Dynamical constraints on the core mass of hot Jupiter HAT-P-13B

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. Owing to the special orbital configuration of the HAT-P-13 system, the magnitude of HAT-P-13b's eccentricity (e_b) is in part dictated by its Love number ($k_{2_b}$), which is in turn a proxy for the degree of central mass concentration in its interior. Thus, the measurement of e_b constrains $k_{2_b}$ and allows us to place otherwise elusive constraints on the mass of HAT-P-13b's core (M_core,b). In this study we derive new constraints on the value of e_b 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 e_b = 0.00700 ± 0.00100. We then use octupole-order secular perturbation theory to find the corresponding $k_{2_b}={0.31}_{-0.05}^{+0.08}$. Applying structural evolution models, we then find, with 68% confidence, that M_core,b is less than 25 Earth masses (M_⊕). The most likely value is M_core,b = 11 M_⊕, 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 and 4.5 μm bands, best match atmospheric model predictions with a dayside temperature inversion and relatively efficient day–night circulation.