# Constraints on the interior structure of HAT-P-13 b

## Constraints on the interior structure of HAT-P-13 b

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

http://arxiv.org/abs/1112.2087

http://arxiv.org/abs/1112.2087

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.

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## Re: Constraints on the interior structure of HAT-P-13 b

Dynamical Constraints on the Core Mass of Hot Jupiter HAT-P-13b

http://arxiv.org/abs/1602.03895

http://arxiv.org/abs/1602.03895

HAT-P-13b is a Jupiter-mass transiting exoplanet that has settled onto a stable, short-period, and mildly eccentric orbit as a consequence of the action of tidal dissipation and perturbations from a second, highly eccentric, outer companion. Due to the special orbital configuration of the HAT-P-13 system, the magnitude of HAT-P-13b's eccentricity (eb) is in part dictated by its Love number (k2b), which is in turn a proxy for the degree of central mass concentration in its interior. Thus, the measurement of eb constrains k2b and allows us to place otherwise elusive constraints on the mass of HAT-P-13b's core (Mcore,b). In this study we derive new constraints on the value of eb by observing two secondary eclipses of HAT-P-13b with the Infrared Array Camera on board the Spitzer Space Telescope. We fit the measured secondary eclipse times simultaneously with radial velocity measurements and find that eb=0.00700±0.00100. We then use octupole-order secular perturbation theory to find the corresponding k2b=0.31+0.08−0.05. Applying structural evolution models, we then find, with 68\% confidence, that Mcore,b is less than 25 Earth masses (M⊕). The most likely value of Mcore,b=11M⊕, which is similar to the core mass theoretically required for runaway gas accretion. This is the tightest constraint to date on the core mass of a hot Jupiter. Additionally, we find that the measured secondary eclipse depths, which are in the 3.6 μm and 4.5 μm bands, best match atmospheric model predictions with a dayside temperature inversion and relatively efficient day-night circulation.

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