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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 of
accretion 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 by
recent 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 the
Millennium 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.