  Peaks in two-dimensional weak lensing (WL) maps contain significant
cosmological information, complementary to the WL power spectrum. This has
recently been demonstrated using N-body simulations which neglect baryonic
effects. Here we employ ray-tracing N-body simulations in which we manually
steepen the density profile of each dark matter halo, mimicking the cooling and
concentration of baryons into dark matter potential wells. We find, in
agreement with previous works, that this causes a significant increase in the
amplitude of the WL power spectrum on small scales (spherical harmonic index
l>1,000). We then study the impact of the halo concentration increase on the
peak counts, and find the following. (i) Low peaks (with convergence 0.02 <
kappa_peak < 0.08), remain nearly unaffected. These peaks are created by a
constellation of several halos with low masses (10^12-10^13 M_sun) and large
angular offsets from the peak center (> 0.5 R_vir); as a result, they are
insensitive to the central halo density profiles. These peaks contain most of
the cosmological information, and thus provide an unusually sensitive and
unbiased probe. (ii) The number of high peaks (with convergence kappa_peak >
0.08) is increased. However, when the baryon effects are neglected in
cosmological parameter estimation, then the high peaks lead to a modest bias,
comparable to that from the power spectrum on relatively large-scales (l<2000),
and much smaller than the bias from the power spectrum on smaller scales
(l>2,000). (iii) In the 3D parameter space (sigma_8, Omega_m, w), the biases
from the high peaks and the power spectra are in different directions. This
suggests the possibility of "self-calibration": the combination of peak counts
and power spectrum can simultaneously constrain baryonic physics and
cosmological parameters.
