<p>There is a relationship between <span class="math-container">$E(B-V)$</span> and the reddening in any other colour. The exact value depends on the type of dust, the extinction value itself and the intrinsic spectrum of the star (as does the 3.0 coefficient mentioned in your question).</p>

<p>However, for the purposes of estimation, the canonical relationship is <span class="math-container">$E(U-B) = 0.72 E(B-V)$</span> (e.g. <a href="https://www.aanda.org/articles/aa/full/2003/01/aa2516/aa2516.html" rel="nofollow noreferrer">Pandey et al. 2003</a>).</p>

<p>Thus you can calculate <span class="math-container">$E(U-B)$</span>, then <span class="math-container">$E(B-V)$</span>, then <span class="math-container">$A_V$</span>, then <span class="math-container">$V_0$</span> and use this with <span class="math-container">$M_V$</span> to get the distance.</p>

CC BY-SA 4.0
2020-03-30T07:02:12.173Z
2020-03-30T07:02:12.173Z
ProfRob
<p>I'm doing the following question:</p>

<blockquote>
  <p>A star is observed with UBV magnitudes <span class="math-container">$m_u = 16.31$</span>, <span class="math-container">$m_b = 14.52$</span>,
  <span class="math-container">$m_v = 13.76$</span>. Spectral analysis gives <span class="math-container">$M_{bol} = 7.31$</span>, <span class="math-container">$BC = -1.02$</span>, <span class="math-container">$(U − B)_0 = 1.222$</span>. Determine the distance to the star.</p>
</blockquote>

<p>As <span class="math-container">$m_u - m_b ≠ (U-B)_0$</span>, I gathered that the distance modulus can't be used directly, since extinction is present. From the bolometric correction (BC), we can determine that the absolute visual magnitude <span class="math-container">$M_v = 8.33$</span>. </p>

<p>After that, I'm unsure of what to do; normally I think in these questions you can obtain the visual extinction <span class="math-container">$A_v = 3.0E_{B-V}$</span>, where <span class="math-container">$E_{B-V}$</span> is the color excess, calculated by <span class="math-container">$E_{B-V} = (m_b - m_v) - (B-V)_0$</span>. Then, the visual extinction can be added to the distance modulus equation to account for extinction in the visual band, and then we can easily obtain distance.</p>

<p>But, while we know <span class="math-container">$m_b$</span>, <span class="math-container">$m_v$</span>, and <span class="math-container">$M_v$</span>, we don't really have a way of obtaining <span class="math-container">$(B-V)_0$</span> to my knowledge, unless there's some way we can relate it to <span class="math-container">$(U-B)_0$</span>. Any help would be much appreciated!</p>

<observational-astronomy><apparent-magnitude><magnitude><absolute-magnitude><extinction>
Distance to star using color index
Alistair
# Distance to star using color index

(Asked by: username_0 on 2020-03-29)

I'm doing the following question:

> A star is observed with UBV magnitudes $m\_u = 16.31$, $m\_b = 14.52$,
> $m\_v = 13.76$. Spectral analysis gives $M\_{bol} = 7.31$, $BC = -1.02$, $(U − B)\_0 = 1.222$. Determine the distance to the star.

As $m\_u - m\_b ≠ (U-B)\_0$, I gathered that the distance modulus can't be used directly, since extinction is present. From the bolometric correction (BC), we can determine that the absolute visual magnitude $M\_v = 8.33$.

After that, I'm unsure of what to do; normally I think in these questions you can obtain the visual extinction $A\_v = 3.0E\_{B-V}$, where $E\_{B-V}$ is the color excess, calculated by $E\_{B-V} = (m\_b - m\_v) - (B-V)\_0$. Then, the visual extinction can be added to the distance modulus equation to account for extinction in the visual band, and then we can easily obtain distance.

But, while we know $m\_b$, $m\_v$, and $M\_v$, we don't really have a way of obtaining $(B-V)\_0$ to my knowledge, unless there's some way we can relate it to $(U-B)\_0$. Any help would be much appreciated!

**Tags:** observational-astronomy, apparent-magnitude, magnitude, absolute-magnitude, extinction


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## 1 answers

### Answer by username_1 on 2020-03-30. Score: 4 | Accepted answer

There is a relationship between $E(B-V)$ and the reddening in any other colour. The exact value depends on the type of dust, the extinction value itself and the intrinsic spectrum of the star (as does the 3.0 coefficient mentioned in your question).

However, for the purposes of estimation, the canonical relationship is $E(U-B) = 0.72 E(B-V)$ (e.g. [Pandey et al. 2003](https://www.aanda.org/articles/aa/full/2003/01/aa2516/aa2516.html)).

Thus you can calculate $E(U-B)$, then $E(B-V)$, then $A\_V$, then $V\_0$ and use this with $M\_V$ to get the distance.


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