1. Sun Lei (孙磊) Peking University
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 Loosely defined: e.g. | z_p - z_s | > 1
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 seen in 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. To estimate the bias on cosmological paramters:
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
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 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!