  Simulations are expected to be the powerful tool to investigate the baryon
effects on dark matter (DM) halos. Recent high resolution, cosmological
hydrodynamic simulations (\citealt{Cintio14}, DC14) predict that the inner
density profiles of DM halos depend systematically on the ratio of stellar to
DM mass ($M_{\ast}/M_{\rm halo}$) which is thought to be able to provide good
fits to the observed rotation curves of galaxies. The DC14 profile is fitted
from the simulations which are confined to $M_{\rm halo}\le 10^{12}M_{\sun}$,
in order to investigate the physical processes that may affect all halos, we
extrapolate it to much larger halo mass, including that of galaxy clusters. The
inner slope of DC14 profile is flat for low halo mass, it approaches 1 when the
halo mass increases towards $10^{12}M_{\sun}$ and decreases rapidly after that
mass. We use DC14 profile for lenses and find that it predicts too few lenses
compared with the most recent strong lensing observations SQLS
(\citealt{Inada12}). We also calculate the strong lensing probabilities for a
simulated density profile which continues the halo mass from the mass end of
DC14 ($\sim 10^{12}M_{\sun}$) to the mass that covers the galaxy clusters
(\citealt{Schaller15}, Schaller15), and find that this Schaller15 model predict
too many lenses compared with other models and SQLS observations.
Interestingly, Schaller15 profile has no core, however, like DC14, the rotation
curves of the simulated halos are in excellent agreement with observational
data. Furthermore, we show that the standard two-population model SIS+NFW
cannot match the most recent SQLS observations for large image separations.
