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 / 3 / 2

The measured mass and radius implyCompared with the supplied composition curves, this is inconsistent with a bare iron-rich or ordinary rock-only planet. A volatile-rich interior and/or an extended low-density gas envelope is needed. A water-rich body with an atmosphere and a rocky core with a modest H/He envelope are different plausible families; mass and radius do not uniquely determine the composition.^[ref]

For the requested H/He estimate, assume a hydrostatic, approximately isothermal terminator at the zero-Bond-albedo, fully redistributed equilibrium temperature. The orbit and temperature areSurface gravity is $g=Gm/R_p^2\simeq 9.58\mathrm{m}{\mathrm{s}}^{-2}$. With molar mass $\mathcal{M}=2.2\times 10^{-3}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$, the atmospheric scale height isA spectral feature spanning $N$ scale heights changes the blocked stellar fraction by the atmospheric annulus area:Thus one scale height is about $338$ parts per million in transit depth; a clear strong feature spanning roughly five scale heights is of order $1.7\times 10^{-3}$. The number of scale heights requires the actual opacity ratio; $N\simeq \ln ({\kappa }_{\mathrm{line}}/{\kappa }_{\mathrm{cont}})$ is a useful isothermal estimate, not a supplied measured value. The true terminator temperature need not equal this redistribution estimate.

A nearly flat spectrum can result from a high-mean-molecular-mass atmosphere with a much smaller scale height, or from optically thick clouds/hazes that hide the deeper absorption features. These are the two qualitative possibilities; detailed precision data can discriminate them. In particular, the pre-2015 HST study favored clouds over the clear high-molecular-mass models it tested, so listing both physical mechanisms is not a claim that all such models fit those data equally well.^[ref]