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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 MMmin Sub-halos Satellite: <Nsat>=(M/M1) , for MMmin 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 mgm(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]