A transit is observed around a star with and (cgs)

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

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

Problem

A transit is observed around a star with

T_{\rm eff}=5500\,\mathrm{K}

and

\log g = 4.05

(cgs), signalling a subgiant rather than a main-sequence star, with transit depth

\delta = 0.00640

. Someone argues: "The depth gives

k^2=\delta

, and every Sun-like star has

R_*\approx1\,R_\odot

, so

R_p=\sqrt{\delta}\times1\,R_\odot = 0.0800\,R_\odot \approx 0.78\,R_J

." Stellar-model fitting to this star's

T_{\rm eff}

and

\log g

gives a catalogued radius

R_*=1.60\,R_\odot

. ((a)) Find the error in the reasoning above. ((b)) Compute the correct planet radius, and state how large the error in the first estimate was.

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