On physical interpretations of the reference transit radius of gas-giant exoplanets

TL;DR

This paper clarifies the physical meaning of the reference transit radius in gas-giant exoplanet spectra, showing it can be interpreted as a continuous optical depth surface rather than a discontinuous or opaque cloud boundary.

Contribution

It demonstrates that the reference transit radius can be understood as a continuous optical depth surface, challenging previous interpretations of it as a cloud deck boundary or discontinuity.

Findings

Optical depth functions can be continuous at the reference radius.

The reference radius can mimic a cloud top in grey cloud models.

Including clouds in opacity calculations is more natural than as a boundary.

Abstract

Two theoretical quandaries involving transmission spectra of gas-giant exoplanets are elucidated. When computing the transit radius as a function of wavelength, one needs to specify a reference transit radius corresponding to a reference pressure. Mathematically, the reference transit radius is a constant of integration that originates from evaluating an integral for the transit depth. Physically, its interpretation has been debated in the literature. Jordan & Espinoza (2018) suggested that the optical depth is discontinuous across, and infinite below, the reference transit radius. Betremieux & Swain (2017, 2018) interpreted the spherical surface located at the reference transit radius to represent the boundary associated with an opaque cloud deck. It is demonstrated that continuous functions for the optical depth may be found. The optical depth below and at the reference transit radius need not take on special or divergent values. In the limit of a spatially uniform grey cloud with constant opacity, the transit chord with optical depth on the order of unity mimics the presence of a "cloud top". While the surface located at the reference pressure may mimic the presence of grey clouds, it is more natural to include the effects of these clouds as part of the opacity function because the cloud opacity may be computed from first principles. It is unclear how this mimicry extends to non-grey clouds comprising small particles.