Faster than SAM: An empirical model for the tidal evolution of dark matter substructure around strong gravitational lenses

Strong gravitational lenses enable direct inference of halo abundance and internal structure, which in turn enable constraints on the nature of dark matter and the primordial matter power spectrum. However, the density profiles of dark subhalos around the main deflector of a strong lens system also depend on tidal evolution inside the host, complicating the interpretation of strong-lensing inferences. We present a model for subhalo tidal evolution that accurately predicts the bound mass function and the density profiles of tidally stripped subhalos that appear near the Einstein radius of a typical deflector for a variety of dark matter models. This model matches predictions from the semianalytic model (SAM) {\sc galacticus}, but enables the simulation of subhalo populations in seconds, rather than hours. We use this model to examine the expected number of subhalos near the Einstein radius of a typical lens, and examine their lensing signals. We show that in cold dark matter the amplitude of the bound mass function is suppressed by a factor of $20$ relative to the infall mass function, and $87 \%$ of subhalos appearing in projection near the Einstein radius of a typical strong lensing deflector have lost more than $80\%$ of their mass since infall. Tidal stripping becomes increasingly severe in dark matter models with suppressed small-scale power, such as warm dark matter. This model will be used to forward model subhalo populations in forthcoming analyses of strong lens systems.