Cosmological studies from tomographic weak lensing peak abundances and
  impacts of photo-z errors
  Weak lensing peak abundance analyses have been applied in different surveys
and demonstrated to be a powerful statistics in extracting cosmological
information complementary to cosmic shear two-point correlation studies. Future
large surveys with high number densities of galaxies enable tomographic peak
analyses. Focusing on high peaks, we investigate quantitatively how the
tomographic redshift binning can enhance the cosmological gains. We also
perform detailed studies about the degradation of cosmological information due
to photometric redshift (photo-z) errors. We show that for surveys with the
number density of galaxies $\sim40\,{\rm arcmin^{-2}}$, the median redshift
$\sim1$, and the survey area of $\sim15000\,{\rm deg^{2}}$, the 4-bin
tomographic peak analyses can reduce the error contours of $(\Omega_{{\rm
m}},\sigma_{8})$ by a factor of $5$ comparing to 2-D peak analyses in the ideal
case of photo-z error being absent. More redshift bins can hardly lead to
significantly better constraints. The photo-z error model here is parametrized
by $z_{{\rm bias}}$ and $\sigma_{{\rm ph}}$ and the fiducial values of $z_{{\rm
bias}}=0.003$ and $\sigma_{{\rm ph}}=0.02$ is taken. We find that using
tomographic peak analyses can constrain the photo-z errors simultaneously with
cosmological parameters. For 4-bin analyses, we can obtain $\sigma(z_{{\rm
bias}})/z_{{\rm bias}}\sim10\%$ and $\sigma(\sigma_{{\rm ph}})/\sigma_{{\rm
ph}}\sim5\%$ without assuming priors on them. Accordingly, the cosmological
constraints on $\Omega_{{\rm m}}$ and $\sigma_{8}$ degrade by a factor of
$\sim2.2$ and $\sim1.8$, respectively, with respect to zero uncertainties on
photo-z parameters. We find that the uncertainty of $z_{{\rm bias}}$ plays more
significant roles in degrading the cosmological constraints than that of
$\sigma_{{\rm ph}}$.
