= Solution
Potential surface habitability requires a stable liquid-water interface, a temperature and pressure outside runaway-greenhouse and high-pressure-ice regimes, and an $\mathrm H_2$ inventory large enough for collision-induced greenhouse warming but not so deep that pressure and temperature sterilize the ocean. Long-term atmospheric retention, tolerable stellar ultraviolet and particle flux, nutrient cycling, and chemical disequilibrium compatible with metabolism are also needed. A location in the <circumstellar habitable zone> alone is insufficient.
For $M_p=5M_\oplus$ and $R_p=2R_\oplus$,
$$
g=\frac{5}{2^2}g_\oplus\simeq12.3\,{\rm m\,s^{-2}}.
$$
Taking $T=300\,{\rm K}$ and hydrogen-rich mean molecular weight $\mu=2.3$ gives the <atmospheric scale height>
$$
H=\frac{k_BT}{\mu m_Hg}\simeq88\,{\rm km}.
$$
If a strong feature spans $N_H=5$ scale heights and $R_s=0.5R_\odot$, the <atmospheric spectral-feature amplitude> is
$$
\boxed{\Delta D\simeq
\frac{2R_pN_HH}{R_s^2}
\simeq9\times10^{-5}\simeq90\,{\rm ppm}}.
$$
Clouds, hazes, refraction, and smaller molecular abundance reduce this estimate.
Back to article page
