The color-color diagram is a plot between $U-B$ vs $B-V$ values.

For a ideal blackbody, what is the equation of this line?

In other words, what does the linear relation between $U-B$ and $B-V$ look like?

  • $\begingroup$ I saw this in a book (carol ostlie) where a st line was given. $\endgroup$ – Agile_Eagle Apr 10 '18 at 14:19

Use Planck's law: $$F(\lambda,T) = c \lambda^{-5} (e^{d/(\lambda T)} - 1)^{-1}$$.

Since magnitude is defined as, $M = -2.5 \log_{10}(F) + \textrm{constant}$, the color index $A-B$ is $$(A - B) = -2.5 \log_{10}(F(\lambda_A,T)/F(\lambda_B,T))$$.

To answer your question, use an appropriate effective wavelength of $U,B,V$. Link $U-B$ and $B-V$ via temperature, you should get $U-B = f(B-V)$.

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  • $\begingroup$ Thanks for the answer, this site has MathJaX enabled, so you can format formulas using $\TeX$ $\endgroup$ – James K Apr 8 '18 at 22:41
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    $\begingroup$ This is only approximately correct. The flux densities have to be integrated over the appropriate filter response functions first. $\endgroup$ – Rob Jeffries Apr 8 '18 at 23:40
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    $\begingroup$ So will it be a straight line? $\endgroup$ – Agile_Eagle Apr 10 '18 at 13:22
  • $\begingroup$ It depends on temperature evolution because $U-B = f(T)$ and $B-V = g(T)$. $\endgroup$ – Kornpob Bhirombhakdi Nov 5 '18 at 11:21

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