deletions | additions       diff --git a/Microlensing.tex b/Microlensing.tex  index 6cee915..90841cd 100644  --- a/Microlensing.tex  +++ b/Microlensing.tex 
...
Microlensing has long been acknowledged as a significant source of potential error when estimating time delays from optical monitoring data \citep[see e.g.][and references therein]{TewesEtal2013a} due to the fact that the relative velocity between the source and lens leads to time dependent fluctuations that are independent between the images. {\bf (GGD: put a microlensing figure here before we reference caustics.)} For caustic crossing events the relevant time scales are months to years, with smoother variations occurring over roughly decade timescales. As expected, the microlensing fluctuations are larger at bluer wavelengths, which correspond to smaller source sizes. The solution to measuring time delays in the presence of these fluctuations (which are uncorrelated between the quasar images) is to model the microlensing in each image individually at the same time as inferring the time delay \citep[e.g.]{Kochanek2004,TewesEtal2013b}.  We create mock microlensing signals in each quasar image light curve by calculating the magnification as the source moves behind a static stellar field. The parameters involved are the source size $R_{\rm src}$, the local convergence $\kappa$ and shear $\gamma$, the fraction of surface density in stars $f_{\star}$, and the relative velocity between the quasar and the lens galaxy $v_[\rm rel}$. We also include a Salpeter mass function for the stars though the amplitude of the fluctuations depends predominantly on the mean mass (which we take to be 1 $M_{\odot}$).  We include realistic microlensing signals in each quasar image lightcurve by tracking the position of the source as it crosses a static starfield with the appropriate stellar density, convergence and shear, with the appropriate velocity, and computing and applying the corresponding microlensing magnification. Our approach is similar to that of \citet{XXX} and \citet{YYY}. For each lens in the OM10 catalog (for which the gravitational lens shear and convergence, $\gamma$ and $\kappa$, are known), we estimate the fraction of mass in stars, $f^*$, at each image position, given a simple model for the stellar mass distribution: we estimate the i-band luminosity given the lens velocity dispersion from the Faber-Jackson relation of \citet{XXX}, and then convert this to a stellar mass assuming a mass to light ratio of XXX \citep{YYY}. We then distribute that stellar mass in a \citet{deVaucoleurs1948} density profile centred on the lens with the given ellipticity and orientation; the effective radius we draw from the Fundamental Plane relation of \citet{}. Given values of $f*$, $\gamma$, $\kappa$ we generate a starfield and compute its magnification map on the source plane following the method of \citet{Wambsganss}.\footnote{The microlensing code used in this work, {\sc MULES} is freely available at \texttt{https://github.com/gdobler/mules}.}   The effect of the source having non-zero size is to smooth out the magnification map; this can be an important effect \citep{DoblerAndKeeton}, not least because it enables the measurement of accretion disk sizes \citep{Kochanek2004}. We draw a source size from a distribution implied by recent disk size estimates, and assume a suitable brightness profile before convolving this profile with the magnification map. We then draw a random 10-year path across this smoothed magnification map, with path length given by the source's velocity relative to the lens, $v_{\rm rel}$, and read off the magnification values. To obtain a plausible value 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.