Estimating the radius of a non-transiting exoplanet

Question

I need to know the timescale of tidal locking of a non-transiting exoplanet. For that, I need to know (or at least have some constraint of) its radius (Gladman et al. 1996):

$$T_{lock} = k \frac{a^6}{G M_{star} R_{planet}^2 Q},$$

where

$T_{lock}$ is the timescale for tidal locking, $k$ is a constant that depends on the properties of the planet and the star, $a$ is the semi-major axis of the planet's orbit, $G$ is the gravitational constant, $M_{star}$ is the mass of the host star, $R_{planet}$ is the radius of the planet and $Q$ is the tidal quality factor, which represents the efficiency of energy dissipation within the planet.

How can I estimate the radius of a given exoplanet?

Answer 1

If you have its mass (and if it's a Doppler-discovered planet then you only have a lower limit to the mass, $M\sin i$), then about the best you can do is plot a mass-radius relationship for all the transiting planets with a known mass and radius and use a best-fit to that in order to estimate the radius of your planet.

Something like this (from Mordasini et al. 2014) :

Note that the relationship is very scattered once you get into the gas-giant regime but that is just an uncertainty you will have to live with.