Limits on the microlens mass function of Q2237+0305

Abstract

Gravitational microlensing at cosmological distances is potentially a powerful tool for probing the mass functions of stars and compact objects in other galaxies. In the case of multiply-imaged quasars, microlensing data has been used to determine the average microlens mass. However the measurements have relied on an assumed transverse velocity for the lensing galaxy. Since the measured mass scales with the square of the transverse velocity, published mass limits are quite uncertain. In the case of Q2237+0305 we have properly constrained this uncertainty. The distribution of light curve derivatives allows quantitative treatment of the relative rates of microlensing due to proper motions of microlenses, the orbital stream motion of microlenses and the bulk galactic transverse velocity. By demanding that the microlensing rate due to the motions of microlenses is the minimum that should be observed we determine lower limits for the average mass of stars and compact objects in the bulge of Q2237+0305. If microlenses are assumed to move in an orbital stream the lower limit ranges between 0.005 and 0.023 solar masses where the the systematic dependence is due to the fraction of smooth matter and the size of photometric error assumed for published monitoring data. However, if the microlenses are assumed to move according to an isotropic velocity dispersion then a larger lower limit of 0.019-0.11 solar masses is obtained. A significant contribution of Jupiter mass compact objects to the mass distribution of the galactic bulge of Q2237+0305 is therefore unambiguously ruled out.