Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S30 / 1 / 3 / Solution

Assume the companion is much less massive than the star, the sinusoid represents a circular Keplerian orbit, and the transit implies $\sin i\simeq 1$. Ignore dilution, limb darkening and grazing geometry when estimating the radius. With $P=5\times 86400\mathrm{s}$,The stellar reflex radial-velocity semi-amplitude gives $K\simeq (m/M_{\odot })(2\pi a/P)$, while transit depth gives $\delta \simeq (R_p/R_{\odot }{)}^2$. ThereforeThe mean density relative to the supplied Jupiter values isThis is a low-density hot gas giant. Strong irradiation can slow contraction or help sustain an inflated envelope; internal heating and a different heavy-element fraction are other possibilities. The inferred low mass also reduces gravitational compression. Mass and radius alone do not determine which inflation mechanism operates.