stellar radius determination

Stellar radius determination is generally approximated by the formula relating luminosity, temperature, and radius:

L = 4πR2sT4

• L,R,T - luminosity, radius, temperature.
• s - Stefan-Boltzmann constant

Or if the values are given in terms of the Sun's values:

R/RSun=(TSun/T)2(L/LSun)1/2

Both L and T need to be measured or estimated. Temperature is generally related to the B-V color index. With a parallax distance measurement, luminosity is related to the apparent magnitude. This yields a very rough estimate: merely basing the temperature on B-V can result in a radius off by as much as 50%. When a parallax distance is not available, an even rougher estimate can be made using the mass-luminosity relation and mass-radius relation. More accurate determination uses:

• Eclipsing binary stars: if their radial velocities can be determined, e.g., by Doppler shift, their separation can be derived and the eclipse yields information about their radii.
• Interferometry (with parallax measurement, for nearby stars).
• Asteroseismology (for stars with observable vibrations): a relatively accurate method for the distances it covers, useful in calibrating other methods.
• Lunar occultation observations.

Only a few hundred stars have been measured by these more accurate methods. Using the more accurate radius in the above formula can sometimes yield a more accurate temperature determination.

Another useful data-point is surface gravity determined from spectral signatures, which depends upon mass and radius, i.e., with it, radius can be estimated from a mass determination, and vice versa.

A determined stellar radius is useful in the study of transiting extra-solar planets, to determine characteristics of the planet's orbit and/or radius.