constraining photometric redshift errors with galaxy two-point correlation functions

8/14/2019 Constraining photometric redshift errors with galaxy two-point correlation functions

1/23

Constraining photometric redshift errors

with galaxy two-point correlations

Michael Schneider

UC Davis

Collaborators: Andy Connolly, Lloyd Knox, Hu Zhan


2/23

Outline

The basic idea

Cross-correlating the photometricsample with itself

Cross-correlating with an overlapping

spectroscopic sample (J. Newman)

Challenges and future directions


3/23

Motivation

Future dark energy surveys (DES, Pan-STARRS, LSST, EUCLID, JDEM)

plan to usephotometric redshifts to measure cosmic shear and

galaxy correlations

Hard to getfair spectroscopic training samples to the depth of the

photometric sample

Conventional photo-z estimation methods may leave intolerably

large errors

Can other calibration methods reduce the size of the fair

spectroscopic training sample needed for a given photo-z

error target?


4/23

Cross correlating galaxies binned

by photometric redshift

astro-ph/0606098


5/23

Photo-z errors induce cross-correlations

bin

Z

Scatter Catastrophic

n(z) A. Schulz

z

n(z)

overlap causes

correlation


6/23

Sensitivity of galaxy power spectrum

10-7

10-6

10-5

10-4

10-3

10-2

10-1

50 100 200 400 800

l2

P(l)/(2)

l

bins (1,1)bins (1,3), var. a13bins (1,3), var. a31

Auto and cross angular

galaxy power spectra

for: 0 < zp < 0.5and 1 < zp < 1.5

Points with errors:

fiducial values (with

photo-z errors)

Lines:1- variation


7/23

Model for photo-z errors

Bin galaxy number density in z and mix values between bins:

dNai

dzd(z, ) =

Nai

1

Na

dNa

dzd(z, )(z)

mean number of galaxies of spectral-type a in photo-z bini that come from true-z bin

Nai

0.01

0.1

1

10

photometric z

spectroscop

ic

z

0 0.5 1 1.5 2 2.5 3

0

0.5

1

1.5

2

2.5

3

Fiducial model:

- Estimate photo-z of 105 simulated galaxy

colors in ugrizy filters (limited in i-band at i


8/23

Model for galaxy correlations

UseLimber approximation to compute linear

angular galaxy power spectrum:

constrain linear galaxy bias jointly with photo-z errorparameters

truncate range to justify Gaussian and Limber

approximationsWith photo-z errors:

C() = NN = NN bb PDM

()

Cij() =

NiNjC()

NN+ Cshotij ()


9/23

- Fractional constraints on

- 10% prior on the galaxy bias

Ni N1

i+ N

2

i

10-3

10-2

10-1

100

0 0.5 1 1.5 2 2.5 3

!

/dN/dz

z

photo-z bin 1

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 2

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 3

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

!

/dN/dz

z

photo-z bin 4

10-3

10-2

10-1

100

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 5

10-3

10-2

10-1

100

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 6

Parameter constraint forecasts

Filled:

full sample

Open:

red/blue split

sample


10/23

Bias and red and blue population

constraints

Galaxy bias constraints

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3

!((b

gal

(z))/b

gal

(z)

z

redblue

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

!

/dN/dz

z

photo-z bin 1

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 2

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 3

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

!

/dN/dz

z

photo-z bin 4

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 5

10-3

10-2

10-1

100

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 6

Red & Blue sub-populations


11/23

Cross correlating with an

overlapping spectroscopic sample

See J. Newman paper:http://astron.berkeley.edu/~jnewman/xcorr/xcorr.pdf
http://astron.berkeley.edu/%257Ejnewman/xcorr/xcorr.pdfhttp://astron.berkeley.edu/%257Ejnewman/xcorr/xcorr.pdfhttp://astron.berkeley.edu/%257Ejnewman/xcorr/xcorr.pdfhttp://astron.berkeley.edu/%257Ejnewman/xcorr/xcorr.pdf


12/23

Model for galaxy correlations

2DAngular

cross-corr

elation

3Dcross-c

orrelation

function

Photometr

icselection

function

At large (linear) scales assume:

In previous notation: Now observable

From A. Schulz Moriond talk

Ci() =

Nib

p ot

bspec

Cspec

()


13/23

Monte Carlo tests (J. Newman)

Assumptions:

Gaussian photo-z errors (fit for 2 parameters)

No bias evolution (so no degeneracy)

25k spec. galaxies per unit z

10 phot. galaxies per arcmin^2clustering of photometric sample independent of z


14/23

How many spectra do we need?

J. Newman


15/23

Near-term spec. samples

Blue: SDSS +

AGES + VVDS +

DEEP2+1700

galaxies/unit z at

high zRed: add

zCOSMOS +

PRIMUS + WiggleZ

+ 5000 galaxies/unit

z at high z

J. Newman


16/23

Test with N-body simulations (A. Schulz)

Boxside (Gpc/h) Boxside (Gpc/h)

Populate 1 (Gpc/h)^3 box with galaxies using HOD

No z evolution of correlations or bias


17/23

Complications

Galaxy bias:

redshift evolution

nonlinear biasMagnification bias

Intrinsic l.o.s. correlations between narrow z-bins

Sample variance

Cosmology dependence

Practical method for reconstruction


18/23

Restricting the number of parameters

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

!

/dN/dz

z

photo-z bin 1

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 2

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 3

10-3

10-2

10-1

0 0.5 1 1.5 2 2.5 3

!

/dN/dz

z

photo-z bin 4

10-3

10-2

10

-1

100

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 5

10-3

10-2

10

-1

100

0 0.5 1 1.5 2 2.5 3

z

photo-z bin 6


19/23

PC decomposition of error distributions

0.0 0.5 1.0 1.5 2.0

0.

0

0.

5

1.

0

1.

5

2.

0

spec. z

ph

ot.z

0.0 0.5 1.0 1.5 2.0

!0.

4

!0.

2

0.0

0.

2

0.

4

z

eigenfunctions

!

!

!

!

!!!!

!!!!!!!!!!! !! !!!!!!!!!!!!!!!!!!!

0 10 20 30 40

0.5

0.6

0.7

0.8

0.9

1.0

Mode number

Cum.prop.ofvarianceSims. from M. Banerji website

(Collister & Lahav 2004, Banerji et al. 2007)

grizY, i < 24.3

Effect on DE

constraints?

http://zuserver2.star.ucl.ac.uk/~mbanerji/DESdata/

Cum.proportionofvariance

Eigenfunctions
http://zuserver2.star.ucl.ac.uk/~mbanerji/DESdata/http://zuserver2.star.ucl.ac.uk/~mbanerji/DESdata/


20/23

Constraints on bias?

Add weak lensing measurementsFit with HOD model(Blake, Collister, & Lahav)

Add 3-point correlations (McBride &Connolly, Ashley & Brunner)


21/23

Conclusions

Amount ofleakage of galaxies between photo-z bins due to catastrophic

errors can be constrained to ~10% of the number of galaxies in each bin if

galaxy bias is known.

Priors on the galaxy bias are necessary to constrain the photo-z error

parameters.

Separation of the galaxy sample according to spectral type may significantly

improve the photo-z errorparameter constraints.

Cross-correlating with a spatially overlapping spectroscopic sample may

provide even tighter constraints on the photo-z errors.

The sizes of the required spectroscopic training samples are not yet

determined.

Might be able tojointly constrain galaxy bias.

Need to test with realistic mocks or data!


22/23

Multipole ranges in galaxy power spectra

photo-z range

0.0 - 0.5 7 114

0.5 - 1.0 23 458

1.0 - 1.5 45 1018

1.5 - 2.0 71 1875

2.0 - 2.5 103 3195

2.5 - 3.0 140 5186

max(z)min(z)


23/23

Fiducial model for red and blue

galaxy spectral types

Total dN/dz normalized to

65 galaxies per sq.

arcmin.

Red and blue dN/dzs are

ad-hoc

Use Cooray 2006 CLFmodels for red and blue

biases

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5 3

dN/dzd!

z

total

red

blue

constraining photometric redshift errors with galaxy two-point correlation functions

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