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Revisiting exoplanet TrES-2 (Kepler-1b)
Kepler's Field of View with inset showing TrES-2, a hot Jupiter-like planet known to cross in front of, or transit, its star every 2.5 days.
Kepler field of view with TrES-2

When determining properties of exoplanets using the transit method, it cannot be overstated how important it is to know the properties of the host star. The paper "The Discovery of Ellipsoidal Variations in the Kepler Light Curve of HAT-P-7" by William Welsh et al (January 2010) has an analysis of the early Kepler observations of the previously discovered transiting planet HAT-P-7b (Kepler-2b) in which the light curve shows the transit of planet across the star, the occultation of the planet by the star (planet going behind the star), and what's known as "ellipsoidal variations" caused by the very nearby planet (only 4 stellar radii away) gravitationally distorting the star, resulting brightness changes twice per orbit.

The paper "Photometrically derived masses and radii of the planet and star in the TrES-2 system" by Thomas Barclay et al, published 2012 Oct 18, concerns precise measurement of the mass and radius of the star and planet in the TrES-2 system using 2.7 years of observations by the Kepler spacecraft. The light curve shows evidence for ellipsoidal variations as well as Doppler beaming, which is a variation in brightness especially associated with a planet transiting a fast spinning star. Careful analyses of the ellipsoidal variations and Doppler beaming can yield a relatively accurate planet-to-star mass ratio. In addition, study of brightness changes caused by internal waves in a star (asteroseismology) can be used to accurately calculate the mass and radius of a star.

The radius of the star is crucial to determining radius of the planet orbiting it, since the amount of drop in brightness of the star only gives the size of the planet relative to the star's size. The paper by Barclay et al further analyzes changes in brightness caused by day/night/rotation of the planet, that can be used to determine the difference in temperature between day and night time sides of the exoplanet, model the atmosphere of the planet and possibly even changing exoplanet weather patterns—an amazing amount of information gleaned from only brightness changes of a star! It is yet another manifestation of the statement by Johannes Kepler, "the ways by which men arrive at knowledge of the celestial things are hardly less wonderful than the nature of these things themselves".

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