Constraining the interior of extrasolar giant planets with the tidal Love number k_2 using the example of HAT-P-13b

TL;DR

This study investigates how the tidal Love number k_2 can constrain the interior structure of exoplanets, using HAT-P-13b as a case, by modeling its interior and comparing calculated k_2 values with observational data.

Contribution

It demonstrates how the tidal Love number k_2 can be used to limit the core mass and metallicity of an exoplanet, providing a new method to probe planetary interiors.

Findings

Maximum core mass for HAT-P-13b is less than 27 Earth masses.

Envelope and bulk metallicity constrained to 1-11 times stellar metallicity.

Lower limits on tidal quality factor Q are between 10^3 and 10^5.

Abstract

Transit and radial velocity observations continuously discover an increasing number of exoplanets. However, when it comes to the composition of the observed planets the data are compatible with several interior structure models. Thus, a planetary parameter sensitive to the planet's density distribution could help constrain this large number of possible models even further. We aim to investigate to what extent an exoplanet's interior can be constrained in terms of core mass and envelope metallicity by taking the tidal Love number k_2 into account as an additional possibly observable parameter. Because it is the only planet with an observationally determined k_2, we constructed interior models for the Hot Jupiter exoplanet HAT-P-13b by solving the equations of hydrostatic equilibrium and mass conservation for different boundary conditions. In particular, we varied the surface temperature and the outer temperature profile, as well as the envelope metallicity within the widest possible parameter range. We also considered atmospheric conditions that are consistent with nongray atmosphere models. For all these models we calculated the Love number k_2 and compared it to the allowed range of k_2 values that could be obtained from eccentricity measurements of HAT-P-13b. We use the example of HAT-P-13b to show the general relationships between the quantities temperature, envelope metallicity, core mass, and Love number of a planet. For any given k_2 value a maximum possible core mass can be determined. For HAT-P-13b we find Mcore < 27 ME, based on the latest eccentricity measurement. We are able to constrain both the envelope and bulk metallicity of HAT-P-13b to 1 -- 11 times stellar metallicity and the extension of the isothermal layer in the planet's atmosphere to 3 -- 44 bar. Assuming equilibrium tidal theory, we find lower limits on the tidal Q consistent with 10^3 - 10^5.