The Extragalactic Lens VLBI Imaging Survey (ELVIS). I. A Search for the Central Image in the Gravitational Lens PMN J1838-3427

The Extragalactic Lens VLBI Imaging Survey (ELVIS) searches for central images of lensed radio quasars, in order to measure the central density profiles of distant galaxies. Here we present sensitive multi-epoch Very Long Baseline Array (VLBA) observations of PMN J1838-3427 at 8 GHz, with a 1 sigma noise level of 38 microJy beam^(-1). Based on the absence of a central image of the background source at this level, we explore the possibilities for the central matter distribution in the lens galaxy. A power-law density profile, rho ~ r^(-gamma), must have gamma > 1.93. Thus the density profile is close to an isothermal profile (gamma = 2) or steeper. The upper limit on any constant-density core in an otherwise isothermal profile is ~< 5 parsecs. We also derive the constraints on models in which the density profile is isothermal on kiloparsec scales, but is allowed to have a different power law in the central ~100 parsecs. If the lens galaxy harbors a supermassive black hole, the galaxy profile is allowed to be shallower, but for the expected black hole mass the galaxy profile must still be close to isothermal or steeper.