An Analysis of Jitter and Transit Timing Variations in the HAT-P-13 System

TL;DR

This paper reanalyzes data from the HAT-P-13 system, revealing that system parameters are less constrained than previously thought due to jitter uncertainties, and discusses how transit timing variations can help refine these parameters.

Contribution

It introduces a new MCMC-based jitter treatment and demonstrates how TTV analyses can better constrain planetary inclinations and eccentricities in the HAT-P-13 system.

Findings

System parameters are less constrained with higher jitter levels.

Current TTV data restricts outer planet eccentricity to less than 0.85.

Future observations could significantly improve constraints on inclinations and eccentricities.

Abstract

If the two planets in the HAT-P-13 system are coplanar, the orbital states provide a probe of the internal planetary structure. Previous analyses of radial velocity and transit timing data of the system suggested that the observational constraints on the orbital states were rather small. We reanalyze the available data, treating the jitter as an unknown MCMC parameter, and find that a wide range of jitter values are plausible, hence the system parameters are less well constrained than previously suggested. For slightly increased levels of jitter ($\sim 4.5\,m\,s^{-1}$) the eccentricity of the inner planet can be in the range $0<e_{inner}<0.07$, the period and eccentricity of the outer planet can be $440<P_{outer}<470$ days and $0.55<e_{outer}<0.85$ respectively, while the relative pericenter alignment, $\eta$, of the planets can take essentially any value $-180^{\circ}<\eta<+180^{\circ}$. It is therefore difficult to determine whether $e_{inner}$ and $\eta$ have evolved to a fixed-point state or a limit cycle, or to use $e_{inner}$ to probe the internal planetary structure. We perform various transit timing variation (TTV) analyses, demonstrating that current constraints merely restrict $e_{outer}<0.85$, and rule out relative planetary inclinations within $\sim 2^{\circ}$ of $i_{rel}=90^{\circ}$, but that future observations could significantly tighten the restriction on both these parameters. We demonstrate that TTV profiles can readily distinguish the theoretically favored inclinations of $i_{rel}=0^{\circ}\,&\,45^{\circ}$, provided that sufficiently precise and frequent transit timing observations of HAT-P-13b can be made close to the pericenter passage of HAT-P-13c. We note the relatively high probability that HAT-P-13c transits and suggest observational dates and strategies.