What can we learn from galaxy clustering?David Weinberg, Ohio State University

Berlind & Weinberg 2002, ApJ, 575, 587

Zheng, Tinker, Weinberg, & Berlind 2002, ApJ, 575, 617

Berlind, Weinberg, Benson, Baugh, Cole, Dav’e, Frenk, Jenkins, Katz, & Lacey 2003, ApJ, 593, 1

Zehavi, Weinberg, Zheng, Berlind, Frieman, et al. 2004, ApJ, 608, 16

Abazajian, Zheng, Zehavi, Weinberg, Frieman, Berlind, Blanton, et al., astro-ph/0408003

Zehavi, Zheng, Weinberg, Frieman, Berlind, Blanton, et al., astro-ph/0408569

Zheng, Berlind, Weinberg, Benson, Baugh, Cole, Dav’e, Frenk, Katz, & Lacey, astro-ph/0408564

Tinker, Weinberg, Zheng, & Zehavi , astro-ph/0411777

Tinker, Weinberg, & Zheng, astro-ph/0501029

Zheng & Weinberg, in preparation

Yoo, Tinker, Weinberg, & Zheng, in preparation

Colless et al. 2001

Sloan Digital Sky Survey

Image courtesy of M. Tegmark

Fundamental Questions

1. What are the matter and energy contents of the universe?

What is the dark energy accelerating cosmic expansion?

2. What physics produced primordial density fluctuations?

3. Why do galaxies exist?

What physical processes determine their masses, sizes, luminosities, colors, and morphologies?

Dark Matter Clustering

Straightforward to predict for specified initial conditions and cosmological parameters.

But where are the galaxies?

Cole et al. 1997

Weinberg 2002

Dark matter clustering is straightforward to predict for specified initial conditions and cosmological parameters.

But where are the galaxies?

SPH simulation of galaxy formation in CDM cosmology.

Weinberg et al. 2004

P(N|M), SPH simulation Mean occupation, SPH & SA

Berlind et al. 2003

Berlind et al. 2003

Dependence on galaxy stellar population age

Berlind et al. 2003

P(N|M), SPH simulation Mean pair count, SPH & SA

Zheng et al. 2004

Halo central galaxies usually more massive, older than satellites. (Berlind et al. 2003)

Convenient to separate central galaxies and satellites.

Central: step function

Satellites: truncated power-law, Poisson statistics

(Kravtsov et al. 2004)

Berlind et al. 2003

Theory predicts that galaxy population depends on halo mass but not on halo’s larger scale environment.

Blanton, Eisenstein, Hogg, & Zehavi 2004

Observations agree.

Contours of local overdensity Contours of blue galaxy fraction

Cosmology + galaxy formation theory HOD

• SPH and semi-analytic model predictions agree.

• Mean occupation function: Low mass cutoff, plateau at N(M) ~ 1-2, roughly linear rise at high mass.

• Strong dependence on galaxy mass and age.

• Sub-Poisson fluctuations at low N, very few pairs in low mass halos. Consequence of large gap (~20) between minimum halo mass for central galaxy and halo mass for first satellite.

• Satellite galaxies have radial profile and velocity dispersion similar to dark matter.

• Predicted HOD depends on halo mass, not environment.

Berlind & Weinberg (2002):

Different clustering statistics respond to different aspects of the HOD. Given assumed halo population, can infer HOD from complementary clustering observations.

Goal: use galaxy clustering to test theories of galaxy formation.

Galaxy 2-point correlation function

gg(r) = excess probability of finding a galaxy a distance r from another galaxy1-halo term: galaxy pairs in the same halo2-halo term: galaxy pairs in separate halos

Projected correlation function of SDSS galaxies:

Not quite a power law!

Zehavi et al. (2004a)

Deviation naturally explained by HOD model.

Zehavi et al. (2004a)

2-halo term

1-halo term

Divided by the best-fit power law

Dark matter correlation function

Hogg & Blanton

Luminosity dependence of correlation function and HOD

Zehavi et al. (2004b)

Minimum halo mass vs. luminosity threshold

Observation

Zehavi et al. (2004b)

Minimum halo mass vs. luminosity threshold

Observation Theory

Zehavi et al. (2004b) Zheng et al. (2004)

Hogg & Blanton

Color dependence of correlation function

Zehavi et al. (2004b)

Qualitative agreement with theoretical predictions

Berlind et al. (2003), Zheng et al. (2004)Zehavi et al. (2004b)

Cross-correlation of red and blue galaxies

Zehavi et al. (2004b)

Consistent with random mix of red and blue populations in halos, given expected means.

Galaxy clustering + cosmology HOD

• With good clustering measurements, specified cosmology, can determine HOD empirically for different galaxy types.

• HOD encodes everything that galaxy clustering can teach us about galaxy formation physics, in physically useful way.

• Progress to date: fitting projected 2-point correlation function with restricted HOD parameterization.

• Natural explanation of observed deviations from power-law correlation function.

• Inferred luminosity and color dependence of HOD in good agreement with theoretical predictions.

Tinker et al. (2004)

Given P(k) shape, 8 , choose HOD parameters to match wp(rp).

Predict cluster M/L ratios.

These are above or below universal value depending on 8/ 8g .

8=0.6

8=0.8

8=0.95

Cluster mass-to-light ratios

Tinker et al. (2004)

Given P(k) shape, 8 , choose HOD parameters to match wp(rp).

Predict cluster M/L ratios.

These are above or below universal value depending on 8/ 8g .

Matching CNOC M/L’s implies (8/0.9)(m/0.3)0.6 =

0.71 0.05.

8=0.6

8=0.8

8=0.95

Cluster mass-to-light ratios

Redshift-space correlation function, 2dFGRS

Peacock et al. (2001)

Redshift-space distortions, SDSS

Zehavi et al. (2004b)

Tinker et al. (2005)

For each (m, 8), choose HOD to match wp(rp).

Large scale distortions degenerate along axis 8 m

0.6, as predicted by linear theory.

Small scale distortions have different dependence on m, 8, v.

HOD modeling of redshift-space distortions

SDSS sample 12, galaxies with Mr<-21

For 8=0.9, m=0.3, large scale distortion is OK, small scale distortion is too strong.

SDSS sample 12, galaxies with Mr<-21

For 8=0.9, m=0.3, large scale distortion is OK, small scale distortion is too strong.

Can fix with strong velocity bias.

For 8=0.9, m=0.3, large scale distortion is OK, small scale distortion is too strong.

Can fix with strong velocity bias.

Or lower 8 and weaker velocity bias.

SDSS sample 12, galaxies with Mr<-21

Galaxy-galaxy weak lensing measures excess surface density around foreground galaxies

Yoo et al. 2005

Yoo et al. 2005

Simple scaling of signal with cosmological parameters

Zheng & Weinberg (2005)

How well can clustering measurements constrain cosmological parameters given “complete” freedom to choose HOD?

Changing m at fixed 8, P(k) shape.

Breaking the degeneracy between bias and cosmology

Zheng & Weinberg (2005)

Forecast of joint constraints on m and 8, for fixed P(k) shape.

Eight clustering statistics, 30 “observables”, each with 10% fractional error.

Abazajian et al. 2004

Joint constraints on m and 8 from SDSS projected galaxy correlation function and CMB anisotropy measurements.

Galaxy clustering cosmology + HOD

• Effects of changing cosmological parameters and HOD parameters are partly, but not completely, degenerate.

• With good measurements and modeling, can hope to constrain both separately.

• Small scale, real space clustering most sensitive to HOD. Dynamically sensitive statistics (redshift space distortions, galaxy-galaxy lensing) and large scale clustering are most sensitive to cosmology.

• Current modeling of cluster M/L ratios, redshift-space distortions implies tension with “concordance” parameter values of m=0.3, 8=0.9.

What can we learn from galaxy clustering?

• The halo occupation distribution for many different types of galaxies. Tests of galaxy formation theory.

So far, good agreement with theoretical predictions.

• The shape of the primordial P(k). Constraints on cosmological parameters, physics of inflation.

• Precise values of m and 8. Constraints on dark energy, gravity wave contribution to the CMB.

Preliminary result: interesting tension with favored values.