Voids

Ravi K. Sheth (UPenn)

Galaxy clustering depends on type Large samples (SDSS, 2dF) now available to quantify this

You can observe a lot just by watching. -Yogi Berra

Light is a biased tracer Not all galaxies are fair tracers of dark matter; To use galaxies as probes of underlying dark matter distribution, must understand ‘bias’

N-body simulations of gravitational clustering in an expanding universe

Hierarchical models Dark matter ‘haloes’ are basic building blocks of ‘nonlinear’structure Models of halo formation suggest haloes have same density whatever their mass Springel et al. 2005

Assume a spherical cow….

(Gunn & Gott 1972; Press & Schechter 1974; Bond et al. 1991)

The Random Walk Model Higher Redshift Critical over density This patch forms halo of mass M smaller mass patch within more massive region MASS

First-crossing distributions • 29 March 1900, Louis Bachelier defends PhD thesis and mathematical finance is born (crossing of constant barrier ~ pricing of options and derivatives) • Schrödinger studied first crossings of linear barrier

From Walks to Halos: Ansätze •

f(

d

c

d

c (z) ,s)ds

at

s

= fraction of walks which first cross ≈ fraction of initial volume in patches of comoving volume

V(s)

which were just dense enough to collapse at

z

≈ fraction of initial mass in regions which each initially contained

m =

r

V(1+

d

c )

≈ and which were just dense enough to collapse at

z

( r r

V(s)

is comoving density of background) ≈

dm m n(m,

d

c )/

r

(Reed et al. 2003) The Halo Mass Function •Small halos collapse/virialize first •Can also model halo spatial distribution •Massive halos more strongly clustered (current parametrizations by Sheth & Tormen 1999; Jenkins etal. 2001)

Random Walk = Accretion history High-z Major merger Low-z over density larger mass at low z small mass at high-z MASS

Other features of the model • Quantify forest of merger histories function of halo mass (formation times, mass accretion, etc.) as • Model spatial distribution of halos: clustering/biasing) (halo – Abundance + clustering calibrates Mass • Halos and their environment: – Nature vs. nurture—key to simplifying models of galaxy formation

Correlations with environment Critical over-dense over density under-dense Easier to get here from over-dense environment This patch forms halo of mass M ‘Top-heavy’ mass function in dense regions MASS

Correlations with environment PAST Critical over-dense over density FUTURE under-dense This patch forms halo of mass M At fixed mass, formation history independent of future/environment MASS

Most massive halos populate densest regions Key to understand galaxy biasing (Mo & White 1996; Sheth & Tormen 2002) over-dense under dense

n(m|

d

) = [1 + b(m)

d

] n(m)

Environmental effects

• Gastrophysics determined by formation history of parent halo • All environmental trends come from fact that massive halos populate densest regions

Massive halos more strongly clustered ‘linear’ bias factor on large scales increases monotonically with halo mass Hamana et al. 2002

Assume a spherical cow….

Hierarchical models Dark matter ‘haloes’ are basic building blocks of ‘nonlinear’structure Models of halo formation suggest haloes have same density whatever their mass Springel et al. 2005

Void Evolution • Large voids expand • Smaller ones get squeezed •Typical void size?

Random Walks • Gaussian initial fluctuation field + spherical evolution model = hierarchical growth of structure (Bond et al. 1991; Lacey & Cole 1993; Sheth 1998; Sheth & van de Weygaert 2003; Shen et al. 2006) ←V v→

Mass function in Voids • Require model for environmental dependence of halo mass function

dN(M|

d

,V)/dM

• Assume subhalo mass function

N(m|M)dm = 0.01 M 12 /m 12 0.9

dm/m

independent of environment

Strong clustering of void galaxies?

• On large scales void subhalos MORE strongly clustered than – dark matter – semi-analytic model of 2dFGRS • Subhalo = Galaxy? dark matter Void subhalos 2dFGRS

M O D E L S S E M I A N A L Y T I C

Halo-model of galaxy clustering • Halo abundances and clustering matter on large scales • Spatial distribution within halos (halo density profiles) only matters on small scales • Different galaxy types populate different halo masses

How to describe different point processes which are all built from the same underlying distribution?

THE HALO MODEL

Void galaxy LF?

• Use halo model – Assume center / satellite different – Assume satellite = halo substructure • Assume all environmental effects from correlation between halo mass and environment SDSS

30% least dense • Environment is number of neighbours within 8Mpc 30% Densest

Environments in SDSS • Least dense regions ~ d < −0.8 ~ voids?

Stochastic Nonlinear Galaxy Bias • Environmental dependence of halo mass function provides accurate framework for describing bias

• Halo-model of galaxy clustering

Three

types of pairs: both in same halo , in different halos but same patch, different patches •

ξ(r|

d

) = ξ 1h (r|

d

) + ξ 2h-1p (r|

d

) + ξ 2h-2p (r|

d

)

• Environment = neighbours within 8 Mpc • Clustering stronger in dense regions • Dependence on density NOT monotonic in less dense regions!

• Same seen in mock catalogs; little room for extra effect!

SDSS Abbas & Sheth 2006

• Galaxy distribution remembers that, in Gaussian random fields, high peaks and low troughs cluster similarly

Summary • Excursion set model has rich structure; can be used to describe clusters

and

voids • Mass function in dense regions ‘top heavy’ • Nonlinear stochastic biasing can be modeled • Clustering is not a monotonic function of density: void galaxies should be strongly clustered • Excursion set based Halo Model captures this complicated behaviour