Determining the microlens mass function from quasar microlensing statistics

The first investigations of the response of the microlensing magnification pattern (at an optical depth of the order of unity) to the mass function of the microlenses found that the resulting statistics depend mainly on the m ean microlens mass <m >. In particular, the mean microlensing caustic cross ing rate was found to be proportional to root <m >. We show that, while thi s is true in the limit of mass functions with a narrow range of mass, in ge neral the magnification pattern shows structure that reflects the contribut ion to the optical depth of microlenses with different masses. We present a better approximation, relating the microlens mass function to light-curve statistics. We show that the variability statistics of quasar microlensing light curves can (in principle) be inverted to obtain the mass function of the microlenses in the mass range over which the mass density remains compa rable, i.e. p(m) dm approximate to Cm-1. A preliminary analysis of the stru cture function for Q2237+0305 suggests that there is not a significant cont ribution to the optical depth from very low-mass objects (10(-3) M-.). Howe ver, observations of multiple microlensed quasars for a period of similar t o 20 yr may in the future yield a detailed p(m) dm. In the mass range where the number density is comparable, i.e. p(m) dm approximate to constant, th e distribution of flux factors could be inverted to find the microlens mass function. This may be used as a probe of the abundance of planets with orb ital radii > 100 au.