# How do you transform between theoretical Hertzsprung-Russell Diagrams and Colour-Magnitude Diagrams?

When discussing stars, theorists tend to use effective temperature $T_\text{eff}$ and luminosity $L$ (on logarithmic scales). Observers, on the other hand, usually talk about observed colours and magnitudes (e.g. $B$ vs. $B{-}V$). These two sets of parameters are obviously related. Temperature corresponds to colour; luminosity to magnitude.

How does one transform between them? That is, given $L$ and $T_\text{eff}$ (from which one can derive $R$ through $L=4\pi R^2\sigma T_\text{eff}^4$), what are $B$ and $B{-}V$, or any other colour/magnitude? Alternatively, given $B$ and $B{-}V$, what are $L$ and $T_\text{eff}$? I figure $(L,T_\text{eff})\to(B,B{-}V)$ is easier.

I'll start trying to answer it myself just by presuming the star is emitting a blackbody spectrum and integrating against the $B$ and $V$ filter functions. I realise this will be a major simplification but it's a start. I'm hoping it's been done (and published) before, maybe with better treatment of reddening etc.

• Are there any stellar specialists on the site? I think you'd have to be one to do much better than than your own googling. Correcting spectra for absorption lines would be the main thing, and that depends heavily on metallicity. I'm doing a lot of radiation transport (though not in a stellar context) for my job now, and the takehome lesson it drives again and again is that as soon as you want to go past the first approximation, things get hairy. – Andrew Oct 24 '11 at 11:17
• OK, not an answer but some clarification: L (luminosity) depends on the distance to your object. Please do not forget the relation between the observed flux of the object and the luminosity. – Tigran Khanzadyan Oct 25 '11 at 8:31
• I was also just wondering, what is the exact problem you are trying to tackle? If you have some specific sample of observed stars with known B and V magnitudes then this is not enough to get the Teff. You would at least need spectra for each object to independently classify it and derive the Teff. This is all nice if you have "proper" main-sequence stars, but if not things will be quite complicated. Probably you could elaborate a bit on what exactly is the problem that you are trying to tackle? If you need a general nice answer then Wikipedia is there... – Tigran Khanzadyan Oct 25 '11 at 8:42