<p>Measuring the (effective) temperature of a star is possible but difficult<span class="math-container">$^\dagger$</span>. It would normally require spectroscopy and a detailed model of the source of the spectrum for comparison.</p>
<p>Measuring the colour of a star is relatively easy - you measure the brightness through two coloured filters and take the flux ratio (and then turn it into a magnitude).</p>
<p>Unfortunately <em>there is no one-to-one mapping between colour and temperature</em>, so although the former is easier to measure it is much preferable to have a direct temperature estimate from a spectrum. That is because the relationship depends on the surface gravity of the star, the composition of the star, and most importantly, the amount of interstellar &quot;extinction&quot; towards the star, which will redden its colour.</p>
<p><span class="math-container">$\dagger$</span> Strictly speaking, to measure the effective temperature of a star in a model-independent way requires (i) a measurement of the flux from the star over a broad range of wavelengths; (ii) the distance to the star (using trigonometric parallax); (iii) a measurement of the star's radius, either from interferometry or in an eclipsing binary system. This is even more difficult and has been accomplished for only a few hundred stars in total.</p>

CC BY-SA 4.0
2022-10-14T09:16:04.083Z
2022-10-14T09:16:04.083Z
ProfRob
<p>You can't measure the temperature of a star.</p>
<p>What you can measure is the properties of the light coming from the star. One way to do this is to view the star in different coloured filters, and compare the brightness of the star.  This gives the colour index.</p>
<p>So the colour index is what is <em>actually</em> measured - and the temperature is deduced from that.</p>

CC BY-SA 4.0
2022-10-13T22:29:23.490Z
2022-10-13T22:29:23.490Z
James K
<p>So I'm learning about the colour-index currently and what is confusing me is why this is useful. The colour of a star is dependent on the temperature, so wouldn't astronomers have a natural idea of what colour a star would be based on its temperature, making the colour index useless? My thought is that perhaps it provides more information about the contents of the surface of the star than the temperature does, but once again wouldn't we automatically know this based on the temperature alone?</p>

CC BY-SA 4.0
2022-10-13T21:40:34.633Z
What do you think is easiest to measure? Is it the temperature? Or the colour?
Rory Alsop
CC BY-SA 4.0
2022-10-13T21:44:52.330Z
When you look at the Hertzsprung-Russell diagram in its form as Luminosity vs. Temperature, then how do you think those *physical* quantities are measured?
AtmosphericPrisonEscape
<color-index>
Why is the colour-index measurement used?
Jackson
# Why is the colour-index measurement used?

(Asked by: username_0 on 2022-10-13)

So I'm learning about the colour-index currently and what is confusing me is why this is useful. The colour of a star is dependent on the temperature, so wouldn't astronomers have a natural idea of what colour a star would be based on its temperature, making the colour index useless? My thought is that perhaps it provides more information about the contents of the surface of the star than the temperature does, but once again wouldn't we automatically know this based on the temperature alone?

**Tags:** color-index
> **Comments:**
> **username_1**: What do you think is easiest to measure? Is it the temperature? Or the colour?  
> **username_2**: When you look at the Hertzsprung-Russell diagram in its form as Luminosity vs. Temperature, then how do you think those *physical* quantities are measured?  

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## 2 answers

### Answer by username_4 on 2022-10-13. Score: 12 | Accepted answer

You can't measure the temperature of a star.

What you can measure is the properties of the light coming from the star. One way to do this is to view the star in different coloured filters, and compare the brightness of the star. This gives the colour index.

So the colour index is what is *actually* measured - and the temperature is deduced from that.


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### Answer by username_3 on 2022-10-14. Score: 6

Measuring the (effective) temperature of a star is possible but difficult$^\dagger$. It would normally require spectroscopy and a detailed model of the source of the spectrum for comparison.

Measuring the colour of a star is relatively easy - you measure the brightness through two coloured filters and take the flux ratio (and then turn it into a magnitude).

Unfortunately *there is no one-to-one mapping between colour and temperature*, so although the former is easier to measure it is much preferable to have a direct temperature estimate from a spectrum. That is because the relationship depends on the surface gravity of the star, the composition of the star, and most importantly, the amount of interstellar "extinction" towards the star, which will redden its colour.

$\dagger$ Strictly speaking, to measure the effective temperature of a star in a model-independent way requires (i) a measurement of the flux from the star over a broad range of wavelengths; (ii) the distance to the star (using trigonometric parallax); (iii) a measurement of the star's radius, either from interferometry or in an eclipsing binary system. This is even more difficult and has been accomplished for only a few hundred stars in total.


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