June 2, 2003
Afternoon session

R. Wechsler
Local clusters z<0.5 
want cluster catalog that is pure, complete
must reliably estimate those
need proxy for mass; calibrate observable-mass rel'n 
--use realistic simulation, run cluster finder as on real data
--optical cluster catalogs
  -test C4 (Miller) & maxBCG (Annis) methods

What is needed in simulation?
 -size
 -match color & luminosity dependent clustering of real data
   E/S0 ridgeline & its evolution ; color-space distribution
 
-->use Hubble volume simulation, 3000Mpc/h, LCDM cosmo
    -gives ~2 sky surveys of area
    -insufficient resolution to do halo population model
    -instead use local density

ingredients:
1. LF from SDSS, only use galaxies brighter than 0.4L* (M_r<-19.9)
2. luminosity dependent bias  P(overdensity|L) tuned to match measured correlation fn.(r|L)
3. Now have sim. with one-band data. Take local density (distance to 10th nearest gal.)
   -find galaxy in real SDSS data with same mag M_r, local dens d_g, and give its colors to 		mock galaxy


How is #2 done:
in simulation, measure DM density d_m at M* scales. Assumes that tuning d_m on this scale will allow proper scaling of corr. fn.
Probability distribution for galaxy of a given mag to be within distance R of 8th nearest neighbor is fit as a log normal (small R) plus gaussian (large R)  
Probability(d_m) tied to corr fn.
corr fn. (r,L) from data
for each L luminosity, what probability distribution fn,
    for each L, now r_0 and gamma. Ask what kind of PDF of chosen form will match these. Can     adjust peak of log normal, gaussian and their width for each L.
      	for instance, bright galaxies are mostly inlog normal at small R, while dim ones are 	mostly gaussian at large R.
Ask what P(d_m) is consistent with corr.fn.(r|L) 


How is #3 done:
In mock catalog, measure distance to 10th nearest neighbor to mag. limit (0.4L*)
Choose galaxy with same local density from SDSS
Kcorrect colors to the redshift in the simulation

now have P(L|z), P(color|z), Corr.fn.(r|L,color)


-with final catalog, estimate completeness/contam of cluster finders
-allows optimization of cluster finders; M. White: can give wrong calibration if model is wrong
-Gus: surprisingly, cluster finders drop below 90% at M~few*10^14 Msun
-what is P(Mass|observable): find 40%-ish scatter for Ngals>30
-can directly predict cluster observable fn. as function of cosmology, if run simulation
 with multiple cosmologies
  sigma_8 does not require new sim, just look at less-evolved time

-allows changing observable to see which one gives best M-observable correlation

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Andreas Berlind
Review of measurements of DM halo occupation by galaxies

Galaxy cluster as DM halo occupation
2 Assumptions:
a. All galaxies live in halos (isolated=field cluster=shared)
b. Galaxy content of a halo depends only on the halo mass M_h
   -so large M_h halo in low-density region should have galaxies with same mass fn. as same
	M_h halo in high-density region  (only now being observationally tested Sheth)

Cosmology (Omega_m, P(k) etc.) --> gives DM halo population halo mass fn., profiles, halo 		correlations

Galaxy Formation (mergers, SF, SN, etc.) --> Halo Occupation Distribution (HOD) P(N|M_h) 	broken into <N(M_h)> and P(N|<N>)
      	spatial distribution of galaxies within halos + velocity distribution

the two together give full galaxy clustering

If we can measure HOD directly, can test cosmo, and vice versa
this talk reviews HOD measurements
currently most measures are of <N(M_h)>
Find characteristic form of <N(>M)> w/ sharp rise (need enough gas to form galaxy),   flattening (one galaxy per halo), then rising power law of slope <1 (groups/clusters)
 -models seem to agree well with each other, but does data? 
 -what is shape for different galaxy types/colors/lums ?
    -red galaxies more of just a power law, blue galaxies shallower slope after turnover

Estimates of N(M_h) in literature:
1. Analytic halo model
   bias on large scales b_g = (1/n_g)^2 * (int[dM dn/dM b(M) <N(M)>])   b(M) from Mo & White   -Zehavi  SDSS corr. fn.
  -Scoccimarro  APM number counts
  -Maliocchetti 2dFGRS
  -Cooray PSCz P(k)
  -Bullock  LBGs b_g, <n> , n_pairs

2. Conditional Lum. Fn.
  -Yang, vanndenBosch  LF(L|M)

3. Populate simulations
  -Jing  LCRS,PSCz
  -Scoccimarro  PTHalos
  -Wechsler  SDSS

4. Group finding to match DM halos
  -Peacock
  -Berlind
  -Kochanek

showed compilation of estimates of slope of <N(M_h)>
  SDSS results agree well; results for red/blue galaxies agree pretty well between surveys
  slope ~0.6 for blue, 1 for red, 0.85 for all galaxies

showed SDSS results for <N(M_h)> for volume-limited samples with different abs. mag cuts
  
Nichol: what is hope for getting down to plateau:
A: None, with groups/clusters. Need to use diff. stats. In regime of 1 gal/halo, no pairs in halos, so they don't contribute to correlation. Only cause shift in large-scale bias (more single halos change mean density). But void stats are very sensitive to this, as are 
galaxy-galaxy lensing and mean galaxy number

Nichol: critical threshold in galaxy density 1/Mpc^2 below which there is no correlation of SFR and local density
A: Unexpected from models. Blue gals. should be more common at low density.

Evrard: how do models put in galaxy distribution in halos?
A: Vary,some put most massive guy in halo center and distribute satellites following DM. Putting in velocity bias can change pairwise veldisp and modify clustering. Jing finds good match to two point corr. fn. but overpredict pairwise veldisp; require overly low Omega of 10-20% velocity bias. Not yet constrained by data.


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Ravi Sheth
Halo models

Assumption in semi-analytic models is that galaxies formed in a halo care ONLY about halo mass

measure corr.fn. xi(r)=pairs in same halo + pairs in separate halos
 = int[dm n(m) m^2 xi(r|M)]  / [int(dm n(m) m)]^2
   + [intdm n(m) m b(m)]^2 xi_dm(r)  / [int(dm n(m) m)]^2

if doing galaxies, m -> N_gal(m)

Split SDSS into dense and void regions
measure xi(r) as a function of density
Now, everything in corr. fn. is density dependent. Mass function , xi(r), etc.
But semi-analytic model says most of these are NOT density dependent, only the mass function of halos.

Can we make a model for how mass fn. depends on environment? Could do from simulations, if believe cosmology. Sheth & Tormen generate analytic model for any cosmology.

n(m|d) where d is density (delta)
  =(1+d)n(m)  more halos in dens regions. Does NOT worl

more massive halos in overdense region, but fewer low mass halos
in underdense regions, get more low mass halos, but fewer high mass halos
-> n(m) not linearly dependent on d
dependence on d depends on cell size

How to understand? Massive guys form from many pieces. Have a merger tree; 
count n(m) at z=0. Can do it at higher z also. Can also think of halos today as subclump of a future single halo. In a dense region today, we are in a halo that will soon merge; just like looking at halo at low-z. In underdense region today, we will not merge for a long time, like a halo at hi-z. Mo & White

Get large change in clustering signal in high vs. low density regions. Both terms of corr. fn. will depend on density. If split SDSS into top & bottom third of density, should get factor of two differences in corr. fn.; easily measured. 

How do we see if analytic assumption works? Fit xi(r) with two part fn. Given a cosmology, get n(m). Do for all sky (all densities), and see if you can recreate low & high density fits. If you can't, then assumption fails. BUT need to get from galaxies to DM halos!
Measure d_gal as f(d_mass). At large scales have small scatter in relation; even though relation is curved, at proper scales it can be represented as linear bias.

Not yet measured in SDSS.

Nichol: plotted xi(LRGS) vs Zehavi xi(main sample). Shapes are quite different; LRGs are power law at all scales. 
A: Cannot play with solo occupation term too much. But n>1 occupation term for LRGS will depend on how LRGS populate halos. If they are all in massive halos, bump up two independent terms in xi(r) by different amounts, such that sum ~ power law. 

Q: How sensitive are results to profile xi(r|m)?
A: If red vs. blue difference is indep. of environment, doesn't matter. But we see they have different profiles within halos, AND the number or red vs. blue depends on halo mass. so Ngal(m) changes AND xi(r|m) changes. As it turns out, Ngal(m) is hugely dominant (see Berlind talk above). 
   Also know from sims that m~veldisp^3; see this in SDSS and sims.

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Andrei Kravtsov
The Dark Side of HOD

What about distribution of halos within halos? Each galaxy is its own halo; galaxies populate large halos

Early, xi(r) is power low; simulations low resoln., no normalization from COBE.
resolution only ~1Mpc
as resolution improves, see strong deviation from power law at scales <1Mpc
historically, bias describes difference between galaxy & DM xi's
b^2 = xi_gg(r)/xi_mm(r)
If bias is nonlinear...need hi-resoln. to see nonlinear regime (clusters, etc)
In hydro sims, can have gas cooling, and can try to identify galaxies as cold clumps, but computationally expensive. In late 90s, get to scales in both N-body & hydro where can see subhalos within cluster-size halos.

Subclumps in halos only 10% of mass, but plotted in log(density) looks a lot more.
Early of these simulations produce power law xi(r) for DM and baryons down to 100kpc; matched APM xi(r) well.
Found galaxies are ANTIbiased: suggestion that clusters have lower efficiency of galaxy formation. But dissipationless models also showed this, which suggests that it is NOT inhibition of galaxy formation but something to do with DM dynamics.

Dissipationless simulations :
LCDM, Omega_0=0.3, h=0.7, sigma_8=1.0, 60h^-1 Mpc  256^3 particles of 1.1*10^9 h^-1 Msun, resolve to ~L*
Kravtsov & Lypin 98, Colin et al. 99 ; at time no Halo occupation models!
Now being redone with Halo models (w/ Wechsler & Berlind)
Now with 80h^-1 Mpc box, sigma_8=0.75, 512^3 particles of 3*10^8 h^-1Msun
identify halos, get <N(m)> vs. m_180; take samples comparable to galaxies in SDSS with
M_r <-16,-18,-19,-20,-21
get characteristic HOD shape : cutoff below certain mass; then about one decade in mass where it is flat (one gal/halo), then power law, reachin up to ~100 gals/halo at m_180 ~ 5*10^15Msun

Shape of HOD is same for all mag limits, with different mass cutoffs and different mass where change to power law occurs. Find slope of power law ~0.85.

Fits of corr. fn. give
M_r	r_0	gamma
-16	4.5	1.65
-18	4.7	
-19	4.7
-20	4.9	1.8
-21	6.3pm0.3 1.93

Budavari results on today's astro-ph agree at bright end (from SDSS)

have flatter slopes at higher redshifts

If you compare objects with the same number density from the two simulations, get same HOD. Therefore sigma_8 unimportant. 

Dynamical evolution of DM halos defines galaxy corr. fn., NOT cluster/SF physics. The galaxy colors, stellar pops may be defined by the latter.

Evrard: How do you select subhalos?
A: Find peaks, check if they are gravitationally bound. Also check visually. Important for completeness at low mass. In each peak, get v_circ(r) for bound particles, and use v_circ as mass proxy.

Q: Do we understand slope of 0.85? 1.0 expected naively.
A: No. Use semi-analytic models where you can turn on/off specific processes. Not yet done.

Sheth: Ben Moore  has paper where he shows subhaloes ~M-1.9 (?,for small objects). If you integrate that , get N(>m) ~ m^0.9, which agrees with Kravtsov results.

Q: What about colors, etc.?
A: This just shows underlying gravitational models ok.

Evrard: Can you reproduce Tully-Fisher, Faber-Jackson?
A: Hard to go from DM veldisp to galaxy veldisp.