  Detections of the tidal disruption flares (TDFs) of stars by supermassive
black holes (SMBHs) are rapidly accumulating as optical surveys improve. These
detections may provide constraints on SMBH demographics, stellar dynamics, and
stellar evolution in galaxies. To maximize this scientific impact, we require a
better understanding of how astrophysical parameters interact with survey
selection effects in setting the properties of detected flares. We develop a
framework for modeling the distributions of optical TDF detections in surveys
across attributes of the host galaxies and the flares themselves. This model
folds in effects of the stellar disruption rate in each galaxy, the flare
luminosity and temperature distributions, the effects of obscuration and
reddening by dust in the host galaxy, and survey selection criteria. We
directly apply this model to the sample of TDFs detected by the Zwicky
Transient Facility and find that the overall flare detection rate is in line
with simple theoretical expectation. The model can also reproduce the
distribution of total stellar mass and redshift of the host galaxies, but fails
to match all details of the detected flares, such as their luminosity and
temperature distributions. We also find that dust obscuration likely plays an
important role in suppressing the TDF detection rate in star-forming galaxies.
While we do not find that the unusual preference of TDFs to have hosts in
post-starburst galaxies in the "green valley" can be entirely explained by
selection effects, our model can help to quantify the true rate enhancement in
those galaxies.
