Greg Dobler edited Microlensing.tex  over 10 years ago

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For each lens in the OM10 catalog we assign an $f_{\star}$ at each image position as follows. The OM10 catalog provides the velocity dispersion for a given lens which we use to estimate the i=band luminosity and effective radius of the galaxy by drawing from the Fundamental Plane [REF]. Assuming a standard \citet{deVaucoleurs1948} profile for the brightness distribution centered on the lens, an isothermal ellipsoid for the total mass distribution, and a mass-to-light ratio of {\bf GGD: what???}, $f_{\star}$ is the ratio of stellar mass density to total mass density at each image position.  The effect of the source having non-zero size is to smooth out Given $\kappa$ and $\gamma$ from  the OM10 catalog and estimating $f_{\star}$ as above, we generate  magnification map; this can maps like the one shown in {\bf (GGD: again, a figure would  be an important effect \citep{DoblerAndKeeton}, not least because it enables nice} which represent  the measurement magnification  ofaccretion disk sizes \citep{Kochanek2004}. We draw  a point  source size from as  a distribution implied function of position in the source plane. To use this make to generate temporal microlensing fluctuations we first smooth it  byrecent disk size estimates, and assume  a suitable brightness profile before convolving this Gaussian source  profile with the magnification map. We a size of {\bf (GGD: Kai, what are you using???)} and  then draw trace  a random 10-year linear  path across this smoothed magnification map, with path length given by along a random direction in  the source's velocity relative map. This path is converted from source plane position  to the lens, time units via  $v_{\rm rel}$, rel}$ [REF]. The effect of having a finite source is to smooth out  and read off reduce  the magnification values. To obtain a plausible value amplitude  of$v_{\rm rel}$, we draw two objects at their given redshifts from  theMillennium Simulation \citep{MS}, and compute their relative velocity \citepp[as in][]{relativevelocity}. The resulting  microlensing magnification curve is then multiplied by that quasar image's flux values to give a microlensed lightcurve. fluctuations.