<p>Yes, there are different relationships between effective temperatures and different colours. That is because the various filters sample different wavelength regions of the stellar spectrum.</p>
<p>You can derive your own formulae (by fitting some suitable polynomial relationship between <span class="math-container">$T_{\rm eff}$</span> and colour), or better just interpolate, from the authoritative and widely-used table supplied by <a href="https://www.pas.rochester.edu/%7Eemamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt" rel="nofollow noreferrer">Pecaut &amp; Mamajek</a>.</p>
<p>Which colour(s) you should use is entirely up to you and the dataset you have. By looking at the table you can see that some colours change with <span class="math-container">$T_{\rm eff}$</span> more quickly than others in certain <span class="math-container">$T_{\rm eff}$</span> ranges.</p>

CC BY-SA 4.0
2023-08-09T17:24:07.287Z
Thank-you. I've looked at the table and the links therein, but I've not been able to see anything that mentions when each range (B-V, U-B, V-R, R-I) should be used. Is it more dependent on availability than the spectral type? 
As for interpolation, I'm afraid I'm not good at all with maths. I probably should have specified that.
Kazon
CC BY-SA 4.0
2023-08-09T07:56:02.613Z
2023-08-09T18:40:25.953Z
2023-08-09T18:40:25.953Z
ProfRob
<p>I'm already familiar with using the difference in B and V magnitudes to calculate temperature, but <a href="https://en.wikipedia.org/wiki/Color_index" rel="noreferrer">Wikipedia</a> (trustworthy source, I know) mentions that U-B, V-R, and R-I are also used depending on colour temperature. Are there different formulae for these, and what constitutes a cooler/midrange/hotter star? I tried using a star's R and I magnitudes in the calculator I made for the standard B-V equation and there's a clear difference.</p>

<star><spectroscopy>
Star surface temperature?
Kazon
# Star surface temperature?

(Asked by: username_0 on 2023-08-09)

I'm already familiar with using the difference in B and V magnitudes to calculate temperature, but [Wikipedia](https://en.wikipedia.org/wiki/Color_index) (trustworthy source, I know) mentions that U-B, V-R, and R-I are also used depending on colour temperature. Are there different formulae for these, and what constitutes a cooler/midrange/hotter star? I tried using a star's R and I magnitudes in the calculator I made for the standard B-V equation and there's a clear difference.

**Tags:** star, spectroscopy

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## 1 answers

### Answer by username_1 on 2023-08-09. Score: 9

Yes, there are different relationships between effective temperatures and different colours. That is because the various filters sample different wavelength regions of the stellar spectrum.

You can derive your own formulae (by fitting some suitable polynomial relationship between $T\_{\rm eff}$ and colour), or better just interpolate, from the authoritative and widely-used table supplied by [Pecaut & Mamajek](https://www.pas.rochester.edu/%7Eemamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt).

Which colour(s) you should use is entirely up to you and the dataset you have. By looking at the table you can see that some colours change with $T\_{\rm eff}$ more quickly than others in certain $T\_{\rm eff}$ ranges.

> **Comments:**
> **username_0**: Thank-you. I've looked at the table and the links therein, but I've not been able to see anything that mentions when each range (B-V, U-B, V-R, R-I) should be used. Is it more dependent on availability than the spectral type?  As for interpolation, I'm afraid I'm not good at all with maths. I probably should have specified that.  

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