I am really confused on how to estimate the luminosity of a made-up star through its lifetime, like say a star with the mass of 0.902 suns, how would I find the luminosity of it say, 6.5 billion years into its life? Or when it's in its red giant phase? What's the max luminosity it will reach in both red giant phases, and how would I calculate that? I've looked it up everywhere and I cannot get a solid answer, so I decided to come and ask here. I really like making up star systems evolution and finding the luminosity over the millions to billions of years of its life have always been really frustrating. I hope y'all can answer my question to help me out a little. Thanks! - some random guy
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2$\begingroup$ You might be interested in this Worldbuilding.SE question and answer: What sets of stellar models are freely available for reference when worldbuilding? Generally, the idea if you don't want to run physical simulations yourself is to look up a similar mass/metallicity/age combination in a big table made by someone who did. $\endgroup$– parasoupCommented Dec 2 at 6:18
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$\begingroup$ There is probably some empirical formula to this, but I am not so sure. $\endgroup$– Polaris5744Commented Dec 2 at 23:21
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$\begingroup$ Can you say what you mean by a 'made-up' star, please? Is that something fictional, or what? $\endgroup$– Robbie GoodwinCommented Dec 3 at 0:21
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$\begingroup$ Just a random Zero-Age star. $\endgroup$– Sayon MearesCommented Dec 3 at 3:19
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Since age is not a direct observable for a star (and in most cases, neither is mass) you would have to look up your answers using evolutionary tracks from a stellar model. In principle, the answer may also depend on the initial chemical composition of the star and its rotation rate. The maximum luminosity of a red giant may also depend on it mass loss rate.
There are lots and lots of publicly available stellar evolution tracks. For example the PARSEC or Geneva models.
A possible empirical alternative is just to use observations of star clusters of known age. Since these contain stars at a range of masses then you get an observational measurement of their luminosity (usually in a restricted wavelength band). The trick then is to also estimate the mass of these stars, which can be done from their colours and $T_{\rm eff}$ for main sequence stars or is just a little higher than the main sequence turn off mass for giants.
