Drinking tea with a fork: Techniques for Photometric redshift surveys

Motivation –Some galaxy scaling relations and clustering from spectroscopic data at low-z –How much of this can be done with photo-z datasets (DES, PanStarrs, LSST) Methods for noisy distance estimates –Typically at higher-z –Also apply to ‘local’ surveys where peculiar velocities contaminate distance estimate –Or to stellar distances from color-magnitude relation

Bernardi et al Scaling relations Slope, amplitude, curvature → nature, formation history

Bernardi et al. 2011

Mark Correlations Weight galaxies when measuring clustering signal; divide by unweighted counts WW(r)/DD(r) means no need for random catalog Error scales as scatter in weights times scatter in pair counts ( Sheth et al ) –If scatter in weights small, can do better than typical cosmic variance estimate –Basis for recent excitement about constraining primordial non-Gaussianity from LSS

Sheth, Jimenez, Panter, Heavens 2006 Close pairs (~ galaxies in clusters) more luminous, older than average

SDSS/MOPED + Mark correlation analysis Predicts inversion of SFR-density relation at z >1 (if densest regions today were densest in the past)

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

A Nonlinear and Biased View Observations of galaxy clustering on large scales are expected to provide information about cosmology (because clustering on large scales is still in the ‘linear’ regime) Observations of small scale galaxy clustering provide a nonlinear, biased view of the dark matter density field, but they do contain a wealth of information about galaxy formation

How much of this information can be got from a photometric redshift survey? - Cosmology mainly wants dN/dz - Galaxy formation wants p(L,R,…|z) - Both want clustering: accurate distances

A fool in a hurry drinks tea with a fork Techniques for Photometric redshift surveys

‘Representative’ spectra required to calibrate mags →z mapping

Typically z phot (mags) So can get p(z phot |z) or p(z|z phot ) More generally, can get p(z|mags)

One mouse dropping ruins the whole pudding Catastrophic failures: dN/dz

Deconvolution: dN/dz phot = ∫dz dN/dz p(z phot |z) Convolution: dN/dz = ∫dz phot dN/dz phot p(z|z phot ) or, more generally, dN/dz = ∫dm dN/dm p(z|m)

De- con- volve (Sheth 2007 uses Lucy 1974) distorted fixed

In SDSS Rossi et al Sheth & Rossi 2010 If = z then ≠ 

All crows in the world are black

Deconvolution

Convolution

For luminosity function in magnitude limited survey, remember that N(M phot ) = ∫dM N(M) p(M phot |M) where N(M) = V max (M)  (M)

(De)convolve to get N(M) … … then divide by V max (M)

= M so ≠ M

Deconvolve

Convolve

Riding a mule while looking for a horse Convolution/deconvolution/ Maximum-likelihood ( Sheth 2007; Christlein et al )/ Weights ( Lima et al. 2008; Cunha et al )

Biased scaling relations can be fixed similarly True, intrinsic Biased because same distance error affects both observables

Similarly for size - L relation

If a single family member eats, the whole family will not feel hungry Cross-correlations: MgII systems and z~0.7 LF in SDSS N.B. ~ 0.1

Churchill et al. 2005

Knowledge of ra, dec, z MgII + correlation length only few Mpc + sufficiently deep photometry = estimate of z~0.7 LF ( Caler et al )

1880 absorbers in DR3 from Procter et al (2006)

Assume all galaxies in same field as absorber have z abs Wrong for all objects except those at z abs Do same for random position Subtract counts

50 kpc 900 kpc 100 kpc 500 kpc

900 kpc 500 kpc 50 kpc

To hit a dog with a meat-bun Only small fraction of absorbers (~400/1900) are in SDSS imaging See Zibetti et al. (2007) for more about SDSS MgII absorbers

Accounting for magnitude limit gives z~0.7 galaxy luminosity function

EW < 1.3 AMore strong 50 kpc 500 kpc More weak

Another view of measurement 1880 fields each ~  (3 arcmin) 2 So LF estimate from total area ~ 10 degrees 2 Comparable to COMBO-17; final data release even larger; can even do evolution Summing over L gives ~ dN/dz from cross correlation/background subtraction, so this is yet another photo-z method

A person is blessed once, But his troubles never come alone dN/dz estimate depends on how correlated objects in photo-sample are with those in spectroscopic sample: in general, this ‘bias’ unknown

In principle, progress from combining all previous methods. Especially if spectra taken to calibrate photo-z’s cover same survey area (…unlikely!)

Water can float a boat But it can sink it too Will calibration spectra themselves provide higher S/N measurement of galaxy scaling relations?

Summary Many complementary methods allow robust checks of derived scaling relations –Honest reporting of photo-z errors crucial Cross-correlating photo/spectro samples useful –SDSS-BOSS LRGs with SDSS photometry –SDSS photometric QSOs with spectroscopic QSO sample (= faint end of QSO LF) –Better if spectra throughout survey volume Deep photometry around absorption line systems interesting even if absorbers not seen

Ongoing... How to measure mark correlations in (magnitude limited) photo-z surveys –Worry about color-selected next –Correlated errors in L,R,color as well as pair separation

The Danaids: Fetching water with a sieve

The standard lore Massive halos form later (hierarchical clustering) Mass function ‘top-heavy’ in dense regions: n(m|  ) = [1+b(m)  ] n(m) Massive halos cluster more strongly than lower mass halos (halo bias):  hh (r|m) = b 2 (m)  dm (r) Dense regions host massive halos

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

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

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

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)

Galaxy distribution remembers that, in Gaussian random fields, high peaks and low troughs cluster similarly 88

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 larger 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

Environment = neighbours within 8 Mpc Clustering stronger in dense regions Dependence on density NOT monotonic in less dense regions! Same seen in mock catalogs; little room for extra effects SDSS Abbas & Sheth 2007

Sheldon et al 2007 Stacking, weak- lensing around clusters gives complementary information (with very different systematics) Data will soon tell us if halos are 200× critical or background density

The Halo Mass Function No evolution in abundance of ~10 12 M sun /h halos from z=2 to present