.73 x 10^24 kg in a volume of 1 cm radius has a density of
1.61 x 10^29 kg/m^3.

The collapsing core of a star should have roughly uniform density.
As it collapses, the density should increase uniformly throughout.
For simplicity, I'll further assume that matter outside the core
doesn't contribute to the collapse.

The collapsing core of a large star would reach a density of
1.61 x 10^20 kg/m^3 before it would reach a density of
1.61 x 10^29 kg/m^3. So an event horizon 1 km in radius would
form before an event horizon 1 cm in radius could form. The
collapsing core would never have an event horizon less than
1 km in radius.

You're using the equations for a static solution of a black hole to the dynamic situation of the formation of that black hole, thereby getting an incorrect result.
Things turn out to be a lot more difficult than that. An isotropic collapse from a homogeneous density with null pressure will form the event horizon at the center, which will then expand outwards. Using more realistic assumptions gets into a whole range of issues. For example using an initial density gradient that increases towards the center will in some cases not develop an event horizon in the first place, getting you a naked singularity.

See the spacetime diagram i linked to in the other thread, here.

What that looks like to me is a description of the apparent horizon which is different then an absolute horizon. I've not read through the paper yet.

I think Jeff and I are just pointing out that before you'd get infinite density at the centre of a collapsing star you'd get the critical density at a Schwarzschild radius > 0

I sort of get it but not quite . I may need to read through this 4 or 5 times before it makes sense . so stick with me . I will eventually get it.

The problem I am having right now is that say you have a dense core . but not quite dense enough for an EH . but then around it there is a collapse so that outside of the core you have more mass closer to the core. All of that mass that is close to the core should also contribute gravitational energy to points within the core.

For example lets take a real EH for example . when a mass comes close to the EH the EH actually will expand outwards towards that mass because the mass is adding gravitational energy to portions of space that are already very warped ( the area just outside the EH ). As that mass comes close the sum of the gravitational energies from the BH AND the mass will warp the BHs EH until the mass is consumed . then the EH will just be larger to because of the extra mass consumed.

Another example is the midpoint between two black holes. If you bring two black hole close to each other the midpoint between them will eventually form a EH at a distance I believe of 1.5 x EH outside of each of the BHs EH. This is because the between the BH has gravitational energy from both black holes ( even though the force could be 0 because they are pulling in opposite directions )

going back to the core. You have the core . PLUS you have the gravitational energy of anything around the core. Once the gravitational energy is high enough an EH will form. Supposing that the gravitational energy doesnt jump from below what is needed for an EH to something for a large EH . a small event horizon would need to form somewhere . that place would be at the center.

I put some effort into getting these numbers right, but I won't
be surprised if I've bungled them totally.


When a quantity of matter is packed inside its Schwarzschild
radius, an event horizon forms at that radius. The matter will
continue collapsing without known limit.

If the same quantity of matter is packed with uniform density into
a volume larger than its Schwarzschild radius, it won't have the
required density, so no event horizon forms.

A mass of 6.73 x 10^29 kg has a Schwarzschild radius of 1 km.

When that mass is packed into a sphere of 1 km radius, an event
horizon forms at the surface and we have a black hole.

If that mass is packed with uniform density into a volume with
a radius larger than 1 km, it won't have the required density
to form an event horizon.

A mass of 6.73 x 10^24 kg has a Schwarzschild radius of 1 cm.

When that mass is packed into a sphere of 1 cm radius, an event
horizon forms at the surface and we have a black hole.

If that mass is packed with uniform density into a volume with
a radius larger than 1 cm, it won't have the required density
to form an event horizon.

6.73 x 10^29 kg in a volume of 1 km radius has a density of
1.61 x 10^20 kg/m^3.

6.73 x 10^24 kg in a volume of 1 cm radius has a density of
1.61 x 10^29 kg/m^3.

The collapsing core of a star should have roughly uniform density.
As it collapses, the density should increase uniformly throughout.
For simplicity, I'll further assume that matter outside the core
doesn't contribute to the collapse.

The collapsing core of a large star would reach a density of
1.61 x 10^20 kg/m^3 before it would reach a density of
1.61 x 10^29 kg/m^3. So an event horizon 1 km in radius would
form before an event horizon 1 cm in radius could form. The
collapsing core would never have an event horizon less than
1 km in radius.


Can a star fall in a super massive black hole without getting destroyed? - Astronomy

IX. Black Holes In Theory: Into the Abyss

Black holes have become a cultural icon. Although few people understand the physical and mathematical innards of black holes that Einstein’s equations reveal, nearly everyone understands the symbolism of black holes as yawning maws that swallow everything and let nothing out. Can there be any compelling reason to understand more deeply a trivialized cultural metaphor? The answer, for anyone interested in the nature of the world around us, is an emphatic yes! Black holes represent far more than a simple metaphor for loss and despair. Although black holes may form from stars, they are not stars. They are objects of pure space and time that have transcended their stellar birthright. The first glimmers of the possibility of black holes arose in the 18th century. Two hundred years later, they are still on the forefront of science. In the domain of astronomy, there is virtual certainty that astronomers have detected black holes, that they are a reality in our Universe. In the domain of physics, black holes are on the vanguard of intellectual thought. They play a unique and central role in the quest to develop a "theory of everything," a deeper comprehension of the essence of space and time, an understanding of the origin and fate of our Universe.

There is a certain inevitability to black holes in a gravitating Universe. Einstein's theory says that for sufficiently compressed matter, gravity will overwhelm all other forces. The reason lies in the fundamental equation, E = mc 2 . Since mass and energy are interchangeable, one of the implications of this equation is that energy has weight. The very energy that is expended to provide the pressure to support a star against gravity increases the pull of the gravitational field. The more you resist gravity, the more you add to its strength. The result is that if an object is compressed enough, gravity becomes overwhelming. Any force that tries to resist just makes the pull all the greater. When gravity exceeds all other forces, the object will collapse to form a black hole.

The first people to contemplate the notion that gravity could become an overwhelming influence were John Mitchell, a British physicist, and the Marquis de Laplace, a French mathematician. Mitchell in 1783 and Laplace in 1796 based their arguments on Newton’s theory of gravity. They used the concept of an escape velocity . The notion is that to escape from the surface of a gravitating object, a sufficiently large velocity must be imposed to overcome the pull of gravity and "escape" into space. If the velocity is too small, the launch will fail. If it is just right, a launched vehicle will just coast to a halt as it gets far away from the gravitating object. With more velocity, a launched vehicle will still have a head of steam as it breaks free of gravity and it will continue to speed away. That is the whole idea behind tying two big, solid-fueled boosters and an external liquid fuel tank to the space shuttle when it goes up from Cape Canaveral. The shuttle must achieve escape velocity, or near it, to get into orbit and that means lifting off the launch pad really fast!

Mitchell and LaPlace used this idea of an escape velocity to argue that an object could be so compact that the escape velocity from the surface would exceed the speed of light. By some coincidence, an algebraic formulation of this escape velocity condition in the context of Newton’s theory of gravity gives the correct result for the "size" of a black hole using the correct theory of gravity, general relativity. Mitchell did not, apparently, coin a zippy short hand name for his intellectual creation. Laplace called his hypothetical compressed entities corps obscurs , or "hidden bodies." (The modern French equivalent is astres occlus , or "closed stars." The literal translation, trous noirs , has also gained acceptance after some initial resistance due to its suggestion of double entendre.)

POSSIBLE FIGURE: illustrate escape velocity

With some hindsight, we can see that Newton’s theory of gravity was flawed. This theory predicted that if two masses got infinitesimally close together the force would go to infinity. A general lesson of physics is that when infinities arise, there is a problem with the mathematical formulation that reflects some omission in the physics. Another problem with Newton’s law of gravity is that while it gave a prescription for how the strength of gravity scaled with the mass of a gravitating object (to the first power) and the distance between objects (inversely as the square of the distance) it did not say how gravity varied in time. Consider two orbiting stars. A literal use of Newton’s law of gravity says that as one star moves, the other instantaneously responds to the fact that the motion has occurred. Thus according to Newton’s law of gravity, the effect of gravity propagates infinitely fast. This second troublesome infinity violates the idea that nothing can move faster than the speed of light. Finally, and perhaps most compelling from a strictly practical point of view, is that Newton’s gravity did not work. Newton’s law of gravity is spectacularly successful in most normal circumstances, when distances are large and speeds are slow. Astronomers still use it to great affect to predict the orbits of most stars. Rocket scientists use it to plot the paths of space craft even as they do complex orbits that carry them around planets, getting a boost from the interaction. The Galileo spacecraft went through a remarkable series of bank shots around the inner planets, picking up speed in the various encounters with Venus and Earth, before being flung to Jupiter. The recently-launched Cassini spacecraft completed the first stage of its voyage to Saturn by first looping inward to circle Venus. Cassini received a kick from the orbital motion of Venus that gave it the momentum to sail out to Saturn. The success of gravitational multiple-bank shots shows that Newton’ s gravity works very well in this regime. For very fine measurements, however, Newton gives the wrong answer! The predictions of Newton do not agree with observation, with the way Nature works. Classic examples are the rate of rotation of the perihelion of Mercury and the deflection of light by the Sun. In contrast, Einstein’s theory of gravity has passed every test of observation. A modern example is the use of global positioning systems in boating, camping, and driving as well as military and industrial uses. This system works by timing the signals from an array of orbiting satellites. It is based on the mathematics of the curved space and warped time of Einstein, not the simple law of gravitation of Newton. If the silicon chips in the GPS detectors knew only about Newton, boaters in the fog and soldiers in the field would get lost!

As we shall see, giving up Newton for Einstein does not represent merely swapping one set of mathematics for another. Rather, Einstein brought with him a revolution in the fundamental concept underlying gravity. Newton crafted his mathematics in the language of a force of gravity as the underlying concept. Physicists and astronomers still use the notion of a gravitational force in casual terms, even though it has become outmoded in a fundamental way. Einstein’s view was radically different. For Einstein, there is no force of gravity. Instead, Einstein’s theory represents gravity as a manifestation of curved space. A gravitating object curves the space around it. A second object then responds by moving as straight as it can in that curved space. The curved space results in deflections of motion that are manifested as gravity even though the object is in free fall, sensing no force whatsoever. Much of this chapter will be devoted to exploring this conception of gravity.

The progress of our understanding of gravity is not over, however. We have come to understand that, while it has passed every experimental test, Einstein’s theory has flaws. It has its own nasty infinities that represent some omission in the physics. Ironically the hints of a new, better theory are again cast in the language of force, but not the force of Newton. In notions being developed today, the force is quantum in nature and may play on a field of ten or eleven dimensions, not the three of space and one of time that sufficed for both Newton and Einstein. We will begin with an exploration of black holes as portrayed in Einstein’s theory and see how deeper issues arise. Some of those issues will be explored in Chapter 12

As described by general relativity, a black hole is a region of space-time bordered by a one-way membrane called an event horizon , as shown schematically in Figure 9.1. Matter or light can pass inward through the event horizon, but nothing that travels at or less than the speed of light, even light itself, can get back out. The term event horizon comes from the notion that if an "event," like a firecracker exploding, occurs just outside the event horizon, the light can reach an observer, and the fact that the event occurred can be registered. If the firecracker goes off just inside the event horizon, however, no information that the event occurred can reach the observer. The event takes place beyond a horizon so that it cannot be seen. Once inside the event horizon, escape is impossible without traveling faster than the velocity of light. The location of the event horizon is thus intimately related to the fact that the speed of light is a speed limit for all normal stuff. The simple argument of Mitchell and Laplace concerning the formation of a corps obscur relates to the size of the event horizon. The size of the event horizon scales with the mass of the black hole. For a black hole with 10 times the mass of the Sun, it would have a radius of 30 kilometers, about 40 miles in diameter. The nature of the event horizon in the context of curved space and time will be explored in more depth below (Section 5).

FIGURE 9.1: The simplest, non-rotating, black hole has two basic elements, the event horizon interior to which nothing can escape, and the singularity, where everything, including space and time, are crushed out of existence.

When Newton was pondering the means by which apples bonked him on the head, and more particularly, how the Earth kept the Moon trapped in orbit, he intuited an important aspect of gravity. He realized that the gravity of the Earth must act from the center of the Earth, not, for instance, from its surface. This was not a trivial conclusion, and he needed to prove that it was true. Newton knocked off his gravity studies for a while and invented the mathematics of calculus in order to prove his conjecture. With his new mathematical tools, Newton was able to prove that although the mass of the Earth is distributed throughout its volume, each little piece of the Earth acts in concert as if it were in the center. The result is that for any object beyond the Earth’s surface, the gravitational attraction of the Earth will act as if all the mass of the Earth were concentrated at a point in the center. This is true for any spherical gravitating body. The gravitational attraction depends only on the distance from the center of the body, not on the radius or volume of that body. Armed with this mathematically proven conclusion, Newton went on to formulate his theory of gravity with a mathematical expression that said that the force of gravity between two spherical objects depended only on the masses of the two objects and on the inverse square of the distance between their centers.

As an example to make this property concrete, imagine that the Sun were suddenly compacted to become a neutron star of the same mass. It would get cold and dark on the Earth, but the Earth would continue in exactly the same orbit, because the gravitational pull it feels from the Sun depends only on the mass of the Sun, not on how big it is. Another implication is that we are in no danger of falling into a black hole. All the black holes we know or suspect are far away. The gravity would be frightful if we were to get near their centers, but at a large distance from their centers, the gravity gets weak as it does at a large distance from any object and vanishingly small if the distance is very large. In this context, there is one interesting difference between normal stars of any kind -- suns, white dwarfs, or neutron stars -- and black holes. The former act as if all their mass were concentrated at a point in the center. For black holes, this is literally true.

Inside the event horizon all mass that falls into a black hole is trapped. Even though there is no material surface at the event horizon, the matter within the black hole still signifies its presence by exerting a gravitational pull. The gravitational acceleration exists outside the event horizon and causes the formation of the event horizon itself. Although the black hole still exerts a gravitational pull, the matter itself is crushed out of all recognizable existence. General relativity predicts that the matter compacts into a region of zero volume and infinite density at the center of the black hole. Even more profound, space and time cease to exist at this point. Such a region is called a singularity , and is illustrated schematically as a point in Figure 9.1. For a black hole, all the mass that creates the gravity is literally at this point in the center, at the singularity.

The infinities associated with the singularity are clues that Einstein’s theory is not a complete theory of gravity, despite its great success. We know in principle what is lacking. Einstein’s theory does not contain any aspects of the quantum theory. The uncertainty principle of the quantum theory tells us that it is not possible to specify the position of anything exactly, including the position of an infinitely small singularity. The notion of a singularity as it arises in Einstein’s theory is thus an intrinsic violation of the quantum theory. With a theory of gravity that properly incorporated quantum effects, which general relativity does not, the singularity would probably be altered to be a region of exceedingly small volume and immense, but not infinite, density. It is the nature of that exceedingly small volume, the singularity that forms inside a black hole, the singularity from which our Universe was born, that is the heart of the quest for a new, deeper understanding of physics.

4. Being a Treatise on the General Nature of Death Within a Black Hole

The manner in which a black hole crushes matter out of existence, save for its gravitational field, is rather graphic. Consider something falling into a black hole, say a human body – feet first. In this case, at every instant the feet are going to be closer to the center of the black hole than is the head. Gravity is thus going to be stronger at the feet and will pull the feet away from the head. The natural forces on an extended body tend to stretch it along the direction toward the center of the gravitation. At the same time all parts of the body are trying to fall toward the center. The left shoulder is trying to fall toward the center. The right shoulder is trying to fall toward the center. As the body gets closer to the center, the distance between separate paths directed at the center gets ever smaller. The shoulders get shoved together, and whatever is in between must suffer the consequences. A body falling into a black hole will be stretched feet from head and crushed side to side. This is known jocularly as the "noodle effect." Anything falling into a black hole will be noodleized, as shown in Figure 9.2.

FIGURE 9.2: Any material body falling into a black hole will have its top pulled from its bottom and its sides crushed together in a tidal "noodleizing" effect.

The technical name for this simultaneous radial stretching and lateral crushing is the tidal force . It is precisely the same effect as causes the tides on the Earth. Here the Moon pulls on the Earth and its oceans, pulling them toward the Moon and pushing them in sideways to form the tidal bulges in the oceans, the faintest form of noodle. As a body falls into a black hole, the tidal forces increase drastically. First the body stretches into a noodle and breaks apart. Then the individual cells stretch into noodles and are destroyed. Next gravity overcomes the electrical forces that bind matter into molecules and atoms. Atoms will be wrenched out of molecules and electrons pulled from atoms. As infall proceeds, the rising tidal forces will overcome the nuclear force, stretching out the atomic nuclei and breaking them apart into individual protons and neutrons. In their turn, the protons and neutrons will break up into quarks, and the quarks into whatever comprises them. These building blocks will in turn be subject to super-noodlization until the singularity is reached and matter as we know it ceases to exist. Another way of characterizing the singularity in Einstein’s theory is that the tidal forces become infinite. Physicists are gaining the first hints of what conditions may be in the "singularity" that will prevent that infinity. A discussion of this topic is postponed to the last chapter.

5. Black Holes in Space and Time

5.1 Curved Space and Black Holes

Black holes are in the most fundamental way a beast of curved space. Visualizing this curvature that occupies all of three dimensions is very difficult for creatures such as us who are limited to a three-dimensional perspective. Even the experts have difficulty picturing the immense complexity of curved space. They have invented tricks to help with the perception. We will describe these tricks because they help, but even they represent only a shadow, and a fairly complicated one, of the truth.

The notion of curved space raises a general question. How do we characterize it? A line inscribed in a wavy two-dimensional space may be straight in some sense from our three-dimensional perspective, but not truly straight at all. Likewise, a properly "straight" line in a curved two-dimensional space may look strangely curved from another perspective. The ability to define and construct straight lines in curved space is fundamental to understanding how curved space works.

What do we mean by a straight line in curved space? There is a rigorous way to decide which lines are straight in a given space, a way that is intuitively reasonable as well. To obtain a straight line in a curved space, start with a small portion of the space where it is for all practical purposes flat. Think of any measure you would normally make on the surface of the Earth, ignoring the fact that the Earth is really a closed spherical surface. In this small, nearly flat portion, use two short straight sticks. Lie one stick down. Now extend the second stick so that it partially overlaps the first, so that you know it is pointed in the same direction as the first, but so that it also extends out a way. Now hold down the second stick and slide the first along, keeping it parallel to the second stick until it extends out a way. Continue in this manner, extending each stick in turn a little way in such a manner that you are always assured that each extension goes in precisely the same direction as the last. As you proceed, draw a line using each stick in turn as a straight edge. Never look off at a distance to orient yourself. This technique depends on the fact that you are looking only at the local little patch of very nearly flat space in which you find yourself at any given instant. This method of drawing a straight line is called parallel propagation since each step consists of extending one of the sticks parallel to the other. One can prove mathematically that the line you draw as a result of this tedious operation is the shortest distance between any two points along it. What more could you want from a truly straight line? The operation of parallel propagation is what you approximate every time you sketch a free hand straight line. You do not make two marks on a paper and then try to make the distance between them as short as possible. Rather you start your pencil off in some direction and then, trying to keep your hand steady, continue the line parallel to itself. That is what makes parallel propagation so intuitive. It is what you really do to sketch a straight line.

In a flat space, parallel propagation will give the ordinary straight lines known and loved by tenth grade geometry teachers. Parallel lines constructed in this fashion will never cross. Triangles made of three such lines will have 180 degrees as the sum of their interior angles. This is the geometry of Euclid, the geometry of flat space. In an arbitrarily curved space, watch out! Viewed from above, lines drawn as straight as possible by the method of parallel propagation will appear wackily curved if the surface is curved but parallel propagated lines are as straight as possible, and will be the shortest distance between two points.

A particular trick the mathematicians have developed for picturing curved space is to project a three-dimensional curved space onto two dimensions in a special way, like casting a shadow. One dimension is suppressed, and the resulting two-dimensional figure is displayed as a two-dimensional surface in three-dimensional space. It becomes something we can look over, around, and under from our three-dimensional perspective and get a feel for the real thing. The technical name for the image that results from projecting the two-dimensional representation into ordinary flat, three-dimensional space is called an embedding diagram , because the two-dimensional "shadow" is embedded in the three-dimensional space.

To perform this trick for a black hole, one of the dimensions of rotation is suppressed. The resulting figure looks like a cone, or as if you were to poke your finger into a rubber sheet, as shown in Figure 9.3. The distant, still flat, parts of the sheet are the simple two-dimensional projection of flat, uncurved, three-dimensional space. The cone made with your finger is a technically proper representation of the curved space around a black hole (at least in qualitative shape, the mathematics of Einstein’s theory tells the precise shape of the cone) .

FIGURE 9.3: A schematic representation of the embedding diagram of the curved, two-dimensional space around a black hole. Far from the black hole the space is flat. Near the black hole, the space appears to be a "cone" to a three-dimensional "hyperspace" observer. A two-dimensional scientist falling into the black hole would be stretched toward the singularity, wrapped in the conical space, and crushed in the singularity. Note that in this view, the space corresponding to the two-dimensional black hole is on the cone. The region "within" the cone as perceived by the hyperspace observer is part of the higher, three-dimensional space that is imperceivable and inaccessible to a two-dimensional inhabitant of the two-dimensional space.

Full appreciation of the manner in which this cone represents the curved space of a black hole takes some time and quiet contemplation. One feature of the cone is immediately

apparent and quite important. Consider the construction of a circle on the surface around the cone. This operation must be done in the confines of the two-dimensional surface. To go off this surface into three dimensions is cheating, because that would be like going from the real three dimensions of a black hole into an unphysical honest-to-gosh fourth spatial dimension. To draw a circle, start at the center of the "black hole," at the bottom of the depression of the cone. Draw a line out along the curved surface directly away from the center. This line is a radius line, despite the fact that from our three-dimensional view of the operation it follows the funny curved surface of the cone. Now stop at some point along the surface of the cone and draw a circle, a line connecting all those points that are equally distant from the center.

Now imagine that you measure the length of the radius line and the circumference of the corresponding circle. Do you see that the radius in this curved surface must always be longer than normal? The ratio of the circumference to 2 p times the radius is always less than one. The process of constructing the cone preserves this aspect of the original curved space and the resulting embedding diagram lets it be seen graphically. In this curved space, the distance inward as represented by the radius is somehow stretched and lengthened. If you were to go off to a flat portion of the rubber sheet and do the same operation, start at a point, go out a certain distance along a radius, make a circle, you would get the standard result -- the circumference is 2 p times the radius. That is the test for flat space.

Let us apply this principle to the curved space around a black hole as portrayed by the projected two-dimensional cone, as illustrated in Figure 6.2. Figure 6.2 shows two scientists drawing lines by parallel propagation in the two-dimensional space which they occupy. Both start at some distance out in the "flat" portion. One draws a parallel-propagated line that passes far from the black hole. This line looks "straight" to an imaginary three-dimensional "hyperspace" observer, the perspective we take whenever we look down from our three-dimensional hyperspace onto a two-dimensional embedding diagram. The other scientist draws a parallel-propagated straight line that skirts the deepest portion of the cone (we do not want anyone crushed by the infinite tidal forces!). As this line nears the lowest portion of the cone, think what happens. A small portion of the space surrounding this point is oriented differently than a small portion of the space out in the flat, away from the cone. The line drawn in this location is going around the axis of the cone, responding to the "aroundness" of the surface, despite the fact that it is going as straight as it can in the curved space of the cone. From this part of space, the line must head off in a direction different from the direction along which it originally aimed in flat space. As this line continues, it will eventually emerge into flat space once more, but in a different direction from the original line segment that started in flat space. This line is also a straight line in the two-dimensional curved space. From the superior three-dimensional position of the "hyperspace observer" the line looks "curved." It is bent toward the center of the cone where the curvature is severe.

Looking from the point of view of the hyperspace observer is useful for perspective, but we must bear in mind that our reality is closer to that of the two-dimensional scientists. We must draw lines, do geometry, and figure out the curvature of space around gravitating objects as three-dimensional people in a three-dimensional space. We do not have the luxury of stepping out into some four-dimensional "hyperspace" and looking back to see how our space curves. We can determine that two initially parallel light rays passing by a star will diverge, just as the two scientists drawing the parallel-propagated lines in Figure 9.4 will determine a real divergence of initially parallel lines. The two-dimensional scientists cannot "see" the conical space around the gravitating object, as it is revealed to the hyperspace observer, but they can deduce its nature by doing careful geometry. They can, for instance, deduce that the radius of a circle in that part of space is long compared to its circumference.

FIGURE 9.4: Two two-dimensional scientists draw parallel-propagated straight lines in their two-dimensional space. The lines begin parallel, but the one that responds to the curvature of the gravitating object will bend toward the center of curvature and emerge in a different direction. Both lines are legitimate straight lines in the two-dimensional space, even though they look curved to a three-dimensional "hyperspace" observer.

We can explore the nature of space around a gravitating object a bit more. Think of an equilateral triangle composed of three "straight" lines surrounding the deepest point of the cone in Figure 9.4. Each line will look like an arc bowed outwards to a three-dimensional hyperspace observer. All observers will agree that the lines will not meet at 60-degree angles, and the sum of the interior angles will be greater than 180 degrees. How about parallel lines? Two lines drawn parallel initially will curve differently as they pass near the cone, and the one closer to the center will be bent more severely. The lines will not be parallel in the flat space to which they emerge. Lines drawn by parallel propagation will be the shortest distance between two points. A line that does not dip down in the cone must travel farther to reach a given point on the far side. Likewise, a line that goes too deeply within the cone will have wasted some motion and will have further to climb out. There is a shortest distance between any two points and the line that is shortest is straight, but there may be more than one straight line between two given points. Think of a line that misses the bottom of the cone narrowly to the left. It will be bent to the right. A line that misses the bottom to the right will be bent to the left. These two lines will cross. From the point of beginning to the point of intersection, there will be two straight lines.

FIGURE 9.5: From the point of view of a hypothetical, three-dimensional, hyperspace observer, the space around the Earth would be a "cone" with the radius of a circle large compared to the corresponding circumference. The Moon moves as straight as it can by parallel propagating in the curved space around the Earth. In this cone-like space, one set of straight lines consists of those that close on themselves around the neck of the cone. This is Einstein’s version of an orbit. The Moon, in turn, causes space to be "cone-like" in its immediate vicinity. This will cause rockets launched from the Earth to be deflected or to orbit even though they, also, are moving as straight as they can in the curved space.

All this is rather abstract, but it applies to Einstein's theory of gravity in general, not just in the vicinity of black holes. Think of the "straight line" that just encircles the neck of the cone and closes on itself, as shown in Figure 9.5. A straight line cannot do that in flat space, but the cone shows that it is not only possible, but demanded of certain straight lines in the curved space. That closed curved straight line in curved space is an orbit! In Einstein’s theory, orbits are not caused by the action of a gravitational force as they are in Newton's theory. For Einstein, the gravitating body causes a curvature in space -- of which our cone is a representation -- and orbiting bodies are moving with no force as straight as they can in that curved space. The Moon is moving as straight as it can in the curved space around the Earth, and the Earth is moving as straight as it can in the curved space around the Sun. For such problems as planetary orbits, both Newton’s theory and Einstein’s give virtually the same numerical results, despite the vastly different concepts on which they are based. That Einstein’s theory explains everything that Newton did in the regime of weak gravity is one of the powers of the theory. In addition, Einstein's theory predicts the nature of black holes that Newton’s is powerless to describe.

Now, perhaps, you are prepared for the mind-bending exercise of attempting to picture the nature of curved space in its three-dimensional glory, with our toy two-dimensional cone as a guide. Figure 9.6 is an attempt to help do that. Draw a radial line out along the cone in the two-dimensional representation. At intervals, draw circles of constant radius, each with its own stretched-out radius. That will give the two-dimensional cone-like surface as perceived by the three-dimensional hyperspace observer. What sort of curved space does the three-dimensional observer see in his own space? That’s us! Imagine, if you can, rotating each of those circles in the two-dimensional space so that the swept-out locus of the rim of the circle is a two-dimensional sphere encompassing a three-dimensional volume. Now you have a set of nested spheres, but the distance from the center to the periphery of each sphere is "stretched out." The distance to the center of each sphere in the empty space around a gravitating object is larger than it would have been in flat space. This is an attempt to represent the curvature of the three-dimensional gravitating space. Neither the three-dimensional observer, nor we, can directly perceive this curvature as a "cone" or anything else. For that, we would have to be a denizen of some fourth-dimensional hyperspace to look "down" on our three-dimensional space. We simply cannot do that. We can do careful three-dimensional geometry in the confines of our own three-dimensional space and work out the nature of the curvature of our space without ever being "outside" of it. If you were to measure the circumference of a given sphere and then measure the distance to the center, you would find that the circumference was in every case less than 2 p times the radius and that the smaller the sphere, the larger would be the discrepancy, just the property preserved in two dimensions and manifes ted in our cone representation. A three-dimensional scientist, cannot, however, perceive where the extra length of the radius "goes." All the scientist can or needs to know is that the radius is long compared to the circumference.

FIGURE 9.6: (top) In the schematic two-dimensional curved space around a gravitating object, one can imagine circles of increasing radius and circumference. The circumference will always be smaller than 2 p times the radius, and the discrepancy will be largest for the innermost circles. Both the two-dimensional resident of the two-dimensional space and the three-dimensional "hyperspace" observer will agree on that general property, but the "hyperspace" observer can "see" the cone-like space and the reason for the large radius is obvious. (bottom) If the nested circles of the top diagram are rotated to map out a series of nested spheres, then one has a crude representation of the space around a three-dimensional gravitating object. Each of the spheres will have a circumference that is less than 2 p times the radius. This is impossible to represent in three-dimensional space (never mind on a flat sheet of paper in this book!). A three-dimensional scientist could determine the curvature by doing careful geometry, but could never "see" the curvature of three dimensions.

The important thing on which to concentrate is that such curvature exists in the space around the Earth, not just near a black hole. If you could draw a huge circle in the space around the Earth and then measure the radius of the circle, you would find that the radius was longer than you would expect if the space were flat. If you were to construct a triangle in the space around Earth consisting of three segments that are the shortest distances between the vertices, you would find that the angles added up to more than 180 degrees. All gravitating bodies curve the space around them! A black hole is only the most extreme example.

With this newfound perspective, let us return to the nature of black holes. Picture again a flat flexible sheet as a two-dimensional representation of flat, empty three-dimensional space. A star would cause a depression in the sheet. The star would be reduced to a two-dimensional spot of finite area (representing volume in the full three dimensions), and the depression representing curved space would extend beyond the star into the surrounding empty space. At no point within the star or beyond its surface is the curvature especially severe.

POSSIBLE FIGURE: illustrate progression from flat space to formation of a black hole and singularity in a one-dimensional representation.

Suppose the star were compacted to become a neutron star. This would be represented by making the spot smaller and the depression in the sheet much deeper. Note that at rather large distances from the neutron star the curvature of the sheet is about the same. Only near the neutron star are the walls of the depression nearly vertical (how one needs that three-dimensional, higher perspective to describe the goings-on!). As in the gravity of Newton, the strength of gravity depends on the distance to the center of the object. At the same relatively large distance, the gravity is the same. A neutron star has greater gravity than a normal star, not in the sense that it reaches out further, but in the sense that, because it is smaller in radius, one can approach much closer to the center of the gravitating star. A measure of the stronger gravity of the neutron star is the severity of the curvature of the flexible sheet at the bottom of the deep depression. The sheet changes directions rapidly at the bottom, a measure of the large curvature.

When a black hole forms, all the matter is crushed into the "singularity." The mass of the star is no longer represented by an area, but by a point. The flexible sheet is stretched to extremes. The curvature undergoes a discontinuity at the bottom of the cone. The sheet changes directions by 180 degrees in an infinitesimal length. One can go "around" the neck of the cone in an infinitesimal distance. This is a representation of the infinite tidal forces that accompany a real singularity. Somewhere down inside the depression of the cone, a circle represents the location of the event horizon. To get the full effect you should picture the space as an escalator moving rapidly inward, flowing down toward the singularity. To move outward you have to run up the down escalator. At the event horizon, the escalator moves inward at the speed of light. Since you cannot run faster than the speed of light in the piece of space you occupy, you are dragged down to the singularity once you cross within the event horizon.

The singularity is a region of mystery, where our present laws of physics break down. That does not mean black holes cannot exist. Einstein’s theory is still quite valid at the event horizon, which is the only part of a black hole anyone will ever observe and live to tell about. The British mathematician Roger Penrose has proved what is called the singularity theorem . This theorem says that once an event horizon forms by any means, some singularity must form. The theorem does not prove that all matter must fall into the singularity once a black hole forms but that conclusion seems somehow inevitable.

5.2 Black Holes and the Nature of Time

Black holes cannot really be understood without a discussion of the nature of time in their vicinity. Like curved space, the flow of time is warped near and within a black hole. This makes temporal events difficult to picture in ordinary terms. One of the fundamental problems with a discussion of time in curved space is that everything depends on whose time you are discussing.

When two things are moving apart at a large relative velocity, the great Doppler shift means that all frequencies are observed to be lower. These frequencies include not only the frequency of light, but also the tick of a clock, even the biological clock. Two people rocketing away from each other at great speeds will each see the other aging more slowly than they themselves are. In the case of large gravity, there is a related effect. To an observer who is not in a large gravitational field, a clock that sits deep within the gravitational pull of some compact star will be seen to run more slowly. A person orbiting around the compact star will be seen to age more slowly.

Two effects happen at once for an object deep in a gravitational field. The photons coming out from the object lose energy as they climb out of the gravitational field so that they have lower frequency by the time they are free of the gravitational pull. The climb out of the region of highly curved space and strong gravity requires some time, so that the rate of arrival of the photons at a distant observer is also slow. There is a long gap between the arrival of one photon and the next. Each photon carries information concerning the "age" of the object that emitted it. Since the photons take longer to get out, they arrive when the outside observer has aged considerably. The outside observer detects the photons and sees the object in the gravitational field as younger.

Consider two investigators. One volunteers to fall down a black hole, giving her life for science. The other, the project scientist, volunteers to remain at a safe distance and monitor the proceedings. The first volunteer falls straight down into the black hole and by her own watch and biological clock passes through the event horizon, is noodleized and dies in a few seconds. The project scientist, watching through his telescope, sees the watch of the falling volunteer running ever more slowly, and the volunteer herself aging more slowly. As the falling volunteer approaches the event horizon, time stops flowing from the vantage point of the distant observer, and he never sees the falling volunteer cross the event horizon.

POSSIBLE FIGURE: illustrate the volunteer falling down the hole

The last photon emitted by the volunteer before crossing the event horizon takes a very long time to reach the distant observer. The distant observer can, in principle, always see some photons from the falling person, no matter how long he waits. When those laggard photons finally arrive, the distant observer sees the falling volunteer before she crossed the event horizon.

In practice the photons that arrive at distant times in the future are highly red-shifted. In addition, the time between their individual arrivals is very long. Most of the time the distant observer sees absolutely nothing. Because of the large red shift and the delay between arrival of photons, the actual perception is that anything falling into the black hole turns black very rapidly.

The term "frozen star" was invented to describe the mathematical solution of Einstein’s theory that corresponded to the result of the absolute collapse of a star. This term focused on the fact that a distant observer can never see the surface of the star fall through the event horizon. There is thus a suggestion that the surface of the star somehow lingers at the event horizon to be touched, and probed and explored. The term "black hole" was coined by John A. Wheeler in 1968 at a meeting on pulsars. Wheeler tried to come up with a graphic term to encourage his colleagues to contemplate even more extreme states of gravitational compaction than white dwarfs and neutron stars. The name "black hole" concentrates on the collapse and the fact that the star rapidly turns completely black and on the fact that after collapse ensues, no part of the star can ever be recovered. If you tried to fly down and grab some of this "frozen star," you would find that the surface receded from your grasp as your time became its time and you could see it fall once more.

The term "black hole" is much more pertinent to the real situation because it directs attention to the actual collapse and to the interior of the black hole. The case is difficult to prove, but there is a sense that the term "black hole" itself spurred some of the marvelous work that followed. With this new term and new mode of thinking came complete mathematical solutions of the interior of black holes, where people’s minds can reach even if their bodies cannot.

6. Black Hole Evaporation: Hawking Radiation

As remarked earlier, Einstein’s theory, for all its magnificence and success, is not complete. This theory is a so-called classical theory in that it incorporates none of the principles of the quantum theory. In Einstein’s theory, as in Newton’s, all motion and changes are smooth, and all positions can, in principle, be specified exactly. Einstein’s theory is not compatible with our understanding of microscopic physics as described accurately by the quantum theory.

6.1 Quantum Event Horizons

The first successful attempt to include some of the principles of the quantum theory was done by the brilliant theoretical physicist from the University of Cambridge, Stephen Hawking. The process by which energy is converted into equal parts matter and antimatter is intrinsically a quantum mechanical process. Hawking’s genius was to see how to add a little of the quantum process into the otherwise classical realm of Einstein’s theory. He showed that the gravitational energy associated with the curved space in the vicinity of an event horizon will create particles and anti-particles. In principle, electrons and positrons, or even protons and anti-protons, could be generated. The easiest particle to make, however, is the photon because it has no mass (technically speaking, a photon and an anti-photon are one and the same thing).

According to the quantum theory, no position can be specified exactly. This applies equally well to the position of the event horizon around a black hole. Because of the intrinsic quantum mechanical nature of things, you cannot say definitely whether something is inside or outside the event horizon, only whether something is probably inside or outside the event horizon. The location of the event horizon is then fuzzy. When two photons are created in the vicinity of the event horizon, there is a probability -- purely quantum mechanical in nature -- that one photon will be inside the event horizon and will disappear down toward the singularity, and the other will be outside the event horizon and fly off to great distances where it can be detected. Hawking’s great discovery was that black holes are not truly black. They shine with their own radiance generated from pure gravitational curvature!

POSSIBLE FIGURE: illustrate Hawking radiation

The physical implications of this discovery were immense and caused a wrenching turnabout in our view of black holes. The energy to create the radiation came from the gravitational field, but the gravitational field came from the mass of the matter that had collapsed to make the black hole. When the photons carry off energy, the energy of the black hole must decline. This can only happen if the mass of the black hole declines as well. As black holes emit Hawking radiation, they are shining away their very mass! Black holes are not completely one-way affairs after all. While it is still true that tidal forces will tear an object beyond recognition as it falls into the singularity, the mass is not gone forever. It will emerge later in the form of the Hawking radiation to permeate the Universe. A black hole is just nature’s way of turning all that bothersome matter into pure random radiation. We will see that nature has yet other tricks with the same fate in mind. Gather ye rosebuds while ye may, a photon yet ye'll be!

Hawking discovered that the black hole radiation does not come out in an arbitrary fashion. The spectrum of the radiation corresponds exactly to a single temperature, when it might have been some odd, non-thermal shape. The temperature is determined in turn by the mass of the black hole. The variation with mass is inverse so that a massive black hole has a low temperature, and a low-mass black hole has a higher temperature. For a black hole of stellar mass the temperature is very low. Little radiation could be emitted in a time as short as the age of the Universe, and so the radiation is of little practical importance. Our standard picture of black holes as gaping one-way maws holds true.

If the mass of the black hole should be less than that of an average asteroid, however, the situation is markedly different. Such small black holes would be very hot and would radiate prodigious amounts of radiation. As these small black holes radiate, their mass shrinks so they get hotter and radiate even faster. The process runs away faster and faster. In less than the age of the Universe, such small black holes could evaporate completely! The final stages of this process are so accelerated that the last energy would emerge in an explosion of high energy gamma rays.

These so-called mini-black holes could not be created in the collapse of an ordinary star. They might have arisen in the turbulence that may have marked the original state of the Big Bang. If this were the case, there could be swarms of mini-black holes in the Universe, some of which would be explosively evaporating at any time. The properties of such explosions have been worked out theoretically, and the radiation has been sought, but so far unsuccessfully.

One can imagine (mathematically) the reverse of a black hole, or a "white hole." A white hole is obtained by running time backwards compared to the flow of events for a black hole. For a black hole, one starts with ordinary space. A star collapses to make a black hole and then you have a black hole forever, gobbling up matter, but releasing nothing (forgetting for the moment Hawking radiation). Now run the movie backwards in time. One must start with a white hole that has existed since the beginning of the Universe, spewing forth matter, but swallowing nothing. At some time the "last stuff" pours forth and one is left with empty, flat space.

Black holes are regarded seriously because we can predict that they might well occur in the course of stellar evolution and because we think we have found them, as the next chapter will show. From the properties of known stars, the properties of the resulting black holes can be predicted. White holes are not regarded on the same footing because they must exist since the beginning of time. Their properties cannot be predicted because we cannot predict the beginning of the Universe. White holes could have any property -- large mass or small. Since we cannot predict their properties, white holes have no firm place on the realm of ordinary pragmatic physics.

Hawking’s discoveries may have been a first step toward putting the notion of white holes on a firmer basis. Hawking has blurred the distinction between white holes and black holes by introducing quantum mechanical properties to the event horizon. Now we see that a black hole can emit radiation, a property previously reserved for white holes. Likewise, a white hole should be able to swallow radiation. Hawking has argued that for very small objects the distinction between white holes and black holes may disappear.

7. Fundamental Properties of Black Holes

For all their exotic nature and the complexity of the theory that treats them, black holes can have only three fundamental intrinsic properties. These properties are their mass, their spin or angular momentum, and their electrical charge. These properties are distinguished because they can be measured from outside the black hole, and therefore determined by ordinary techniques. The mass can be determined by putting an object in orbit around the black hole and seeing how fast it moves. The charge can be determined by holding a test charge and detecting the force of attraction or repulsion from the hole. In practice, one expects real black holes to be electrically neutral because they should rapidly attract enough opposite charge from their surroundings to neutralize any charge that might build up. Measurement of the spin of a black hole is a more subtle process. As the black hole rotates, it drags the nearby space around with it. This dragging can be measured in principle, like the currents in the ocean. Once the mass, spin and charge of a black hole are known, all of its other intrinsic properties are set. For instance, for a non-charged, non-spinning black hole, the size given by the radius of the event horizon is strictly proportional to the mass. The temperature of the Hawking radiation varies inversely with the mass. Other properties that a black hole might have, but cannot, are mountains like the Earth or sunspots and flares like a star. On a more fundamental level, black holes cannot have the property of a lepton number or a baryon number. The forces associated with leptons and baryons are short range and cannot extend outside the event horizon where they can be measured. Black holes do not so much violate the "laws" of conservation of lepton and baryon number as transcend them. In the realm of black holes, these fundamental physical laws of ordinary space are irrelevant. John A. Wheeler has coined an aphorism to describe this raw simplicity of black holes -- he says &quo tblack holes have no hair."

To illustrate the power of this notion, consider two compact stars. Let one be made of neutrons, an ordinary neutron star. Let the other be made of anti-neutrons, an anti-neutron star! If these two stars were to collide, the neutrons and anti-neutrons would annihilate to produce pure energy and an explosion of unprecedented proportions. Suppose, however, we dump a few too many neutrons on the first star and it collapses into a black hole. Then we add some anti-neutrons to the second star so that it, too, collapses to make a black hole. Do we now have a black hole and an anti-black hole? No, we have two identical black holes because the black holes transcend the law of baryon (neutron and anti-neutron) number. If the two black holes combine, the result is not an explosion, but one larger black hole. The form of mass that originally collapsed to make a black hole becomes irrelevant once it has passed through the event horizon. Then only the total mass counts. While he was warming up, Stephen Hawking presented to the world the laws by which black holes combine to make larger ones, an exercise that alone would have assured his reputation as a brilliant physicist.

Just because black holes have only three fundamental properties does not mean that their nature, which derives entirely from specifying the values of those three properties, is not complex. Apart from quantum effects, the exterior of a black hole, the event horizon, is a model of simplicity: smooth, perfect, and unperturbed. The insides, however, as exposed by the powerful techniques of mathematics, are a wonder such as to strain one’s credibility to the limits.

When we discussed the oddities of the flow of time near black holes (Section 5.2), we omitted the oddest twist of all. This aspect can never be observed directly, but is the real factor that accounts for the existence of the event horizon that blocks our view. Inside the event horizon, space takes on the aspects of time. No matter how rockets are fired or forces applied, any object must move inward toward the singularity (or outward, if we are dealing with a white hole) as it ages. There is no choice in the matter, just as you have no choice in the matter of your aging from eighteen to thirty-one. The same principle that drags you on into old age drags an object within the event horizon ever closer to the singularity. Within the event horizon space is no longer the entity in which you can move around in three dimensions with impunity. There is only one direction, inward. The one-way nature of this space is intimately related to the one-way nature of time. Inside a black hole space is time-like! The time-like nature of space is the reason that everything goes inward inside a black hole, and nothing can get out. It is the reason black holes are black.

8.2 Schwarzschild Black Holes

The simplest black hole is one with mass, but no charge or spin. This kind is called a

Schwarzschild black hole after the physicist who first gave a mathematical description of such a beast, shortly after Einstein presented his general theory of relativity. There is a poetry to this name that is rendered as "black shield" from the German. This was the type of black hole illustrated schematically in Figure 9.1.

For a Schwarzschild black hole, the event horizon coincides exactly with what is called the surface of infinite red shift . A photon emitted from this surface will have an infinitely long wavelength by the time it escapes to great distances. The event horizon is round for a Schwarzschild black hole and the singularity is a point at the center of the black hole.

Mathematical investigations have shown that even the lowly Schwarzschild black hole is not so simple. In the idealized case where one assumes that all the mass is confined to the singularity and that a vacuum exists everywhere else, a black hole is really twain, two equal geometries sharing the same singularity. Each black hole has its own Universe of empty flat space. These two Universes exist at the same instant but in different places. When moving at less than the speed of light, one cannot travel from one to the other, but will instead fall into the singularity. This idealized mathematical description does not apply to a black hole that has formed from the collapse of a star. Then the matter of the star introduces other changes in the geometry and curvature of space that are, as yet, too complicated for anyone to have been able to calculate. The "other Universe" is undoubtedly just a mathematical fiction, but it gives a portent of the richness to come.

One has only to introduce some rotation to the black hole to complicate affairs in the most interesting fashion. The first basic mathematical solution corresponding to rotating black holes was discovered by the New Zealand physicist Roy Kerr in 1963. Subsequently, the complete solution of the interior of a rotating black hole was worked out, but these black holes are still referred to as Kerr black holes to distinguish them from Schwarzschild black holes.

If a black hole rotates rapidly enough, the event horizon disappears completely. In this case one could look directly into the fearsome maw of the singularity. Such a beast is known as a naked singularity , a singularity unclothed by an event horizon. There is no formal proof as yet, but a strong belief that no black hole can rotate fast enough to create a naked singularity. Certainly any star that rotated so fast would fling itself apart before it could collapse to make a black hole. Firing matter into a black hole tangentially would spin it up. Calculations show, however, that as the black hole nears the limit where the last veil might be dropped, gravitational radiation will become so intense as to carry away any increment in rotational energy. Perhaps there is some way to create a naked singularity, but it seems very difficult. Many researchers have adopted the as yet unproven doctrine that naked singularities cannot exist in the real world of astrophysics. This doctrine that nature denies freedom of expression to unclothed singularities is known informally as "cosmic censorship." Stephen Hawking, a firm believer in cosmic censorship, bet Kip Thorne of Caltech that naked singularities cannot exist. He paid off on the bet when carefully designed computer models yielded naked singularities. No one has yet found one in their back yard.

Real rotating black holes may have matter swarming around inside the event horizon that will substantially alter the geometry of the inner reaches. The best we can do is to follow the mathematician’s description of the idealized case where, once again, the assumption is made that all mass is confined to the singularity, and that all the rest of space is pure vacuum. Welcome to Wonderland, Alice!

The first thing one discovers in the study of rotating black holes is that the singularity is not a point but a ring! One can imagine an intrepid explorer plunging through the center of the ring, avoiding the infinite tidal forces of the singularity itself. Retreating now to the outside, we find that for a rotating black hole the surface of infinite red shift separates from the event horizon. Both surfaces are oblate, flung out around the equator by centrifugal forces, but the surface of infinite red shift is more extended. There is a finite distance between the surface of infinite red shift and the event horizon at the equator. At the poles of the rotation axis the two surfaces are still contiguous.

The surface of infinite red shift has another property. It is also the stationary limit with respect to sideways motion. The rotation of the black hole drags the local space around in the same sense as the hole rotates. The effect is stronger the closer one is to the black hole. At a moderate distance one could fire rockets and overcome the effect in order to hover in one place. This requires some effort like swimming upstream or walking up the down escalator. At the stationary limit, all efforts to remain still are fruitless. To resist moving around in the same sense as the black hole spins, one would have to fly backwards in the local space faster than the speed of light. Inside the stationary limit, all material objects, including photons of light, are forced to rotate with the hole.

On the other hand, because the surface of infinite red shift is removed from the event horizon at the equator, one can, in principle (ignoring the huge tidal forces), fly inside the surface of infinite red shift and return. This can be done by moving with the rotation of the black hole, the path of least resistance. Some paths lead into the event horizon and there will be no return but with a rotating black hole, the option exists to emerge from within the surface of infinite red shift.

The region between the surface of infinite red shift and the event horizon is called the ergosphere . This phrase was coined by Roger Penrose (of the singularity theorem) who investigated its properties. It derives from the Greek word "ergo," meaning work or energy. Penrose found that under proper circumstances energy could be extracted from the black hole. If one of a pair of particles is fired down the hole in a counter-rotating sense from within the ergosphere, the recoil will throw the other particle out with more energy than both particles had originally, including their mass energy, E=mc 2 . You do not get something for nothing. In this case the excess energy in the ejected particle comes from the rotational energy of the black hole. After the particle is ejected, the black hole will be rotating less rapidly.

There is some question as to whether this Penrose process for tapping the energy of a rotating black hole can be of real astrophysical interest. The problem is that a considerable investment of energy must be made in firing the first particle into the event horizon in the proper fashion. A puny nuclear explosion would be far from sufficient the particle must be moving at nearly the speed of light. Such reactions with massive particles may not occur spontaneously in nature with any reasonable probability. On the other hand, photons are already moving at the speed of light. There have been discussions of Penrose processes operating to swallow some photons and eject others at high energy. This process is also driven by the rotational energy of the black hole and is termed superradiance . There is some speculation that the gamma rays seen from quasars could be produced in this way, starting with photons in the more conventional X-ray or ultraviolet range that are produced in the inner edges of the hot accretion disk.

Let us now journey into the event horizon. As we pass within, we come to a region of time-like space in which we must move inward as we age. There is a crucial difference, however, for there is an inner boundary to this time-like region. At this inner boundary is another event horizon, which prevents a return to the space beyond. Within this second event horizon is a region of normal, if highly curved, space. This event horizon prevents a return to the time-like space, rather than preventing a return to normal space.

Within this inner volume of normal space is another surface of infinite red shift, but since one can move in and out of such a surface if appropriate moves are taken, it has no direct consequence. Around the equator of this inner surface of infinite red shift is the line we devoutly wish to avoid. That equatorial line is the location of the ring-shaped singularity. If we stumble against that we are doomed by the infinite tidal forces.

The special property of this inner region of normal space is that we could elect to stay here forever. By careful choice of movement we can orbit around and never strike the singularity itself. This is very different from the case for a non-rotating black hole. There the time-like space leads inexorably to the singularity.

Other options await if we continue our imaginary journey within the spinning black hole. At the same place, but in the future, there is a similar space-time structure. Here, however, the sense of the event horizons and time-like space are reversed. As one flies about, one could in principle elect to head outward, passing through an event horizon into a region of out-going time-like space. This would be bounded by an outer event horizon, and beyond that would be an ergosphere, a surface of infinite red shift, and finally free space. Formally, mathematically, this is not the space from which we entered, but another, separate Universe. The mathematical solution shows that in this new Universe there will be another in-going black hole like the original one we entered, so one can plunge down again and come out in yet a third Universe. The idealized mathematical solution we are exploring has an infinite number of Universes, all connected by rotating black holes!

Let us return to the central regions of the rotating black hole. We found there a more or less spherical region of normal space inside of which lay the ring singularity. Watch carefully now, Alice! The plane of the ring singularity divides the volume into two halves. You can maneuver from the top half, out through the surface of infinite red shift, and back in, to come to the bottom half. Alternatively, you could elect to plunge straight through the hole in the middle of the ring. In so doing, you would come to a bottom half, but not the one accessed by going out and around the ring. If from this new lower half you went out and around, you would be in a top half, but again not the one from which you started. The space through the ring is not the space you get to by going around the ring. If this is not passing through the looking glass, what is? You can imagine looking down through the ring and seeing another creature, perhaps a puce-colored eight-legged cat. If you go out around the singularity and look, you will not see the creature. Its space is only through the ring, not behind it.

If you join the creature through the ring you can seek, in the future, a set of outgoing horizons. These will again lead to an outer, flat Universe, which is none of the ones we have discussed previously. As you leave this black hole, you will feel it pushing you. Unlike the others we have explored, this out-going solution that exists through the ring anti-gravitates!

Having entertained ourselves thus, we must return to more sober reality. We do not diminish the wonder of the tale to point out again that what has just been described is an idealized mathematical solution. It is a marvelous, exact solution to the full set of equations describing general relativity. Nevertheless, a crucial assumption has been made in order to solve the equations at all. The assumption is that there is no mass anywhere except in the singularity. The presence of any matter or energy within the first set of event horizons would cause a change in the curvature and geometry, and the wonderful world of multiple Universes would probably vanish. The solution to the equations with even a little matter present throughout the volume would not contain any of the extra spaces, in the future or through the ring. Even the presence of an explorer such as we imagined ourselves to be could change the whole situation.

Some research has been done to see what happens to the mathematical solution if the tiniest bit of extra matter is added inside the black hole. There is a strong suggestion that the whole geometry would begin to rattle and shake with the resultant generation of an intense flux of gravitational radiation. This radiation alone would alter the physical and mathematical situation, to eliminate the reality of the extra spaces and Universes. At the very least, in the real Universe photons of light will continue to flood down the black hole. As they plummet in, they are blue shifted and attain incredible energies. This energy will build up at the event horizon in what has been termed a blue sheet . This sheet of energy would warp the geometry and wipe out any of the multiply-connected interior geometry.

The mathematical "vacuum" solution to the Kerr black hole is a marvelous, mind-stretching exercise. It probably has nothing to do with the guts of a real star-born black hole, rotating or not. On the other hand, the reality is fantastic enough as we shall see in the next chapter, and the mystery of the singularity remains.


Monster Black Hole Caught Swallowing Unlucky Star

Call it a Cosmic Scene Investigation: For the first time, scientists have identified a stellar victim of a giant black hole — an unlucky star whose death may ultimately provide more clues on the inner workings of the enigmatic gravitational monster that devoured it.

Supermassive black holes are objects millions to billions times the sun's mass that lurk in the hearts of most galaxies. They lay quietly until victims, such as stars, wander close enough to get shredded apart by their extraordinarily powerful gravitational pull.

Scientists first caught a black hole red-handed in a stellar murder last year. Now researchers have determined not only the culprit in a similar cosmic homicide but the casualty as well: a star rich in helium gas.

"This is the first time we've actually been able to pinpoint what kind of star was disrupted," study lead author Suvi Gezari, an astronomer at Johns Hopkins University, told SPACE.com. [Photos: Black Holes of the Universe]

Hungry black holes

Astronomers say supermassive black holes rip apart stars very rarely, maybe just once every 10,000 years per galaxy. To detect one such event, Gezari and her colleagues monitored hundreds of thousands of galaxies in ultraviolet light with the space-based Galaxy Evolution Explorer (GALEX) and in visible light with the Hawaii-based Pan-STARRS telescope.

In June 2010, the researchers spotted a bright flare from the previously dormant black hole at the center of a galaxy approximately 2.7 billion light-years away.

"When the star is ripped apart by the gravitational forces of the black hole, some part of the star's remains falls into the black hole while the rest is ejected at high speeds," Gezari said. "We are seeing the glow from the stellar gas falling into the black hole over time."

The flare of light reached peak brightness a month after it was detected, then slowly faded over the next 12 months. By measuring the rise of the flare's brightness, the scientists calculated the rate at which the star's gas was getting sucked into the black hole. This in turn helped reveal at what point and time the black hole had begun disrupting the star, revealing how powerful its gravitational field was and thus its mass.

The astronomers estimate the black hole's mass to be 3 million suns, comparable to our Milky Way's central black hole.

"These spectacular events provide a glimpse into otherwise unobservable black holes, telling us about their masses," Gezari said. "We know that there are strong connections between black holes and the galaxies they reside in, and it turns out that somehow the mass of the black hole and the mass of a galaxy influence each other, so we want to better know what's going on there. Also, people want to understand the physics of black holes and how they affect the geometry of space-time around them. We need to know its mass to help pinpoint a lot of those details."

Cosmic scene investigation

In addition, Gezari and her colleagues analyzed the spectrum of the ejected gas — that is, the specific colors making up its light — using data from the Multiple Mirror Telescope Observatory on Mount Hopkins in Arizona. Each element has a unique spectral fingerprint, and the spectrum of the gas revealed it was mostly helium.

"It is like we are gathering evidence from a crime scene," Gezari explained.

The fact there was mostly helium and very little hydrogen in the gas suggests "the slaughtered star had to have been the helium-rich core of a stripped star," Gezari said.

Gezari and her team suspect the destroyed star was once enveloped with hydrogen, but this was ripped away by the black hole. [Video: How Astronomers Find Giant Black Holes]

"This likely happened when the star went through the red giant phase, where it expanded to 100 times its original radius," Gezari said. "When it puffed up like that, it became vulnerable to the gravitational tidal forces of the black hole, and it would have been very easy to strip off the tenuous hydrogen envelope.

"However, the star then had to approach much closer, 100 times closer in, before it was completely disrupted by the black hole. We think it approached all the way in to one-third of an astronomical unit, similar to the orbit of Mercury [about one-third the distance between the Earth and sun]. We then saw the helium gas streaming into the black hole."

The scientists detailed their findings online today (May 2) in the journal Nature.

"This is the first time where we have so many pieces of evidence, and now we can put them all together to weigh the perpetrator — the black hole — and determine the identity of the unlucky star that fell victim to it," Gezari said. "These observations also give us clues to what evidence to look for in the future to find this type of event."

The upcoming Large Synoptic Survey Telescope, capable of scanning half the sky every night, should detect far more of this carnage.

"We can measure at what rate stars are being disrupted by black holes as a function of the type of galaxy, measure the masses of the black holes, see what types of stars orbit black holes in the centers of galaxies, and try and better understand the evolution of galaxies over time," Gezari said. "There's a lot more to be done."


2012 Meteor Showers

"Bright X-ray novae are so rare that they're essentially once-a-mission events and this is the first one Swift has seen," said Neil Gehrels, the mission's principal investigator, at NASA's Goddard Space Flight Center in Greenbelt, Md. "This is really something we've been waiting for."

An X-ray nova is a short-lived X-ray source that appears suddenly, reaches its emission peak in a few days and then fades out over a period of months. The outburst arises when a torrent of stored gas suddenly rushes toward one of the most compact objects known, either a neutron star or a black hole.

The rapidly brightening source triggered Swift's Burst Alert Telescope twice on the morning of Sept. 16, and once again the next day.

Named Swift J1745-26 after the coordinates of its sky position, the nova is located a few degrees from the center of our galaxy toward the constellation Sagittarius. While astronomers do not know its precise distance, they think the object resides about 20,000 to 30,000 light-years away in the galaxy's inner region.

Ground-based observatories detected infrared and radio emissions, but thick clouds of obscuring dust have prevented astronomers from catching Swift J1745-26 in visible light.

The nova peaked in hard X-rays -- energies above 10,000 electron volts, or several thousand times that of visible light -- on Sept. 18, when it reached an intensity equivalent to that of the famous Crab Nebula, a supernova remnant that serves as a calibration target for high-energy observatories and is considered one of the brightest sources beyond the solar system at these energies.

Even as it dimmed at higher energies, the nova brightened in the lower-energy, or softer, emissions detected by Swift's X-ray Telescope, a behavior typical of X-ray novae. By Wednesday, Swift J1745-26 was 30 times brighter in soft X-rays than when it was discovered and it continued to brighten.

"The pattern we're seeing is observed in X-ray novae where the central object is a black hole. Once the X-rays fade away, we hope to measure its mass and confirm its black hole status," said Boris Sbarufatti, an astrophysicist at Brera Observatory in Milan, Italy, who currently is working with other Swift team members at Penn State in University Park, Pa.

The black hole must be a member of a low-mass X-ray binary (LMXB) system, which includes a normal, sun-like star. A stream of gas flows from the normal star and enters into a storage disk around the black hole. In most LMXBs, the gas in the disk spirals inward, heats up as it heads toward the black hole, and produces a steady stream of X-rays.

But under certain conditions, stable flow within the disk depends on the rate of matter flowing into it from the companion star. At certain rates, the disk fails to maintain a steady internal flow and instead flips between two dramatically different conditions -- a cooler, less ionized state where gas simply collects in the outer portion of the disk like water behind a dam, and a hotter, more ionized state that sends a tidal wave of gas surging toward the center.

"Each outburst clears out the inner disk, and with little or no matter falling toward the black hole, the system ceases to be a bright source of X-rays," said John Cannizzo, a Goddard astrophysicist. "Decades later, after enough gas has accumulated in the outer disk, it switches again to its hot state and sends a deluge of gas toward the black hole, resulting in a new X-ray outburst."

This phenomenon, called the thermal-viscous limit cycle, helps astronomers explain transient outbursts across a wide range of systems, from protoplanetary disks around young stars, to dwarf novae -- where the central object is a white dwarf star -- and even bright emission from supermassive black holes in the hearts of distant galaxies.

Swift, launched in November 2004, is managed by Goddard Space Flight Center. It is operated in collaboration with Penn State, the Los Alamos National Laboratory in New Mexico and Orbital Sciences Corp. in Dulles, Va., with international collaborators in the United Kingdom and Italy and including contributions


AstroGeek

This story is getting bigger and bigger (pun intended).

At the bottom of this post, I have a set of links that I’m updating as I find more. [Last update 5/19/2007]

I first saw a mention of the supernova SN2006gy, in a post over at Tom’s Astronomy Blog. SN2006gy is now being called ‘the largest supernova ever observed’, and it may be the first observation of a specific type of supernova (see below for details). This supernova occurred in NGC 1260, a galaxy about 240 million light years away. Observations of the very unusual light curve indicate that the progenitor star (i.e., the star that exploded) was a hyper-massive star between 140 and 250 Solar Masses (M⊙). Phil Plait (The Bad Astronomer) has a post about it on Astronomybuz.com, and I have posted a followup link swarm over there as well.

This massive supernova was first observed by University of Texas graduate student Robert Quimby on September 18, 2006. It was detected by an optical robotic telescope as part of the Texas Supernova Search project. NGC 1260 is a very faint (Mag 14.1) spiral galaxy located in the constellation Perseus, about 1° 48 ‘ 13″ away from Algol in the opposite direction of Triangulum. It’s not visible to the naked eye, and you’ll need a pretty good scope to pick it out. There is a cluster of faint galaxies in the middle of Perseus, and NGC 1260 is just one of them.

The apparent magnitude at its peak was 15, making it a very faint object, visible only with a powerful telescope. However, due to the distance, the absolute magnitude is calculated at -22. In over-simplified terms, the absolute magnitude is the calculated brightness of an object if viewed from a fixed reference distance. That distance is called the ‘standard luminosity distance’ and is about 10 parsecs or 32.616 light years. Our sun has an absolute magnitude of 4.83, but a much larger apparent magnitude of −26.73 because we are so close to it. The apparent magnitude of the full moon is −12.6. If Eta Carinae (another hyper-massive star about 7,500 light years away in the constellation Carina) were to explode in the same way, it would quite possibly be bright enough to be seen during full daylight, and to read by at night, because it is much closer to us (7,500 light years instead of 240 million light years). It would have a much higher apparent magnitude than SN2006gy.

So, since this supernova was observed in September 2006, why is it making news now? It turns out there are several very good reasons.

First of all, it is behaving very differently than a typical supernova. Typically, supernovae reach their peak brightness in a few days to a few weeks. They then fade into obscurity a few months later. SN2006gy took 70 days to reach it’s full brightness (see the light curve above). And boy, was it bright. It was brighter than any previously observed supernova. Then, it stayed brighter than any previously observed supernova for more than three months. Nearly eight months later, it still is as bright as a typical supernova at its peak, outshining its host galaxy.

Second, this object is so unusual, there was a lot of debate about what it actually is. Many scenarios were considered and rejected. It did not behave according to the usual ways that stars evolve. Some astronomers initially thought it may be an outburst from an active galactic nucleus (AGN), however further observations showed that there was a clear separation between the nucleus of NGC1260 and SN2006gy. It did not show the typical spectral lines of a Wolf-Rayet star (also see “The Physical Properties of Wolf-Rayet Stars“). They could tell early on that it was embedded in a cloud of matter, and there was debate as to if this was a dense region of the inter-stellar medium (ISM), or if it was the outer layers of a super-massive progenitor star similar to Eta Carina that had been previously ejected to form the circum-stellar medium (CSM). However, it ejected too much mass to be a type Ia supernova that exploded in a hydrogen-rich cloud. It was suggested early on that it was something else, something new and unusual.

Now, it appears that it is that ‘something else’, specifically a different kind of supernova, theorized but never before observed a ‘‘pair instability’ (aka ‘pair production’, ‘pair-producing’ or ‘pair production instability’) supernova‘. To save wear and tear on my fingers, I’m going to adopt the abbreviation ‘PISn’ for the rest of this article. This type of supernova was first theorized in the 1960’s, but has never been observed, until (perhaps) now. This type of supernova requires an immensely heavy progenitor star, somewhere between 140-260 M⊙. Theoretically, a PISn can only occur in a supermassive but low metallicity star (in astronomy parlance, everything heavier than helium is ‘metal’), in other words star very much like a Population III star. Population III stars were the first generation of stars that condensed out of the Big Bang. They were composed of only hydrogen and helium, virtually no heavier elements at all. (NOTE: The progenitor of SN20006gy was not a Population III star, it is far too recent. Supermassive stars burn out quickly, within a million years or so as opposed to 10 Billion years for yellow dwarf stars like our Sun.) Stars without the right amount of mass (either too much, or too little) don’t turn into this kind of supernovae, and stars with too high metallicity don’t get big enough to cause this kind of supernova.

It turns out that PISns are very important to our understanding of the early phases of the universe. As noted above, the Population III stars had very low metallicity, almost no elements heavier than Helium. Because of this, they could form so-called “supermassive” stars (stars greater than 100 M⊙) more readily than today. Supermassive stars are not formed as frequently now as they were in the early universe, and when they do form, they tend to rip themselves apart, shedding huge amounts of mass in outbursts like Eta Carinae. (Eta Carinae was the site of a giant outburst about 150 years ago, when it became one of the brightest stars in the southern sky. Though the star released as much visible light as a supernova explosion, it survived the outburst. The outburst produced two huge ‘blobs’ of ejected material and a large thin equatorial disk, all moving outward at about 1.5 million miles per hour.) Supernovae in general, including PISNs, were important vehicles in forming the heavier elements (meaning everything heavier than helium) and spreading them across the universe.

The observations of SN2006gy showed that a huge amount of energy was being released 3吆^44 ergs / second (in contrast, our sun outputs about 3.86 x 10^33 ergs/second or 386 billion billion megawatts), which indicated a dense CSM. From this, scientists (See Ofek, et. al below) have inferred a mass loss rate of the progenitor is was about 1 tenth of a solar mass per year over a period of about 10 years prior to explosion. The total radiated energy in the first two months was about 1.1 × 10^51 ergs, which is only a factor of two less than that available from a super-Chandrasekhar Ia explosion (Another recently observed oddball type of supernovae). Therefore, given the presence of a star forming region in the vicinity of the SN and the high energy requirements, a plausible scenario is that SN 2006gy is related to the death of a massive star (e.g., a PISn) (See Smith, et. al below).

In the theoretical model of a PISn the temperature at the core becomes so great so quickly, that before the typical supernova fusion cascade (hydrogen -> helium -> carbon etc.) can complete, gamma rays in the core of the star become so energetic that they begin interacting with each other and with the core material, creating matter-antimatter particle pairs. Gamma radiation is the energy that provides the most of the radiation pressure which prevents collapse of the outer layers of the star. The conversion of gamma radiation into particle-antiparticle pairs in the core removes the radiation pressure (the energy is held in the core instead of radiating out of it). Once that gamma radiation starts to disappear, the outer layers of the star fall inward. This creates more pressure in the core, which creates even more energetic gamma rays, which create even more particle-antiparticle pairs. This is where the name ‘pair production instability’ comes from. This process occurs sooner in the lifetime of the star than the typical fusion cascade would complete. The result is a runaway thermonuclear explosion that, theoretically, would be brighter than any typical supernova.

Why would it be brighter? Most of the light of a supernova is generated by the conversion of lighter elements into a radioisotope of nickel, nickel-56. Nickel-56 has a half-life of just over 6 days, and is produced in large quantities in type Ia supernovae. As it decays into other elements, it gives off significant amounts of radiation. The shape of the light curve of type Ia supernovae corresponds to the decay of nickel-56 to cobalt-56 and then to iron-56. In most supernovae, a significant amount of mass is ‘locked up’ in the form a stellar remnant, either a black hole or a neutron star. However, in a PISn, the star is completely annihilated, blown apart from the inside, leaving behind no black hole or neutron star remnant. Instead the entire mass of the star is spewed out in the explosion with enough velocity that it does not fall back to form a neutron star or black hole. The result is huge amounts of ejecta in the form of heavy elements. In fact, the amount of matter ejected from the explosion would pretty much match up with the total amount of matter that would be theoretically available in the star. By studying the light curve of the explosion, it is estimated that SN2006gy ejected about 20 M⊙ of nickel-56 alone, a huge amount. That’s why it was so bright.

It’s not very often that a single event propels a section of theory from the purely theoretical to observed instance, but this event appears to be doing just that. Check out this new stellar evolution graphic courtesy of the Chandra team.

After analyzing the images from the Chandra X-Ray Observatory and ground-based observations from observatories like James Lick and the Keck Observatory, the scientists have determined that:

Of all exploding stars ever observed, this was the king… We were astonished to see how bright it got, and how long it lasted.”


Contents

Protostar Edit

Stellar evolution starts with the gravitational collapse of a giant molecular cloud. Typical giant molecular clouds are roughly 100 light-years (9.5 × 10 14 km) across and contain up to 6,000,000 solar masses (1.2 × 10 37 kg). As it collapses, a giant molecular cloud breaks into smaller and smaller pieces. In each of these fragments, the collapsing gas releases gravitational potential energy as heat. As its temperature and pressure increase, a fragment condenses into a rotating ball of superhot gas known as a protostar. [3] Filamentary structures are truly ubiquitous in the molecular cloud. Dense molecular filaments will fragment into gravitationally bound cores, which are the precursors of stars. Continuous accretion of gas, geometrical bending, and magnetic fields may control the detailed fragmentation manner of the filaments. In supercritical filaments, observations have revealed quasi-periodic chains of dense cores with spacing comparable to the filament inner width, and embedded two protostars with gas outflows. [4]

A protostar continues to grow by accretion of gas and dust from the molecular cloud, becoming a pre-main-sequence star as it reaches its final mass. Further development is determined by its mass. Mass is typically compared to the mass of the Sun: 1.0 M (2.0 × 10 30 kg) means 1 solar mass.

Protostars are encompassed in dust, and are thus more readily visible at infrared wavelengths. Observations from the Wide-field Infrared Survey Explorer (WISE) have been especially important for unveiling numerous galactic protostars and their parent star clusters. [5] [6]

Brown dwarfs and sub-stellar objects Edit

Protostars with masses less than roughly 0.08 M (1.6 × 10 29 kg) never reach temperatures high enough for nuclear fusion of hydrogen to begin. These are known as brown dwarfs. The International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives (13 Jupiter masses ( M J), 2.5 × 10 28 kg, or 0.0125 M ). Objects smaller than 13 M J are classified as sub-brown dwarfs (but if they orbit around another stellar object they are classified as planets). [7] Both types, deuterium-burning and not, shine dimly and fade away slowly, cooling gradually over hundreds of millions of years.

Stellar mass objects Edit

For a more-massive protostar, the core temperature will eventually reach 10 million kelvin, initiating the proton–proton chain reaction and allowing hydrogen to fuse, first to deuterium and then to helium. In stars of slightly over 1 M (2.0 × 10 30 kg), the carbon–nitrogen–oxygen fusion reaction (CNO cycle) contributes a large portion of the energy generation. The onset of nuclear fusion leads relatively quickly to a hydrostatic equilibrium in which energy released by the core maintains a high gas pressure, balancing the weight of the star's matter and preventing further gravitational collapse. The star thus evolves rapidly to a stable state, beginning the main-sequence phase of its evolution.

A new star will sit at a specific point on the main sequence of the Hertzsprung–Russell diagram, with the main-sequence spectral type depending upon the mass of the star. Small, relatively cold, low-mass red dwarfs fuse hydrogen slowly and will remain on the main sequence for hundreds of billions of years or longer, whereas massive, hot O-type stars will leave the main sequence after just a few million years. A mid-sized yellow dwarf star, like the Sun, will remain on the main sequence for about 10 billion years. The Sun is thought to be in the middle of its main sequence lifespan.

Eventually the star's core exhausts its supply of hydrogen and the star begins to evolve off the main sequence. Without the outward radiation pressure generated by the fusion of hydrogen to counteract the force of gravity the core contracts until either electron degeneracy pressure becomes sufficient to oppose gravity or the core becomes hot enough (around 100 MK) for helium fusion to begin. Which of these happens first depends upon the star's mass.

Low-mass stars Edit

What happens after a low-mass star ceases to produce energy through fusion has not been directly observed the universe is around 13.8 billion years old, which is less time (by several orders of magnitude, in some cases) than it takes for fusion to cease in such stars.

Recent astrophysical models suggest that red dwarfs of 0.1 M may stay on the main sequence for some six to twelve trillion years, gradually increasing in both temperature and luminosity, and take several hundred billion years more to collapse, slowly, into a white dwarf. [9] [10] Such stars will not become red giants as the whole star is a convection zone and it will not develop a degenerate helium core with a shell burning hydrogen. Instead, hydrogen fusion will proceed until almost the whole star is helium.

Slightly more massive stars do expand into red giants, but their helium cores are not massive enough to reach the temperatures required for helium fusion so they never reach the tip of the red-giant branch. When hydrogen shell burning finishes, these stars move directly off the red-giant branch like a post-asymptotic-giant-branch (AGB) star, but at lower luminosity, to become a white dwarf. [2] A star with an initial mass about 0.6 M will be able to reach temperatures high enough to fuse helium, and these "mid-sized" stars go on to further stages of evolution beyond the red-giant branch. [11]

Mid-sized stars Edit

Stars of roughly 0.6–10 M become red giants, which are large non-main-sequence stars of stellar classification K or M. Red giants lie along the right edge of the Hertzsprung–Russell diagram due to their red color and large luminosity. Examples include Aldebaran in the constellation Taurus and Arcturus in the constellation of Boötes.

Mid-sized stars are red giants during two different phases of their post-main-sequence evolution: red-giant-branch stars, with inert cores made of helium and hydrogen-burning shells, and asymptotic-giant-branch stars, with inert cores made of carbon and helium-burning shells inside the hydrogen-burning shells. [12] Between these two phases, stars spend a period on the horizontal branch with a helium-fusing core. Many of these helium-fusing stars cluster towards the cool end of the horizontal branch as K-type giants and are referred to as red clump giants.

Subgiant phase Edit

When a star exhausts the hydrogen in its core, it leaves the main sequence and begins to fuse hydrogen in a shell outside the core. The core increases in mass as the shell produces more helium. Depending on the mass of the helium core, this continues for several million to one or two billion years, with the star expanding and cooling at a similar or slightly lower luminosity to its main sequence state. Eventually either the core becomes degenerate, in stars around the mass of the sun, or the outer layers cool sufficiently to become opaque, in more massive stars. Either of these changes cause the hydrogen shell to increase in temperature and the luminosity of the star to increase, at which point the star expands onto the red-giant branch. [13]

Red-giant-branch phase Edit

The expanding outer layers of the star are convective, with the material being mixed by turbulence from near the fusing regions up to the surface of the star. For all but the lowest-mass stars, the fused material has remained deep in the stellar interior prior to this point, so the convecting envelope makes fusion products visible at the star's surface for the first time. At this stage of evolution, the results are subtle, with the largest effects, alterations to the isotopes of hydrogen and helium, being unobservable. The effects of the CNO cycle appear at the surface during the first dredge-up, with lower 12 C/ 13 C ratios and altered proportions of carbon and nitrogen. These are detectable with spectroscopy and have been measured for many evolved stars.

The helium core continues to grow on the red-giant branch. It is no longer in thermal equilibrium, either degenerate or above the Schönberg–Chandrasekhar limit, so it increases in temperature which causes the rate of fusion in the hydrogen shell to increase. The star increases in luminosity towards the tip of the red-giant branch. Red-giant-branch stars with a degenerate helium core all reach the tip with very similar core masses and very similar luminosities, although the more massive of the red giants become hot enough to ignite helium fusion before that point.

Horizontal branch Edit

In the helium cores of stars in the 0.6 to 2.0 solar mass range, which are largely supported by electron degeneracy pressure, helium fusion will ignite on a timescale of days in a helium flash. In the nondegenerate cores of more massive stars, the ignition of helium fusion occurs relatively slowly with no flash. [14] The nuclear power released during the helium flash is very large, on the order of 10 8 times the luminosity of the Sun for a few days [13] and 10 11 times the luminosity of the Sun (roughly the luminosity of the Milky Way Galaxy) for a few seconds. [15] However, the energy is consumed by the thermal expansion of the initially degenerate core and thus cannot be seen from outside the star. [13] [15] [16] Due to the expansion of the core, the hydrogen fusion in the overlying layers slows and total energy generation decreases. The star contracts, although not all the way to the main sequence, and it migrates to the horizontal branch on the Hertzsprung–Russell diagram, gradually shrinking in radius and increasing its surface temperature.

Core helium flash stars evolve to the red end of the horizontal branch but do not migrate to higher temperatures before they gain a degenerate carbon-oxygen core and start helium shell burning. These stars are often observed as a red clump of stars in the colour-magnitude diagram of a cluster, hotter and less luminous than the red giants. Higher-mass stars with larger helium cores move along the horizontal branch to higher temperatures, some becoming unstable pulsating stars in the yellow instability strip (RR Lyrae variables), whereas some become even hotter and can form a blue tail or blue hook to the horizontal branch. The morphology of the horizontal branch depends on parameters such as metallicity, age, and helium content, but the exact details are still being modelled. [17]

Asymptotic-giant-branch phase Edit

After a star has consumed the helium at the core, hydrogen and helium fusion continues in shells around a hot core of carbon and oxygen. The star follows the asymptotic giant branch on the Hertzsprung–Russell diagram, paralleling the original red-giant evolution, but with even faster energy generation (which lasts for a shorter time). [18] Although helium is being burnt in a shell, the majority of the energy is produced by hydrogen burning in a shell further from the core of the star. Helium from these hydrogen burning shells drops towards the center of the star and periodically the energy output from the helium shell increases dramatically. This is known as a thermal pulse and they occur towards the end of the asymptotic-giant-branch phase, sometimes even into the post-asymptotic-giant-branch phase. Depending on mass and composition, there may be several to hundreds of thermal pulses.

There is a phase on the ascent of the asymptotic-giant-branch where a deep convective zone forms and can bring carbon from the core to the surface. This is known as the second dredge up, and in some stars there may even be a third dredge up. In this way a carbon star is formed, very cool and strongly reddened stars showing strong carbon lines in their spectra. A process known as hot bottom burning may convert carbon into oxygen and nitrogen before it can be dredged to the surface, and the interaction between these processes determines the observed luminosities and spectra of carbon stars in particular clusters. [19]

Another well known class of asymptotic-giant-branch stars is the Mira variables, which pulsate with well-defined periods of tens to hundreds of days and large amplitudes up to about 10 magnitudes (in the visual, total luminosity changes by a much smaller amount). In more-massive stars the stars become more luminous and the pulsation period is longer, leading to enhanced mass loss, and the stars become heavily obscured at visual wavelengths. These stars can be observed as OH/IR stars, pulsating in the infrared and showing OH maser activity. These stars are clearly oxygen rich, in contrast to the carbon stars, but both must be produced by dredge ups.

Post-AGB Edit

These mid-range stars ultimately reach the tip of the asymptotic-giant-branch and run out of fuel for shell burning. They are not sufficiently massive to start full-scale carbon fusion, so they contract again, going through a period of post-asymptotic-giant-branch superwind to produce a planetary nebula with an extremely hot central star. The central star then cools to a white dwarf. The expelled gas is relatively rich in heavy elements created within the star and may be particularly oxygen or carbon enriched, depending on the type of the star. The gas builds up in an expanding shell called a circumstellar envelope and cools as it moves away from the star, allowing dust particles and molecules to form. With the high infrared energy input from the central star, ideal conditions are formed in these circumstellar envelopes for maser excitation.

It is possible for thermal pulses to be produced once post-asymptotic-giant-branch evolution has begun, producing a variety of unusual and poorly understood stars known as born-again asymptotic-giant-branch stars. [20] These may result in extreme horizontal-branch stars (subdwarf B stars), hydrogen deficient post-asymptotic-giant-branch stars, variable planetary nebula central stars, and R Coronae Borealis variables.

Massive stars Edit

In massive stars, the core is already large enough at the onset of the hydrogen burning shell that helium ignition will occur before electron degeneracy pressure has a chance to become prevalent. Thus, when these stars expand and cool, they do not brighten as dramatically as lower-mass stars however, they were more luminous on the main sequence and they evolve to highly luminous supergiants. Their cores become massive enough that they cannot support themselves by electron degeneracy and will eventually collapse to produce a neutron star or black hole. [ citation needed ]

Supergiant evolution Edit

Extremely massive stars (more than approximately 40 M ), which are very luminous and thus have very rapid stellar winds, lose mass so rapidly due to radiation pressure that they tend to strip off their own envelopes before they can expand to become red supergiants, and thus retain extremely high surface temperatures (and blue-white color) from their main-sequence time onwards. The largest stars of the current generation are about 100-150 M because the outer layers would be expelled by the extreme radiation. Although lower-mass stars normally do not burn off their outer layers so rapidly, they can likewise avoid becoming red giants or red supergiants if they are in binary systems close enough so that the companion star strips off the envelope as it expands, or if they rotate rapidly enough so that convection extends all the way from the core to the surface, resulting in the absence of a separate core and envelope due to thorough mixing. [21]

The core of a massive star, defined as the region depleted of hydrogen, grows hotter and more dense as it accretes material from the fusion of hydrogen outside the core. In sufficiently massive stars, the core reaches temperatures and densities high enough to fuse carbon and heavier elements via the alpha process. At the end of helium fusion, the core of a star consists primarily of carbon and oxygen. In stars heavier than about 8 M , the carbon ignites and fuses to form neon, sodium, and magnesium. Stars somewhat less massive may partially ignite carbon, but are unable to fully fuse the carbon before electron degeneracy sets in, and these stars will eventually leave an oxygen-neon-magnesium white dwarf. [22] [23]

The exact mass limit for full carbon burning depends on several factors such as metallicity and the detailed mass lost on the asymptotic giant branch, but is approximately 8-9 M . [22] After carbon burning is complete, the core of these stars reaches about 2.5 M and becomes hot enough for heavier elements to fuse. Before oxygen starts to fuse, neon begins to capture electrons which triggers neon burning. For a range of stars of approximately 8-12 M , this process is unstable and creates runaway fusion resulting in an electron capture supernova. [24] [23]

In more massive stars, the fusion of neon proceeds without a runaway deflagration. This is followed in turn by complete oxygen burning and silicon burning, producing a core consisting largely of iron-peak elements. Surrounding the core are shells of lighter elements still undergoing fusion. The timescale for complete fusion of a carbon core to an iron core is so short, just a few hundred years, that the outer layers of the star are unable to react and the appearance of the star is largely unchanged. The iron core grows until it reaches an effective Chandrasekhar mass, higher than the formal Chandrasekhar mass due to various corrections for the relativistic effects, entropy, charge, and the surrounding envelope. The effective Chandrasekhar mass for an iron core varies from about 1.34 M in the least massive red supergiants to more than 1.8 M in more massive stars. Once this mass is reached, electrons begin to be captured into the iron-peak nuclei and the core becomes unable to support itself. The core collapses and the star is destroyed, either in a supernova or direct collapse to a black hole. [23]

Supernova Edit

When the core of a massive star collapses, it will form a neutron star, or in the case of cores that exceed the Tolman–Oppenheimer–Volkoff limit, a black hole. Through a process that is not completely understood, some of the gravitational potential energy released by this core collapse is converted into a Type Ib, Type Ic, or Type II supernova. It is known that the core collapse produces a massive surge of neutrinos, as observed with supernova SN 1987A. The extremely energetic neutrinos fragment some nuclei some of their energy is consumed in releasing nucleons, including neutrons, and some of their energy is transformed into heat and kinetic energy, thus augmenting the shock wave started by rebound of some of the infalling material from the collapse of the core. Electron capture in very dense parts of the infalling matter may produce additional neutrons. Because some of the rebounding matter is bombarded by the neutrons, some of its nuclei capture them, creating a spectrum of heavier-than-iron material including the radioactive elements up to (and likely beyond) uranium. [25] Although non-exploding red giants can produce significant quantities of elements heavier than iron using neutrons released in side reactions of earlier nuclear reactions, the abundance of elements heavier than iron (and in particular, of certain isotopes of elements that have multiple stable or long-lived isotopes) produced in such reactions is quite different from that produced in a supernova. Neither abundance alone matches that found in the Solar System, so both supernovae and ejection of elements from red giants are required to explain the observed abundance of heavy elements and isotopes thereof.

The energy transferred from collapse of the core to rebounding material not only generates heavy elements, but provides for their acceleration well beyond escape velocity, thus causing a Type Ib, Type Ic, or Type II supernova. Current understanding of this energy transfer is still not satisfactory although current computer models of Type Ib, Type Ic, and Type II supernovae account for part of the energy transfer, they are not able to account for enough energy transfer to produce the observed ejection of material. [26] However, neutrino oscillations may play an important role in the energy transfer problem as they not only affect the energy available in a particular flavour of neutrinos but also through other general-relativistic effects on neutrinos. [27] [28]

Some evidence gained from analysis of the mass and orbital parameters of binary neutron stars (which require two such supernovae) hints that the collapse of an oxygen-neon-magnesium core may produce a supernova that differs observably (in ways other than size) from a supernova produced by the collapse of an iron core. [29]

The most massive stars that exist today may be completely destroyed by a supernova with an energy greatly exceeding its gravitational binding energy. This rare event, caused by pair-instability, leaves behind no black hole remnant. [30] In the past history of the universe, some stars were even larger than the largest that exists today, and they would immediately collapse into a black hole at the end of their lives, due to photodisintegration.

After a star has burned out its fuel supply, its remnants can take one of three forms, depending on the mass during its lifetime.

White and black dwarfs Edit

For a star of 1 M , the resulting white dwarf is of about 0.6 M , compressed into approximately the volume of the Earth. White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy pressure of the star's electrons, a consequence of the Pauli exclusion principle. Electron degeneracy pressure provides a rather soft limit against further compression therefore, for a given chemical composition, white dwarfs of higher mass have a smaller volume. With no fuel left to burn, the star radiates its remaining heat into space for billions of years.

A white dwarf is very hot when it first forms, more than 100,000 K at the surface and even hotter in its interior. It is so hot that a lot of its energy is lost in the form of neutrinos for the first 10 million years of its existence, but will have lost most of its energy after a billion years. [31]

The chemical composition of the white dwarf depends upon its mass. A star of a few solar masses will ignite carbon fusion to form magnesium, neon, and smaller amounts of other elements, resulting in a white dwarf composed chiefly of oxygen, neon, and magnesium, provided that it can lose enough mass to get below the Chandrasekhar limit (see below), and provided that the ignition of carbon is not so violent as to blow the star apart in a supernova. [32] A star of mass on the order of magnitude of the Sun will be unable to ignite carbon fusion, and will produce a white dwarf composed chiefly of carbon and oxygen, and of mass too low to collapse unless matter is added to it later (see below). A star of less than about half the mass of the Sun will be unable to ignite helium fusion (as noted earlier), and will produce a white dwarf composed chiefly of helium.

In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarfs to exist yet.

If the white dwarf's mass increases above the Chandrasekhar limit, which is 1.4 M for a white dwarf composed chiefly of carbon, oxygen, neon, and/or magnesium, then electron degeneracy pressure fails due to electron capture and the star collapses. Depending upon the chemical composition and pre-collapse temperature in the center, this will lead either to collapse into a neutron star or runaway ignition of carbon and oxygen. Heavier elements favor continued core collapse, because they require a higher temperature to ignite, because electron capture onto these elements and their fusion products is easier higher core temperatures favor runaway nuclear reaction, which halts core collapse and leads to a Type Ia supernova. [33] These supernovae may be many times brighter than the Type II supernova marking the death of a massive star, even though the latter has the greater total energy release. This instability to collapse means that no white dwarf more massive than approximately 1.4 M can exist (with a possible minor exception for very rapidly spinning white dwarfs, whose centrifugal force due to rotation partially counteracts the weight of their matter). Mass transfer in a binary system may cause an initially stable white dwarf to surpass the Chandrasekhar limit.

If a white dwarf forms a close binary system with another star, hydrogen from the larger companion may accrete around and onto a white dwarf until it gets hot enough to fuse in a runaway reaction at its surface, although the white dwarf remains below the Chandrasekhar limit. Such an explosion is termed a nova.

Neutron stars Edit

Ordinarily, atoms are mostly electron clouds by volume, with very compact nuclei at the center (proportionally, if atoms were the size of a football stadium, their nuclei would be the size of dust mites). When a stellar core collapses, the pressure causes electrons and protons to fuse by electron capture. Without electrons, which keep nuclei apart, the neutrons collapse into a dense ball (in some ways like a giant atomic nucleus), with a thin overlying layer of degenerate matter (chiefly iron unless matter of different composition is added later). The neutrons resist further compression by the Pauli exclusion principle, in a way analogous to electron degeneracy pressure, but stronger.

These stars, known as neutron stars, are extremely small—on the order of radius 10 km, no bigger than the size of a large city—and are phenomenally dense. Their period of rotation shortens dramatically as the stars shrink (due to conservation of angular momentum) observed rotational periods of neutron stars range from about 1.5 milliseconds (over 600 revolutions per second) to several seconds. [34] When these rapidly rotating stars' magnetic poles are aligned with the Earth, we detect a pulse of radiation each revolution. Such neutron stars are called pulsars, and were the first neutron stars to be discovered. Though electromagnetic radiation detected from pulsars is most often in the form of radio waves, pulsars have also been detected at visible, X-ray, and gamma ray wavelengths. [35]

Black holes Edit

If the mass of the stellar remnant is high enough, the neutron degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. The mass at which this occurs is not known with certainty, but is currently estimated at between 2 and 3 M .

Black holes are predicted by the theory of general relativity. According to classical general relativity, no matter or information can flow from the interior of a black hole to an outside observer, although quantum effects may allow deviations from this strict rule. The existence of black holes in the universe is well supported, both theoretically and by astronomical observation.

Because the core-collapse mechanism of a supernova is, at present, only partially understood, it is still not known whether it is possible for a star to collapse directly to a black hole without producing a visible supernova, or whether some supernovae initially form unstable neutron stars which then collapse into black holes the exact relation between the initial mass of the star and the final remnant is also not completely certain. Resolution of these uncertainties requires the analysis of more supernovae and supernova remnants.

A stellar evolutionary model is a mathematical model that can be used to compute the evolutionary phases of a star from its formation until it becomes a remnant. The mass and chemical composition of the star are used as the inputs, and the luminosity and surface temperature are the only constraints. The model formulae are based upon the physical understanding of the star, usually under the assumption of hydrostatic equilibrium. Extensive computer calculations are then run to determine the changing state of the star over time, yielding a table of data that can be used to determine the evolutionary track of the star across the Hertzsprung–Russell diagram, along with other evolving properties. [36] Accurate models can be used to estimate the current age of a star by comparing its physical properties with those of stars along a matching evolutionary track. [37]


Captain Planet VS The Magic School Bus: The Fight

Exiting the cobblestone building in town square, strolled a group of children being led by a rather encentric looking woman. She had bright red-orange hair held up in a beehive hairdo and wore a purple dress with various scientific objects adorning it. Planets, equations, test tubes, and even a dinosaur or two were scattered over the frill. Some might say they were even moving.

"Alright class, everyone back onto the Bus. I hope you all had fun at the Natural History Museum!" The students followed her down the step of the building, most of them looking slightly dissapointed. All but one, of course.

Arnold: "I sure did Mrs. Frizzle. Glad I didn't stay home today!"

"Yeah it was great. " Said Wanda, "but a little underwhelming. I mean, last week we went to space! This just doesn't give the same thrills." Several of the other students nodded or voiced their agreements, not wanting to upset their favorite teacher but certainly expecting more from her in the field trip department.

"Ohh, sorry kids. I had something better planned, but my friend Doc had to cancel. Something about clearing up Cyber Pollen before they raise the dead. That Doc, always a joker.”

"Exactly!" replied his teacher “To the Bus kids, two by two please.”

Several Blocks away

"Can you see them Mati?" asked Wheeler, asking his friend and fellow planeteer looking into the Binoculars.

"Yep, that's her alright. Just like Gaia described her. Crazy outfit, big hair, and a bus with a face." Mati replied, the little monkey sitting on his shoulder screeching and hollering in anticipation.

Gi approached them, joining the conversation. "Are we sure this is the right bus? We don't want any kids to get hurt."

"We'll make sure all the kids are safe." Kwame said. "Besides, we all know Cap can handle this. That bus needs to be destroyed, it once made it so recycling didn't exist! If it fell into the wrong hands, who knows what damage could be done!"

The other Planeteers gasped in fear and astonishment, just like they did earlier the first time they were told this. Mati's monkey screeched even louder, and cowered behind Mati's head.

"Vhat are ve vaiting for then? Let's save the planet." Shouted Linka. “Then let our powers combine!” Kwame said as he held his ring high into the air, the others following suit.

"Long ago the four element lived in peace. Then everything changed when-" Katara was cut off as she realized all the Planeteers were giving her ugly looks. She also realized this was not the recording studio she had just been in. "Oopps, sorry about that." She shirked away awkwardly, uncomfortable to be in the situation.

Ignoring her as she left,the Planeteers turned and watched as their bright beams of energy formed together in the sky as it began to take form, followed with a seemingly bodiless voice that began to speak as the surge of energy began to finalize it’s form.

A green and blue leotard wearing man appeared above them, striking a heroic pose.
"I AM CAPTAIN PLANET!" He shouted to the heavens.

“GO PLANET!” The Planeteers cheered to their planetary savior as he landed near them.
“What seems to the the problem Planeteers?” He asked with confidence.

“That yellow school bus is dangerous, Cap! It can take away recycling!” Gi called out as she pointed behind Captain Planet to the yellow school bus driving away.

“Well then, it looks like I’m gonna have to revoke that bus’ permit!” Cap said as he levitated into the air and flew off after the bus.

Swiftly flying down to the street, Captain Planet landed with a powerful punch to the concrete right in front of the bus. His landing caused cracks in the pavement, as well as a small indentation. "Stop right there, buzzhair. Your anti-recycling days are over!"

Mrs. Frizzle slammed on the breaks in order to avoid hitting the rejected Blue Man Group member. "Oh my, it seems your not much of a fan. I take it your from the School board for all those permission slips huh?"

"What? No, I'm here to destroy your anti-recycling machine so it can never be used to hurt the environment. For I am Captain Planet! Defender of Earth and its resources!"

"An environmentalist huh? Do you know my old friend Al? He's actually my third cousin twice remo-"

"Enough Talk!" Planet shouted, "Time to compound this carbon spewing car!"

"Ohohoho, You can try" responded Mrs. Frizzle, winking slyly.

"FIGHT!" Yelled Mrs. Frizzle, gunning the engine and driving straight towards the blue clad hero. The Bus's tires screeched as it took off, causing massive skid marks in a snake pattern. The speedometer jumped upwards as the kids were pushed back into their seats by the sudden acceleration. It looked as if they were going to ram the blue clad superhero head on.

"Looks like someone's got some road rage" said Planet, catching the bus as it came closer and tossing it into the air behind him. The bus spun like a blocked football, flipping front to back at an incredible rate. The kids, their hands in the air, screamed in a mix of joy and terror, depending on who you asked.

Not flustered by this in the slightest, Mrs Frizzle pushed a single button on the Bus's dashboard. While still in mid air and nearing the peak of its arc, the Bus began to twist and bulgde, its shape changing before any bystanders eyes. When it was done, it had taken the shape of a modern byplane and regained it's balance, leveling out in midair.

Sporting a pair of aviator goggles that she did not have earlier, Mrs. Frizzle turned to her students. "Alright, that's as good a seatbelt check as any, everyone ok?"

All the children responded yes, except for a paniced Arnold who had locked himself into a death grip on the seat. Turning back, Frizzle saw Planet flying right at them, looking very serious.

“What’s the rush? Got a hot foot on the accelerator do you?” Upon saying this, from Planet's hands shot forth a burst of flames, arching towards the Bus with such force and heat that nearby clouds evaporated. The children watched this, amazed to an extent. They had all seen, and had been, water molecules going through the water cycle before, but this was new.

"You see class, the sudden change in temperature causes the molecules to accelerate and expand, to the point whe-"

Mrs. Frizzle was cut off by a loud thud, as Planet was plastered against the windshield, like an unfortunate bug. Flipping another switch, Frizz turned on the wipers, brushing him aside. He fell for several feet before regaining his balance.

"Looks like you won that game of chicken. But I have a striking surprise up my sleeve." From the eco-friendly hero's hands shot forth massive bolts of lightning, the beams arching in an erratic zig-zag as they approached the nearest metal object, namely the Bus.

Frizzle scrambled at the controls, all the while looking as calm as if she was taking a stroll down the road. "I'll show you chicken!" she yelled, and the Bus followed her lead and transformed into. well, a chicken. With surprising speed and agility, the Busken out-manuvered the bolts of lighting, and fired it's own projectiles at Captain Planet.

Two eggs splattered on Planets head, briefly obscuring his vision. Wiping the yolks off his eyes, he muttered to himself. "Well that was certainly fowl." Looking up, he saw the bus, once again looking like a bus, flying away and to the ground. Scowling, Planet took off in pursuit, not about to let this end so early. "Looks like the yolks on you!"

The Bus landed back onto the street, and began to drive back to the school. "Well class, I hope that was the kind of excitement you were all looking for. I haven't had to fight like that in years!"

Carlos spoke up, knowing this was his moment to shine. "I guess we could say that we flew the coo-"

With a grinding and sudden halt, the Bus stopped, as if some immovable object had placed itself in front of them. And so it had. Captain Planet stood in front of the bus, stopping it in its tracks, having shrugged off the blow and barely moved an inch.

"Ooooh, your persistant, I like it!" Frizzle cried out, having more fun by the minute. Planet responded curtly, obviously not having nearly as good a time. "Let's see whats under this hood. Hmm, well I’d say your carburetor’s out of tune and your brake’s close to disconnecting. Don’t worry, I’ll take all of those out for you, free of charge!" he said, aiming to sabatoge the vehicle from the inside out. With physical strength alone, he lifted off the hood from the Bus.

"Oh bad oh bad bad bad!" said Kesha, hanging onto the seat tightly. However, the second Planet opened the front of the Bus, a cloud of smoke floated into his face. Coughing and stuttering, he stumbled backwards, almost falling over himself in the process.

"cough* c-carbon monoxide! cough* cough*" Planet stuttered out, as he slowly stood back up-

Only to have the breath knocked out of him as the Bus ran his ass over. Hit first by the bumper, he tumbled underneath the grill as the rough bottom of the bus scratched him up badly. Eventually, he came out the other side, rolling on the pavement. He sprung up, ready for almost anything.

Anything except the Bus backing up incredibly fast.

“Hnngh, you’re not gonna run me down again.” Stamping his foot on the ground, the road beneath the Bus shot upwards, once again propelling the Bus high into the air. Planet shot after it, the very ground beneath him following him up as if a liquid. The Bus attempted to transform in midair, likely into some kind of flying vehicle, but was forced to stop midway due to a massive gust of wind coming from Planet's direction. Having twirled his hands, Planet caused a giant tornado to catch the bus, preventing it's escape and spinning it through the air.

Flying in from underneath, the Captain grabbed the Bus by the wheel well and hurled it downwards. Just after, he shot a hand into the air and summoned a massive lightning bolt, which struck downwards. Tumbling through the air, Mrs. Frizzle held her arms in the air, squealing in delight, like a child at a candy store. The rest of the students weren't so happy, save Wanda, who was practically cheering for more. Struck and being forced downward even faster by the electricity, the Bus landed harshly on a building, crashing through the roof with ease.

Planet arrived moments later, but all he saw was a crater surrounded by many cardboard boxes. In fact, nearly everything he saw was a cardboard box. This must have been some kind of factory. Confused, he started looking around for any sign of the Bus, just to be sure it was destroyed. Meanwhile, a hushed conversation was going on a few feet away.

"Mrs. Frizzle, are you sure this was a good hiding place?" asked Arnold, somehow still functioning after all of the traumatic events that had just taken place.

"Absolutely my boy. He'll never find us here."

"Bu-but, a box? Do you really think that's enough?"

"It's like my old uncle Serpentes used to tell me, 'never underestimate the power of a cardboard box'." Frizzle responded, putting a hand over her eye and speaking as gruff as she could.

Hearing their voices, Captian Planet noticed the only yellow box in the building. At nearly the speed of light, he dashed forward and flipped it over, only to reveal nothing underneath. "But I was sure I heard them from under the box. "

"Your clooooooooose, we're not under the box" Mrs. Frizzles voice said, as the yellow cardboard box twisted and turned, changing shape and growing. "We are the box!" Suddenly it was not a box in front of Planet, but a massive black bear. It reared back one of its huge paws and slugged Planet across the face, sending him reeling backward.

The Bear-Bus charged forward, and struck again, but this time Planet was ready, and caught the bears paws in his hands. "You’ll have to bear with me, if I'm not careful this could end grizzly for me."

Summing the strength of the very Earth itself, he flung the Bear-Bus so hard it crashed through the buildings ceiling and flew upwards, eventually leaving the atmosphere and tumbling through space. Even in the vaccum of space, the Bear-Bus looked non worse for wear.

"Alrighty then, lets set a course for victory! Make it so!" Frizzle exclaimed, pulling a crank near the roof of the bus. It expanded in size and shape, forming a disk connected to two large cynlinders behind it. Suffice to say, it was a rather familiar design.

Planet was watching the skies, happy at a day’s work saving the world, despite the countless collateral damage he created, but since when was any of that his fault?
“Looks like that bus finally found it’s place in the universe.” Captain Planet mused as he prepared to return to the Earth when a peculiar sound filled his ears.

The look on his face changed from smug confidence to a staggering disbelief as a large, yellow starship that looked awfully familiar barreled down from above. To add insult to injury, twin photon torpedos were fired from the ship and struck the good Captain where he stood, completely obliterating the surrounding buildings in a firey blaze.

Aboard the USS Busterprise, the student crew and captain Frizzle watched the destruction. "Two direct hits!" said Tim, sporting Jordie's visor.

"According to my research" began Dorothy Ann "That amount of force should be more than enough to keep him down."

"Excellent!" Mrs. Frizzle replied. "Carlos, full power to the engine, Ralphie, turbines to speed, Arnold!-"

"Why am I the one in the red shirt?" asked a very nervous Arnold.

"You just stay there, Wesley. We don't need you getting hurt."

"Mrs. Frizzle!" cried out Phoebe, distressed at something on the moniter. "He's still alive and coming right for us!"

"Fire the torpedos! All of them!" Yelled Frizzle, more in enthusiasm then worry. The USS Busterprise fire off more flashes of energy beams, most of which Planet skillfully dodged. One of the charges hit him directly though, causing a massive explosion in the low atmosphere.

“Better prime those engines, Scotty, cause you’re about to make First Contact!” Captain Planet flew through the explosion, seemingly unphazed by the plasma blast. Not flinching in the slightest, Mrs. Frizzle gunned the engine, quickly moving up the warp factors as she played the most dangerous game of chicken ever.

The two collided, Planet catching but barely holding back the speeding starship. It's engines strained against the strength before it. Muscles straining and teeth gritting, Planet was engaged in a giant shoving contest with a ship the size of a city.

At that moment, Captain Planet snapped.

"You need to make like a tree, and F***ING LEAVE!" he said through baited breath, and with a mighty heave tossed the starship aside and sent it tumbling through the air. Gathering an energy around him, Captain Planet charged, then fired a massive beam, which followed at the dissipearing starship. Its struck head on, and in the ships place formed a giant tree, rotted into the ground and thousands of feet tall. It's yellow bark stood out in contrast to the many leaves sported above it.

"I, I made them a tree." Said Planet, as if in shock. "I'll. I'll make them all trees. ALL OF THEM!"

Planet began to fire off various bursts of energy, in every direction. People, animals, and objects below him unfortunate enough to be in the way was painfully transformed into many species of trees. Laughing maniacally, he continued his barrage of beams, until nothing was visible save a massive forest. He floated above it, awed and consumed by his own power.

Master Bison would have been proud.

Snapping him out of his stupor, the giant tree that had been a starship shrunk and shifted, until a small yellow vehicle remained. It was almost identical to the original Bus, but with fins and a massive exhaust tube on the end. It bore a slight resemblance to a Space Shuttle. Planet scowled in response. “I’ve heard of clear-cutting problems, but this is ridiculous.”

Frizzle paid this no mind, still enjoying the ride. "And that class, is how water transpiration works inside of a tree. Any questions?"

Raising her hand patiently, Phoebe looked out the window to observe a very disturbing image. Hundreds of vines were growing from the forest below and ensnaring the Bus itself, slowly but surely wrapping it into a cocoon. "Mrs. Frizzle, how do we get out of this?"

"A little off topic but excellent question!" she exclaimed, happy to entertain.

Her hand hovered over a round, multicolored button, which had a shape of a large robot on it. Then she thought better of it. "Maybe next time" she said to no one in particular. Instead she activated the shrinkerscope, causing the sudden decrease in mass. Before Captain Planet's very eyes, the Bus shrunk until it was invisible, and then some. It had become so small, that it passed through the atoms of the vine holding it in place.

"So class, can anyone tell me what those are?" Frizzle asked, pointing to the many quick moving spheres around them.

"Protons!" Phoebe called out.

"Electrons!" Wanda exclaimed.

"Destructons!" Yelled Planet. Looking above them, they saw a massive blue hand reaching for them. He had shrunken down somewhat, but remained much larger than the Bus itself. The hand was the size of an island in comparison, and was moving to swat them like a fly.

The massive blue hand closed over the Bus, capturing it in an enclosed fist. Raising the fist to his face, Planet opened his palm, studying the tiny vehicle sitting there. "I think it's time we cooled off a bit." Taking in a deep breath, Planet exhaled, the cold breeze causing a small glacier to form over the Bus. While tiny to the massive form of Captain Planet, the Bus had become completly covered in ice, frozen solid.

"Chill Out." Planet said, then cringed. That pun was bad, even by HIS standards.

Before he could come up with something better, or dispose of the piece of ice in his hand, Planet's super vision (Which he has??) zoomed in on the tiny iceberg. Having noticed movement to some degree, he saw the Bus, equipped with a massive drill on it's front, exit the ice block. His ears picked up tiny dialogue to go along with it.

"-then the friction from the drill creates heat, melting the ice even faster to escape!" Frizzle explained the physics of getting out of an iceberg.

High above them, Planet took a deep breath, then blew a jet of flames at the microscopic Bus. They bounced off it's hull once again, and the tiny Bus flew forwards, taking advantage of the open oppertunity before them. Namely Planet's open mouth. Zooming through the protectors jaws, the Bus grew in size not fully, but about to the size of an orange. It lost no momentum, forcing it's way through Planet's digestive tract much too quickly.

The Captain writhed in pain, twisting his body in agony as the miniature Bus plowed through his body. Organs were pushed out of the way painfully, and his intestines were stretched to their max. He twisted and turned, bending with the movements of the Bus, his arms and legs twitching in a spasm and his face tightly clenched. After almost 5 minutes of this pain, he screamed as the Bus made it's untimely exit, breaking his red tighty-whitey's as they left.

Frizzle looked back as the Bus returned to normal size and began to put some distance between them and the protector of Earth. "Well class, I think this superhero could use a laxative or two after that field trip." The entire class, Arnold included, burst into laughter at the well-timed burn.

Regaining whatever composure he had left, Planet turned to look at his fleeting foe. He scowled, never having been pushed to this breaking point before, even in his immortal life. Crossing his arms, he knew things were about to get serious. "Only a coward attacks from behind, but maybe that's what it will take to beat you" he said to no one in particular. Dashing forward, he quickly caught up with the speeding Bus.

Flying up from behind, Captain Planet landed on the roof of the bus with a mighty clang. “Now let’s peel back this tin can here.” Planet quipped, digging in his fingers, he heaved with great force as the roof ripped apart. Peering inside, he saw all of the students looking up at him, frightened to say the least.

"Huh, it's bigger on the inside" Planet commented, not expecting to see so much space inside.

Frizzle spun in her chair, not a care in the world. She pulled what looked like the stopper on a pinball machine, but did not release it, instead looking to her adversary. "I prefer to think of it as smaller on the outside!"

Releasing the stopper, it sprang back into position. As a reflex, a boxing glove on a spring shot upwards from the floor of the bus, smacking Planet in the face and knocking him off the Bus itself. Within seconds of impact, the Bus's roof reformed, repairing itself as it changed into another type of spaceship, this one boomerang in shape.

"MRS. FRIZZLE" The class called out in fear. Looking back, she saw something she had never seen on her students faces. Actual, real fear, not caused by something she had control of. For the first time ever, they had been in actual, real danger.

That would not stand. NO ONE messed with her kids.

Strapping herself in, Frizzle turned around the Bus, facing the source of the kids terror. Captain Planet hovered in the air, having recovered from the oddly powerful punch. The two stared each other down, the tension maleable. This would end today. One of their ideals would stand with them, and the other would fall.

"Kids" Mrs. Frizzle said, her voice much more calm than usual. "I think it's time we took some chances!"

Across the sky, Planet became cloaked in fire. The very air around him began to swirl, and electricity bounced through the air.

Water shot upwards like a snake, swirling in a ring around the Captain. Balls of concentrated earth and stone did the same, and several plates of metal attached themselves to his body, forming a medival armor.

"And maybe get a little bit messy." she ended, winking at her students.

Planet flew forward at over twice the speed of light, the sphere of elemental energy following suit, one massive ball of earth's wrath concentrated in one location. Fire, Water, Air, Earth, Metal, and Electricity danced around him, giving Planet the look of some mythical godly being.

Two giant, mechanical gloved hands emerged from the sides of the Bus, seemingly out of no where. One hand caught Planet, stopping all his momentum at once without flinching. The second hand bitch slapped him across the face hard.

The blow sent Planet reeling, tumbling through the air at a breakneck speed. He crashed into the ground miles below, skidding to a halt on the sand of some godforsaken dessert. Every part of him ached, a feeling the embodiment of Earth was not familiar with.

Getting up, he shook his head into clearity and looked upwards. Using enhanced vision, he saw the Bus floating multiple miles in the air. "No, I cannot fail." Planet readied himself, about to charge forward, when the Bus played it's trump card.

With an unrealistic and shocking acceleration, the Bus moved so fast only Planet's semi-omnipotence keyed him in to what had happened. It shot forward, ducking around the defender of Earth and slamming into him, knocking him sideways and spinning him about. It's great speed unchecked, the Bus came to a slow halt, accompanied with a cartoonish screech of the tires.

Before he could even take advantage of this, Planet was bombarded again. Taking a sharp turn, the Bus spun on its axel and faced Captain Planet. In such a short time that the Hero of Earth could not perceive, the Bus rammed into him and carried him out of the atmosphere.
/>
Almost blacking out from the sheer speed, Planet watched as stars and planets rushed past at a blinding speed. The only thing he could make out clearly was the Bus itself, with the red haired teacher staring him down. She had a crazy glint in her eye that caused Planet to fear her immensely. “Hnngh…powers…weakening…have to…get back…to Earth…”

"Liz, plot a course to the farthest star system you can find" she said, turning the wheel to the tiny lizard.

The Captain struggled to shake himself off, but just as he was sliding from the bumper, two giant hands extended from the Bus's side and held him in place. Their grip was excrutiatingly painful, and try as he might he could not escape their grasp.

After a surprisingly short trip, the Bus came to a sudden stop. It was so jarring Planet would have been launched several galaxies away had he not been trapped within the grip of two giant gloved hands.

Feeling s searing pain all around him, Captain Planet quickly realized where he was. The heat was immensely intense, and all around him at once, as a unimaginable pressure was being exerted on him from all angles. His chemist mind could feel all the nitrogen, hydrogen, and other highly reactive elements flowing around him.

He was being held inside a sun.

His vision had begun to cloud, but he could still make out the Bus that was holding him in place. It had changed, gaining a circular dial around its front window. It loosely resembled H.G.Wells Time Machine, but it couldn't possibly be-

"Class, reset your watches, cause it's time to travel!" shouted Mrs. Frizzle, spinning a dial on the inside of the Bus, completely safe from the dangers of the sun. Slowly but surely, Planet began to feel the eons pass by. Even though he was immortal, the sheer length of time going by was staggering, like nothing he could ever have imagined.

From inside the Bus, he could hear the teacher taunting him. “Oh what a fantastic learning experience this will be, Mr. Planet. Do you know where we are? We’re inside a star! Oh this isn’t just any star, this one is set to expire over 10 billion years from now! Do you know what happens when a sun expires?” Captain Planet’s eyes widened in shock.

“N-No…” Captain Planet said weakly, Ms Frizzle only grinned.

" When the core runs out of hydrogen, these stars fuse helium into carbon just like out Sun. However, after the helium is gone, their mass is enough to fuse carbon into heavier elements. Once the core has turned to iron, it can burn no longer. The star collapses by its own gravity and the iron core heats up. The core becomes so tightly packed that protons and electrons merge to form neutrons. In less than a second, the iron core, which is about the size of the Earth, shrinks to a neutron core with a radius of about 6 miles (10 kilometers)."

Captain Planet immediately knew where she was going with this as he tried his best to break free. “But it gets better! The outer layers of the star fall inward on the neutron core, thereby crushing it further. The core heats to billions of degrees and explodes! T hereby releasing large amounts of energy and material into space. The shock wave from the supernova can initiate star formation in other interstellar clouds. The remains of the core can form a neutron star or a black hole depending upon the mass of the original star."

Planet didn't respond. As the millions of years passed by, the pressure increased, causing him immense pain. The sun grew, and he could feel things going on around him that almost perfectly matched her description.

It was then Planet realized just what he had gotten himself into. That he had challeneged a force far beyond his own bearing. And he saw, by him strange omnipresence, that this wasn't some force of evil. He saw that this woman had been teaching people ways to preserve the planet, and being successful in it as well.

Struggling to breath, Planet managed to erk out one finale sentence with a smile. "You've. beaten me. at my own game….I guess…the power…really is…yours…”

"Oh Mr. Planet, don't flatter yourself. You were never even a player."

Right as their exchange ended, the star collapsed inwards on itself, launching a massive explosion that destroyed the entire solar system around it. The energy expanded outwards, followed by a reversal caused by a newly form Black Hole, as it sucked in all the material around for light years. All forms of matter, even those like light itself, were taken in. Everything had been absorbed or crushed.

. And then, blasting from the center of the Black Hole, was a tiny yellow dot exited, being the only object known able to escape the massive force behind it. If sound had carried through space, one might have heard a faint "Yaaahoooooooooooooo!".

Back inside the Bus, Mrs. Frizzle turned to her students. "Well class, I hope you all enjoyed that surprise field trip."

The entire class, save one, cheered in agreement, having had a blast during the entire episode. Arnold had his head between his legs, leaning over a trash can.

"That was amazing!" Wanda declared in excitement.

"That was totally wicked!" Ralphie said in agreement.

"Looks like Captain Planet fell from star. dom." Carlos joked

"Carlos!" The entire class called out before they all broke into laughter as they floated out in space to admire the newly formed black hole.

K.O.

Natalie: "Hell f*cking yeah! Now THAT'S educational!"

Lucas Zaboot: "But- how- why- I-. I am at a loss for words. and that don't happen too often. "

Johnny Zealous: "Luckily, not all of us are. While at first glance, this match seemed to be in the bag for Captain Planet, The Magic School Bus proved to be more effectively faster and stronger than the Hero of Earth."

Lucas Zaboot: (still dumb-founded) "How. How can a bus be stronger than a blue man with the powers of Earth. "

Johnny Zealous: "I'm glad you asked." (taking off his thick-rimmed glasses and putting on a pair of thin-rimmed glasses labeled "Math Tutor Glasses" as he turns to Kra) "Kra? Would you care to assist me in demonstrating?"

Kra: (putting on his own pair of glasses labeled "Smart Human Glasses") "I would be delighted. Ahem* To fully understand how a bus can beat the Champion of Earth, we had to take some extra time to calculate, estimate and measure the Speed, Strength and Durability of both combatants, starting with the Magic School Bus. Play it DJ!"

MAGIC SCHOOL BUS

Johnny Zealous: "While it has been established the bus can go 400 times the speed of light minimum, we decided to try and find a more certain and determined way to calculate the Bus' speed. In the very first episode, the Bus flew out into space and went on a tour around the solar system in the span of 30 minutes, crossing paths with Earth again before it went out towards the planet Pluto. The speed of light is 186,287 miles per second, yet scientists have calculated it takes five hours for the sunlight to reach Pluto, whereas our blue orb of a planet gets the sun in only 8 minutes."

Kra: "The estimated distance between the Earth and Pluto is 4.67 billion miles. While humans haven't found the technology to send one of their own there yet, the fastest pod sent by NASA to fly past there is the New Horizons Pluto module, a module launched in 2006 for the sole purpose of flying all the way to Pluto and beyond to see what lies beyond. That was 8 years ago. Currently, NASA announced the module will reach Pluto by July of this year to begin collecting visual data. With this in mind, we took the to calculator to see how fast it could take the bus to get there."

Johnny Zealous: "Our results concluded that in order for the bus to reach Pluto in 30 minutes, the bus would have had to have gone 2,980,592 miles per second. Four times the speed of light."

Kra: "After witnessing a supernova first-hand, the bus grew a pair of hands large enough to collect the stellar remnant scientists call "a neutron star" and compacted it into a white dwarf. There's a very elaborate equation to determine how to do this, but thankfully, some human on the internet did it for us." (holds up a sheet of paper)

“The average density of material in a neutron star of radius 10 km is 7012110000000000000 1.1吆 12 kgcm 𕒷 . Therefore, 5 ml of such material is 7012550000000000000 5.5吆 12 kg, or 5 500 000 000 metric tons.”

Johnny Zealous: "From these calculations, we were able to determine the bus is strong enough to lift 60 billion tons, that's more than enough to move the moon out of orbit."

Kra: "Remember when we said the bus witnessed a supernova first-hand? That's because it saw it explode right in it's face."

Johnny Zealous: "Recalculating our original assessment, we instead use, for point of comparison, an atomic bomb, which displaces 500,000 tons of force, while a supernova is scientifically estimated to blow with over an octillion tons in force. So, calculate the numbers and the resounding answer is 1,000,000,000,000,000,000,000,000,000,000,000,000 megatons, or 1 Undecillion atomic bombs."

Kra: "Count it for yourself, that's 36 zeroes in that number enough impact to permanently wipe out Europe and ensure nothing grows ever again. You know, if there's still an Earth left as well."

Johnny Zealous: "Not only that, since a supernova's destructive capability differs with the size of a star, they can range between 500,000 Kelvins to 800,000 Kelvins, we managed to determine a supernova going off would top over a million degrees Fahrenheit."

Kra: "But then we come to Captain Planet, a guy who can make up powers on the fly. So to determine his maximum potential, we originally started with what feats he has been able to demonstrate on the show. However we quickly came to realize that this was not a helpful or productive method of getting the correct calculation."

Johnny Zealous: "So, instead of looking towards man-made science to determine Captain Planet's potential, we looked to Mother Nature and calculated from that."

CAPTAIN PLANET

SPEED

Kra: "In the episode "A Good Bomb is Hard to Find," Captain Planet flew into Earth's orbit carrying an atomic bomb set on a timer and flung it into outer space to let it explode harmlessly in a minute. While we determined earlier that Captain Planet's Speed was Mach 10, we found a little fact that would have contradicted this fact."

Johnny Zealous: "Mach 10 is 10 times the speed of sound, around 7,600 mph. In order for rockets to break through Earth's escape velocity, they have to be going over 25,000 mph, therefore, Captain Planet's Mach 10 speed couldn't even break him out of earth's escape velocity in time if he was going this distance."

Kra: "Thankfully, human scientists have and they even took calculative note how long it took them to do it."

"This is the Saturn V, the three-stage liquid-fueled launch vehicle NASA used on July 16, 1969 when human astronauts flew into space to land on the moon. NASA's logs recorded it took the rocket 12 minutes at the speed of 25,000 mph to break escape velocity and arrive in orbit above the Earth."

Johnny Zealous: "With that information, we were able to determine that in order for Captain Planet to fly out into Earth's orbit with a bomb in a minute, he would have had to have gone over 300,000 miles per hour, 394 times the speed of sound and just short of twice the speed of light."

Lucas Zaboot: "Wait, isn't the speed of light in seconds-"

Kra: "Since Captain Planet is described as being Class 100, we decided to look past man-made machinery and look to a feat of strength caused by our very own planet."

Johnny Zealous: "Behold the Valdivia Chilean Earthquake of 1960, the most powerful earthquake ever recorded in human history, resulting in the deaths of 6,000 people and leaving 40% of the city's population without homes."

Kra: "This earthquake devastating magnitude was measured on the Richter Scale at 9.5, the same amount as 2.7 gigatons of TNT, which, when calculated, is 3 billion tons of the earth itself moving."

Johnny Zealous: "To determine Captain Planet's durability, we looked at the second most devastating natural disaster in the world: Volcanoes.

Kra: "What you're looking at is the the Puyehue-Cordón Caulle eruption of 2011. When this erupted, it pumped out 100 million tons of ash and pumice into the air, forcing all manner of aircraft in South America to be grounded. Not only that, it pumped so much ash into the sky, it took two weeks for it to circumnavigate the globe and it still kept pumping ash. Scientists estimated the amount of force required to pull that off required 70 atomic bombs of force, the same equivalent of one thermo-nuclear bomb."

Johnny Zealous: "Ah, but that's not completely devastating. While super volcanos do exist, they have not yet been measured by modern scientists for their destructive force after all the years since their initial eruption. Luckily, we do have one volcanic eruption in recorded history that can give us a close approximation of the devastating power of Mother Nature, precisely 200 years ago."

Kra: "What you're looking at is an artist's rendition of the 1815 Mt. Tambora eruption in Indonesia. When this blew, anyone living 1,000 miles away heard it. It killed over 71,000 humans in the ensuing eruption and the amount of ash it pumped into the air caused the planet to go into a global cooling effect that resulted in wide-spread harvest failure and causing 1816 to be referred to as "The Year Without a Summer." You want devastating, this is it."

Johnny Zealous: "Now scientists were able to estimate from witness accounts and personal letters that detailed the eruption that the eruption produced 3.3 quintillion joules, that's about 78,871 megatons of force.
For comparison, we used the most powerful bomb mankind has ever tested: The Tsar Bomba.

Kra: "What you're watching is 50 megatons of TNT at work. If that's scary, try to imagine 1,577 of these things going off at once 200 years ago. That's enough destructive force to wipe out the United States of America and half of Canada."

Johnny Zealous: "All right, we crunched the numbers and placed them on a graph to show their respective differences. The result?"

Kra: "As you can see, numbers speak for themselves."

Lucas Zaboot: "J-Jesus. science is fucking scary. "

Natalia: "In the words of Boomstick, "Not Even Close."

Johnny Zealous: "Though keep in mind, we were able to get these numbers based on the potential both characters can demonstrate and the scientific studies done to look at our own planet and beyond ours. When taking that into consideration, it becomes clear to see why the bus COULD win. The Bus CAN leave Earth's orbit and fly around into the far reaches of space for exploration and knowledge, Captain Planet cannot."

Kra: "Furthermore, had Planet tried to transform the Bus into something else, the Bus could have changed back easily. It's interior never changes much when it transforms, and it's been transformed against it's will before as well. And had Planet tried to dismantle the Bus, he would have been stopped by the Bus's regular Ol' engine, full of chemicals and gases that would be toxic to him."

Johnny Zealous: "When you take that major limitation into our factors, it's clear to see why the bus won this fight, in more ways then one really. "

Kra: "When you really break it down, the moral stance of Captain Planet is "Earth is the only planet we have to live on, do your part to clean it up." However, the optimism for the future comes from Captain Planet guilting the young impressionable viewers to take action by presenting negative stereotypes of big business tycoons as being pollution-happy and uncaring about the planet and it's limited resources in order to take action to clean up the mistakes of humans who are too dumb to realize their actions. The Magic School Bus, is different in this regard. "

Johnny Zealous: "The Bus has broken out of earth's orbit many times, shrunk to sub-atomic size, entered the bodies of humans to look at their digestive track, their skin cells and their muscles. But the core principle of the show is the optimism and encouragement to LEARN. Ms. Frizzle doesn't take her students on field trips to guilt them to learn something about science and the universe, she encourages her students to learn from seeing these mysteries and let them come to their conclusions, always praising them the kids when they understand but also never putting them down for getting it wrong."

Kra: "After all, her catchphrase is "It's time to take chances, make mistakes and get messy." Why? Because THAT is learning."

Lucas Zaboot: "Wait. I think I get it now. Captain Planet's a condescending douchebag for putting the blame of Earth's problems on kids who don't know any better and the Magic School Bus is about encouraging kids to make mistakes so they'll know not to f*ck up again!"

Kra: "Exactly! It's because of this that Captain Planet not only loses the Death Battle, but the nostalgia battle as well. He's not the hero for our time, he's the hero for the finger-pointing social justice warriors of Tumblr."

Natalie: (awkward silence) "the fuck was that?"

Johnny Zealous: "Referential humor, our- um- sponsor has that habit. "

Kra: ". it's weird.." (removing his "smart human glasses")

Johnny Zealous: (changing his glasses back to their typical wide-brim lens) "I don't choose them, I just take the money."

Lucas Zaboot: "And so am I! All the bets I made on this fight that is! heh heh heh! F*ck you, Captain Planet, power is mine, ya bitch."

Kra: "Looks to me Captain Planet just got schooled."

Natalia: "The Winner is the Magic School Bus."

The Magic School Bus:
+Many times faster
+Many times more durable
+Many times Stronger
+More versatile and adaptable
+Mrs. Frizzle is much smarter than Captain Planet
-Poor ranged options
-No combat experience
-Inconsistency is still an issue

Captain Planet:
+More experience in battle
+Better range
+Can make up powers on the fly
-Speedblitz'd
-No where near as strong
-No where near as durable
-Horribly inconsistent
-Weakened the farther he is from Earth
-Cannot Kill


Fremont Peak 5/26

Well, I’m going to be taking the first trip of the season up to the Fremont Peak observatory.

Things have been a bit delayed this year so far, because my oldest daughter was in some local theater productions. I’m a bit worried, because I have some issues going on with my neck, which could make observing painful. I’ve been having the issues for a while (gradual onset of pain over the last couple of years), but they got bad enough for me to go back to my doctor and bug him for a diagnosis. I was sent to get an MRI, and it turns out that I have a bulging or herniated disk between C5 and C6. This is what was causing the pain from my neck down my right arm to my fingertips, and is now causing intermittent tingling/numbness as well.

So, we’ll just have to take things as they come, and see how it goes.

If you are in the South San Francisco Bay Area, and are interested in having me come to your elementary/Jr. High classroom and speak about astronomy, please let me know.


Forerunners vs Interim Coalition of Governance

The Forerunners vs our favorite xenocidal species: Xeeleeverse Exultant-Era Humanity!

Bonus round is winner vs the Silentium Flood

Disagreeable

Enraged Antimatter God

The Forerunners vs our favorite xenocidal species: Xeeleeverse Exultant-Era Humanity!

Bonus round is winner vs the Silentium Flood

Onlinemph

ICG had time prescience, along with some pretty impressive ships, correct?

I remember reading about black hole guns and what not.

Disagreeable

Enraged Antimatter God

ICG had time prescience, along with some pretty impressive ships, correct?

I remember reading about black hole guns and what not.

Onlinemph

It's been a while since I read the book but were not they fighting with the xeelee in just one galaxy? Where as the the Forerunner had around three million planets. I also remember some impressive construction feats for the Forerunners also.

Still it's all irrelevant in the face of time pre-science and pulling copies of yourself from individual planck times.

Zak757

Time travel, that is all. Interim Coalition of Grimdark Xenophobic Pricks wins because of it, unfortunately. FTL in Xeeleeverse breaks causality like that.

Hopefully the Forerunners find a way to reverse engineer their technology during the war so they can tear those child killing assholes to pieces.

Hazimat

Analysising Blueprints.

Losses of 100 Billion lives per decade and whatever material they commited for however many decades they had been assaulting the Xeelee.

Even without their tech, the ICG put up a good fight on sheer numbers alone.
Then you factor in that they were disassembling stars in real time for resources, CTC computer, IIRC nano-second reaction "virtual copies" of pilots who are the one really piloting the greenships, starbreakers, blackhole guns, the library of possible futures.

Mist2123

What title?

No amount of forerunner wank and reverse engineer wank is going to save them from the ICG from tearing them a new one. Look at what happened to the Silver Ghosts, they were using similar technologies and still got crushed by humanity.

We're talking about people who have no moral compunctions about doing stupid shits like throwing away an average of 10 billion loves per year in space-trench warfare for 20,000 years+ (200000000000000) and pants down retarded ideas like blowing up Chandra the home of the MonadsPissing-off God.

They can sustain those losses in with their war Xeelee in the Milky way alone, and they can keep chugging with those kind of losses, and counting, for the next million years.

Shit man they suffered an average of 10 billion losses per year for 20,000 years+ (200000000000000) with their war Xeelee in the Milky way alone, and they can keep chugging with those kind of losses, and counting, for the next million years.
The coalition maybe dumb, but they aren't terminally dumb.

I mean they did successfully exterminate the Silver Ghost The same species that created the Ghost pits and Gravstar Shields.

Ghost pits: Area Denial weapons by imposing a radically alien physics on a large area. Where any non-biological weapon basically falls apart because of the physics that govern those weapons don't exist anymore.
Gravstar Shield: Pocket universe bubbles that block FLT-foreknowledge.

Forerunners get swarmed in less than a year.

TLDR
This ends up with Didact and the Qax stroking their hate boners for humanity in the next million years.


Watch the video: Πως μία μαύρη τρύπα μπορεί να σε σκοτώσει (February 2023).