The Galaxy Dark Matter Connection

The Galaxy Dark Matter Connection constraining cosmology & galaxy formation Frank C. van den Bosch (MPIA) Collaborators: Houjun Mo (UMass), Xiaohu Yang (SHAO) Marcello Cacciato, Surhud More (MPIA) Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 1/20

Outline, Motivation & Techniques Why study the Galaxy-Dark Matter Connection? Outline, Motivation & Techniques To constrain the physics of Galaxy Formation To constrain Cosmological Parameters Two Methods to Constrain Galaxy-Dark Matter Connection New Cosmological Constraints Precision cosmology using non-linear structure Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 2/20

The The Conditional Luminosity Function The CLF Model In order to parameterize the Halo Occupation Statistics we introduce the (CLF), Φ(L M), which is the direct link between the halo mass function n(m) and the galaxy luminosity function Φ(L): Φ(L) = R 0 Φ(L M) n(m) dm The CLF contains a wealth of information, such as: The average relation between light and mass: L (M) = R 0 Φ(L M) L dl The occupation numbers of galaxies: N (M) = R L min Φ(L M) dl We have constrained CLF using four different, independent techniques Galaxy Group Catalogues Satellite Kinematics Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 3/20

The CLF Model The Conditional Luminosity Function The CLF Model Motivated by results obtained from galaxy group catalogue, we split CLF in central and satellite components Φ(L M)dL = Φ c (L M)dL +Φ s (L M)dL For centrals we adopt a log-normal distribution Φ c (L M)dL = 1 2π σ c exp» ln(l/l 2 c) 2σ c dl L For satellites we adopt a modified Schechter function Φ s (L M)dL = Φ s Ls L Ls α s exp[ (L/Ls ) 2 ]dl Note that L c, L s, σ c, φ s and α s all depend on halo mass M Free parameters are constrained by fitting data Use Monte-Carlo Markov Chain to sample the posterior distribution of free parameters, and to put confidence levels on derived quantities Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 4/20

Occupation Statistics from Clustering Galaxies occupy dark matter halos. Occupation Statistics from Clustering Luminosity & Correlation Functions Results Cosmology Dependence CDM: more massive halos are more strongly clustered. Clustering strength of given population of galaxies indicates the characteristic halo mass Clustering strength measured by correlation length r 0 Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 5/20

Occupation Statistics from Clustering Galaxies occupy dark matter halos. Occupation Statistics from Clustering Luminosity & Correlation Functions Results Cosmology Dependence CDM: more massive halos are more strongly clustered. Clustering strength of given population of galaxies indicates the characteristic halo mass Clustering strength measured by correlation length r 0 WMAP1 Ω m = 0.30 Ω Λ = 0.70 σ 8 = 0.90 - WMAP3 Ω m = 0.24 Ω Λ = 0.76 σ 8 = 0.74 CAUTION: Results depend on cosmological parameters Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 5/20

Luminosity & Correlation Functions Occupation Statistics from Clustering Luminosity & Correlation Functions Results Cosmology Dependence cccc DATA: More luminous galaxies are more strongly clustered. cccc ΛCDM: More massive haloes are more strongly clustered. More luminous galaxies reside in more massive haloes REMINDER: Correlation length r 0 defined by ξ(r 0 ) = 1 Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 6/20

Results Occupation Statistics from Clustering Luminosity & Correlation Functions Results Cosmology Dependence (Cacciato, vdb et al. 2008) Model fits data extremely well with χ 2 red 1 Same model in excellent agreement with results from SDSS galaxy group catalogue of Yang et al. (2008) Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 7/20

Cosmology Dependence Occupation Statistics from Clustering Luminosity & Correlation Functions Results Cosmology Dependence Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 8/20

Cosmology Dependence Occupation Statistics from Clustering Luminosity & Correlation Functions Results Cosmology Dependence (Cacciato, vdb et al. 2008) Mass-to-Light ratios tightly constrained, but with strong dependence on cosmology Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 8/20

The mass associated with galaxies lenses background galaxies background sources lensing due to foreground galaxy The Measurements How to interpret the signal? Comparison with CLF Predictions WMAP3 vs. WMAP1 Cosmological Constraints 0 1 0 1 Lensing causes correlated ellipticities, the tangential shear, γ t, which is related to the excess surface density, Σ, according to γ t (R)Σ crit = Σ(R) = Σ(< R) Σ(R) Σ(R) is line-of-sight projection of galaxy-matter cross correlation: Σ(R) = ρ R D S 0 [1 + ξ g,dm (r)] dχ Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 9/20

The Measurements Number of background sources per lens is limited. Measuring γ t with sufficient S/N requires stacking of many lenses Σ(R L 1, L 2 ) has been measured using the SDSS by Mandelbaum et al. (2005) for different bins in lens luminosity The Measurements How to interpret the signal? Comparison with CLF Predictions WMAP3 vs. WMAP1 Cosmological Constraints Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 10/20

How to interpret the signal? Stacking The Measurements How to interpret the signal? Comparison with CLF Predictions WMAP3 vs. WMAP1 Cosmological Constraints Because of stacking the lensing signal is difficult to interpret In order to model the data, what is required is: P cen (M L) P sat (M L) f sat (L) These can all be computed from the CLF Using Φ(L M) constrained from clustering data, we can predict the lensing signal Σ(R L 1, L 2 ) Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 11/20

Comparison with CLF Predictions The Measurements How to interpret the signal? Comparison with CLF Predictions WMAP3 vs. WMAP1 Cosmological Constraints NOTE: This is not a fit, but a prediction based on CLF Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 12/20

WMAP3 vs. WMAP1 The Measurements How to interpret the signal? Comparison with CLF Predictions WMAP3 vs. WMAP1 Cosmological Constraints χ 2 =29.5 χ 2 =3.1 WMAP3 cosmology clearly preferred over WMAP1 cosmology Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 13/20

Cosmological Constraints The Measurements How to interpret the signal? Comparison with CLF Predictions WMAP3 vs. WMAP1 Cosmological Constraints Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 14/20

Cosmological Constraints Ω m = 0.21 ± 0.01 (95% CL) σ 8 = 0.73 ± 0.03 (95% CL) The Measurements How to interpret the signal? Comparison with CLF Predictions WMAP3 vs. WMAP1 Cosmological Constraints Precision Cosmology using non-linear structure!! Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 14/20

For a given cosmology, luminosity dependence of clustering yields tight constraints on CLF, and thus on galaxy formation Combining clustering and galaxy-galaxy lensing we obtain tight constraints on cosmological parameters, which are in excellent agreement with CMB constraints Current (preliminary) results suggest Ω m = 0.21±0.01 (95% CL) σ 8 = 0.73±0.03 (95% CL) This technique is competative with and complementary to BAO, cosmic shear, SNIa and Lyα forest If anything, our results indicate that our model for structure formation is accurate on non-linear scales Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 15/20

Galaxy Formation in a Nutshell Galaxy Formation in a Nutshell Satellite Weighting or Host Weighting? Implications for Galaxy Formation Stochasticity Comparison with other Constraints Halo Occupation Numbers Perturbations grow due to gravitational instability and collapse to produce (virialized) dark matter halos Baryons cool, accumulate at center, and form stars galaxy Dark matter halos merge, causing hierarchical growth Halo mergers create satellite galaxies that orbit halo central orbit halos merge galaxies merge satellite central Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 16/20

Satellite Weighting or Host Weighting? Galaxy Formation in a Nutshell Satellite Weighting or Host Weighting? Implications for Galaxy Formation Stochasticity Comparison with other Constraints Halo Occupation Numbers Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 17/20

Satellite Weighting or Host Weighting? Galaxy Formation in a Nutshell Satellite Weighting or Host Weighting? Implications for Galaxy Formation Stochasticity Comparison with other Constraints Halo Occupation Numbers (More, vdb et al. 2008) The combination of σ sw and σ sw allows one to determine mean and scatter of P(M L c ) Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 17/20

Implications for Galaxy Formation Stochasticity Galaxy Formation in a Nutshell Satellite Weighting or Host Weighting? Implications for Galaxy Formation Stochasticity Comparison with other Constraints Halo Occupation Numbers log L 0 1 0000 1111 0 1 000 111 0000 1111 0 1 0 1 00 11 00 11 000 111 0 1 0000 1111 000 111 00 11 0 1 01 01 01 log M The scatter in P(L cen M) is independent of M The scatter in P(M L cen ) increases strongly with L cen Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 18/20

Implications for Galaxy Formation Stochasticity Galaxy Formation in a Nutshell Satellite Weighting or Host Weighting? Implications for Galaxy Formation Stochasticity Comparison with other Constraints Halo Occupation Numbers log L 0 1 0000 1111 0 1 000 111 0000 1111 0 1 0 1 00 11 00 11 000 111 0 1 0000 1111 000 111 00 11 0 1 0000 0000 1111 1111 0000 000 111 1111 Our results on satellite kinematics imply that σ logl (M) = 0.16 ± 0.04 with no significant dependence on halo mass. log M The scatter in P(L cen M) is independent of M The scatter in P(M L cen ) increases strongly with L cen Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 18/20

Comparison with other Constraints Galaxy Formation in a Nutshell Satellite Weighting or Host Weighting? Implications for Galaxy Formation Stochasticity Comparison with other Constraints Halo Occupation Numbers Probability Distribution from Satellite Kinematics Constraints from Galaxy Group Catalogue (Yang et al. 2008) Constraints from Clustering Analysis (Cooray 2006) Predictions from Semi Analytical Model (Croton et al. 2006) Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 19/20

Halo Occupation Numbers Galaxy Formation in a Nutshell Satellite Weighting or Host Weighting? Implications for Galaxy Formation Stochasticity Comparison with other Constraints Halo Occupation Numbers Unlike 2dFGRS, the SDSS reveals clear shoulders at N M = 1 Most likely this is an artefact of the functional form of the CLF Kunming, February 27, 2009 The Galaxy-Dark Matter Connection - p. 20/20