Implicit biases in transit models using stellar pseudo-density

The transit technique is responsible for the majority of exoplanet discoveries to date. Characterizing these planets involves careful modeling of their transit profiles. A common technique involves expressing the transit duration using a density-like parameter, $\tilde{\rho}$, often called the "circular density." Most notably, the Kepler project -- the largest analysis of transit lightcurves to date -- adopted a linear prior on $\tilde{\rho}$. Here, we show that such a prior biases measurements of impact parameter, $b$, due to the non-linear relationship between $\tilde{\rho}$ and transit duration. This bias slightly favors low values ($b \lesssim 0.3$) and strongly disfavors high values ($b \gtrsim 0.7$) unless transit signal-to-noise ratio is sufficient to provide an independent constraint on $b$, a criterion that is not satisfied for the majority of Kepler planets. Planet-to-star radius ratio, $r$, is also biased due to $r{-}b$ covariance. Consequently, the median Kepler DR25 target suffers a $1.6\%$ systematic underestimate of $r$. We present a techniques for correcting these biases and for avoiding them in the first place.