2024ApJ...976L..14L

We present constraints on the shape of Kepler-51d, which is a superpuff with a mass ∼6 M_⊕ and a radius ∼9 R_⊕, based on detailed modeling of the transit light curve from James Webb Space Telescope (JWST) NIRSpec. The projected shape of this extremely low-density planet is consistent with being spherical, and a projected oblateness f_⊥ > 0.2 can be excluded regardless of the spin obliquity angles. If this is taken as the limit on the true shape of the planet, Kepler-51d is rotating at ≲50% of its breakup spin rate, or its rotation period is ≳33 hr. In the more plausible situation that the planetary spin is aligned with its orbital direction to within 30°, then its oblateness is <0.08, which corresponds to a dimensionless spin rate ≲30% of the breakup rotation and a dimensional rotation period ≳53 hr. This seems to contradict the theoretical expectation that planets with such low masses may be spinning near breakup. We point out the usefulness of the stellar mean density and the orbital eccentricity in constraining the shape of the transiting planet, so planets with well-characterized host and orbital parameters are preferred in the detection of planetary oblateness with the JWST transit method.