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, how we can measure measure them, and how they can be used to indicate of infall onto large scale overdensities in the local universe. Keep in mind that peculiar velocity studies aren't easy: the universe is a messy place!

The task of this team is to understand the methodology of deriving peculiar velocities and the amplitude of Note: Team C is looking into aspects of the Virgo cluster including the distribution (on the sky and in redshift space) of the galaxies believed to be members of it.

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 Be aware that the details are a bit out of date; note that the distance of the Virgo cluster they assumed in making this model was 15 Mpc, and we know it is larger than that (more like 16.7 Mpc).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 a long list of 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). The axes are simply labeled X and Y = SGX and SGY. 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 use all of this information and our flow model to explore and understand the distribution of galaxies in the local universe.

    Infall of galaxies into the Virgo Cluster

    Numerous groups are engaged in the process of using HST observations to measure the distances of galaxies in redshift-independent ways. The most accurate distances come from measuring "standard candles" like the tip of the red giant branch (TRGB). An interesting paper for your team to investigate is Infall of Nearby Galaxies into the Virgo Cluster as Traced with Hubble Space Telescope (Karachentsev et al 2014, Ap. J. 782, 4. Here are Figures 1 and 6 from that paper.

  •   Be sure that you understand what these two figures show. How do they indicate evidence for infall onto the Virgo cluster? How are they different?

  •   Why does Figure 6 show more points at lower distances and only one point at large ones (in the Virgo background)?

  •   How do the errors in distances obtained using the TRGB method compare to those obtained with the baryonic Tully-Fisher relation?

    Using the Tully-Fisher relation

    Peculiar velocity studies require a lot of hard work both in obtaining the observational dataset, in converting the observational quantities into useful galaxy properties, in understanding the uncertainties, biases and limitations, and finally, in using the data to map the deviations from Hubble flow.

    Some years ago, some of us conducted a survey of peculiar velocities in the local universe. You can find it at SFI++. II. A New I-Band Tully-Fisher Catalog, Derivation of Peculiar Velocities, and Data Set Properties Springob et al 2007, ApJSupp 172, 599. Note that this predates the SDSS; in fact, we acquired both the HI dataset and the images needed to measure magnitudes, sizes, inclinations etc. Here is a file containing the final (useful) data for galaxies in the SFI++ compliation with recessional velocities less than 12000 km/s.

  •   What is the "I-band"?

  •   What parts of the sky have been sampled by SFI++? What parts have not?

  •   What is the difference btween the Tully-Fisher relation and the baryonic Tully Fisher relation?

  •   Construct the Tully-Fisher diagram for the galaxies. Be sure that the luminosity increases towards the top.

  •   The recessional velocity here is given as "vcmb". What is the "CMB rest frame"?

  •   Plot the relation between distance (horizontal axis) and the recessional velocity (vertical axis) in the CMB frame. How does the scatter around the mean relation vary with distance? Why?

    Infall into the PPS using the Tully-Fisher relation

    Simply put, there were not enough galaxies in the region of the PPS for this older survey to detect infall into PPS. There was a tantalizing hint, but we never felt fully confident in the results.

  •   Here is a file containing the galaxies in the α.70 catalog in the region of APPSS. How many of them are also contained in the SFI++ sample? Hint: Think carefully: what is the easiest way to match the two catalogs?.

  •   Make the plot of distance versus recessional velocity for the galaxies in PPS, α.70 and SFI++. If there were galaxies infalling into PPS with a peak velocity of 1000 km/s (and the data were otherwise perfect), what would this diagram look like?

  •   Use what you have learned to explain to the other UATers what the APPS survey will (hopefully) do .... in the future!

    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: Sat Jun 11 10:03:46 EDT 2016 by martha