An Introduction to Modern Astrophysics · Problem 10.21

The Sun — Carroll & Ostlie

Physics — Astrophysics · main-sequence-hydrogen-burning-lifetimes

Problem

Estimate the hydrogen-burning lifetimes of stars near the lower and upper ends of the main sequence. The lower end of the main sequence occurs near

0.072\,\mathrm{M}_\odot

, with

\log_{10} T_e = 3.23

and

\log_{10}(L/L_\odot) = -4.3

. On the other hand, an

85\,\mathrm{M}_\odot

star near the upper end of the main sequence has an effective temperature and luminosity of

\log_{10} T_e = 4.705

and

\log_{10}(L/L_\odot) = 6.006

, respectively. Assume that the

0.072\,\mathrm{M}_\odot

star is entirely convective so that, through convective mixing, all of its hydrogen, rather than just the inner 10\%, becomes available for burning.