Quantitative Interpretation of Quasar Microlensing Light Curves

We develop a general method for analyzing the light curves of microlensed quasars and apply it to the OGLE light curves of the four-image lens Q2237+0305. We simultaneously estimate the effective source velocity, the average stellar mass, the stellar mass function, and the size and structure of the quasar accretion disk. The light curves imply an effective source plane velocity of 10200 km/s < v_e h / sqrt(<M>) < 39600 km/s (68% confidence). Given an independent estimate for the source velocity, found by combining estimates for the peculiar velocity of the lens galaxy with its measured stellar velocity dispersion, we obtain a mean stellar mass of <M>=0.037h^2 solar masses (0.0059h^2 < <M>/Msun < 0.20h^2). We were unable to distinguish a Salpeter mass function from one in which all stars had the same mass, but we do find a strong lower bound of 50% on the fraction of the surface mass density represented by the microlenses. Our models favor a standard thin accretion disk model as the source structure over a simple Gaussian source. For a face-on, thin disk radiating as a black body with temperature profile T_s ~ R^(-3/4), the radius r_s where the temperature matches the filter pass band (2000 Angstroms or T_s(r_s)=70000K) is (1.4 x 10^15)/h cm < r_s < (4.5 x 10^15)/h cm. The flux predicted by the disk model agrees with the observed flux of the quasar, so non-thermal or optically thin emission processes are not required. From the disk structure we estimate a black hole mass of M_BH = (1.1_(-0.7)^(+1.4) x 10^9) h^(-3/2) (L/L_E)^(-1/2) solar masses, consistent with the mass estimated under the assumption that the quasar is radiating at the Eddington luminosity (L/L_E=1).

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