Baryon effects on the dark matter haloes constrained from strong gravitational lensing

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.