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, M•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:

gg(r), gh(r)

VPF

v12,

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

High

What is happening... What we observe...

obs.

This effect is modeled well by linear theory (Kaiser 1987):

22 )1)(()( kPkP rz

bM

6.0

Redshift Space Distortions

Linear theory does not take into account velocities from non-linear collapse.

Coherent infall

Virialized core

Total observation:

)/||exp()( vvvf

)/||exp()( vvvf

2222

22

)2/1(

)1)(()(

k

kPkP r

z

obs.

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 =M0.6/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 = f(Mh,r)

•Develop analytic form of h() and test this against N-body models of different cosmologies.

•Once h is determined, use the HOD to extend it to galaxy correlation function, g() .

•This will be applied to Sloan results.

Voids

Mathis & White, 2002

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.

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 ( ~ 0.15 h-1Mpc)

Explore parameter space of cosmological models:

M, , ns, 8

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.