A CALIBRATION OF THE STELLAR MASS FUNDAMENTAL PLANE AT z ∼ 0.5 USING THE MICRO-LENSING-INDUCED FLUX RATIO ANOMALIES OF MACRO-LENSED QUASARS

We measure the stellar mass surface densities of early-type galaxies by observing the micro-lensing of macro-lensed quasars caused by individual stars, including stellar remnants, brown dwarfs, and red dwarfs too faint to produce photometric or spectroscopic signatures. Instead of observing multiple micro-lensing events in a single system, we combine single-epoch X-ray snapshots of 10 quadruple systems, and compare the measured relative magnifications for the images with those computed from macro-models. We use these to normalize a stellar mass fundamental plane constructed using a Salpeter initial mass function with a low-mass cutoff of 0.1 M-circle dot and treat the zeropoint of the surface mass density as a free parameter. Our method measures the graininess of the gravitational potential produced by individual stars, in contrast to methods that decompose a smooth total gravitational potential into two smooth components, one stellar and one dark. We find the median likelihood value for the normalization factor F by which the Salpeter stellar masses must be multiplied is 1.23, with a one sigma confidence range, dominated by small number statistics, of 0.77 < F < 2.10.