Galaxy Clustering and Mergers

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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 virial 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
• Criteria for galaxies to merge may vary with the
  model

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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
• Calculate the expected 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
  neighbour 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 10MPc
• 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
• Assume radius e is related to m
• Assume galaxies have the same density
• 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 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
• In time ?t, change in number of galaxies of mass
  m is given by

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Timestep computation

• Given 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(earlier
  time), the mass function at a lower
  redshift(later time) can be computed

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Final objectives

• Obtain the rate of galaxy mergers by comparing
  mass functions for different redshifts
• Provide insight into the time-evolution of b
• Obtain the expected radius of a galaxy given its
  mass
• Infer the expected size of a galaxys halo

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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
• 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)