Slow Rotation for the Super-puff Planet Kepler-51d

Super-puffs are low-density planets of unknown origin and composition. If they form by accreting nebular gas through a circumplanetary disk, one might expect super-puffs to be spinning quickly. Here, we derive upper limits on the rotational oblateness of the super-puff Kepler-51d, based on precise transit observations with the NIRSpec instrument on board the James Webb Space Telescope. The absence of detectable oblateness-related anomalies in the light curve leads to an upper limit of about 0.15 on the planet's sky-projected oblateness. Assuming the sky-projected oblateness to be representative of the true oblateness, the rotation period of Kepler-51d is ≳40 hr, or equivalently, its rotation speed is ≲42% of the breakup speed. Alternatively, if the apparently low density of Kepler-51d is due to an opaque planetary ring, the ring must be oriented within 30^∘ of face on and have an inner radius smaller than 1.2 times the planet's radius. Separately, the lack of anomalies exceeding 0.01% in the ingress and egress portions of the light curve places a constraint on the model of Wang & Dai, in which the planet's apparently low density is due to a dusty outflowing atmosphere.