Solution (source code)

= Solution

The measured mass and radius imply
$$
\bar\rho_p=\rho_\oplus\frac{6.6}{2.6^3}\simeq2.1\,\mathrm{g\,cm^{-3}}.
$$
Compared 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.<Mass-radius relationships for solid exoplanets by Sara Seager and others>[2007, abstract and solid-composition mass-radius models; the observed radius can also include a gas envelope]{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 are
$$
a=\left[\frac{G(0.16M_\odot)P^2}{4\pi^2}\right]^{1/3}=0.0144\,\mathrm{AU},\qquad
T_{\rm eq}=3000\sqrt{\frac{0.21R_\odot}{2a}}\simeq552\,\mathrm K.
$$
Surface gravity is $g=Gm/R_p^2\simeq9.58\,\mathrm{m\,s^{-2}}$. With molar mass $\mathcal M=2.2\times10^{-3}\,\mathrm{kg\,mol^{-1}}$, the <atmospheric scale height> is
$$
\boxed{H=\frac{R_uT}{\mathcal M g}\simeq2.18\times10^5\,\mathrm m\simeq218\,\mathrm{km}.}
$$
A spectral feature spanning $N$ scale heights changes the blocked stellar fraction by the atmospheric annulus area:
$$
\boxed{\Delta\delta\simeq\frac{2R_pNH}{R_*^2}\simeq3.38\times10^{-4}N.}
$$
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 $1.7\times10^{-3}$. The number of scale heights requires the actual opacity ratio; $N\simeq\ln(\kappa_{\rm line}/\kappa_{\rm cont})$ 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.https://arxiv.org/abs/1401.0022[2014 transmission-spectrum study, abstract: featureless near-infrared spectrum and rejection of tested cloud-free high-molecular-mass models]{ref}