If luminosity is proportional to M^3.5, how does the main sequence lifespan ( au_MS) scale with mass (M)?

Answer

au_MS proportional M^{-2.5}

Since lifespan is inversely related to luminosity (the consumption rate) and directly related to available fuel (mass), the relationship simplifies to a sharp inverse correlation with mass raised to the power of 2.5.

If luminosity is proportional to M^3.5, how does the main sequence lifespan (	au_MS) scale with mass (M)?
astronomystarmain-sequencemasslifetime