Galaxy Clustering and Mergers

1
Galaxy Clustering and Mergers

• Abel Yang
• Supervisors Dr. Phil Chan Dr. Bernard Leong

Image Cluster 1E 0657-56 with hot gas X-ray
emission(red) superimposed on dark matter
gravitational lens(blue). Credit X-ray
NASA/CXC/CfA/M.Markevitch et al. Optical
NASA/STScI Magellan/U.Arizona/D.Clowe et
al. Lensing Map NASA/STScI ESO WFI
Magellan/U.Arizona/D.Clowe et al.
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Introduction

• Counts in cells distribution describes galaxy
  clustering
• Describes how many galaxies can be found in a
  fairly sampled region of space
• Galaxy clustering may depend on dark matter and
  other factors
• Isothermal halos soften the gravitational
  potential and modify virial equilibrium
• Variations in galaxy clustering may reveal new
  insights into the nature and evolution of the
  universe

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Counts in Cells Distribution

• Given by
• Dependent on virial parameter b and average
  number of galaxies in a cell N
• May be derived using thermodynamics (Saslaw and
  Hamilton 1984, ApJ 27613) or statistical
  mechanics (Ahmad, Saslaw and Bhat 2002, ApJ
  571576)
• Contains information about the parameter b
• b1.0 indicates fully virialized b0.0 indicates
  unvirialized (Poisson distribution)

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Use of Galaxy Merger Statistics

• Galaxy mergers will change the counts in cells
  distribution as average number of galaxies in a
  cell changes
• Change of b due to the adiabatic expansion of the
  universe can be found (Saslaw 1992, ApJ 391423)
• We can calculate the expected value of b at a
  particular scale length R using galaxy merger
  statistics by finding the form of db/dR
• db/dR can take into account the change in the
  number of galaxies
• Criteria for galaxies to merge may vary with the
  model used

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Procedure

• Show that mergers are not likely to occur across
  cell boundaries for certain cell sizes
• Shows that the counts in cells distribution is
  preserved even with galaxy mergers
• Consider the merger cross-section and derive
  the merger rate
• Involves the mean free path of a galaxy
• Infer the most likely radius of a galaxy
• Consider changes in the distribution of galaxy
  masses
• Radius of a galaxy may be related to halo size

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Cross-Cell Mergers and Movement

• Consider a spherical cell containing a test
  galaxy
• Guaranteed region exists where nearest neighbour
  is in the same cell
• From 2-point correlation function, probability of
  a neighbour occuring in the rest of the cell can
  be calculated

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Cross-Cell Mergers and Movement

• Same procedure can apply to nearest neighbour
  midpoint
• Using observed parameters for 2-point correlation
  function, minimum cell size where cross-cell
  nearest neighbour probability is negligible is
  approximately 2Mpc
• Upper limit of cell size given by upper limit of
  2-point correlation function at 5Mpc
• Power law form breaks down at 10Mpc
• With suitable cell sizes, mergers are most likely
  to occur within the same cell

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Merger Rates

• Consider a moving test galaxy of mass m1
• Test galaxy has a merger cross-section
• Given by the maximum separation in merger
  criteria
• Depends on the mass of merger candidate m2
• Describes the disc perpendicular to its movement
  where mergers may take place
• Galaxy covers a volume where mergers may occur in
  time ?t

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Merger Rates

• Merger cross-section S is dependent on galaxy
  masses m1, m2, galaxy radii e1, e2, and relative
  velocity v(Garcia-Gomez et. al. 1996, AA
  313363)
• Comes from conditions for a galaxy merger to take
  place
• Various merger criteria may be considered
• Merger rate is given by integrating over all v
  where f(v) is the velocity distribution, n(m) the
  number of galaxies of mass m

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Merger Criteria

• Consider merger criteria given by
• Aarseth and Fall 1980 (ApJ 23643)
• Garcia-Gomez et. al. 1996 (AA 313363)
• Fit to n-body simulations in parameter space
• Defines required separation for galaxies to merge
  given velocity, radius and mass
• Merger cross section S can be obtained
• Obtained through solving for r2

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Galaxy Radii

• Assume e is related to m
• Assume galaxies have the same density ?
• For galaxies as spheres
• For galaxies as discs
• Radius k is related to mass of galaxy by the
  relations
• For galaxies as spheres
• For galaxies as discs

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Merger Rates

• From the merger rates, we can consider the number
  of galaxies
• that increase in mass from mass m (merge out) and
• that increase in mass to become mass m (merge in)
• Merge out component is given by
• Merge in component is given by

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Timestep computation

• In time ?t, change in number of galaxies of mass
  m is given by
• With the form of ?n(m), we can simulate the
  effects of galaxy mergers on a mass function
• Number of galaxies of mass m per unit volume is
  given by the Schechter mass function
• Given a mass function at a high redshift, the
  mass function at a lower redshift can be computed

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Datasets
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Data Treatment

• Normalize total mass based on mass to light
  ratio
• Assume mass to light ratio is the same for all
  galaxies
• Local value of mass density at 3x108 M?
  Mpc-3(SDSS, Rudnick et. al. 2003, ApJ 599847
  COMBO-17, Borch et. al. 2006, AA 453869)
• Assumes the presence of variations in local mass
  density or incomplete observational data
• Mass is not uniformly distributed
• Average mass density is of interest
• Unseen mass and Constant density corrections
• Allow total starting mass to be the same as the
  total ending mass

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Constant Density Correction

• Assumes that the discrepancies are due to
  variations in the local density
• Also assume that the shape of the distribution is
  the same for all fields
• Normalize the mass function to add up to the
  observed local stellar mass density
• Assume that the shape of the mass function is
  correct
• Scale the mass function to obtain the same total
  mass
• Corrected mass function given by
• Where C is the correction factor

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Unseen Mass Correction

• Assumes that there is matter that cannot be seen
• This matter may be too faint to be observed
• These galaxies make up the low end tail
• Add the correction to the first bin to make up
  for the discrepancy
• May introduce a spike at the faint end tail
• Corrected mass function given by
• Where D is the correction factor

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Data Used

• 2 test ranges
• Selected to compare data from different surveys
• Low range z0.05 to z0.75
• Data from Autofib, COMBO-17 and VIMOS-VLT B-Band
• VIMOS-VLT B-Band to match Autofib in B-Band
• High range z0.50 to z1.50
• Data from VIMOS-VLT R-Band, LCIR and Bright Ages
• VIMOS-VLT R-Band to match LCIR in R-Band
• Faint end cutoff at 1010 M?

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Simulations

• Uses both merger criteria
• Considers the cases for
• Galaxies are spheres
• Galaxies are discs
• Infer the most likely value of k and obtain the
  most likely simulated mass distribution
• Start from higher z and end at lower z
• Match resulting mass distribution with observed
  data
• Obtain the Schechter parameter fit to the
  resulting distribution where we fix ? at the
  value as observed

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Results

• Low Range
• Only Autofib Data returned results
• High Range
• Only VIMOS-VLT and LCIR data returned results
• Results for Constant density and Unseen mass
  correction were the same to working precision
• Most results favour galaxies as spheres
• VIMOS-VLT(High Range) simulation results for
  galaxies as discs using the Aarseth and Fall
  criteria fits observed results better

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Results - Low RangeAutofib

• Aarseth and Fall
• Best fit results
• Galaxy as spheres
• k 1.56
• a -1.04
• M -19.28

• Garcia-Gomez et. al.
• Best fit results
• Galaxy as spheres
• k 2.90
• a -1.23
• M -19.31

• Observed results
• a -1.16 (0.05, -0.05)
• M -19.30 (0.15, -0.12)

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Results - High RangeVIMOS-VLT

• Aarseth and Fall
• Best fit results
• Galaxy as discs
• k 2.60
• a -1.53
• M -22.41

• Garcia-Gomez et. al.
• Best fit results
• Galaxy as spheres
• k 4.90
• a -1.17
• M -22.33

• Observed results
• a -1.42 (0.04, -0.04)
• M -22.30 (0.27, -0.35)

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Results - High RangeLCIR

• Aarseth and Fall
• Best fit results
• Galaxy as spheres
• k 2.54
• a -0.97
• M -21.01

• Garcia-Gomez et. al.
• Best fit results
• Galaxy as spheres
• k 4.79
• a -1.00
• M -21.02

• Observed results
• a -1.00 (0.06, -0.02)
• M -21.03 (0.03, -0.10)

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Discussion

• Inferred value of k ranges from 0.010 to 0.050
• Indicates a galaxy of 1011 M? has a radius of
  about 10kpc to 50kpc
• Large range of values indicate uncertainty in
  merger criteria
• Other factors have not been considered in merger
  criteria
• Internal velocity dispersion
• Mass loss during mergers
• Variations in local density highlight need for
  data over more fields
• Most surveys focus on HDF-S and CDF-S fields

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Future Work

• Using the counts in cells distribution at high
  redshifts, the galaxy merger rate can be obtained
  through the time evolution of b.
• Galaxy radii can be predicted independently
• Merger criteria and model can be verified
• Using merger criteria that takes into account the
  behaviour of dark matter can provide an measure
  of the distribution of dark matter by fitting to
  the observed statistics
• Dark matter is observed to not behave like
  ordinary matter in a collision (Clowe et. al.
  2006, ApJL 648109)