Temperature Distributions on Tidally-locked Hot Exoplanets

Introduction: The discovery of over 250 exoplanets, many of which exist in conditions unlike any Solar System bodies, has motivated researchers to study these planets and place them within the greater context of planetary science. Of these discovered exoplanets, most are massive (Jupiter masses) and orbit very close to the parent-star, with orbital periods on the order of several days [1]. Additionally, near Earth-mass planets orbiting in habitable zones of other solar systems are being discovered with new detection techniques. The planet GI 581c, discovered in 2007, is an example of such a planet [2]. Atmospheres have been detected on giant exoplanets and with the advent of new telescopes and techniques, will also be detected on smaller planets. We primarily focus on hot super-Earth planets, rocky planets up to 20 Earth masses that orbit close to the parent star. The closest analog in our solar system to these hot exoplanets is Mercury, a planet with a composition whose exact nature remains to be determined [3]. We present a preliminary computational method to understand possible surface and interior temperatures and atmospheric compositions of hot, rocky exoplanets by modeling solid-state heat transfer using conductive and radiative transport. These methods allow us to characterize these planets and provide a theoretical context for observational data. Methods: We use the finite element code SSAXC, a spherical axisymmetric version of ConMan (Convection in the Mantle) to study heat transfer in tidallylocked planets. The code uses the Petrov-Galerkin finite element method to solve the time-dependent twodimensional heat equation for an axially symmetric geometry [4]. The code is modified to include heat flux onto and radiative heat loss from the surface at each time interval to compute the steady-state temperature profile. This code can accomodate both conductive and convective cases for a variety of planetary conditions and materials, though in this preliminary study, only the conductive case is considered. In the case of exoplanets, various planetary radii, orbital distances, and parent-star types and fluxes will be considered. We will be considering planets up to 20 Earth masses with varying metallic core size and surface compositions. Results: A steady-state temperature profile was computed for a conductive planet with stellar heating as the sole heat source. The pole is the axis of symmetry and represents the point closest to the star. Stellar heat flux is treated with latitudinal dependence, as it drops off as a cosine function from the pole. A core region is treated at a constant temperature that is 10% (T=0.1) of the surface polar temperature (T=1). Temperatures and radii have been normalized, such that R = 1 represents the planet radius and T =1 is the peak temperature (Fig. 1). At steady-state, there are regions where the planet may exist in a molten state that could be depleted of volatile materials that have either escaped or are constituents of an atmosphere. Future laboratory experiments will elucidate information of what materials would preferentially evaporate from a range of possible silicate compositions. Additionally, there are regions of intermediate temperature that could be considered habitable even on a hot exoplanet.