<p>They are mostly empirical. Found by measuring the <span class="math-container">$B-V$</span> for stars of known <span class="math-container">$T_{\rm eff}$</span> (which are in turn measured by knowing the luminosity and radius of a star, and this is only known for a small number of stars). The relationships also depend on stellar surface gravity and composition.</p>

<p>An alternative approach is to derive "synthetic" relationships by folding spectra calculated from model atmospheres through the appropriate filter responses.</p>

CC BY-SA 4.0
2019-12-07T19:08:52.233Z
2019-12-07T19:08:52.233Z
ProfRob
<p>Is there an exact relationship between color indices and temperature? 
I have seen some numerical formulas relating B - V color index to temperature, of the form <span class="math-container">$B - V = a_1 + \frac{a_2}{T} $</span> . </p>

<p>I am wondering is there any way to derive these formulas or are they completely empirical?  </p>

<observational-astronomy><temperature><hubble-telescope><photometry>
Relationship between Color Index and Temperature
Hrsht
# Relationship between Color Index and Temperature

(Asked by: username_0 on 2019-12-07)

Is there an exact relationship between color indices and temperature?
I have seen some numerical formulas relating B - V color index to temperature, of the form $B - V = a\_1 + \frac{a\_2}{T} $ .

I am wondering is there any way to derive these formulas or are they completely empirical?

**Tags:** observational-astronomy, temperature, hubble-telescope, photometry


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## 1 answers

### Answer by username_1 on 2019-12-07. Score: 3 | Accepted answer

They are mostly empirical. Found by measuring the $B-V$ for stars of known $T\_{\rm eff}$ (which are in turn measured by knowing the luminosity and radius of a star, and this is only known for a small number of stars). The relationships also depend on stellar surface gravity and composition.

An alternative approach is to derive "synthetic" relationships by folding spectra calculated from model atmospheres through the appropriate filter responses.


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