1. 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

2. 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’

3. How to describe different point processes which are all built from the same underlying distribution? THE HALO MODEL

4. Environmental effects In hierarchical models, close connection between evolution and environment (dense region ~ dense universe ~ more evolved ~ more massive halos ~ more clustering) n(m|  ) = [1+b(m)  n(m) Observed correlations with environment test hierarchical galaxy formation models

5. Halo-model of galaxy clustering Two types of pairs: only difference from dark matter is that number of pairs in m-halo is not m 2 ξ dm (r) = ξ 1h (r) + ξ 2h (r) Spatial distribution within halos is small-scale detail

6. Halo-model of un-weighted correlations Write 1+ξ = DD/RR as sum of two components: ξ 1gal (r) ~ ∫dm n(m) g 2 (m) ξ dm (m|r)/  gal 2 ξ 2gal (r) ≈ [∫dm n(m) g 1 (m) b(m)/  gal ] 2 ξ dm (r) ≈ b gal 2 ξ dm (r) g 2 (m) is mean number of galaxy pairs in m-halos (= m 2 for dark matter) g 1 (m) is mean number of galaxies in m-halos (= m for dark matter)

7. Satellite galaxy counts ~ Poisson Write g 1 (m) ≡ ‹g(m)› = 1 + ‹g s (m)› Think of ‹g s (m)› as mean number of satellite galaxies per m halo Minimal model sets number of satellites as simple as possible ~ Poisson: So g 2 (m) ≡ ‹g(g-1)› = ‹g s (1+g s )› = ‹g s › + ‹g s 2 › = 2‹g s › + ‹g s › 2 = (1+‹g s ›) 2 - 1 Simulations show this ‘sub-Poisson’ model works well ( Kravtsov et al. 2004 )

8. Two approaches … Halo Occupation Distribution ( Jing et al., Benson et al.; Seljak; Scoccimarro et al. ) –Model N gal (>L|M halo ) 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 M halo ( Tinker et al., Skibba et al.): Conditional Luminosity Function ( Peacock, Smith ): –Model LF as function of M halo, and infer HOD ( Yang, Mo, van den Bosch; Cooray) …both separate centrals/satellites

9. 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

10. Why is … Luminosity dependence of SDSS clustering well described by halo model with g 1 (m|L) ≈ 1 + m/[23 m 1 (L)] g 1 (m|L) nonzero only if m>m 1, where m 1 (L) adjusted to match decrease of number density with increasing L (Assume Poisson distribution, with mean g 1, for non-central, ‘satellite’ galaxies)

11. 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(>V circ ) works well for all clustering analyses to date, including z~3 ( Conroy et al. 2006 )

13. Halo substructure = galaxies? N sub (>m|M) = (M/10 12 h -1 M sun ) 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 M stellar /L

14. Ongoing debate over ‘orphan’ galaxies … ( e.g. Nagai & Kravtsov 2005 )

15. Predicted correlation between luminosity and mass Skibba, Sheth, Connolly, Scranton 2006 ~ ln(1 + M/M crit ) ~ independent of M Prediction based on halo-model interpretation of clustering in SDSS for galaxy samples with various L cuts ( Zehavi et al. 2005 ) central satellite total

16. Halo model fits of Zehavi et al. (SDSS) imply mean satellite luminosity only weak function of halo mass Provides good description of group catalog of Berlind et al. (SDSS), Yang et al. (SDSS) Worth reconsidering Scott (1957) effect, but for satellites?

17. Skibba & Sheth 2007 Berlind et al Yang et al HOD prediction

18. Assumptions (to test) Halo profiles depend on mass, not environment Galaxy properties, so p(N gal |L,m), and so g 1 (m) and g 2 (m), depend on halo mass, not environment All environmental dependence comes from correlation between halo mass and environment: n(m|  ) = [1+b(m)  n(m) –Mass function ‘top-heavy’ in dense regions

19. Halo-model of environmental trend Three types of pairs: both in same halo, in different halos but same patch, in different patches ξ(r|  ) = ξ 1h (r|  ) + ξ 2h-1p (r|  ) + ξ 2h-2p (r|  )

20. Environments in SDSS Least dense regions ~  < −0.8 ~ voids

21. Aside 1: Poisson cluster models (thermodynamic, Neg. Binomial) quite accurate, N.B. Counts are in cells centered on particles

22. Environment is number of neighbours within 8Mpc 30% densest 30% least dense

23. Assume cosmology → halo profiles, halo abundance, halo clustering Calibrate g(m) by matching n gal and ξ gal (r) of full sample Make mock catalog assuming same g(m) for all environments Measure clustering in sub-samples defined similarly to SDSS SDSS Abbas & Sheth 2007 M r <−19.5

24. Highest density Lowest density Mass function top heavy in dense regions z-space

25. Aside 2: Stochastic Nonlinear Bias Environmental dependence of halo mass function provides accurate framework for describing bias (curvature = ‘nonlinear’; scatter = ‘stochastic’) G 1 (M,V) = ∫dm N(m|M,V) g 1 (m)

26. 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

27. Galaxy distribution remembers that, in Gaussian random fields, high peaks and low troughs cluster similarly

28. 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 2dFGRS Void halos Colberg & Sheth 2007

29. 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  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  Little room for additional (e.g. assembly bias) environmental effects

30. Gastrophysics determined by formation history of parent halo

31. Correlations with environment Traditional approach requires separation into ‘cluster’ and ‘field’, ‘dense’ and ‘under-dense’ ( Berlind et al. 2006; Yang et al. 2006 ) Non-trivial in redshift-space, given that many environmental trends small, so accurate separation required

32. 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)

33. Luminosity as mark in SDSS Skibba, Sheth, Connolly, Scranton 2006 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 centre not special centre special Unweighted signal

34. Luminosity as mark in SDSS Skibba, Sheth, Connolly, Scranton 2006 Close pairs more luminous only in redder bands Qualitatively consistent with models

35. Color as mark in SDSS Skibba, Sheth, Connolly, Scranton 2006 Close pairs are redder than average Long-tailed distributions show clearer signal?

36. 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

38. 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

41. 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

42. 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

43. Color- magnitude relation ~ independent of group properties Distribution of galaxies in relation does depend on group properties Blanton, Berlind, Hogg 2006

44. Assume split between red and blue depends on luminosity (determine directly from data); mass dependence entirely from correlation between luminosity and halo mass

45. SATELLITES CENTRALS Assume bimodal colors = centre- satellite … rather than centre-satellite or centre-satellite

46. 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 )

47. Passive evolution of the most massive galaxies? White et al. 2007 Match number densities of most luminous galaxies at two redshifts ( e.g. NDWFS of Brown et al. 2006 )

48. If no merging … G(M) = ∫ dm N(m|M) [g cen (m) + g sat (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

49. Hi-z Low-z

51. 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)

52. 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 )