A warm Neptune-mass planet has equilibrium temperature

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Celestial mechanics and planetary systems · Celestial mechanics and planetary systems

Stars from the Inside, Ch Planetary systems: formation estimates, transits and the atmospheres of other worlds

Problem

A warm Neptune-mass planet has equilibrium temperature T=900 KT = 900\,\mathrm{K}, surface gravity gp=12 m s−2g_p = 12\,\mathrm{m\,s^{-2}}, mean molecular weight μ=2.3\mu = 2.3, and radius Rp=0.35 RJR_p = 0.35\,R_J. Its host star has radius R∗=0.90 R⊙R_* = 0.90\,R_\odot. ((a)) Compute the atmospheric scale height HH. ((b)) Compute the extra transit depth Δδ≈2RpH/R∗2\Delta\delta \approx 2R_pH/R_*^2 contributed by one scale height of atmosphere.

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