Analysis of the exoplanet containing system Kepler-13

Abstract

We have applied the close binary system analysis program WinFitter, with its physically detailed fitting function, to an intensive study of the complex multiple system Kepler-13 using photometry data from all 13 short cadence quarters downloaded from the NASA Exoplanet Archive (NEA) (http://exoplanetarchive.ipac.caltech.edu). The data-point error of our normalized, phase-sequenced and binned (380 points per bin: 0.00025 phase interval) flux values, at 14 ppm, allows the model’s specification for the mean reference flux level of the system to a precision better than 1 ppm. Our photometrically derived values for the mass and radius of KOI13.01 are $6.8\pm0.6~\mbox{M}_{\mathrm{J}}$ and $1.44\pm0.04~\mbox{R}_{\mathrm{J}}$. The star has a radius of $1.67\pm0.05~\mbox{R}_{\odot}$. Our modelling sets the mean of the orbital inclination $i$ at $94.35\pm0.14^{\circ}$, with the star’s mean precession angle $\phi_{p}$—$49.1\pm5.0^{\circ}$ and obliquity $\theta_{o}$ $67.9 \pm 3.0^{\circ}$, though there are known ambiguities about the sense in which such angles are measured.

Our findings did not confirm secular variation in the transit modelling parameters greater than their full correlated errors, as argued by previous authors, when each quarter’s data was best-fitted with a determinable parameter set without prejudice. However, if we accept that most of the parameters remain the same for each transit, then we could confirm a small but steady diminution in the cosine of the orbital inclination over the 17 quarter timespan. This is accompanied by a slight increase of the star’s precession angle (less negative), but with no significant change in the obliquity of its spin axis. There are suggestions of a history of strong dynamical interaction with a highly distorted planet rotating in a 3:2 resonance with its revolution, together with a tidal lag of $\sim30~\mbox{deg}$. The mean precessional period is derived to be about 1000 y, but at the present time the motion of the star’s rotation axis appears to be supporting the gravitational torque, rather than providing the balance against it that would be expected over long periods of time.

The planet has a small but detectable backwarming effect on the star, which helps to explain the difference in brightness just after transit and just before occultation eclipses. In assessing these findings it is recognized that sources of uncertainty remain, notably with possible inherent micropulsational effects, variations from other components of the multiple star, stellar activity, differential rotation and the neglect of higher order terms (than $r_{1}^{5}$) in the fitting function, where $r_{1}$ is the ratio of the radius of the star to the mean orbital separation of planet and host star.