Evolution and environment
• The halo model
– Environmental effects in the SDSS
– Halo mass vs. local density
• Mark correlations
– SDSS galaxies and their environments
– Centre-satellite split and galaxy SEDs
• Passive evolution models
– Conditional mass function + halo model
predicts nonlinear correlation function
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’
How to describe different point
processes which are all built from
the same underlying distribution?
THE HALO MODEL
Environmental effects
• In hierarchical models, close connection
between evolution and environment (dense
region ~ dense universe ~ more evolved ~
more massive halos ~ more clustering)
n(m|d) = [1+b(m)d] n(m)
• Observed correlations with environment test
hierarchical galaxy formation models
Halo-model of galaxy clustering
• Two types of pairs: only difference from dark matter
is that number of pairs in m-halo is not m2
• ξdm(r) = ξ1h(r) + ξ2h(r)
• Spatial distribution within halos is small-scale detail
Halo-model of un-weighted correlations
Write 1+ξ = DD/RR as sum of two components:
ξ1gal(r) ~ ∫dm n(m) g2(m) ξdm(m|r)/rgal2
ξ2gal(r) ≈ [∫dm n(m) g1(m) b(m)/rgal]2 ξdm(r)
≈ bgal2 ξdm(r)
g2(m) is mean number of galaxy pairs in m-halos
(= m2 for dark matter)
g1(m) is mean number of galaxies in m-halos
(= m for dark matter)
Satellite galaxy counts ~ Poisson
• Write g1(m) ≡ ‹g(m)› = 1 + ‹gs(m)›
• Think of ‹gs(m)› as mean number of satellite
galaxies per m halo
• Minimal model sets number of satellites as
simple as possible ~ Poisson:
• So g2(m) ≡ ‹g(g-1)› = ‹gs (1+gs)› = ‹gs› +
‹gs2› = 2‹gs› + ‹gs›2 = (1+‹gs›)2 - 1
• Simulations show this ‘sub-Poisson’ model
works well (Kravtsov et al. 2004)
Two approaches …
• Halo Occupation Distribution
(Jing et al., Benson et al.; Seljak; Scoccimarro et al.)
– Model Ngal(>L|Mhalo) for range of L (Zehavi et al.;
Zheng et al.; Berlind et al.; Kravtsov et al.; Conroy et al.; Porciani,
Magliochetti; Collister, Lahav)
– Differentiating gives LF as function of Mhalo
(Tinker et al., Skibba et al.):
• Conditional Luminosity Function (Peacock, Smith):
– Model LF as function of Mhalo , and infer HOD
(Yang, Mo, van den Bosch; Cooray)
…both separate centrals/satellites
Luminosity dependent clustering
Zehavi et al. 2005
SDSS
• Deviation from power-law statistically significant
• Centre plus Poisson satellite model (two free parameters)
provides good description
Why is …
• Luminosity dependence of SDSS clustering
well described by halo model with
g1(m|L) ≈ 1 + m/[23 m1(L)]
• g1(m|L) nonzero only if m>m1, where m1(L)
adjusted to match decrease of number
density with increasing L
• (Assume Poisson distribution, with mean g1,
for non-central, ‘satellite’ galaxies)
Halo Substructure
• Halo substructure = galaxies is good model
(Klypin et al. 1999; Kravtsov et al. 2005)
• Agrees with semi-analytic models and SPH;
gas only cools in deep potential wells
(Berlind et al. 2004; Zheng et al. 2005; Croton et al. 2006)
• Setting n(>L) = n(>Vcirc) works well for
all clustering analyses to date, including z~3
(Conroy et al. 2006)
Halo substructure = galaxies?
• Nsub(>m|M) = (M/1012 h-1Msun)0.1 (M/m)0.9 /90
– Factor 90 (required to have one subhalo) > 23
(required to have one satellite galaxy), suggests that
tidal stripping is factor of ~ 4 in mass
– So M/L for centrals (no stripping) larger than for
satellites (lots of stripping) of same L (consistent with
lensing analysis of Limousin et al. 2007)
• Also, if stars closer to halo center, M/L different
from Mstellar/L
Ongoing debate over ‘orphan’ galaxies … (e.g. Nagai & Kravtsov 2005)
Predicted
correlation
between
luminosity
and mass
Prediction based on
halo-model
interpretation of
clustering in SDSS
for galaxy samples
with various L cuts
(Zehavi et al. 2005)
total
satellite
central
<Lcen|M> ~ ln(1 + M/Mcrit)
<Lsat|M> ~ independent of M
Skibba, Sheth, Connolly, Scranton 2006
Skibba & Sheth 2007
HOD prediction
Yang et al
Berlind et al
Assumptions (to test)
• Halo profiles depend on mass, not
environment
• Galaxy properties, so p(Ngal|L,m), and so
g1(m) and g2(m), depend on halo mass, not
environment
• All environmental dependence comes from
correlation between halo mass and
environment:
n(m|d) = [1+b(m)d] n(m)
– Mass function ‘top-heavy’ in dense regions
Halo-model of environmental trend
• Three types of pairs: both in same halo, in different
halos but same patch, in different patches
• ξ(r|d) = ξ1h(r|d) + ξ2h-1p(r|d) + ξ2h-2p(r|d)
Environments
in SDSS
• Least dense
regions
~ d < −0.8
~ voids
Aside 1:
Poisson cluster
models
(thermodynamic,
Neg. Binomial)
quite accurate,
N.B. Counts are in
cells centered on
particles
30% least dense
• Environment is
number of
neighbours within
8Mpc
30% densest
• Assume
cosmology →
halo profiles,
halo abundance,
halo clustering
• Calibrate g(m) by
matching ngal and
ξgal(r) of full
sample
• Make mock
catalog assuming
same g(m) for all
environments
• Measure clustering
in sub-samples
defined similarly
to SDSS
M
r<−19.5
SDSS
Abbas & Sheth 2007
Highest density
z-space
Lowest density
z-space
Mass function top heavy in dense regions
Aside 2: Stochastic Nonlinear Bias
• Environmental
dependence of halo
mass function
provides accurate
framework for
describing bias
(curvature =
‘nonlinear’; scatter =
‘stochastic’)
• G1(M,V) =
∫dm N(m|M,V) g1(m)
• Environment
= neighbours
within 8 Mpc
• Clustering
stronger in
dense regions
• Dependence
on density
NOT
monotonic in
less dense
regions!
• Same seen in
mock catalogs
SDSS
Abbas & Sheth 2007
• Galaxy
distribution
remembers
that, in
Gaussian
random
fields, high
peaks and
low troughs
cluster
similarly
Predicts unexpectedly(?) strong
clustering of void galaxies
• On large scales
void halos indeed
MORE strongly
clustered than
– dark matter
– semi-analytic
model of 2dFGRS
dark matter
Void halos
2dFGRS
Colberg & Sheth 2007
• Environment
= neighbours
within 8 Mpc
• Clustering
stronger in
dense regions
• Dependence
on density
NOT
monotonic in
less dense
regions!
• Same seen in
mock catalogs
 Choice of scale not important
 Mass function ‘top-heavy’ in dense
regions
 Massive halos have smaller radii
(halos have same density whatever
their mass)
 Gaussian initial conditions?
 Void galaxies, though low mass,
should be strongly clustered
SDSS
 Little room for additional (e.g.
assembly bias) environmental effects
Gastrophysics determined by
formation history of parent halo
Correlations with environment
• Traditional approach requires separation
into ‘cluster’ and ‘field’, ‘dense’ and ‘underdense’ (Berlind et al. 2006; Yang et al. 2006)
• Non-trivial in redshift-space, given that
many environmental trends small, so
accurate separation required
Marks in the SDSS
• WW/DD as function of pair separation r
– Measure number of pairs separated by r,
weighted by some observable (the ‘mark’)
– Divide by number of pairs each weighted by
mean value of ‘mark’
• Observed marks (luminosity, color)
• Derived marks (stellar mass, age, SFR)
Luminosity as mark in SDSS
Large scale signal
consistent with halo
bias prediction; no
large scale
environmental trends
Small scale signal
suggests centre
special; model with
gradual threshold
(rather than step) is
better
Unweighted signal
centre not special
centre special
Skibba, Sheth, Connolly, Scranton 2006
Luminosity
as mark in
SDSS
Close pairs more
luminous only in
redder bands
Qualitatively
consistent with
models
Skibba, Sheth, Connolly, Scranton 2006
Color as
mark in
SDSS
Close pairs are
redder than average
Long-tailed
distributions show
clearer signal?
Skibba, Sheth, Connolly, Scranton 2006
MOPED Marks in SDSS
• MOPED evidence
for ‘downsizing’
(Heavens et al. 2004)
• Dependence on
environment?
• Expect because
luminous galaxies
populate denser
regions
Luminous galaxies
Lower luminosity
galaxies
Sheth, Jimenez, Panter, Heavens 2006
Sheth, Jimenez, Panter, Heavens 2006
• Radius of circle
represents total
mass in stars
formed, in units
of average
stellar mass
formed at same
redshift
• Star formation
only in less
dense regions at
low z?
Sheth, Jimenez, Panter, Heavens 2006
Sheth, Jimenez, Panter, Heavens 2006
Combination of MOPED marks
+ mark correlations shows
star formation rates in regions that
are dense today was above average
at hi-z, below average at low-z
Ultimate goal
• Halo model not just of luminosity,
but of entire SED
• First step: luminosity and color
– Allows model of stellar mass, star
formation history as function of halo
mass, and hence environment
• Colormagnitude
relation ~
independent
of group
properties
• Distribution
of galaxies in
relation does
depend on
group
properties
Blanton, Berlind, Hogg 2006
Assume split
between red
and blue
depends on
luminosity
(determine
directly from
data); mass
dependence
entirely from
correlation
between
luminosity and
halo mass
Assume
bimodal
colors =
centresatellite
… rather than
centre-satellite or
centre-satellite
CENTRALS
SATELLITES
CENTRALS
Model with red satellites
works quite well; so can
model stellar mass.
Yet to include ‘conformity’;
blue central = blue satellites
(Weinmann et al. 2006 based on
Yang et al. 2005 group catalog)
Passive evolution
of the most
massive galaxies?
Match number densities of most
luminous galaxies at two redshifts
(e.g. NDWFS of Brown et al. 2006)
White et al. 2007
If no merging …
• G(M) = ∫ dm N(m|M) [gcen(m) + gsat(m)]
• Low-z bias = ∫ dM n(M) G(M) B(M)
• High-z bias = ∫ dm n(m) g(m) b(m)
– Check that two bias factors evolve as expected from
linear theory/continuity equation calculation for large
scales
• Get small scales by assuming ‘satellites’ trace halo
(NFW) profile
…halo model provides complete
analytic description
Hi-z
Low-z
Can also …
• Assume mergers are of old centrals (tests
assumption that dynamical friction primary
mechanism for mergers)
• This predicts fraction of ‘merged satellites’
(e.g. White et al. NDWFS ‘satellite’ merger
models)
Conclusions
• Mark statistics useful for quantifying trends with
environment
• Halo model simple, powerful
– useful for understanding environmental trends (halo
mass-based description more efficient than density?)
– allows simple description of evolution in no merger
models
– first step to building halo-model of SED says satellites
are old and red
• Allows one to use abundance and clustering to
constrain models (a la Sheth-Tormen for halo mass function)