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{sub b}) is in part dictated by its Love number (k{sub 2{sub b}}), which is in turn a proxy for the degree of central mass concentration in its interior. Thus, the measurement of e{sub b} constrains k{sub 2{sub b}} and allows us to place otherwise elusive constraints on the mass of HAT-P-13b's core (M{sub core,b}). In this study we derive new constraints on the value of e{sub 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{sub b} = 0.00700 ± 0.00100. We then use octupole-order secular perturbation theory to find the corresponding k{sub 2{sub b}}=0.31{sub −0.05}{sup +0.08}. Applying structural evolution models, we then find, with 68% confidence, that M{sub core,b} is less than 25 Earth masses (M{sub ⊕}). The most likely value is M{sub core,b} = 11 M{sub ⊕}, 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.