Schechter versus Schechter: Subarcsecond gravitational lensing and inner halo profiles

Subarcsecond lensing statistics depend sensitively on the inner mass profiles of low-mass objects and the faint-end slopes of the Schechter luminosity function and the Press-Schechter mass function. By requiring the luminosity and mass functions to give consistent predictions for the distribution of image separation below 1", we show that dark matter halos with masses below cannot have a single type of profile, be it the singular isothermal 10(12) M-. sphere (SIS) or the shallower "universal" dark matter profile. Instead, consistent results are achieved if we allow a fraction of the halos at a given mass to be luminous with the SIS profile and the rest to be dark with an inner logarithmic slope shallower than -1.5 to compensate for the steeper faint-end slope of the mass function compared with the luminosity function. We quantify how rapidly the SIS fraction must decrease with decreasing halo mass, thereby providing a statistical measure for the effectiveness of feedback processes on the baryon content in low-mass halos.