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The Average Size and Temperature Profile of Quasar Accretion Disks

We use multi-wavelength microlensing measurements of a sample of 10 image pairs from 8 lensed quasars to study the structure of their accretion disks. By using spectroscopy or narrow band photometry we have been able to remove contamination from the weakly microlensed broad emission lines, extinction and any uncertainties in the large-scale macro magnification of the lens model. We determine a maximum likelihood estimate for the exponent of the size versus wavelength scaling ($r_s\propto λ^p$ corresponding to a disk temperature profile of $T\propto r^{-1/p}$) of $p=0.75^{+0.2}_{-0.2}$, and a Bayesian estimate of $p=0.8\pm0.2$, which are significantly smaller than the prediction of thin disk theory ($p=4/3$). We have also obtained a maximum likelihood estimate for the average quasar accretion disk size of $r_s=4.5^{+1.5}_{-1.2} $ lt-day at a rest frame wavelength of $λ= 1026~{\mathrm Å}$ for microlenses with a mean mass of $M=1 M_\sun$, in agreement with previous results, and larger than expected from thin disk theory.