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

1. 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

2. Cosmic Shear Tyson et al 2002

3. Cosmic shear and the systematics powerful ! • measure: DA(z) & G(z) • bias-free Hu Zhan (06) Knox, Song, & Zhan (06) But systematics control is crucial !! Huterer et al. (06)

4. Catastrophic errors LSST without u band SNAP standard filters z_phot Catastrophic error 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

5. Catastrophic errors seenin a realistic galaxy z-distribution n(z) Brodwin et al.03 (CFDF) Gavazzi & Soucail 06 (CFHT)

6. How do the lensing signals depend on the source galaxy distribution n(z) bias ! Refregier 2003 n(z) n(z) z

7. SNAP : a space-based survey survey geometry area:1000 deg² number densigy:100 gal/arcmin² depth:zmed = 1.26 Its weak lensing design: Employ 5 tomographic z bins: fidicual n(z) of galaxy: with  = 2,  =1.5

8. Lensing tomography: how many redshift bins to use? wa w0

9. 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.

10. n(z) C for signal ‘S’ ‘Bin-0’: M S for model ‘M’ To estimate the bias on cosmological paramters: Extension of Fisher matrix: Chi-square fitting analysis:

11. Biases on dark energy equation of state (w0, wa): ² fitting: Fisher matrix approximation: fiducial values biased values 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.

12. 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]

13. 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 = - ' , so still bias the parameter estimate!

14. 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 w0 w0 Scatter of bias is large: significant compared to statistical errors Notable descrepancy between results of fit / Fisher when residual (f – f ‘) is large

15. 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 w0 w0 Scatter of bias is small: getting insignificant Descrepancy between fit / Fisher is vanishing since residual (f – f ‘) keeps small

16. To fight against catastrophic failure: spectroscopic calibration How many spectra is sufficient ? 2(w0-wa) (w0-wa) A calibration size of 500-600 spetra at z ~ [3,4] is necessary Might not be easy at such high-z but hopeful

17. To fight against catastrophic failure: other methods including u band : fcata: ~1%  ~ 0.1 % But technical difficulty exists…

18. To fight against catastrophic failure: other methods Cutting out galaxies at z < 0.5 & z>2.5 : re-define 5 narrower z-bins consider original 3 z-bins left But with notable statistical loss…

19. 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

20. Thank you!