Exoplanets are illuminated by their host star and one can calculate how this illumination varies over the exoplanet’s surface, or the top of its atmosphere. For our purposes, we will use the term “surface” to refer to which of these applies. This illumination is called instellation, and it is determined by adding up the light received by each point on the surface from all visible parts of the host star. For large star-planet separations, this is easily accomplished by assuming that the star is very far from the planet and its rays reach the planet as plane parallel rays. In this case, the flux received is proportional to the inverse square of the star-planet separation for all points (see 1). This assumption breaks down for small star-planet separations, where the flux received is proportional to the inverse square of the separation of points on the exoplanet and those of the stellar surface, which varies across the surface of the exoplanet.
In using the plane parallel ray approximation, researchers effectively treat the exoplanet as if it has two zones, a dayside that is fully illuminated by the hemisphere of the host star facing it, and a nightside that receives no light as shown in 1. The terminator separates these two zones and bisects the exoplanet into two hemispheres. Such a model is not realistic, and if it were the sun would appear to set instantly at the terminator!
For star-planet separations that are on the order of a few stellar radii, this approximation breaks down, and one must take into account the finite angular size of the host star, i.e. treat it like a sphere. When this is done, the surface of the exoplanet is split into more than two zones. The fully illuminated zone (the yellow region of the exoplanet in 2), is the one that receives light from the apparent disk of the host star, which is the region between the inner tangent lines (dashed lines in 2). The region beyond the outer tangent lines (dot-dashed lines in 2) is unilluminated, note that it does not begin until after the traditional terminator. The two remaining zones are the two penumbral zones, which receive less light than the fully illuminated zone. The first penumbral zone receives light from more than half of the apparent disk of the host star (between the dashed lines and dotted lines in 2), and the second zone from less than half (between the dotted and dot-dashed lines in 2).
For extremely close-in exoplanets, much more than half of the exoplanet can be illuminated. For example, the hot jupiter Kepler-91 b is about 70% illuminated, with about 40% of that illumination being within the penumbral zones. As a comparison, Earth’s penumbral zone is only 0.5% of its surface. This illumination is not accounted for in any known atmospheric or climate modeling software.
The goal of this project is to analytically and/or numerically determine the illumination as a function of position on an exoplanet surface while accounting for the finite angular size of the host star. This will then be incorporated into a global climate model, such as ROCK-3D, and tested on potentially habitable exoplanets. In addition, the illumination model sets the initial conditions for Exoplanet Reflection models. Incorrectly modeling the illumination will result in incorrect estimates of exoplanet properties, such as temperature, planetary albedo, and planetary radius.
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