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Marked Correlations in Hierarchical Models

Marked Correlations in Hierarchical Models. Why environmental trends? How to quantify? How to test? Halo-model description. Ravi K. Sheth (UPenn). Environmental effects. Gastrophysics determined by formation history of parent halo

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Marked Correlations in Hierarchical Models

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  1. Marked Correlations in Hierarchical Models • Why environmental trends? • How to quantify? How to test? • Halo-model description Ravi K. Sheth (UPenn)

  2. Environmental effects • Gastrophysics determined by formation history of parent halo • Formation history correlates with mass (massive objects form later) • All environmental trends come from fact that massive halos populate densest regions

  3. Most massive halos populate densest regions over-dense under-dense Key to understand galaxy biasing (Mo & White 1996; Sheth & Tormen 2002) n(m|d) = [1 + b(m)d] n(m)

  4. How to quantify trends with environment? • Traditional approach requires separation into cluster and ‘field’ • Non-trivial in redshift-space, given that many environmental trends small, so accurate separation required

  5. There’s more to the point(s) • Multi-band photometry becoming the norm • CCDs provide accurate photometry; possible to exploit more than just spatial information • How to estimate clustering of observables, over and above correlations which are due to spatial clustering? • Do galaxy properties depend on environment? Standard model says only dependence comes from parent halos…

  6. Marked correlation functions Weight galaxies by some observable (e.g. luminosity, color, SFR) when computing clustering statistics (standard analysis weights by zero or one) No need to define ‘cluster’ and ‘field’

  7. Marked correlations (usual correlation function analysis sets m = 1 for all galaxies) W(r) is a ‘weighted’ correlation function, so … marked correlations are related to weighted ξ(r)

  8. Estimator • For un-weighted: 1 + x(r)= DD/RR • For weighted: 1 + W(r) = WW/RR • So ratio is WW/DD: no need for random catalog---very easy to estimate! • Rough estimate of errors from randomizing marks and repeating measurement many times

  9. Luminosity as a mark • Mr from SDSS • BIK from semi-analytic • model (GIF) • Little B-band light • associated with • close pairs; more B-band • light in ‘field’ than ‘clusters’ • Vice-versa in K • Feature at 3/h Mpc in all • bands: Same physical • process the cause? • e.g. galaxies form in groups • at the outskirts of clusters Sheth, Connolly, Skibba (2005)

  10. Colors and star formation • Close pairs tend to be redder • Scale on which feature • appears smaller at higher z: • clusters smaller at high-z? • Amplitude drops at lower z: • close red pairs merged? • Close pairs have small • star formation rates; scale • similar to that for color even • though curves show • opposite trends! • Same physics drives both • color and SFR?

  11. How to separate correlations which arise from statistics of initial distribution (i.e. correlation between halo mass and environment) from those which arise from physics?

  12. Halo-model of galaxy clustering • Two types of pairs: only difference from dark matter is that number of pairs in m-halo is not m2 • ξdm(r) =ξ1h(r) + ξ2h(r) • Spatial distribution within halos is small-scale detail

  13. Halo-model of marked correlations Write as sum of two components: W1gal(r) ~∫dm n(m) g2(m)‹W|m›2ξdm(m|r)/rgal2 W2gal(r) ≈ [∫dm n(m) g1(m) ‹W|m›b(m)/rgal]2ξdm(r) So, on large scales, expect 1+W(r) 1+ξ(r) 1 + BWξdm(r) 1 + bgalξdm(r) M(r) = =

  14. Type-dependent clustering: Why? populate massive halos populate lower mass halos Spatial distribution within halos second order effect (on >100 kpc)

  15. Gastrophysics determines typical marks of galaxies as function of mass of halo which hosts them … Sheth 2005

  16. If physics wrong, theory should not match measured marked statistics (same LF per halo as before, only now central galaxy is not special)

  17. Sheth 2005 …all the rest is statistics Curves show two models for the physics (solid = central galaxy special; dashed = central galaxy same as others) If physics wrong, theory does not match

  18. Comparison of two marks gives information about how correlation between marks depends on environment (e.g. FP?) E.g., on scales larger than a few Mpc, environmental dependence of Mass-to-Light ratio is entirely a consequence of correlation between halo mass and environment

  19. Weighted correlations in SDSS early-type sample z~0.06 z~0.09 z~0.12 Can use observables or derived parameters as marks

  20. Conclusions (mark these words!) • Marked correlations represent efficient use of information in new high-quality multi-band datasets (there’s more to the points…) • No ad hoc division into cluster/field, bright/faint, etc. • Trivial change to existing clustering algorithms (and no need for random catalog) • Describes environmental trends in same language as other clustering measurements (halo-model) • Comparison with SDSS ongoing (no surprises yet!) • test Ngalaxies(m); • then test if rank ordering OK; • finally test actual values

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