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. 2011

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. 2005) – 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

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 zphot(mags)

• So can get p(zphot|z) or p(z|zphot)

• More generally, can get p(z|mags)

One mouse droppingruins the whole pudding

Catastrophic failures: dN/dz

Deconvolution:dN/dzphot = ∫dz dN/dz p(zphot|z)

Convolution:dN/dz = ∫dzphot dN/dzphot p(z|zphot)

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

De-con-volve

(Sheth 2007 uses

Lucy 1974)

distortedfixed

In SDSS

Rossi et al. 2009 Sheth & Rossi 2010

If <|z> = z then <z|> ≠

All crows in the world are black

Deconvolution

Convolution

For luminosity function in magnitude limited survey,

remember that

N(Mphot) = ∫dM N(M) p(Mphot|M)where

N(M) = Vmax(M) (M)

(De)convolve to get N(M) …

… then divide by Vmax(M)

<M|M> = M so <M|M> ≠ M

Deconvolve

Convolve

Riding a mule while looking for a horse

Convolution/deconvolution/Maximum-likelihood

(Sheth 2007; Christlein et al. 2010)/Weights (Lima et al. 2008; Cunha et al. 2009)

Biased scaling

relations can be fixed

similarlyTrue, 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. <zspec> ~ 0.1

Churchill et al. 2005

Knowledge of ra, dec, zMgII + correlation length only few Mpc

+ sufficiently deep photometry = estimate of z~0.7 LF

(Caler et al. 2010)

1880 absorbers in DR3 from Procter et al (2006)

•Assume all galaxies in same field as absorber have zabs

•Wrong for all objects except those at zabs

•Do same for random position •Subtract counts

50 kpc

900 kpc100 kpc

500 kpc

900 kpc

500 kpc50 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 A More strong

50 kpc

500 kpc

More weak

Another view of measurement

• 1880 fields each ~ (3 arcmin)2 • So LF estimate from total area ~ 10 degrees2

• 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 boatBut 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) = b2(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 ngal and ξgal(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

Mr<−19.5

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

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

The Halo Mass

Function

No evolution in abundance of ~1012 Msun/h halos from z=2 to present