Transit timing effects due to an exomoon II

TL;DR

This paper extends the analysis of transit timing variation effects caused by exomoons to more general orbital inclinations, revealing additive and deductive effects based on orbit direction, and discusses how to determine the moon's orbital separation.

Contribution

It introduces a generalized model for TDV effects considering inclined exomoon orbits and identifies new components and asymmetries in the signals.

Findings

TDV signals have two main components: velocity variation and impact parameter variation.

Prograde and retrograde orbits produce additive and deductive effects, respectively.

The ratio of TDV to TTV effects can still determine the moon's orbital separation in inclined systems.

Abstract

In our previous paper, we evaluated the transit duration variation (TDV) effect for a co-aligned planet-moon system at an orbital inclination of i=90 degrees. Here, we will consider the effect for the more general case of i <= 90 degrees and an exomoon inclined from the planet-star plane by Euler rotation angles $\alpha$, $\beta$ and $\gamma$. We find that the TDV signal has two major components, one due to the velocity variation effect described in our first paper and one new component due to transit impact parameter variation. By evaluating the dominant terms, we find the two effects are additive for prograde exomoon orbits, and deductive for retrograde orbits. This asymmetry could allow for future determination of the orbital sense of motion. We re-evaluate the ratio of TDV and TTV effects, $\eta$, in the more general case of an inclined planetary orbit with a circular orbiting moon and find that it is still possible to directly determine the moon's orbital separation from just the ratio of the two amplitudes, as first proposed in our previous paper.