Taking Kepler data out for a spin

The recent announcement by the space telescope Kepler team of 706 exoplanetary candidates, of which around half they kept to themselves and half the data went public for, has enabled researchers to start making use of the data that was released. For some, it means using it to look for actual exoplanets, hoping that the low probability half of the data will still yield a gem or two they can follow up from the ground. For others, it provides a chance to use very high quality data to look at existing systems and test out a hypothesis or two.

Once such system is the hot Jupiter exoplanet TrES-2b. In orbit of the star GSC (Guide Star Catalogue) 03549-02811 A, the discovery of the planet by the Trans-Atlantic Exoplanet Survey in 2006, the second discovery made by TrES, showed a body with a mass nearly a fifth greater than Jupiter and a radius more than one and a quarter times as large as that of our gas giant. The planet orbitted a Sun-like star, now known as TrES-2 in exoplanet circles, in nearly two and a half days. It is likely to be tidally locked, with the same face pointed toward its host star, and orbits in pretty much a circular fashion less than one twenty-fifth the Earth-Sun orbital distance. The star has a binary companion and together they shine at a magnitude just above fifteen, making for a difficult observational target for casual observers.

TrES-2b was known to be in the field of view of Kepler and so an examination of its light curve was one of the first things published to show the probe was working. As such, the exoplanet gained another name – Kepler-1b. Studies of orbital parameters and careful observations of the light curve and other parameters had followed the 2006 discovery such as Doppler observations of the stellar wobble induced by the planet in 2006 and in separate observations in 2007 and 2008. As such, Kepler was able to use this known signal, and two others in its field of view, as a calibration tool.

Kepler runs in two modes, short and long cadence data – essentially short (one minute) and long (30 minute) exposures. The long cadence data results in a smeared out, flatter curve, but preserves bandwidth, as such 99% of Kepler data is long cadence. Once the calibration had been dealt with, the data went out to other researchers to see what could be dredged from the curves. David Kipping (who tweets here) and Gaspar Bakos went at the data with their own research tools.

David writes up his results and an introduction to things like the Kepler mission at his website here, and the paper, for the more technical minded, can be downloaded from here. The data used can be found here, Data Release 5, using zeroth and first quarter data releases. The aims of the investigation were to examine reports published last year suggesting secondary transits, transit time variations and even changes in the inclination of the orbit. These suggestions came from data sources inferior to Kepler, suggesting the new instrument could firm up or rule out each hypothesis.

Excellent instrument or not, the data still had to go through the usual wash, exploring alternate explanations for what’s happening, examining the limits of the data and looking for interfering systems. One such bit of interference, possibly an instrument effect, possibly a starspot one quarter the size of the Earth and very black, was seen. The researchers then investigated noise inherent in the signal and removed outliers with a few initial fits of the data.

A model of the data is computed using the primary eclipse (planet in front of star, blocking light) and the secondary eclipse (planet behind star, suddenly no longer reflecting light – exoplanets act as inferior planets like Mercury and Venus, showing phases). The model makes no assumptions about even the eccentricity of the orbit, preferring to rely on the data and propagating errors in the data in the proper fashion.

In this system, the planet has a grazing eclipse, catching the limb of the star. As stellar limbs tend to glow less brightly than the middle of their discs (limb darkenning due to the star being translucent), this can have an effect on the shape and depth of the light curve, which cuts off a darker than average part of the star. Another problem that can affect the depth of the light curve is the binary companion of the main star, which will happilly shine away constantly while the first is getting slightly blotted. An unresolved partner signal is referred to as blending. There is also blending by planetary emissions, but these are expected to be mostly outside of the wavelengths examined by Kepler.

The model shows that there is a very weak secondary eclipse, showing a low albedo exoplanet (it doesn’t reflect much light at all). The albedo suggests a planet as dark as black paint, though the error bars are rather large on this, so conclusions should be taken with caution. The model also shows the data to be consistent with a circular orbit. Planetary parameters derived fit well with previous studies, but stellar parameters suggest a smaller, more massive star than previously considered. Working at the very limits of the data, some care is taken to examine a possible periodic signal overlaid into the planetary data that may suggest an exomoon. However, even Kepler can only be pushed so far and when the data fails to provide a conclusive yes or no, investigations into other explanations suggest that the signal is simply due to Kepler binning the parts of the signal in exposure time sized blocks which catch the start and end of the transit at different parts of the block each time, known as ‘phasing’. Upper limits are set on the masses of any unseen moons at given orbital periods and inclinations. A Transit Duration Variation was detected, but a curious one for which no explanation has been provided and many ruled out. Additionally, the possibly that the exoplanet is altering its inclination required more than the 18 transits in the Kepler data. No evidence was found of additional dips in the light curve.

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