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According to the Hertzsprung-Russell diagram, they would roughly have the same temperature, but I've read in bibliography that the surface temperature of the red giant is about 5000K and the one of the red dwarf can be down to 2000K. Which one would have the higher effective temperature?

In case they had the same. Would the color of a star define its effective temperature, regardless its size?

Many thanks!

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It is more the case that the effective temperature defines the colour, and not the other way round.

At a temperature of 5000K, the star would be a K2 and the colour would be described as "orange". Giants like this, such as Pollox, might get described as "red giants" (as the have formed in the same way as red, M class, giants) but you could argue that that is a misnomer.

On the other hand, an orange K0 dwarf, such as Sigma Draconis, is hotter than an M class giant like Betelgeuse. Betelgeuse has an effective temperature of about 3500K.

So there are dwarf stars that have a higher temperature than giants, and there are giants that are hotter than dwarves. The temperature is the main determiner of the colour.

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    $\begingroup$ I understand it now. Thanks. $\endgroup$
    – user9867
    Dec 16, 2022 at 20:17

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