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

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

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

CC BY-SA 3.0
2018-04-08T22:41:47.033Z
Thanks for the answer, this site has MathJaX enabled, so you can format formulas using $\TeX$
James K
CC BY-SA 3.0
2018-04-08T23:40:11.760Z
This is only approximately correct. The flux densities have to be integrated over the appropriate filter response functions first.
ProfRob
CC BY-SA 3.0
2018-04-10T13:22:04.343Z
So will it be a straight line?
Agile_Eagle
CC BY-SA 4.0
2018-11-05T11:21:50.707Z
It depends on temperature evolution because $U-B = f(T)$ and $B-V = g(T)$.
Kornpob Bhirombhakdi
CC BY-SA 3.0
2018-04-08T20:46:09.227Z
2018-04-08T22:40:46.507Z
2018-04-08T22:40:46.507Z
Kornpob Bhirombhakdi
<p>The color-color diagram is a plot between $U-B$ vs $B-V$ values. </p>

<p>For a ideal blackbody, <strong>what is the equation of this line?</strong></p>

<p>In other words, <strong>what does the linear relation between $U-B$ and $B-V$ look like?</strong></p>

CC BY-SA 3.0
2018-04-10T14:19:04.963Z
I saw this in a book (carol ostlie) where a st line was given.
Agile_Eagle
<star><observational-astronomy><astrophysics><data-analysis><photometry>
What is equation of straight line for a ideal blackbody on the color color diagram?
Agile_Eagle
# What is equation of straight line for a ideal blackbody on the color color diagram?

(Asked by: username_0 on 2018-04-08)

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?**

**Tags:** star, observational-astronomy, astrophysics, data-analysis, photometry
> **Comments:**
> **username_0**: I saw this in a book (carol ostlie) where a st line was given.  

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## 1 answers

### Answer by username_1 on 2018-04-08. Score: 2 | Accepted answer

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 $U-B = f(B-V)$.

> **Comments:**
> **username_2**: Thanks for the answer, this site has MathJaX enabled, so you can format formulas using $\TeX$  
> **username_3**: This is only approximately correct. The flux densities have to be integrated over the appropriate filter response functions first.  
> **username_0**: So will it be a straight line?  
> **username_1**: It depends on temperature evolution because $U-B = f(T)$ and $B-V = g(T)$.  

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