What is the basic physical model relationship for estimating main sequence lifetime ($t$)?
Answer
t is proportional to Mass divided by Luminosity ($t propto M/L$)
The foundational physical model used to estimate a star's main sequence lifetime ($t$) is derived from a simple ratio: the amount of available fuel divided by the rate at which that fuel is consumed. Since the amount of fuel available (primarily hydrogen) is generally proportional to the star's initial mass ($M$), and the rate of consumption is determined by its luminosity ($L$), the relationship simplifies mathematically to $t$ being proportional to the ratio of mass over luminosity, or $t propto M/L$. Because luminosity scales so steeply with mass ($L propto M^{3.5}$), this ratio leads to the drastic lifetime differences observed across the stellar spectrum.
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