Catastrophic errors of photo-z: biasing Catastrophic errors of photo-z: biasing dark energy parameter estimates with dark energy parameter estimates with

cosmic shearcosmic shear

Sun Lei (Sun Lei ( 孙磊孙磊 ))

Peking UniversityPeking University

Collaborators: Z.-H. Fan, C. Tao, J.-P. Kneib, S. Jouvel, A. TilquinCollaborators: Z.-H. Fan, C. Tao, J.-P. Kneib, S. Jouvel, A. Tilquin

Tys

on e

t al

200

2

Cosmic Shear

Cosmic shear and the systematicsCosmic shear and the systematics

Knox, Song, & Zhan (06)Hu Zhan (06)

Huterer et al. (06)

powerful !

measure: DA(z) & G(z)

bias-free

But systematics control is crucial !!

Catastrophic errors Catastrophic errors

Catastrophic errorCatastrophic error

by A.Conollyby S.Jouvel

LSST without u band SNAP standard filters

Causes: e.g. Lyman break(~1000 A) & Balmer break (~4000 A) confused

Catastrophic errorCatastrophic error

z_spec

z_ph

ot

Loosely defined: e.g. | z_p - z_s | > 1

Brodwin et al.03 (CFDF) Gavazzi & Soucail 06 (CFHT)

Catastrophic errors seen in a realistic galaxy z-distribution n(z)Catastrophic errors seen in a realistic galaxy z-distribution n(z)

How do the lensing signals depend on the source galaxy How do the lensing signals depend on the source galaxy distribution n(z)distribution n(z)

n(z)

bias !

Ref

regi

er 2

003

z

n(z)

SNAP : a space-based survey

survey geometry

area: 1000 deg²

number densigy: 100 gal/arcmin²

depth: zmed = 1.26

with = 2, =1.5

fidicual n(z) of galaxy:

Employ 5 tomographic z bins:

Its weak lensing design:

Lensing tomography: how many redshift bins to Lensing tomography: how many redshift bins to use?use?

wa

w0

fcata=1 % at z_spec ~ 0.4 z_phot ~ 3.5

with zm = 0.4, = 0.1, Acata determined by fcata.

SNAP Photo-z simulation results: with its standard 9 filter set

To characterize true n(z) of :

To estimate the bias on cosmological paramters:

Extension of Fisher matrix:

Chi-square fitting analysis:

C

for signal ‘S’

for model ‘M’

n(z)

SM‘Bin-0’:

Assume a 7-param fiducial model [m, w0, wa, 8, h, b, n], with a Gaussian priors (pi)=0.05 applied on all hidden params except (b)=0.01.

² fitting: Fisher matrix approximation:

Biases on dark energy equation of state (w0, wa):

fiducial values

biased values

To fight against catastrophic failure: spectroscopic calibrationTo fight against catastrophic failure: spectroscopic calibration

Sampling N spectra out of our simulated 1300 galaxies whose photo-zs fall in z_phot = [3, 4]

To fight against catastrophic failure: spectroscopic calibrationTo fight against catastrophic failure: spectroscopic calibration

'

(one realization of calibration)

there is residual fcata = - ' , so still bias the parameter estimate!

If Nspec is not enough :

for signal ‘S’

for model ‘M’

S

M

w0 w0

wa

To fight against catastrophic failure: spectroscopic calibrationTo fight against catastrophic failure: spectroscopic calibration

Sampling 100 spectra (with 100 realizations)

5 z-bins with all Cij: 5 z-bins with auto Cii only:

Scatter of bias is large: significant compared to statistical errors

Notable descrepancy between results of fit / Fisher when residual (f – f ‘) is large

w0 w0

wa

To fight against catastrophic failure: spectroscopic calibrationTo fight against catastrophic failure: spectroscopic calibration

Sampling 500 spectra (with 100 realizations)

5 z-bins with all Cij: 5 z-bins with auto Cii only:

Scatter of bias is small: getting insignificant

Descrepancy between fit / Fisher is vanishing since residual (f – f ‘) keeps small

To fight against catastrophic failure: spectroscopic calibrationTo fight against catastrophic failure: spectroscopic calibration

How many spectra is sufficient ?

A calibration size of 500-600 spetra at z ~ [3,4] is necessary

Might not be easy at such high-z but hopeful

(w0-wa)

2(w0-wa)

To fight against catastrophic failure: other methods To fight against catastrophic failure: other methods

fcata: ~1% ~ 0.1 %

But technical difficulty exists…

including u band :

To fight against catastrophic failure: other methodsTo fight against catastrophic failure: other methods

consider original 3 z-bins left re-define 5 narrower z-bins

But with notable statistical loss…

Cutting out galaxies at z < 0.5 & z>2.5 :

• Catastrophic error is frequently seen in photo-z catalogs and is an important source biasing the galaxy z-distribution.

• The bias induced by catastrophic errors on DE parameter estimate from cosmic shear:

SNAP with std-type filters: ~1 % fcata significant compared to statistical error in tomography 5-z

bins case

• To resist the bias by catastrophic errors: * spectroscopic calibration useful, needs a relatively large sample at high-z * Including u band useful, may be not easy for space-based telescope e.g. SNAPu : ~ 0.1% fcata bias much smaller than statistical error * Cutting out galaxies with suspicious z useful, with a price paid for

statistical loss

summarysummary

Thank you!Thank you!