Volume 538, February 2012
|Number of page(s)
|Planets and planetary systems
|16 February 2012
Constraining the interior of extrasolar giant planets with the tidal Love number k2 using the example of HAT-P-13b
1 Institute of Physics, University of Rostock, 18051 Rostock, Germany
2 Dept. of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA
3 Astrophysical Institute and University-Observatory, Schillergässchen 2–3, 07745 Jena, Germany
Received: 23 September 2011
Accepted: 15 November 2011
Context. 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.
Aims. 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 k2 into account as an additional, possibly observable parameter.
Methods. Because it is the only planet with an observationally determined k2, 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 k2 and compared it to the allowed range of k2 values that could be obtained from eccentricity measurements of HAT-P-13b.
Results. 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 k2 value a maximum possible core mass can be determined. For HAT-P-13b we find Mcore < 27 M⊕, based on the latest eccentricity measurement. We favor models that are consistent with our model atmosphere, which gives us the temperature of the isothermal region as ~2100 K. With this external boundary condition and our new k2-interval 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 103−105.
Conclusions. Our analysis shows that the tidal Love number k2 is a very useful parameter for studying the interior of exoplanets. It allows one to place limits on the core mass and estimate the metallicity of a planet’s envelope.
Key words: methods: numerical / planets and satellites: interiors / planets and satellites: individual: HAT-P-13b
© ESO, 2012
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