Galaxy Groups

The purpose of this project is to study the properties of groups of galaxies. We will measure several global properties of groups including size and mass and mass-to-light ratios.

Data

The data for this project can be found in a file here:

  • 2mrs.11.25.LDGroups.dat.

    The data file contains the galaxies in groups of galaxies identified in the 2 Micron All-Sky Survey (2MASS) Redshift Survey. The columns in the ascii file are labeled with their content There are 1604 groups and over 11,000 galaxies in this catalog.

  •     Name is the coordinate name of the object from the 2MASS catalog

  •     RA, DEC are the right ascension and declination in hours, minutes and seconds or degrees, minutes and seconds format.

  •         RA runs from 0 to 24 hours,

  •        Dec runs from -90 to + 90 degrees,

  •        but the Virgo cluster is centered around 1.5 hours and + 12 degrees.

  •     Vh is the heliocentric radial velocity The cluster is centered around 1000 km/s/

  •     K is the K band (2.2 micron) magnitude

  •     Distance in Megaparsecs computed from the corrected velocity

    • Group Masses

    The mass of each group can be calculated from the data two ways, one by applying the Virial estimator and one by applying the Projected mass estimator. I've written a more complete description of these two estimators and of the Virial Theorem from which the first is derived which can be viewed in the following power-point file: Mass Estimators. This gives you the general formula to use in either of these calculations.

    The Viral estimator, after corrections for projection effects both in the projected radius (to go from 2-D to 3-D, and in the radial velocity (to go from 1-D to 3-D), is:

  •               MVT = (3&pi N)/(2G)   (&sum vi2)/ &sum i < j (1/Rij)

    • where Rij is the separation between the ith and jth particle (the limitation i < j is meant to eliminate double counting) and vi is the velocity if the ith galaxy w.r.t. the average cluster velocity.

    The Projected Mass estimator of Heisler, Bahcall & Tremaine is:

  •               MPM = fp/GN   (&sum vi2 Ri,c)

    • where Ri,c is the projected separation between the galaxy and the cluster center, and vi is as above. The projection factor, fp, depends on the average orbital eccentricity of the system,

  •             fp = 32/&pi    for primarily radial orbits
  •              = 16/&pi    for isotropic orbits (the usual choice)
  •              =   8/&pi    for primarily circular orbits

    • How different are the PM and Virial estimates of Virgo's mass?

    Mass-to-Light Ratio

    Well now you have it. With the group mass and the group luminosity you can compute the group mass-to-light ratio.

    We do have a determination of the absolute luminosity density from the whole survey. This is about to be published by Mark Hartmann et al.

  •               L = 6.7 x 108 h LSun Mpc-3
    • where the h symbol means that the value depends on the assumed value of the Hubble Constant. h = 1 is for H0 = 100 km/s/Mpc, so for the best current value of H0 = 70 km/s/Mpc,
  •               L = 4.7 x 108 LSun Mpc-3

    • The Mean Mass Density of the Universe and &Omega

    Given an M/L and an integrated luminosity density, we can calculate the mean mass density:

  •               &rho = (M/L) x L

    • The critical mass density depends only on the Hubble Constant and the gravitational constant. The formula for the critical density is in section 5 of our book,

  •               &rhocrit = 3 H02 / 8 &pi G

  •                         = 8.9 x 10-30 g/cm3

    • So now you can calculate &Omega by comparing the mass density you have measured --- assuming all galaxies have the same mass-to-light ratio as the integral of the Virgo Cluster --- to the critical mass density. Go for it!

  •                         &Omega = &rho / &rhocrit

    • After you do that, however, write down what you think are all the assumptions that have gone into this determination. Are they reasonable? Again, how does your value compare to those in the literature (for gravitating matter, since that's what you measure when you measure the mass of Virgo via either the PM or Virial estimators).

    Structure of the Cluster

    The last thing to look at is the structure of the cluster. Can you find a program for making contour diagrams? If so, try making these spatial plots:

  • Spiral Galaxies Types > -1
  • Elliptical Galaxies Types < 0

    • You may need to estimate morphological types for the cluster members or possibly look them up in the NASA Extragalactic Database .

    Then split the sample into 3 equal bins in radial velocity and plot

  • The lowest third in v
  • The middle third in v
  • The highest third in v

    • What do you see?

    Back to the Future

    FAS Seminar Link

    Faculty Seminar Link

    FAS 21x. Link



    Copyright John P. Huchra <huchra@cfa.harvard.edu> 2005