SH #3: Understanding Galaxies         Group Project

Team B:       Large scale structure in the local Universe

In this activity, you will investigate the distribution of galaxies in the local universe and the impact of clustering on Hubble's Law locally. Because the distributions of galaxies and dark matter are not uniform in the nearby universe (i.e. both tend to cluster), the expansion of the universe locally is not perfectly smooth. Galaxies are accelerated towards overdensities in the mass, especially clusters. Your task is to understand the importance of "peculiar velocities", the deviations from smooth Hubble expansion in the local universe and then to investigate some of the local structures. Keep in mind that many surveys only cover part of the sky. Your task will include trying to understand the importance of "cosmic variance", the effect of not having a fully "fair sample" of the universe. The universe, in both space and time, is a messy place!

Hint: you can view a bigger version of the images by clicking on them.

Deviations from Hubble expansion

We know that locally, the expansion of the universe is "perturbed" by the fact that galaxies tend to cluster. As depicted in the cartoon to the right, taken from a publication in the 1980's, it has been known for some time that the Local Group is falling towards the Virgo Cluster, even as the local universe expands.

  •   Use this cartoon to understand why the "peculiar velocity" of galaxies nearby limits our ability to use Hubble's Law to derive distances from velocities.

  •   If we measure the redshift (radial velocity) of a galaxy in the direction of the Virgo cluster but closer to us than the cluster, would we expect its observed velocity to be higher or lower than its distance would suggest if we invoked Hubble's Law?

  •   What if the galaxy were located in the direction of Virgo but at a larger distance?
  • Credit:
    Aaronson et al 1986
    ApJ 302, 536

    Hubble expansion around the Virgo cluster

    To demonstrate the concept, the next diagram shows the results of a model of the local flow field in the plane of the Local Supercluster very close to us. It is taken from a review article by Davis and Peebles in 1983. Be aware that the details are a bit out of date; note that the distance of the Virgo cluster they assumed in making this model was 15 Mpc, and we know it is larger than that (more like 16.7 Mpc). However, the diagram should be useful to help you understand the local flow field.

    The x axis shows the distance from us. The angular scale (in degrees) measures the angular distance from the direction of the Virgo cluster as viewed from the Sun. The heavy contours trace the heliocentric velocity expected for a galaxy at a given distance away from us in different directions. The short dashed circles show the velocities we would expect if the velocity field were not perturbed, that is, if the Virgo cluster were not there.

  •   Be sure you understand how to interpret this diagram.

  • Credit: Davis and Peebles, 1983, ARA&A 21, 109

    Predicting distances using a flow model: a case study

    The galaxy NGC 4565 is a spiral galaxy viewed almost perfectly edge-on. It is located at an angular distance of about 13 degrees from the center of the Virgo cluster. Use the tools you know about (e.g. NED and SKYDEG) to learn more about this galaxy.

  •   What is the observed heliocentric recessional velocity of NGC 4565?

  •   According to the model velocity field of the Local Supercluster, at what distance would a galaxy seen 14 degrees from the Virgo cluster have a heliocentric velocity equal to that of NGC 4565? Remembering that the model underestimates the distance of Virgo, use the diagram to predict the galaxy's distance based on the model and its observed recessional velocity.

  • Credit: R. Ritter
  •   NED gives 21 values of "redshift independent distances"; individual distances have to be used with a grain of salt, because they are a very inhomogeneous and complex set of data which adopt different distances to Virgo, different values of the Hubble constant, etc. The NED folks try to correct for those things to adopt a "mean metric distance". What value do they get? How does it compare with the value you predicted from the model?

    Supergalactic coordinates

    In the mid 1950's, Gerard deVaucouleurs noticed (as we shall soon) that the nearby galaxies within about 40 million galaxies are not distributed evenly around the sky, but rather the majority of them trace a band around the sky. The distribution of "nebulae" in a continuous band was actually noticed by William Herschel more than 200 years earlier. DeVaucouleurs realized that the distribution could be explained if the galaxies were mainly found in a flattened disk-like structure which he referred to as the "supergalactic plane".

    Galaxies with supergalactic latitude SGB = 0 degrees lie in this plane. Supergalactic longitude SGL is measured along the plane with its origin (SGL = 0 degrees, SGB = 0 degrees) lying near Galactic longitude l = 138 degrees and latitude b = 0 degrees (i.e. in the Galactic plane too).

    An alternative system, called the cartesian supergalactic coordinates SGX, SGY, SGZ. It requires knowledge of distance because its units are in Megaparsecs. SGX is directed towards the point SGL = 0 degrees, SGB = 0 degrees and the SGZ axis towards the north supergalactic pole, SGB = +90 degrees. With this definition, SGX and SGY are in the supergalactic plane, where SGZ = 0 degrees.

    Credit: R. Powell
    Find the NED entry for the Virgo cluster to find its coordinates in various systems. Write them in decimal degrees in epoch J2000. Then think about where Virgo must lie in the SGX, SGY, SGZ system.

    R.A. & Dec.  
    l, b  
    SGL, SGB  
    SGX, SGY, SGZ  

    Mathematically, we can use a galaxy's equatorial position (R.A. and Dec.) to calculate its "supergalactic coordinates", supergalactic longitude (SGL) and latitude (SGB). And, if we know the distance to a galaxy, the "cartesian supergalactic coordinates" SGX, SGY, SGZ can be assigned using some fairly simple mathematical formulae:
                  SGX = distance*cos(SGL)*cos(SGB)
                  SGY = distance*sin(SGL)*cos(SGB)
                  SGZ = distance*sin(SGB)

    Calculating distances for real: What the Cornell EGG does!

    Since one of the main aims of ALFALFA is to take a census of galaxies in the local universe, members of the Cornell ExtraGalactic Group are always trying to figure out how best to determine distances to nearby galaxies. It's one of those never-ending projects that has to be revisted every few years as new and better observational data, obtained by many people using many different methods, become available. (We could spend all week talking just about this, but we won't!)

    To calculate distance, we use a "hybrid flow model" developed by Karen Masters (CU PhD 2004, now at the University of Portsmouth, UK) to calculate the distance to each object. Since we know that Hubble's Law does not apply locally, Karen's approach to assigning distances is a bit complicated. It uses "primary distances" where they are available and has a built-in assignment of some galaxies to their parent groups or clusters (most notably, the Virgo cluster). In the absence of some redshift- independent distance measurement, it uses a model of the local velocity field (predicting the distance to a galaxy of a given observed heliocentric velocity in a specific direction) that Karen devised by examining all of the galaxies with known distances. It's not perfect, but it is better than using Hubble's Law.

    Notice that Karen's diagram extends to larger distances that the one from Davis and Peebles which we used above.

    from Masters, 2004, CU Ph.D. thesis.

    Above, to the right is Karen's flow model velocity field for the supergalactic plane (SGZ = 0 degrees). It is centered on "us" (the Local Group). The contours trace the velocity a galaxy would have at a certain distance from us. It's more complicated than the diagram from Davis and Peebles that we used before because it extends further away from us and includes more "attractors" than just the Virgo cluster.

  •   Find the Virgo cluster in this diagram.

  •   What other features do you see in the flow model? How can you explain them?

    We can use all of this information and our flow model to explore and understand the distribution of galaxies in the local universe.

    The distribution of galaxies in the Local Supercluster on the sky:

    For your use, I have identified a set of galaxies, distributed all around the sky, with measured heliocentric recessional velocities less than 3000 km/s. Here is the file in CSV format or ASCII text format. You can use TOPCAT to generate the plots needed to answer the questions below

    First, make a simple sky plot of the positions of these galaxies on the sky, that is, Right Ascension versus Declination. The center of the plot should be at R.A. = 12hours, with Right Ascension increasing toward the right in this rendition.

  •   Mark on the plot the location of the Virgo cluster.

  •   What does this diagram tell us?

  •   Why is this a bad way of showing how celestial objects are distributed on the sky?

    For a fairer rendition, we can use TOPCAT to generate a spherical plot of the galaxies contained in our datafile, using the "sky" plot capability. The center of the plot is at R.A. = 12h, with Right Ascension increasing toward the right in this rendition.

  •   Where are we in this diagram?

  •   Mark on the plot the location of the Virgo cluster.

  •   What does this diagram tell us?

    In this case, having TOPCAT offers an advantage, because the tool allows you to rotate the diagram.

    Next, look at the same type of plot but now using the supergalactic coordinates, SGL and SGB.

  •   What structure is evident in this plot?

  •   Going back to the previous diagram, can you get the same impression?

    To convince you, let's go back to the 2nd plot (equatorial coordinates on the spherical sky plot) but identify with red symbols the objects that we can consider to lie in the "supergalactic plane", that is galaxies with supergalactic latitudes less than 20 degrees: -20o < SGB < +20o (low supergalactic latitudes).

  •   What structure is evident in the two plots?

  •   What does their comparison tell you?

    And, to further illustrate, go back to the cartesian R.A. vs Dec. plot, but now plot the distribution of galaxies in the supergalactic longitude-latitude coordinate system.

  •   What structure is evident in this plot?

  •   What does it tell you?

  •   As the team which is investigating large scale structure on the largest scale, what conclusions can you make on the importance of large scale structure on the scale of the Local Supercluster?

    The distribution of galaxies in the Local Supercluster in velocity:

    The above plots made no use of the third observable dimension -- the velocity. We can use the same file to examine how the distance, derived from our flow model, depends on the heliocentric velocity. Again, using TOPCAT, plot distance on the x-axis and heliocentric velocity on the y-axis.
  •   Why is there a vertical line of points at distance ~ 17 Mpc?

  •   Use this plot to investigate how large the uncertainty is in the estimate of distance if Hubble's law is invoked. How large is the uncertainty at 10 Mpc? At 30 Mpc?

    The Pisces-Perseus Supercluster

    One of the most prominent features in the northern hemisphere (as viewed from Earth) extragalactic sky in the direction opposite the Virgo cluster is the Pisces-Perseus Supercluster.

    Below are two diagrams showing the distribution of galaxies on the sky. The top shows all galaxies with measured redshifts and brighter than mag=15.7. The bottom one shows only the subset with measured heliocentric velocities between 4000 km/s and 6500 km/s. Even in this very simple plot, the filamentary structure of the supercluster is very evident.

  •  The supercluster itself contains a number of clusters of galaxies listed in the table to the right. Mark the locations of the clusters on the plot. Where do they lie with respect to the prominent filament

  •   Perseus is a much rich cluster than Abell 262, yet it does not show up as prominently in this diagram. Why might that be?

  • Cluster R.A.,Dec. Helio. velocity
    Pegasus cluster 350.1, 8.2 3888
    NGC 383 cluster 17.7, 32.2 5186
    NGC 507 cluster 20.9, 33.2 5702
    Abell 262 28.2, 36.2 4887
    Abell 347 36.5, 41.9 5516
    = Abell 426
    49.7, 41.5 5366
    Values from NED

  •   What are the linear dimensions of the main ridge of the supercluster?

    Other things to consider

  •   Look up some more information about the clusters, and perhaps find some interesting images of them and their notable galaxies.

  •   What other issues/questions are raised in your mind?

    Last modified: Sun Jan 12 12:18:33 EST 2014