The total density profile of DM halos fitted from strong lensing
  In cosmological N-body simulations, the baryon effects on the cold dark
matter (CDM) halos can be used to solve the small scale problems in
$\Lambda$CDM cosmology, such as cusp-core problem and missing satellites
problem. It turns out that the resultant total density profiles (baryons plus
CDM), for halos with mass ranges from dwarf galaxies to galaxy clusters, can
match the observations of the rotation curves better than NFW profile. In our
previous work, however, we found that such density profiles fail to match the
most recent strong gravitational lensing observations. In this paper, we do the
converse: we fit the most recent strong lensing observations with the predicted
lensing probabilities based on the so-called $(\alpha,\beta,\gamma)$ double
power-law profile, and use the best-fit parameters ($\alpha=3.04, \beta=1.39,
\gamma=1.88$) to calculate the rotation curves. We find that, at outer parts
for a typical galaxy, the rotation curve calculated with our fitted density
profile is much lower than observations and those based on simulations,
including the NFW profile. This again verifies and strengthen the conclusions
in our previous works: in $\Lambda$CDM paradigm, it is difficult to reconcile
the contradictions between the observations for rotation curves and strong
gravitational lensing.
