Is there a formlua or equation to calculate a star's B-V index based on it's observed frequencies in the B and V spectrums ? I have unfortunately not been able to find anything...
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$\begingroup$ I'd actually say astronomy.stackexchange.com/q/23346/24157 is a better match to this question, although that one was closed as a duplicate of a question that's not really related. $\endgroup$– user24157Commented Nov 26, 2019 at 16:00
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I found :
$$B-V = -2.5 \log_{10} \left(\frac{f_B}{f_V}\right)$$
From this question. It works for my purposes.
Those are magnitudes on the left. Five magnitudes are a factor of 100, so 2.5 magnitudes are a factor of 10. So if $f_B/f_V =$ 100 (i.e. 10$^2$) then $B-V =$5.
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2$\begingroup$ This is from the standard relationship between flux and magnitude e.g. en.m.wikipedia.org/wiki/Apparent_magnitude (Note: $f_B$ here is flux in the Bessell/Johnson B filter, not frequency) $\endgroup$ Commented Nov 23, 2019 at 18:35
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1$\begingroup$ I made a small edit and noted that that's base-10 log. Feel free to edit further if this helps, or roll back if it doesn't. In a few days if nobody leaves an answer you find more helpful, you can also accept your own answer. $\endgroup$– uhohCommented Nov 24, 2019 at 12:04