Analysis and interpretation of 15 quarters of Kepler data of the disintegrating planet KIC 12557548 b


Context. The Kepler object KIC 12557548 shows irregular eclipsing behaviour with a constant 15.685 h period, but strongly varying transit depth. The object responsible for this is believed to be a disintegrating planet forming a trailing dust cloud transiting the star. A 1D model of an exponentially decaying dust tail was found to reproduce the average eclipse in intricate detail. Based on radiative hydrodynamic modelling, the upper limit for the planet mass was found to be twice the mass of the Moon.
Aims: In this paper we fit individual eclipses, in addition to fitting binned light curves, to learn more about the process underlying the eclipse depth variation. Additionally, we put forward observational constraints that any model of this planet- star system will have to match.
Methods: We manually de- correlated and de-trended 15 quarters of Kepler data, three of which were observed in short cadence mode. We determined the transit depth, egress depth, and stellar intensity for each orbit and search for dependencies between these parameters. We investigated the full orbit by comparing the flux distribution of a moving phase window of interest versus the out-of-eclipse flux distribution. We fit short cadence data on a per-orbit basis using a two-parameter tail model, allowing us to investigate potential dust tail property variations.
Results: We find two quiescent spells of åisebox-0.5ex~30 orbital periods each where the transit depth is <0.1%, followed by relatively deep transits. Additionally, we find periods of on-off behaviour where >0.5% deep transits are followed by apparently no transit at all. Apart from these isolated events we find neither significant correlation between consecutive transit depths nor a correlation between transit depth and stellar intensity. We find a three-sigma upper limit for the secondary eclipse of 4.9 × 10$^-5$, consistent with a planet candidate with a radius of less than 4600 km. Using the short cadence data we find that a 1D exponential dust tail model is insufficient to explain the data. We improved our model to a 2D, two-component dust model with an opaque core and an exponential tail. Using this model we fit individual eclipses observed in short cadence mode. We find an improved fit of the data, quantifying earlier suggestions by Budaj (2013, A&A, 557, A72) of the necessity of at least two components. We find that deep transits have most absorption in the tail, and not in a disk-shaped, opaque coma, but the transit depth and the total absorption show no correlation with the tail length.