Catastrophic errors of photoz biasing dark energy parameter
Catastrophic errors of photo-z: biasing dark energy parameter estimates with cosmic shear Sun Lei (孙磊) Peking University Collaborators: Z. -H. Fan, C. Tao, J. -P. Kneib, S. Jouvel, A. Tilquin
Tyson et al 2002 Cosmic Shear
Cosmic shear and the systematics l! u f r e pow u measure: DA(z) & G(z) u bias-free Hu Zhan (06) Knox, Song, & Zhan (06) But systematics control is crucial !! Huterer et al. (06)
Catastrophic errors Catastrophic error SNAP standard filters z_phot LSST without u band Catastrophic error by A. Conolly by S. Jouvel z_spec Loosely defined: e. g. | z_p - z_s | > 1 Causes: e. g. Lyman break(~1000 A) & Balmer break (~4000 A) confused
Catastrophic errors seen in a realistic galaxy z-distribution n(z) Brodwin et al. 03 (CFDF) Gavazzi & Soucail 06 (CFHT)
How do the lensing signals depend on the source galaxy distribution n(z) Refregier 2003 bias ! n(z) z
SNAP : a space-based survey Its weak lensing design: survey geometry area: 1000 deg² number densigy: 100 gal/arcmin² depth: zmed = 1. 26 fidicual n(z) of galaxy: with = 2, =1. 5 Employ 5 tomographic z bins:
Lensing tomography: how many redshift bins to use? wa w 0
SNAP Photo-z simulation results: with its standard 9 filter set To characterize true n(z) of : fcata=1 % at z_spec ~ 0. 4 z_phot ~ 3. 5 with zm = 0. 4, = 0. 1, Acata determined by fcata.
n(z) C for signal ‘S’ ‘Bin 0’: M for model ‘M’ To estimate the bias on cosmological paramters: Extension of Fisher matrix: Chi-square fitting analysis: S
Biases on dark energy equation of state (w 0, wa): ² fitting: Fisher matrix approximation: fiducial values biased values Assume a 7 -param fiducial model [ m, w 0, wa, 8, h, b, n], with a Gaussian priors (pi)=0. 05 applied on all hidden params except ( b)=0. 01.
To 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 calibration S for signal ‘S’ for model ‘M’ ' M (one realization of calibration) If Nspec is not enough : there is residual fcata = bias the parameter estimate! ' , so still
To 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: wa w 0 Scatter of bias is large: significant compared to statistical errors Notable descrepancy between results of fit / Fisher when residual (f – f ‘) is large
To 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: wa w 0 Scatter of bias is small: getting insignificant w 0 Descrepancy between fit / Fisher is vanishing since residual (f – f ‘) keeps small
To fight against catastrophic failure: spectroscopic calibration How many spectra is sufficient ? 2 ( w 0 - (w 0 -w a) A calibration size of 500 -600 spetra at z ~ [3, 4] is necessary Might not be easy at such high-z but hopeful wa)
To fight against catastrophic failure: other methods including u band : fcata: ~1% ~ 0. 1 % But technical difficulty exists…
To fight against catastrophic failure: other methods Cutting out galaxies at z < 0. 5 & z>2. 5 : consider original 3 z-bins left re-define 5 narrower z-bins But with notable statistical loss…
summary • 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
Thank you!
- Slides: 20