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We present {\em Spitzer} secondary-eclipse observations of the hot JupiterHAT-P-13 b in the 3.6 {\micron} and 4.5 {\micron} bands. HAT-P-13 b inhabits atwo-planet system with a configuration that enables constraints on the planet'ssecond Love number, \math{k\sb{2}}, from precise eccentricity measurements,which in turn constrains models of the planet's interior structure. We exploitthe direct measurements of \math{e \cos \omega} from our secondary-eclipse dataand combine them with previously published radial velocity data to generate arefined model of the planet's orbit and thus an improved estimate on thepossible interval for \math{k\sb{2}}. We report eclipse phases of \math{0.49154\pm 0.00080} and \math{0.49711 \pm 0.00083} and corresponding \math{e \cos\omega} estimates of \math{-0.0136 \pm 0.0013} and \math{-0.0048 \pm 0.0013}.Under the assumptions of previous work, our estimate of \math{k\sb{2}} of 0.81{\pm} 0.10 is consistent with the lower extremes of possible core masses foundby previous models, including models with no solid core. This anomalous resultchallenges both interior models and the dynamical assumptions that enable them,including the essential assumption of apsidal alignment. We also report eclipsedepths of 0.081\% {\pm} 0.008\% in the 3.6 {\micron} channel and 0.088 \% {\pm}0.028 \% in the 4.5 {\micron} channel. These photometric results arenon-uniquely consistent with solar-abundance composition without any thermalinversion.

The Atmosphere and Interior Structure of HAT-P-13b from Spitzer Secondary Eclipses