Probing the dark matter radial profile in lens galaxies and the size of X-ray emitting region in quasars with microlensing

We use X-ray and optical microlensing measurements to study the shape of the dark matter density profile in the lens galaxies and the size of the (soft) X-ray emission region. We show that single epoch X-ray microlensing is sensitive to the source size. Our results, in good agreement with previous estimates, show that the size of the X-ray emission region scales roughly linearly with the black hole mass, with a half light radius of $R_{1\mathrm{/}2}\simeq (24\pm 14)r_g$ where $r_g=G{M}_{BH}\mathrm{/}{c}^2$. This corresponds to a size of $\log (R_{1\mathrm{/}2}\mathrm{/}cm)=15.6_{-0.3}^{+0.3}$ or $\sim$ 1 light day for a black hole mass of $M_{BH}={10}^9{M}_{\text{sun}}$. We simultaneously estimated the fraction of the local surface mass density in stars, finding that the stellar mass fraction is $\alpha =0.20\pm 0.05$ at an average radius of $\sim 1.9R_e$, where $R_e$ is the effective radius of the lens. This stellar mass fraction is insensitive to the X-ray source size and in excellent agreement with our earlier results based on optical data. By combining X-ray and optical microlensing data, we can divide this larger sample into two radial bins. We find that the surface mass density in the form of stars is $\alpha =0.31\pm 0.15$ and $\alpha =0.13\pm 0.05$ at $(1.3\pm 0.3)R_e$ and $(2.3\pm 0.3)R_e$, respectively, in good agreement with expectations and some previous results.