Help understanding ring diagram analysis used in helioseismology

Help understanding ring diagram analysis used in helioseismology

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I need help understanding something. In global helioseismology we study the modes directly (stationary waves characterized by 3 integers numbers: $n$, $l$ and $m$). As the angular degree $l$ becomes bigger, the acoustic waves don't form a stationary wave (mode) anymore (they don't have enough lifetime anymore).

But, I'm working with ring diagram analysis (one of the techniques of local helioseismology) for these waves that don't form a mode. And in the data we still have and integer number $n$ (number of nodes in radial direction) and a non-integer number of $l$ (because the wave is not stationary).

I don't understand, what does that mean?? I have an $n$ and $l$ describing a propagating wave? What is the physical mean of that?

Local Helioseismology of Sunspots: Current Status and Perspectives

Mechanisms of the formation and stability of sunspots are among the longest-standing and intriguing puzzles of solar physics and astrophysics. Sunspots are controlled by subsurface dynamics, hidden from direct observations. Recently, substantial progress in our understanding of the physics of the turbulent magnetized plasma in strong-field regions has been made by using numerical simulations and local helioseismology. Both the simulations and helioseismic measurements are extremely challenging, but it is becoming clear that the key to understanding the enigma of sunspots is a synergy between models and observations. Recent observations and radiative MHD numerical models have provided a convincing explanation for the Evershed flows in sunspot penumbrae. Also, they lead to the understanding of sunspots as self-organized magnetic structures in the turbulent plasma of the upper convection zone, which are maintained by a large-scale dynamics. Local helioseismic diagnostics of sunspots still have many uncertainties, some of which are discussed in this review. However, there have been significant achievements in resolving these uncertainties, verifying the basic results by new high-resolution observations, testing the helioseismic techniques by numerical simulations, and comparing results obtained by different methods. For instance, a recent analysis of helioseismology data from the Hinode space mission has successfully resolved several uncertainties and concerns (such as the inclined-field and phase-speed filtering effects) that might affect the inferences of the subsurface wave-speed structure of sunspots and the flow pattern. It is becoming clear that for the understanding of the phenomenon of sunspots it is important to further improve the helioseismology methods and investigate the whole life cycle of active regions, from magnetic flux emergence to dissipation. The Solar Dynamics Observatory mission has started to provide data for such investigations.

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Features of the H–R Diagram

Following Hertzsprung and Russell, let us plot the temperature (or spectral class) of a selected group of nearby stars against their luminosity and see what we find ([link]). Such a plot is frequently called the Hertzsprung–Russell diagram, abbreviated H–R diagram. It is one of the most important and widely used diagrams in astronomy, with applications that extend far beyond the purposes for which it was originally developed more than a century ago.

Figure 3. In such diagrams, luminosity is plotted along the vertical axis. Along the horizontal axis, we can plot either temperature or spectral type (also sometimes called spectral class). Several of the brightest stars are identified by name. Most stars fall on the main sequence.

It is customary to plot H–R diagrams in such a way that temperature increases toward the left and luminosity toward the top. Notice the similarity to our plot of height and weight for people ([link]). Stars, like people, are not distributed over the diagram at random, as they would be if they exhibited all combinations of luminosity and temperature. Instead, we see that the stars cluster into certain parts of the H–R diagram. The great majority are aligned along a narrow sequence running from the upper left (hot, highly luminous) to the lower right (cool, less luminous). This band of points is called the main sequence. It represents a relationship between temperature and luminosity that is followed by most stars. We can summarize this relationship by saying that hotter stars are more luminous than cooler ones.

A number of stars, however, lie above the main sequence on the H–R diagram, in the upper-right region, where stars have low temperature and high luminosity. How can a star be at once cool, meaning each square meter on the star does not put out all that much energy, and yet very luminous? The only way is for the star to be enormous—to have so many square meters on its surface that the total energy output is still large. These stars must be giants or supergiants, the stars of huge diameter we discussed earlier.

There are also some stars in the lower-left corner of the diagram, which have high temperature and low luminosity. If they have high surface temperatures, each square meter on that star puts out a lot of energy. How then can the overall star be dim? It must be that it has a very small total surface area such stars are known as white dwarfs (white because, at these high temperatures, the colors of the electromagnetic radiation that they emit blend together to make them look bluish-white). We will say more about these puzzling objects in a moment. [link] is a schematic H–R diagram for a large sample of stars, drawn to make the different types more apparent.

Figure 4. Ninety percent of all stars on such a diagram fall along a narrow band called the main sequence. A minority of stars are found in the upper right they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram they are both hot and dim, and must be white dwarfs.

Now, think back to our discussion of star surveys. It is difficult to plot an H–R diagram that is truly representative of all stars because most stars are so faint that we cannot see those outside our immediate neighborhood. The stars plotted in [link] were selected because their distances are known. This sample omits many intrinsically faint stars that are nearby but have not had their distances measured, so it shows fewer faint main-sequence stars than a “fair” diagram would. To be truly representative of the stellar population, an H–R diagram should be plotted for all stars within a certain distance. Unfortunately, our knowledge is reasonably complete only for stars within 10 to 20 light-years of the Sun, among which there are no giants or supergiants. Still, from many surveys (and more can now be done with new, more powerful telescopes), we estimate that about 90% of the true stars overall (excluding brown dwarfs) in our part of space are main-sequence stars, about 10% are white dwarfs, and fewer than 1% are giants or supergiants.

These estimates can be used directly to understand the lives of stars. Permit us another quick analogy with people. Suppose we survey people just like astronomers survey stars, but we want to focus our attention on the location of young people, ages 6 to 18 years. Survey teams fan out and take data about where such youngsters are found at all times during a 24-hour day. Some are found in the local pizza parlor, others are asleep at home, some are at the movies, and many are in school. After surveying a very large number of young people, one of the things that the teams determine is that, averaged over the course of the 24 hours, one-third of all youngsters are found in school.

How can they interpret this result? Does it mean that two-thirds of students are truants and the remaining one-third spend all their time in school? No, we must bear in mind that the survey teams counted youngsters throughout the full 24-hour day. Some survey teams worked at night, when most youngsters were at home asleep, and others worked in the late afternoon, when most youngsters were on their way home from school (and more likely to be enjoying a pizza). If the survey was truly representative, we can conclude, however, that if an average of one-third of all youngsters are found in school, then humans ages 6 to 18 years must spend about one-third of their time in school.

We can do something similar for stars. We find that, on average, 90% of all stars are located on the main sequence of the H–R diagram. If we can identify some activity or life stage with the main sequence, then it follows that stars must spend 90% of their lives in that activity or life stage.


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Astronomy Lab and Clay Telescope

Your Final Report for Evelab is meant for you to summarize your Observations and data Reductions for EL-Obs 3 (M39 H-R diagram) and EL-Obs 4 (M57, the Ring Nebula, and M31, the Andromeda galaxy) and to carry out some simple analysis of all 3 objects to learn some basic properties of these 3 different "extended" objects: a star cluster, a Planetary Nebula, and a galaxy. Since all 3 objects are photometry projects, your Introduction section of the paper should briefly refer to EL-Obs 2 and what you did and learned about Albireo. You will derive some basic characteristics of each of the 3 objects in your Analysis section, and in your Discussion section you can inter-compare them: how they each provide key insights into properties of stars, stellar evolution, and the vast conglomeration of stars that form a galaxy. You should summarize your observations, data reduction and analysis for each of these 3 objects ias the first 3 sections (following a general Introduction section) of your Report and then in a Discussion section inter-compare them. Following are the principal data reduction and data analysis tasks to carry out for each object:

In EL-Obs 3, you have already prodcued your H-R diagram which is the results of your observations being reduced to photometry. Use your "final" H-R diagram plot to draw the cluster main-sequence on your plot of V vs. (B-V) for all teh stars measured and incorporating any comments we made on your EL-Obs 3 Report. You H-R diagram will include stars from ALL the fields combined. Then circle or color red the stars on the plot from only the central field (i.e. not NW, SE, etc.) that are on or near the m-s turnoff and count the number of these central field stars, Nstars, (NOTE: since all data & fields were combined, TFs will send to everyone the B and V mad values for all stars measured in just the central field, including any that are in the central field but might have been actually measured in anothr field due to field overlaps.)

First, derive the distance (in pc) to M39 by plotting a line for the main sequence (hereafter m-s) for absolute magnitude MV vs. (B-V) using the figure B-V vs. MV HR diagram. Pick TWO values of your measured M39 m-s line for V vs. (B-V) at (B-V) values of 0.4 and 0.8. Your observed m-s line should be roughly parallel to the m-s line for MV vs. (B-V) from the reference figure over this range of the m-s. Take the difference, mV - MV, at 2 points along the line (at B-V values 0.4 and 0.8) and average those two differences for your best estimate of mV - MV, the distance modulus, and derive d in pc. Your estimated error in mV - MV could be the difference of either or both of your "end points" from the average value of mV - MV you derived, and from the hight vs. low values of mV - MV (on either side of your average) you can derive the corresponding distance to give your error in the cluster distance.

Second, derive the approximate age of the M39 cluster. Mark the turnoff point on your observed m-s where the stars begin to fall above (brighter than) the m-s line you have drawn for stars fainter and redder. Note the (B-V) color of this turnoff and compare with the template H-R diagra figure B-V vs. MV HR diagram. What is the Spectral Type for your estimated (B-V) at the Turnoff? Then using the table M-S mass vs SpType Table, estimate the mass of stars at the turnoff point. You could estimate the uncertainty on this by estimating the uncertainty of where you marked the B-V color and from that comparing the max vs. min mass estimates. Finally, for your estimated turnoff mass, derive the age of M39, using our equation for m-s lifetime, Tm-s 10 10 /(M/Msun) -2.5 years. Once again, from your approximate uncertainty on the turnoff mass, you can estimate a rough uncertainty on the cluster age.

Third, use your derived distance d(pc) and the skinny triangle formula to derive the width, W(pc) of the cluster central field, give the angular size of the field of view of our CCD camera which is A(arcmin) = 13 arcmin. Convert this to radians using conversion 1 arcmin = 1/60 degree and 1 degree = &pi/180 radians = 3.14/180 radians. Then derive the density of stars in a box in M39 with side W(pc) in the central field: Density(stars) = Nstars/W(pc) 3 where Nstars is the number of stars on or near the m-s and turnoff in your H-R diagram for stars in the central field that you should have circled and counted (see above). How does the central M39 stellar density, in units stars/pc 3 , compare with the density of stars near the Sun, which is about 0.1 stars/pc 3 ?

M57 (Ring Nebula)

In your EL4-Obs Report, you (should) have derived B and V magnitudes (ideally each as the average of 2 measurements) for the central 4 pixel radius surrounding the central white dwarf (WD) as well as B and V magnitudes for the Ring, between 12 pixel radius and either 17 or 20 pixel radius.

First, given the distance to the Ring Nebula of d=700pc, derive the absolute magnitude in the V band, MV, for the WD and for the Ring shell. What are the luminosities in solar units for each source in the V band? (use the absolute magnitude definition: MV = -2.5logLV+ const to derive LV(WD or Ring)/LV(Sun) = 10 -0.4(MV(WD or Ring) - MV(Sun)) , where MV(Sun) = +4.7.

Second, derive the approximate temperature of the WD and the Ring, assuming both are black bodies, from the B-V mag and the scale of B-V color vs. temperature as plotted on the H-R diagram figure B-V vs. MV HR diagram or use the plot from Lecture, namely the figure Temp vs. B-V m-s stars. Note the WD B-V is "contaminated" by the nebula (in V) so temperature will likely be too low.

Third, check your estimated temperature for the Ring Nebula against what its radius and luminosity would say it should be (in solar units) if the Ring is a black body. You need to first derive the Ring radius in km to compare it with the Sun (since your luminosity is also in solar units). For that you need to know 1 pixel = 1.56 arcsec and convert to radians and use the Skinny Triangle formula for the M57 distance given above. Use the Ring radius as the "Outer shell" radius of 17 or 20 pixels as listed above. What about the WD temperature? It is a (relatively) massive WD, with mass M

0.007 Rsun. For this radius, and your measured MV for the WD, what should its Black Body temperature be?

M31 (Andromeda)

Once again, use your Reductions to magnitudes from your EL-Obs 4 Report and you Table of B and V magnitudes for the 4 apertures of radii 16, 32, 48, and 96 pixels.

First, given the distance to M31 of 780 kpc, derive the absolute magnitude of the enclosed light from M31 in the V band in each of the 4 apertures. These absolute magnitudes, MV, should be derived from your average observed V magnitude (if you indeed had 2 measurements in each aperture).

Second, derive the B-V color of the 4 regions of the Bulge of M31 and for each, estimate the spectral type by using the conversion from B-V spectra type given in the H-R diagram plot B-V vs. MV HR diagram. Estimate the sub-type (e.g. G2 vs. G5) by interpolating on the scale across the top of this diagram.

Third, derive the approximate total mass in each of the 4 aperture regions by using your derived absolute magnitude MV and the corresponding value for the Sun (MV = 4.7). The difference in these absolute magnitudes is of course the ratio of the luminosities, just as you did above for M57. The ratio of the luminosities is then teh ratio of the masses (assuming a fixed mass/luminosity ratio = 1 in solar units). From your 4 mass-enclosed numbers, make two plots: 1) Mass enclosed(solar masses) vs. Radius(pc) and 2) mass in each annulus (the central 12 pixel radius aperture is still enclosed mass) derived by subtracting the total luminosityor mass in aperture 1 from aperture 2 aperture 2 from aperture 3 etc. For BOTH plots, try using logarithmic scales, since the values for mass will range over more than a factor of 10. So plot on y-axis log(mass) and on x-axis log(radius) values. [you can also make plots without log scales for comparision, if you like]. For plot 2, on log scales, what is the approximate slope of a rough fit line through your 4 points? Summarize your results for both plots with two Tables showing values for each aperture radius. The Tables should have the following column headings:

Radius(pix) | Radius(pc) | B mag | V mag | (B-V) | MV | L/Lsun | M/Msun

The final 2 columns in each row should give the enclosed or annulus luminosity and mass for that aperture in solar units using the same formalism as above for M57, and see below for deriving the enclosed mass for each aperture (assuming a constant M/L ratio).

Fourth, and finally, what kind of stars are responsible for most of the light in each aperture? Use the figure B-V vs. MV HR diagram to convert from B-V to spectral type.

Discussion Section: Combined for all 3 "Nebulae" (at the end of the Report)

Here you can put your own words down to describe your understanding of these 3 very different, but related, "nebulae". Only on of them (the Ring) is a true nebula, of course, but all 3 are Messier Catalog objects which means they are extended and not "just" single stars. Here are a few items you can discuss in this

1.5 page sections of your Report:

  • Is M39 still in the process of forming stars? If not, why not? (hint: is there any obvious nebular gas or dust?)
  • Why is there not a "Ring Nebula" as one of the "stars" in M39? Could there have been one? (hint: how long does a Planetary nebula "live"?)
  • Why does hte Ring Nebula (the Ring part) not resemble a BB? Why is the WD so blue? (you may not be able to detect it in R and just barely in V?)
  • For M31 with a total mass in stars of

Format of the Evelab Final Report

0.5 page) to measure these 3 very different "extended" objects? How did they all "build" on what you did in EL-Obs 2?

Observations: Describe (briefly 0.5-1 page) the observations you did for your ObsReports 3-4 and your observations and your estimate of measurement uncertainties - e.g., your approximate uncertainties in your V and B magnitudes (rough estimate) from scatter (if you have more than one measurement) or from how well you centered on M57 or M31

Data reductions: Brief summary (

0.5-1 page) of how you "reduced" your measured observations and derived your measurement uncertainties. Estimate your uncertainty in HOW you fit the m-s in M39 and thus its distance. What is your rough estimate of the uncertainty in your distance estimate (in pc units) for M39 and the corresponding uncertainty in stellar density? What is your estimated uncertainty in the mass within the 4 regions of M31?

Data analysis:In this section (

4-5 pages you need at least a page for each of your 3 objects), you describe how you used your measurements to derive the values for the items listed above. As noted below, please show your work in the Appendix.

Discussion (1-2 pages): Here you can have some fun: in your own words, interpret your data. What do the numbers of bright vs. faint stars on the m-s tell us about hte distribution of stellar mass in M39? How do M39 and M57 show stellar evolution? What do the V magnitudes and derived MV and masses in the 12-96 pixel apertures tell you about how luminosity and mass per unit area in each annulusrise toward the center?

News & seminars


Prof. Laurent Gizon (Principal Investigator)- top left

Dr. Vasilis Archontis (Principal Investigator) - top right

Prof. Mats Carlsson (Principal Investigator) - bottom left

Dr. Allan Sacha Brun (Corresponding Principal Investigator) - bottom right

Preparation of the ERC Synergy oral at the end of August 2018.

Fernando Moreno-Insertis (Co-Investigator)

Host Institutions

Teams members

Prof. Laurent Gizon
Dr. A. Birch
Dr. R. Cameron

F. Kupka, Senior Postdoc
(05/01/19 – 06/30/20)
K. Mandal, Postdoc
(11/01/19 - )
D. Fournier, PhD
(10/01/20 -)
C. Goddard, Postdoc
(05/01/19 – 06/01/20)
S. Cloutier, PhD
(01/01/20 - )
Y. Bekki, PhD, Postdoc
(03/01/20 - )

Dr. Vasilis Archontis
Prof. A. Hood

P. Syntelis, Postdoc
(05/01/19 – 10/01/19)
A. Borissov, Postdoc
(09/01/20 - )
G. Chouliaras, PhD
(09/27/20 - )

Oslo University

Prof. Mats Carlsson
Prof. V. Hansteen
Associate Prof. B. Gudiksen

K. Krikova, PhD
(09/01/20 - )
R. Robinson, PhD
(09/23/19 - )
Andrius Popovas, Research Software Engineer
(01/03/2020 - )

Dr. Allan Sacha Brun
Dr. P. Kestener
Associate Prof. M. Browning
Assistant Prof. L. Jouve
Dr. A. Strugarek

Q. Noraz, PhD
(10/08/19 - )
R. Pinto, Senior postdoc
(01/06/20 - )
A. Finley, Postdoc
(12/01/20 - )
M. Delorme, Senior postdoc/HPC researcher

Prof. F. Moreno-Insertis
Dr. M. Collados
Prof. J. Trujillo-Bueno
Dr. E. Khomenko

B. Coronado, PhD, in kind contribution
(11/01/20 - )
D. Nobrega,Postdoc
(03/01/21 - )
Manuel Luna, Senior postdoc, in kind contribution (05/19 - ) .


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Astronomy Lab and Clay Telescope

Photometry is the quantitative measurement of both the flux and color of a star. This lab will guide you to understand how to calculate the magnitudes of the stars from CCD images. We will observe two bright stars in the constellation Orion, Betelgeuse and Rigel. Because the telescope and camera are so sensitive, and Betelgeuse and Rigel are so bright, we will use an Aperture Mask when taking images to prevent our CCD camera from saturating. Using this aperture mask effectively makes our telescope aperture smaller and allows us to collect moreaccurately measure the star flux without the complications of saturated images (which would introduce large systematic errors).

Procedure (at the telescope):

    First, we'll take our calibration images of Alcyone, which is the brightest star in the Pleiades Cluster. This star will be the standard that we base our observations on. Slew the telescope to Alcyone.
      Move the filter to B and take 3 images making sure that Alcyone has no more than 40,000 counts in its peak pixel for each exposure. Start with a short exposure time of 0.5 seconds and adjust accordingly to get

    Astronomy Lab and Clay Telescope

    Photometry is the quantitative measurement of both the flux and color of a star. This lab will guide you to understand how to calculate the magnitudes of the stars from CCD images. Because the telescope and camera are so sensitive, and Albireo and Vega are so bright, we will use an Aperture Mask when taking images to prevent our CCD camera from saturating. Using this aperture mask effectively makes our telescope aperture smaller and allows us to collect moreaccurately measure the star flux without the complications of saturated images (which would introduce large systematic errors.

    Procedure (at the telescope):

    • First, we'll take our calibration images of Vega. Slew the telescope to Vega.
    • Move the filter to B and take 3 images making sure that Vega has no more than 40,000 counts in its peak pixel for each exposure. Start with a short exposure time of 0.5 seconds and adjust accordingly to get


    This article has at best only managed a superficial introduction to the very interesting field of Graph Theory and Network analysis. Knowledge of the theory and the Python packages will add a valuable toolset to any Data Scientist’s arsenal. For the dataset used above, a series of other questions can be asked like:

    1. Find the shortest path between two airports given Cost, Airtime and Availability?
    2. You are an airline carrier and you have a fleet of airplanes. You have an idea of the demand available for your flights. Given that you have permission to operate 2 more airplanes (or add 2 airplanes to your fleet) which routes will you operate them on to maximize profitability?
    3. Can you rearrange the flights and schedules to optimize a certain parameter (like Timeliness or Profitability etc)

    If you do solve them, let us know in the comments below!

    Network Analysis will help in solving some common data science problems and visualizing them at a much grander scale and abstraction. Please leave a comment if you would like to know more about anything else in particular.

    When one become two: Separating DNA for more accurate nanopore analysis

    A new software tool developed by Earlham Institute researchers will help bioinformaticians improve the quality and accuracy of their biological data, and avoid mis-assemblies. The fast, lightweight, user-friendly tool visualises genome assemblies and gene alignments from the latest next generation sequencing technologies.

    Called Alvis, the new visualisation tool examines mappings between DNA sequence data and reference genome databases. This allows bioinformaticians to more easily analyse their data generated from common genomics tasks and formats by producing efficient, ready-made vector images.

    First author and post-doctoral scientist at the Earlham Institute Dr Samuel Martin in the Leggett Group, said: "Typically, alignment tools output plain text files containing lists of alignment data. This is great for computer parsing and for being incorporated into a pipeline, but it can be difficult to interpret by humans.

    "Visualisation of alignment data can help us to understand the problem at hand. As a new technology, several new alignment formats have been implemented by new tools that are specific to nanopore sequencing technology.

    "We found that existing visualisation tools were not able to interpret these formats Alvis can be used with all common alignment formats, and is easily extensible for future ones."

    A key feature of the new command line tool is its unique ability to automatically highlight chimeric sequences -- weak links in the DNA chain. This is where two sequences -- from different parts of a genome or different species -- are linked together by mistake to make one, affecting the data's accuracy.

    Chimera sequences can be problematic for bioinformaticians when identifying specific DNA. The chimera formation can physically happen to the DNA molecules during either sequencing library preparation, during the sequencing process on some platforms, and by assembly tools when trying to piece together a genome.

    During the development of the tool, the team compared genome assemblies with and without using Alvis chimera detection. The vector image produced shows an example output, where the intuitive tool tracks all reads it recognises as chimeras.

    "Although chimeric sequences don't make up a large proportion of samples, they can have a significant effect, so we have to be careful that we have identified them during analysis," said Dr Martin.

    "In the Alvis diagram example of chimera data, each rectangle across the page represents a read, and the coloured blocks inside them represent alignments. Most chimeras are easy to see because their alignments are different colours, meaning they map to different genomes. Others are more subtle because both alignments are to the same genome, but different regions."

    The Alvis tool can pinpoint visualisation of only chimeric sequences for further inspection, and output numerical data describing the chimeras. This demonstrates that by applying the tool and then bioinformatically splitting the chimeras, the quality of the assemblies is significantly improved.

    Accessed over 600 times since being made available at the beginning of March this year, Dr Martin, adds: "We hope that Alvis continues to be useful to other researchers working with, for example, nanopore sequencing improving their understanding of their data by visualising alignments,''.

    "Alignments are so fundamental to bioinformatics that it could be of use to anyone working with long read sequencing data, as well as alignments generated by sequencing data from short-read platforms. The diagrams that Alvis generates can be easily exported to directly use in publications, demonstrated in our study already."

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