= Solution
In transmission, the leading scaling is the <atmospheric spectral-feature amplitude>
$$
\Delta D\sim\frac{2R_pN_HH}{R_*^2}.
$$
Observability therefore improves for a small bright host star, a large planet, low surface gravity, high atmospheric temperature, low mean molecular mass, large molecular abundance, and cloud-free limbs. Stellar activity and heterogeneity, refraction, aerosols, limited transit count, detector noise, and spectral overlap reduce it.
In emission, the contrast scales approximately as
$$
\left(\frac{R_p}{R_*}\right)^2
\frac{B_\lambda(T_p)}{B_\lambda(T_*)}.
$$
It depends on dayside temperature, vertical temperature gradient, molecular opacity, heat redistribution, orbital geometry, stellar brightness, and instrumental background.
Back to article page
