Microlensing Analysis for the gravitational lens systems SDSS0924+0219, Q1355-2257, and SDSS1029+2623

We use spectroscopic observations of the gravitationally lensed systems SDSS0924+0219(BC), Q1355-2257(AB), and SDSS1029+2623(BC) to analyze microlensing and dust extinction in the observed components. We detect chromatic microlensing effects in the continuum and microlensing in the broad emission line profiles of the systems SDSS0924+0219(BC), and Q1355-2257(AB). Using magnification maps to simulate microlensing and modeling the emitting region as a Gaussian intensity profile with size $r_s \propto \lambda ^p$, we obtain the probability density functions for a logarithmic size prior at $\lambda_{rest-frame}=3533$ {\AA}. In the case of SDSS0924+0219, we obtain: $r_s = 4^{+3}_{-2}$ $\sqrt{M/M_{\odot}}$ light-days (at $1 \sigma$), which is larger than the range of other estimates, and $p = 0.8 \pm 0.2$ (at $1 \sigma$), which is smaller than predicted by the thin disk theory, but still in agreement with previous results. In the case of Q1355-2257 we obtain (at $1 \sigma$): $r_s = 3.6^{+3.0}_{-1.6}$ $\sqrt{M/M_{\odot}}$ light-days, which is also larger than the theoretical prediction, and $p = 2.0 \pm 0.7$ that is in agreement with the theory within errors. SDSS1029+2326 spectra show evidence of extinction, probably produced by a galaxy in the vicinity of image C. Fitting an extinction curve to the data we estimate $\Delta E \sim 0.2$ in agreement with previous results. We found no evidence of microlensing for this system.