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Using the Halo Occupation
Distribution to Constrain
Cosmological Models
Oral Section of the Ph.D. General Exam,
November 8, 2002
Current Issues in Cosmology:
Current Issues in Cosmology:
Determining the density of the
universe, WM.
•Assumption: Large scale structure is a consequence
of gravitational collapse.
•To test this assumption, observe the redshift space
distortions of the galaxy distribution.
•The matter density is a key cosmological parameter.
Current Issues in Cosmology:
Voids in the Galaxy Distribution
•To test your cosmological model, compare it to
the observed distribution of galaxies.
•Easy to do for bright objects in dense areas,
harder for the lower luminosity objects in
underdense locations.
•New surveys (2dF, Sloan) will make this
comparison easier.
The Halo Occupation Distribution:
What is the HOD?
•Statistical description of the relationship between dark
matter halos and their galaxies.
•The HOD can tell us everything about the statistics of
galaxy clustering for a given cosmological model:
xgg(r), xgh(r)
VPF
v12, s12
etc...
The Halo Occupation Distribution
How does the HOD
work?
•Navg(M) - average number of
galaxies in halo of mass M.
•P(N|Navg) - probability
distribution of galaxy
numbers.
•Relationship between
galaxies and mass within a
single halo.
Berlind & Weinberg, 2001
Redshift Space Distortions
What is happening...
What we observe...
High r
This effect is modeled well
by linear theory (Kaiser
1987):
Pz (k )  Pr (k )(1   2 ) 2
obs.
W0M.6

b
Redshift Space Distortions
Linear theory does not take into
account velocities from nonlinear collapse.
Total observation:
f (v)  exp(  | v | / s v )
f (v)  exp(  | v | / s v )
Coherent infall
obs.
Virialized core
Pr (k )(1   2 ) 2
Pz (k ) 
(1  k 2s 2  2 / 2) 2
Current Issues in Cosmology:
The effect is measurable
with the new large
galaxy redshift surveys
(i.e. 2dF; Peacock et al
2001)
Redshift Space Distortions
Using the HOD to obtain the matter density:
•We want to measure =WM0.6/b, where b=bias parameter.
•Need analytic function of the halo velocities-- obtained from
fitting N-body simulations:
Zheng, Tinker, Weinberg, & Berlind 2002
Redshift Space Distortions
What I plan to do:
•Use N-body simulations to obtain functions
v = f(Mh,r) and s = f(Mh,r)
•Develop analytic form of xh(s,p) and test this against
N-body models of different cosmologies.
•Once xh is determined, use the HOD to extend it to
galaxy correlation function, xg(s,p) .
•This will be applied to Sloan results.
Voids
What is a void?
(1) A region devoid of any
galaxies brighter than L*.
(2) A region where the
number density of galaxies
falls below some threshold
value.
Mathis & White, 2002
Voids
Why are voids important?
•Statistical test of galaxy clustering: void probability
function (VPF), nearest neighbor statistic.
•Test theory of galaxy formation: If galaxy type is
environmentally dependent (i.e. Dressler effect) then
voids should contain unique set of galaxies. Peebles
(2001) terms this the “void phenomenon”.
•Unanswered theoretical questions:
-How much mass is in the voids?
-How much of that mass is in virialized halos?
-What galaxies populate those halos?
Voids
Simulation techniques:
•Particle Mesh (PM) - Fastest method, memory limited and
therefore low spatial resolution.
•Tree code (GADGET) - O(NlnN) algorithm, excellent spatial
resolution but CPU time limited.
r (h-1 Mpc)
Zheng et al, 2002
Voids
Simulation techniques:
•Nested-Grid Particle Mesh (NGPM).
Insert higher-resolution mesh inside of
a larger simulation volume, increasing
resolution but subverting the memory
limitation problem.
•This method is well suited for
multiscale simulation techniques that
will be employed (Bertschinger 2001).
Splinter 1995
Voids
The HOD can give you the VPF very easily:
Calculate from N-body simulations (once populated with
galaxies).
Analytical form if you have an analytic theory of halo
clustering (e.g. Mo & White 1996).
Berlind & Weinberg 2001
Voids
Higher resolution simulations are needed to properly
simulate the halo population inside voids.
v ~ 30 km s-1 halos (l ~ 0.15 h-1Mpc)
Explore parameter space of cosmological models:
WM, L, ns, s8
Use the HOD to create galaxy populations in the voids.
Create predictions and/or theoretical tools to use with
the surge of new data to come out in the next few years.