Question

The estimated lifetime of the Sun on the main sequence is ~ 1010 years. Calculate the main sequence lifetime of stars of masses (i) 100 MΘ and (ii) 5 MΘ.

Answer 1

An expression for the main sequence life-time is:

$$\frac{t_{MS}}{t_{Sun}}={\frac{M_{MS}}{M_{Sun}}}^{-2.5}$$

So, is we know relative star mass, life-time is estimated to be:

$$t_{MS}=t_{Sun}{\frac{M_{MS}}{M_{Sun}}}^{-2.5}$$

i)

$$t_{MS}=t_{Sun}{\frac{M_{MS}}{M_{Sun}}}^{-2.5}=10^{10}*{100}^{-2.5}=10^5 years$$

ii)

$$t_{MS}=t_{Sun}{\frac{M_{MS}}{M_{Sun}}}^{-2.5}=10^{10}*{5}^{-2.5}=1.8*10^8 years$$