Angular clustering and Angular clustering and halo occupation propertieshalo occupation properties

of COSMOS galaxiesof COSMOS galaxies

Cristiano PorcianiCristiano Porciani

Overview

• Brief summary of clustering studies performed at ETH-Zurich:

correlation functions

counts in cells

theoretical interpretation: halo occupation models

• A few suggestions for optimizing the photometric redshift catalog for LSS studies (many thanks to P. Capak and B. Mobasher for producing it!)

LSS from COSMOS

Finite volume effects: integral constraint, lack of fluctuations on large-scales.

Spatially-dependent photometry

Poor sampling, (lack of close galaxy pairs) mask accuracy, galaxy size and identification in crowded regions

The COSMOS galaxy catalog is ideal for surveying the LSS of the universe beyond the local volumes probed by the 2dFGRS and the SDSS

COSMOS data (LSE)

Power-law fit

Coil et al. (2004) - 5 deg2 over 5 fields

Wilson (2003) - 1.5 deg2 over 6 fields

Our preliminary mask is probably too little conservative

Our preliminary masksampled with a Poisson point process containing 106 points [my “random catalog” for computing ()].

COSMOS galaxies with I<25

COSMOS galaxies with I<25 and no photometric redshift

Sample variance and the IC

The shape of the PDF, the variance and the bias of an estimator for () depends on:• the adopted estimator • the angular separation (nearly Gaussian PDF for small , strongly skewed PDF for large )• the higher-order moments of the galaxy distribution• shot-noise• finite volume effects

IC

Poisson errors strongly underestimate the variance and do not give the covariance matrix; groupwise bootstrap (e.g. Porciani & Giavalisco 2002) or mock catalogs (need

many!!!) are better alternatives.

Clustering amplitude vs apparent magnitude

Points with errorbars represent COSMOS data.

The dashed lines are the best-fitting power-laws from Coil et al. (2004).

Clustering amplitude vs apparent magnitude

COSMOS

Coil et al. (2004)

Postman et al. (1998)

Millennium mock COSMOS created by Kitzbichler et al.

Clustering amplitude vs color

All COSMOS galaxies with

I<24

Clustering amplitude vs color

COSMOS

Coil et al. (2004)

Millennium mock COSMOS by Kitzbichler et al.

All COSMOS galaxies with

I<24

All COSMOS galaxies with

I<25

Clustering amplitude vs color

Adding the redshift information

Joint distribution of z and z for our photometric redshifts

A non-negligible fraction of our galaxies have very uncertain redshifts

COSMOS galaxies with I<24 and 0.2<z<0.5

COSMOS galaxies with I<24, 0.2< z<0.5 andz < 0.2 (1+z)

The clustering amplitude differs by 25%!

Clustering amplitude and redshift errors

Clustering amplitude and redshift errors

It would be crucial to have information regarding the likelihood function of the photometric redshifts. This way each galaxy could be associated with a statistical weight to measure ().

If it is not possible to have the likelihood function of each COSMOS galaxy, a good proxy (e.g. a substantial number of percentiles) would be very helpful as well.

This would also increase the accuracy of the Limber inversion.

Likelihood functions are essential to accurately estimate ()

Redshift evolution

IAB< 24

The halo model for large-scale structure

The halo model provides a phenomenological understanding of LSS in the non-linear clustering regime.

Motivations

• Galaxies are expected to form within DM halos but a detailed understanding of the physics is still lacking

• The number density and the clustering properties of DM halos can be readily and reliably computed as a function of their mass

• It is therefore of great interest to try to establish a connection between these halos and different classes of cosmic objects

• This phenomenological description is useful to guide and constrain galaxy formation models and to build mock galaxy catalogues (in order to understand systematic effects in galaxy surveys)

• The halo model successfully reproduces low order mass and galaxy correlations (and pair velocities) in numerical simulations.

The halo occupation distribution

The key ingredient of the halo model for galaxy clustering is the halo occupation distribution, P(N | M), which gives the probability for a halo of virial mass M to contain N galaxies of a given type.

In principle, its moment of order n can be determined by studying the n-point clustering properties of the galaxy population.

Relying on measurements of the mean density (need completeness corrections) and the 2-point correlation function of COSMOS galaxies, only the first 2 moments of the halo occupation function can be determined from the data. These strongly constrain galaxy formation models!

2-point statistics in the halo model

Two-point correlation function:

Mean density of galaxies:

Halo mass function Halo occupation number

Galaxy number density profile

Second factorial moment of the HOD

Halo correlation funct.

Previous experience with the halo model

LBGs: Porciani & Giavalisco (2002)

2dFGRS: Magliocchetti & Porciani (2003)

2QZ: Porciani, Magliocchetti & Norberg (2004) Porciani & Norberg (2005)

All the machinery is in place,ready to be applied to the final COSMOS data

Potential to study redshift, luminosity, morphology and color dependent clustering in

terms of halo occupation properties

COSMOS 2dFGRS

Further activities at ETH-Zurich

• Counts-in-cells analysis higher-order moments

• Clustering of drop-out galaxies at high-z

• Preliminary theoretical studies to investigate the potentiality of ZCOSMOS