Stellar radius ($R_{\ast }$)

A stellar radius is the radius assigned to a star using a stated surface convention. A gaseous star has no sharp solid boundary: in a model, a commonly used reference is a layer near outward optical depth of order one. Different spectral bands can sample different layers, particularly in very extended stellar atmospheres.

For an approximately spherical star, a measured angular diameter $\theta$ and distance $d$ give $R_{\star }\simeq d\theta /2$ for small $\theta$ in radians. Alternatively, luminosity and effective temperature give $L=4\pi R_{\star }^2\sigma T_{\mathrm{eff}}^4$ through the Stefan–Boltzmann law. Eclipsing binaries offer another route through orbital geometry. This measurement matters directly for exoplanet transit photometry, whose exoplanet transit depth primarily supplies the planet-to-star radius ratio.