Transcript Document

Zheng Zheng
Dept. of Astronomy, Ohio State University
Collaborators:
David Weinberg (Advisor, Ohio State)
Andreas Berlind (NYU)
Josh Frieman (Chicago)
Jeremy Tinker (Ohio State)
Idit Zehavi
(Arizona)
SDSS et al.
Light traces mass?
Light traces mass?
Snapshot @ z~1100
Light-Mass relation well understood
CMB from WMAP
Snapshot @ z~0
Light-Mass relation not well understood
Galaxies from SDSS
Cosmological Model
initial conditions
energy & matter contents
Galaxy Formation Theory
gas dynamics, cooling
star formation, feedback
m 8 n 
Dark Halo Population
n(M)
(r|M)
v(r|M)
Weinberg 2002
Halo Occupation Distribution
P(N|M)
spatial bias within halos
velocity bias within halos
Galaxy Clustering
Galaxy-Mass Correlations
Halo Occupation Distribution (HOD)
• P(N|M)
Probability distribution of finding N galaxies in a halo of virial mass M
mean occupation <N(M)> + higher moments
• Spatial bias within halos
Difference in the distribution profiles of dark matter and galaxies within halos
• Velocity bias within halos
Difference in the velocities of dark matter and galaxies within halos
e.g., Seljak 2000, Scoccimarro et al. 2001, Berlind & Weinberg 2002
Part I
Constraining Galaxy Bias (HOD) Using
SDSS Galaxy Clustering Data
HOD modeling of two-point correlation functions
• Departure from a power law
• Luminosity dependence
• Color dependence
Two-point correlation function of galaxies
1-halo term
2-halo term
HOD Parameterization
Zheng et al. 2004
HOD of sub-halos
Central:
<Ncen>=1, for MMmin
Sub-halos
Satellite:
<Nsat>=(M/M1) , for MMmin
Galaxies
Close to Poisson Distribution (~1)
Kravtsov et al. 2004
Two-point correlation function:
Departures from a power law
SDSS measurements
Zehavi et al. 2004a
Two-point correlation function:
Departures from a power law
The inflection around 2 Mpc/h can be naturally
explained within the framework of the HOD:
It marks the transition from a large scale
regime dominated by galaxy pairs in
separate dark matter halos (2-halo term)
to a small scale regime dominated by
galaxy pairs in same dark matter halos
(1-halo term).
2-halo term
1-halo term
Dark matter
correlation function
Divided by the
best-fit power law
Zehavi et al. 2004a
Two-point correlation function:
Departures from a power law
Fit the data by assuming an
r-1.8 real space correlation
function
 r0 ~ 8Mpc/h
 host halo mass > 1013 Msun/h
HDF-South
Strong clustering of a population
of red galaxies at z~3
+ galaxy number density
 ~100 galaxies in each halo
Daddi et al. 2003
Two-point correlation function:
Departures from a power law
Less surprising models from HOD modeling
Signals are dominated by 1-halo term
M > Mmin ~ 6×1011Msun/h
(not so massive)
<N(M)>=1.4(M/Mmin)0.45
Predicted r0 ~ 5Mpc/h
HOD modeling of the clustering
of z~3 red galaxies
Zheng 2004
Luminosity dependence of galaxy clustering
Zehavi et al. 2004b
Luminosity dependence of galaxy clustering
Divided by a power law
Zehavi et al. 2004b
Luminosity dependence of galaxy clustering
The HOD and its luminosity
dependence inferred from
fitting SDSS galaxy
correlation functions have a
general agreement with galaxy
formation model predictions
Luminosity dependence of the HOD
predicted by galaxy formation models
Berlind et al. 2003
Luminosity dependence of galaxy clustering
• From 2-point correlation
functions
(Zehavi et al. 2004b)
• From group multiplicity
functions
(Berlind et al. 2004)
• From populating Virgo
simulations
(Wechsler et al. 2004)
Comparison of HODs derived
from different methods
Agreement at high mass end
Systematics at low mass end
Luminosity dependence of galaxy clustering
Zehavi et al. 2004b
Zheng et al. 2004
SA model
HOD parameters as a function of galaxy luminosity
Luminosity dependence of galaxy clustering
Zehavi et al. 2004b
Predicting correlation functions for luminosity-bin samples
Luminosity dependence of galaxy clustering
Predicting the conditional
luminosity function (CLF)
Zehavi et al. 2004b
Conditional luminosity
function (CLF) predicted
by galaxy formation models
Zheng et al. 2004
Color dependence of galaxy clustering
Zehavi et al. 2004b
Color dependence of galaxy clustering
Zehavi et al. 2004b
Berlind et al. 2003, Zheng et al. 2004
Inferred from SDSS data
Predicted by galaxy formation model
Color dependence of galaxy clustering
Zehavi et al. 2004b
-20<Mr<-19
-21<Mr<-20
Color dependence of galaxy clustering
What we learn:
Red and blue galaxies
are nearly well-mixed
within halos.
Red-blue cross-correlation:
Prediction vs Measurement
Zehavi et al. 2004b
Tegmark et al. 2004
Part II
Constraining Galaxy Bias (HOD)
and Cosmology Simultaneously
Using Galaxy Clustering Data
A Theoretical Investigation
Why useful ?
• Consistency check
• Better constraints on cosmological parameters (e.g., 8, m)
• Tensor fluctuation and evolution of dark energy
• Non-Gaussianity
Cosmology
A
HOD
A

Halo Population
A
Galaxy Clustering
Galaxy-Mass Correlations
A
Cosmology
B
Halo Population
B

=
HOD
B
Galaxy Clustering
Galaxy-Mass Correlations
B
Halo populations from
distinct cosmological models
Changing m with
8, n, and  Fixed
Zheng, Tinker,
Weinberg, & Berlind
2002
Halo populations from
distinct cosmological models
•
Changing m only
Halo mass scale shifts (m)
Same halo clustering at same M/M*
Pairwise velocities at same M/M* m0.6
•
Changing m but keeping Cluster-normalization
Similar halo clustering and pairwise velocities at fixed M
Different shapes of halo mass functions
•
Changing m and P(k) to preserve the shape of halo MF
Similar halo mass functions
Different halo clustering and halo velocities
Halo Populations from distinct cosmological models are NOT degenerate.
(Zheng, Tinker, Weinberg, & Berlind 2002)
Cosmology
A
HOD
A
Halo Population
A
Galaxy Clustering
Galaxy-Mass Correlations
A



=
Cosmology
B
Halo Population
B
HOD
B
Galaxy Clustering
Galaxy-Mass Correlations
B
HOD parameterization
• P(N|M)
Motivated by results from
semi-analytic galaxy
formation models and SPH
simulations
Mean occupation <N>M
2nd momentum <N(N-1)>M
[Transition from a narrow distribution to a wide distribution]
• Spatial bias within halos
Different concentrations of galaxy distribution and dark
matter distribution (c)
• Velocity bias within halos
vg= vvm
Observational quantities
•
•
•
•
•
•
•
•
Galaxy overdensity g(r)
Group multiplicity function ngroup(>N)
Two-point correlation function of galaxies gg(r)
m0.6/bg
Pairwise velocity dispersion v(r)
Average virial mass of galaxy groups <Mvir(N)>
Galaxy-mass cross-correlation function mgm(r)
3-point correlation function of galaxies
Constraints on HOD and
cosmological parameters
Changing m with
8, n, and  Fixed
Zheng & Weinberg 2004
Constraints on HOD parameters
Changing m with
8, n, and  Fixed
Constraints on cosmological parameters
Changing m only
Cluster-normalized
Changing 8 only
Halo MF matched
Summary and Conclusion
• HOD is a powerful tool to model galaxy clustering.
• HOD modeling aids interpretation of SDSS galaxy clustering.
* HOD leads to informative and physical explanations of galaxy
clustering (departures from a power law in 2-point correlation
function, the luminosity dependence, and the color dependence) .
* It is useful to separate central and satellite galaxies.
* HODs inferred from the data have a general agreement with
those predicted by galaxy formation models.
• Galaxy bias and cosmology are not degenerate w.r.t.
galaxy clustering.
* Using galaxy clustering data, we can learn the HOD of different
classes of galaxies, and thus provide useful constraints to the
theory of galaxy formation.
* Simultaneously, cosmological parameters can also be determined
from galaxy clustering data. [future applications to SDSS data]