How to Calculate Luminosity of an RR Lyrae Star?

[Gregg]

Homework Statement

Given pulsation period in days, (surface temperature) and mass of an RR Lyra variable star. How do you find luminosity?

Homework Equations

The relevant equations seem to be for finding the luminosity of Cepheids... there are no equations for Lyrae... Other than, absolute magnitude is 49 solar masses luminosities, for all RRs.

Should I use

$$ \Pi \approx \sqrt{\frac{3\pi}{2 \gamma G \rho}} $$ to get L from

$$\frac{L}{L_{\odot}} = {\left ( \frac{R}{R_{\odot}} \right )}^2 {\left ( \frac{T}{T_{\odot}} \right )}^4 $$ ?

 

[member 553083]

The Attempt at a SolutionI think that the first equation can be used to get an approximation of luminosity, but I'm not sure if it's the correct approach.