1. Large scale structure in the SDSS
The ISW effect
The Ly-alpha forest
Galaxies and Clusters
Marked correlations: There’s more to the points
Ravi K. Sheth (UPitt/UPenn)

2. The ISW effect Cross-correlate CMB and galaxy distributions
Interpretation requires understanding of galaxy population

3. Expected scaling of signal
Expect NO signal in Einstein de-Sitter!
Recent (2003) detections in X-ray and radio-selected catalogs

4. Cross-correlate LRGs with CMB
Measured signal
combination of
ISW and SZ effects
Estimate both using
halo model (although
signal dominated by
linear theory);
Signal predicted to
depend on
b(a) D(a) d/dt [D(a)/a]

5. Evolution and bias Work in progress to disentangle evolution of
bias from z dependence
of signal
(Scranton et al. 2004)

6. Spherical harmonic analysis similar (Padmanabhan et al 2004)

7. The Ly-a forest Evolution measured over 2.2<z<4.2
Consistent with WMAP LCDM cosmology (hi-z universe ~ EdS)
Series of papers by McDonald, Seljak et al. (2004)
(Alternative analysis by Hui et al. 200?)

8. Galaxy Surveys

9. Spatial Clustering
Large scale measurements can detect baryon wiggles/bump:
LRG clustering
QSO clustering
Smaller scale measurements constrain galaxy formation models

10. (Cole et al. 2000)

11. Kauffmann, Diaferio, Colberg & White 1999
Also
Cole et al., Benson et al.,
Somerville & Primack,
Colin et al.
Colors indicate age

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

13. Comparison with simulations
Sheth et al. 2001
steeper
Halo model calculation of x(r)
Red galaxies
Dark matter
Blue galaxies
Note inflection at scale of transition from halo term to 2-halo term
Bias constant at large r
shallower
x1h›x2h
x1h‹x2h →

15. Power-law: x(r) = (r0/r)g
slope g = -1.8
Totsuji & Kihara 1969

16. Not a power law
Feature on few Mpc scale; expected as transition from 1halo to 2halo term
(Zehavi et al. 2004)

17. N-body simulations of
gravitational clustering
in an expanding universe
Lots of substructure!
(Model by Lee 2004)

18. Galaxies and halo substructure
Better to think in terms of center + satellite:
g1(m) = 1 + [m/23m1(L)]a(L) for m>m1(L)
Higher order moments from assumption that satellite distribution is Poisson
Poisson model consistent with assumption that halo substructure = galaxies

19. Linear bias on large scales

20. Color dependence and cross-correlations consistent with simplest halo model

21. fingers of god
Redshift space trends qualitatively consistent
with v2 ~ m2/3 scaling—quantitative agreement
also?

22. Galaxy formation models ~ correctly identify the halos in which galaxies form Galaxy ~ halo substructure is reasonable model

23. Extensions
Poisson model implies a complete model of point distribution
Can now make mock catalogs that have correct LF and 2pt function---check using n-pt, Minkowski’s,…
Assume monotonic relation between subclump mass and galaxy luminosity to get L-s relations
Include correlations between L, size, color, etc.
Relate galaxy distribution to cluster distribution (what is better tracer of mass: L? Ngal? S?)
Model of BCGs (e.g. use C4 catalog)

24. Successes and Failures
Distribution of sizes ~ Lognormal: seen in SDSS
Morphology-density relation (oldest stars in clusters/youngest in field)
Type-dependent clustering: red galaxies have steep correlation function; clustering strength increases with luminosity
Distribution of luminosities
Correlations between observables (luminosity/color, luminosity/velocity dispersion)

25. Sizes of disks and bulges
Observed distribution ~ Lognormal
Distribution of halo spins ~ Lognormal
Distribution of halo concentrations ~ Lognormal
(Bernardi et al. 2003; Kauffmann et al. 2003; Shen et al. 2003)

26. Environmental effects
Fundamental assumption: all environmental trends come from fact that massive halos populate densest regions

27. Color and Luminosity
Hogg et al. 2004

28. Density and Lumi-nosity
Hogg et al. 2004

29. Marked correlation functions
Weight galaxies by some observable
(e.g. luminosity, color, SFR) when computing clustering statistics (standard analysis weights by zero or one)

30. 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…

31. Early-type galaxies
Models suggest cluster galaxies older, redder, more massive
Weak, if any, trends seen

32. Age and environment

33. Marked correlations (in volume-limited catalogs)
Close pairs are redder, and have larger D4000, suggesting they are older, even though no strong trend seen with s
Environment matters!
low-z
hi-z
D4000

34. 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)

35. Luminosity as a mark Mr from SDSS BIK from semi-analytic model
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

36. 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?

37. Stellar mass Circles show M*, crosses show LK
Similar bumps, wiggles in both: offset related to rms M*, L
Evolution with time: M* grows more rapidly in dense regions

38. Halo-model of marked correlations
Again, write in terms of two components:
W1gal(r) ~ ∫dm n(m) g2(m) ‹W|m›2 ξdm(m|r)/rgal2
W2gal(r) ≈ [∫dm n(m) g1(m) ‹W|m› b(m)/rgal]2 ξdm(r)
So, on large scales, expect
1+W(r)
1+ξ(r)
1 + BW ξdm(r)
1 + bgal ξdm(r)
M(r) = =

39. 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)

40. 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.
Comparison of SDSS/SAMs ongoing
test Ngalaxies(m);
then test if rank ordering OK;
finally test actual values
Halo-model is natural language to interpret/model