Catastrophic Photo-z Errors and the Dark Energy Parameter Estimates with Cosmic Shear

We study the impact of catastrophic errors occurring in the photometric redshifts of galaxies on cosmological parameter estimates with cosmic shear tomography. We consider a fiducial survey with 9-filter set and perform photo-z measurement simulations. It is found that a fraction of 1% galaxies at z_{spec}~0.4 is misidentified to be at z_{phot}~3.5. We then employ both chi^2 fitting method and the extension of Fisher matrix formalism to evaluate the bias on the equation of state parameters of dark energy, w_0 and w_a, induced by those catastrophic outliers. By comparing the results from both methods, we verify that the estimation of w_0 and w_a from the fiducial 5-bin tomographic analyses can be significantly biased. To minimize the impact of this bias, two strategies can be followed: (A) the cosmic shear analysis is restricted to 0.5<z<2.5 where catastrophic redshift errors are expected to be insignificant; (B) a spectroscopic survey is conducted for galaxies with 3<z_{phot}<4. We find that the number of spectroscopic redshifts needed scales as N_{spec} \propto f_{cata}\times A where f_{cata}=1% is the fraction of catastrophic redshift errors (assuming a 9-filter photometric survey) and A is the survey area. For A=1000 {deg}^2, we find that N_{spec}>320 and 860 respectively in order to reduce the joint bias in (w_0,w_a) to be smaller than 2\sigma and 1\sigma. This spectroscopic survey (option B) will improve the Figure of Merit of option A by a factor \times 1.5 thus making such a survey strongly desirable.