How to Calculate Combined Apparent Magnitude for Binary Star Systems

[nicedazed]

Hi guys, first post (hopefully not only).

If 2 stars are in an apparent binary system, how do you calculate the "combined apparent magnitude" of the system if you know both their apparent magnitudes and their distance from you.

I can work out the apparent magnitude (even though that's not required) but the combined one is troubling me and other examples on the internet are either unclear to me or using variables i don't have.

Thanks.

 

[cepheid]

Welcome to PF nicedazed!

The definition of the apparent magnitude m of a source is:

m = -2.5log₁₀(F/F₀)

where F is the flux (the energy per unit time and per unit area) being received from the source, and F₀ is the flux of a reference source that has been defined to have an apparent magnitude of 0 (I believe that at one time this reference source was Vega, but now a more complicated set of references is used).

Here, flux is really the meaningful physical quantity. It's what you measure directly, making it overall just more useful to work with. In particular, fluxes are additive, whereas magnitudes are not. So, the total flux being received from the two sources in a binary system is just equal to the sum of the individual fluxes from each source.

Does that last statement give you an idea of how to determine the combined apparent magnitude of the system?