Caption: A cartoon of the mass-luminosity relation for main-sequence stars. It is NOT quantitatively accurate.

Features:

1. Note that luminosity increases approximately as a power of stellar mass:
   1. L/L_☉ ≅ 0.23*(M/M_☉)**2.3
             for M < 0.43 M_☉.
   2. L/L_☉ ≅ (M/M_☉)**4
             for M ∈[0.43 M_☉,2 M_☉].
             Probably the range for most stars.
   3. L/L_☉ ≅ 1.4*(M/M_☉)**3.5
             for M ∈[2 M_☉, 55 M_☉].
   4. L/L_☉ ≅ 3200*(M/M_☉)**1
             for M > 55 M_☉.
   (Wikipedia: Mass-luminosity relation).

2. The plot is for the M ∈[0.43 M_☉,2 M_☉] case: i.e., L/L_☉ ≅ (M/M_☉)**4.

   For this case, if stellar mass increases by 2, luminosity increases by 16.

3. The best representative case for the whole main sequence is probably the formula L/L_☉ ≅ 1.4*(M/M_☉)**3.5.

4. An important consequence of the mass-luminosity relation is that main-sequence stellar lifetime decreases rapidly with stellar mass even though the amount of hydrogen fuel increases with stellar mass. The more massive the star, the more efficient its hydrogen burning and this more than negates having more hydrogen fuel to use.

5. To be quantitative, we can assume that the amount of hydrogen fuel is proportional to stellar mass M. In which case:

          t_lifetime ∝∼  M/L ∝∼ M**(-2.5) = 1/M**2.5 

   assuming the representative case L/L_☉ ≅ 1.4*(M/M_☉)**3.5.

   From this formula, if stellar mass increases by 10, then main-sequence stellar lifetime decreases by 10**2.5 ≅ 300. By this result, a star of 10 M_☉ would have a main-sequence stellar lifetime of 1/300 that of the Sun. Thus its main-sequence stellar lifetime would be 10 Gyr/300 = 10**4 Myr/300 = 30 Myr which is roughly correct (see file star_lifetimes.html).