Quantifying the Biases of Spectroscopically Selected Gravitational
  Lenses
  Spectroscopic selection has been the most productive technique for the
selection of galaxy-scale strong gravitational lens systems with known
redshifts. Statistically significant samples of strong lenses provide a
powerful method for measuring the mass-density parameters of the lensing
population, but results can only be generalized to the parent population if the
lensing selection biases are sufficiently understood. We perform controlled
Monte Carlo simulations of spectroscopic lens surveys in order to quantify the
bias of lenses relative to parent galaxies in velocity dispersion, mass axis
ratio, and mass density profile. For parameters typical of the SLACS and BELLS
surveys, we find: (1) no significant mass axis ratio detection bias of lenses
relative to parent galaxies; (2) a very small detection bias toward shallow
mass density profiles, which is likely negligible compared to other sources of
uncertainty in this parameter; (3) a detection bias towards smaller Einstein
radius for systems drawn from parent populations with group- and cluster-scale
lensing masses; and (4) a lens-modeling bias towards larger velocity
dispersions for systems drawn from parent samples with sub-arcsecond mean
Einstein radii. This last finding indicates that the incorporation of
velocity-dispersion upper limits of \textit{non-lenses} is an important
ingredient for unbiased analyses of spectroscopically selected lens samples. In
general we find that the completeness of spectroscopic lens surveys in the
plane of Einstein radius and mass-density profile power-law index is quite
uniform, up to a sharp drop in the region of large Einstein radius and steep
mass density profile, and hence that such surveys are ideally suited to the
study of massive field galaxies.
