Implicit biases in transit models using stellar pseudo-density

TL;DR

This paper identifies and corrects biases in transit parameter measurements caused by implicit priors on stellar pseudo-density, which affect impact parameter and planet radius estimates in exoplanet studies.

Contribution

It demonstrates how linear priors on stellar pseudo-density bias transit parameters and proposes methods to correct and avoid these biases.

Findings

Bias in impact parameter $b$ favors low values and disfavors high values.

Median Kepler DR25 target has a 1.6% underestimate of planet radius.

Proposed techniques effectively correct and prevent these biases.

Abstract

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.