# H-R diagram, Double stars

Can someone help me? I have a case, like, we have H-R diagram and two stars on it. One of them is a blue star on main sequence, another is a red giant. They have equal luminosity. If they are in a double star system and seen from Earh as one star, then where on the diagram should I place this star? What luminosity amd temperature will it have?

Maybe I should sum up their luminosity and then, using Stefan Boltzmann law, calculate the temperature? But does the law work for red giants? And can I sum the luminosity?

• I've never known (or admittedly noticed) double stars being listed as one aggregate star on an HR diagram, even if they're close together. What are the complications with listing them both separately?
– user10106
May 16 '18 at 13:31
• It may be optical double system, or, like, what temperature does an object have when one star is over another for observer from earth. May 16 '18 at 14:03
• I suspect that if the luminosities are similar, they can be spectroscopically separated, and if they are not similar, you can more or less ignore the less luminous star. You wouldn't want to plot two stars of similar luminosity but highly different spectral types as a single point, that would really confuse the diagram. I'm not saying it's always possible to separate the stars, but one must try. May 16 '18 at 14:30
• It depends on what information you intend to present. More info? May 17 '18 at 14:23

It seems like you have a point source which you know that it is a combination of two stars: one blue, and the other redder. You can apply two-component blackbody: $F_{\lambda,total} = C_1 \times F_{\lambda,1}(T_1) + C_2 \times F_{\lambda,2}(T_2) ; T_1 \ne T_2$ where $F_{\lambda,total}$ is the observed specific fluxes from the point source, $F_{\lambda,1}, F_{\lambda,2}$ are blackbodies with temperature $T_1, T_2$ respectively, $C$s are normalization constants.
You can sum fluxes, since fluxes are normalized for the luminosity distance. Since luminosity $L$ is $L = F \times 4 \pi D_L^2$ where $D_L$ is the luminosity distance, the total luminosity is $L_1 + L_2 = 4 \pi D_{L,1}^2 \times F_1 + 4 \pi D_{L,2}^2 \times F_2 = C_1 \times F_1 + C_2 \times F_2$. Therefore, you can sum the luminosity when $D_{L,1} \approx D_{L,2}$.