Estimation of Planetary Photometric Emissions for Extremely Close-in Exoplanets

Abstract

The fine precision of photometric data available from missions like Kepler provide researchers with the ability to measure changes in light on the order of tens of parts per million (ppm). This level of precision allows researchers to measure the loss of light due to exoplanet transits as well as the light emitted by an exoplanet, or planetary photometric emissions. The planetary photometric emissions are due to the thermal emissions of the exoplanet, and reflected stellar light. In many cases it is assumed that the incident stellar light may be modeled as plane parallel rays. For extremely close-in exoplanets the finite angular size of the host star must be taken into account and the plane parallel ray model breaks down. One consequence of modeling the incident stellar radiation in this manner is the creation of three distinct zones as opposed to the two zones present in the plane parallel ray model. The three zones are the fully illuminated, penumbral, and un-illuminated zones. The existence of the penumbral zone means that more than half of the exoplanet will be at least partially illuminated by the host star. In this work we will present a complete derivation of the reflective luminosity of the fully illuminated zone. In addition, we will present an outline for the derivation of the reflected intensity distribution of the penumbral zone. Within this work we will also derive a new expression for the thermal luminosity of an exoplanet by treating each of the three zones as a blackbody emitting at a constant temperature. Finally, it will be shown that an estimation of the radius of the exoplanet requires proper accounting of light from the penumbral zone during the primary transit. Not doing so risks underestimating the radius of the exoplanet and an overestimation of its geometric albedo and nightside temperature.