1. Values shown in the image were obtained from Carlos A. Bertulani, Nuclei in the Cosmos, 2013. The values are subject to revision, of course, with improved calculations, but are unlikely to change very much.

  2. Yours truly thinks these are main-sequence lifetimes. However, since the post-main-sequence phase of stellar evolution is relatively brief (∼ 10 % ??? of the main-sequence lifetime), there is NO great difference between main-sequence lifetime and total nuclear burning lifetime.

  3. The most obvious conclusion from the image is that as mass increases, stellar lifetime decreases rapidly. The more massive the star, the more efficiently is burns its nuclear fuel.

  4. The most massive K-type main-sequence stars have mass ∼ 0.8 M_☉ and have stellar lifetime of ∼ 15 Gyr.

    Now ∼ 15 Gyr is greater than age of the observable universe = 13.797(23) Gyr (Planck 2018) (i.e, the time since Big Bang) according to the Λ-CDM model (which fits almost all observations very well circa 2020).

    In fact, all stars ≤ ∼ 0.9 M_☉ probably have main-sequence lifetime longer than ∼ 14 Gyr.???

    So such stars have never left the main sequence. All the stars ≤ ∼ 0.9 M_☉ ever formed are still around, relics of earlier generations of star formation. We identify these old stars by their low metalliticity.

    The post-main-sequence phase of stars ≤ ∼ 0.9 M_☉ is entirely theoretical since there are none in that phase to observe.

    The image shows that stars of 0.1 M_☉ live more than 10**3 Gyr. Those stars will be around a long time.

  5. The Sun is a middling mass star (of exactly 1 M_☉) and will live about 10 Gyr on the main sequence and will live as a nuclear burning star (i.e., a post-main-sequence star) for about 1.5 Gyr thereafter (Wikipedia: Sun: After core hydrogen exhaustion). The Sun's current age ≅ 4.6 Gyr, and so it has ≅ 5.4 Gyr left on the main sequence (Wikipedia: Sun: After core hydrogen exhaustion). These values are, of course, subject to revision.

  6. Stars with initial mass ≥ ∼ 8 M_☉ (the more massive B-type main-sequence stars and O-type main-sequence stars) explode as core-collapse supernovae after lifetimes of ≥ ∼ 30 Myr.???

We can give a derivation of an approximate main sequence lifetime formula making use of some assumed results:

  1. First, the hydrogen burning rate (i.e., rate of burning to helium-4 (He-4)) is easily found.

  2. We know the atomic masses of hydrogen (H, Z=1) and helium-4 (He-4, Z=2): respectively, 1.008 (fiducial value) and 4.002602 in atomic mass units (AMU).

    When 4 hydrogen nuclei are hydrogen burned to 1 helium-4 (He-4), there is a relative atomic mass loss from reactants to product of 0.007291 = 0.7291 % ≅ 0.7 %.

  3. Recall conservation of energy principle. So the rest mass is lost by the reactants is converted into some other form of energy. In fact, it is converted heat energy which can be calculated using E=mc**2.


     E = mc**2, and thus 1 kilogram of rest mass in energy terms is
       1 kg * (3*10**8 m/s)**2 = 9*10**16 joules
       = about 2.5*10**10 KW-hours  (Note 1 kW-hr = 3.6*10**6 J )
       = the explosion energy yield of about 20 megatons of TNT
            ( 1 megaton TNT = about 4*10**15 J )  .  

  4. Now let's find the hydrogen burning rate in fiducial values:
      R = (rate of rest mass converted to heat energy)*[(H mass burnt)/(H mass converted)]
        = (L/c**2)*κ ,  where κ = [(H mass burnt)/(H mass converted)] = (1/0.007291)
        = (L_☉/c**2)*(L/L_☉)(1 M_☉ / 1.98855*10**30 kg)*(3.1557600*10**16 s / 1 Gyr)*κ
        = 9.270*10**(-3)*(L/L_☉)*(M_☉/Gyr)  .  
    We now assume the approximate mass-luminosity relation known from a combination of observations and stellar structure modeling: L = L_☉*(M/M_☉)**3.5 which holds approximately for the stellar mass 0.1--50 M_☉ (see Wikipedia: Main sequence: Lifetime, Wikipedia: Mass-luminosity relation). This gives us
      R = 9.270*10**(-3)*[(M/M_☉)**3.5]*(M_☉/Gyr)  .  

  5. Next, assuming luminosity is constant on the main sequence (which is approximately true), the main sequence lifetime formula is
      t_lifetime = fM/R = (10 Gyr)*(f/f_☉)*[(M_☉/M)**2.5] 
    in general where we have rounded the coefficient from 10.78 to 10 since the 0.78 quantity is insignificant to the accuracy we are working at. Note f is the general hydrogen burning efficiency factor and f_☉ = 0.1 is a fiducial value for the Sun NOT an exact value. Thus,
      t_lifetime = fM/R = (10 Gyr)*(f/f_☉)*[(M/M_☉)**(-2.5)] in general  ,
                        = 10 Gyr for the Sun  ,
                        ≅ 3000 Gyr for a 0.1 M_☉ star assuming f ≅ 0.1  ,
                        ≅ 3*10**(-2) Gyr = 30 Myr for a 10 M_☉ star assuming f ≅ 0.1  . 

  6. Note the hydrogen burning rate is for the hydrogen mass burnt. The rate of rest mass converted to heat energy is smaller by a factor of the relative atomic mass loss 0.007291.

    Also note that if an initially pure hydrogen star converted all its hydrogen to helium-4 (He-4), it would decrease in mass by the same factor 0.007291.

  7. Since the main-sequence lifetime of a star is overwhelmingly its longest phase as a nuclear burning object, our approximate main sequence lifetime formula applies to the whole nuclear burning lifetime of stars as well as the main-sequence lifetime.

  8. Using our main sequence lifetime formula, we have calculated the values in Table: Approximate Main-Sequence Lifetimes.
      Table:  Approximate Main-Sequence Lifetimes
          M                       t
        (M_☉)                (Gyr or Myr)
          0.1                 3,200 Gyr
          0.5                    57 Gyr
          0.88                   13.8 Gyr ≅ Gyr the age of the observable universe
          0.9                    13 Gyr
          1.0                    10 Gyr ≅ lifetime of a G2 V star (e.g., the Sun)
          1.5                     3.6 Gyr
          3                     640 Myr
          5                     180 Myr
          8                      55 Myr
         10                      32 Myr
         20                       5.6 Myr
         30                       2.0 Myr
         60                       0.36 Myr
  9. Our approximate stellar lifetimes in the above Table: Approximate Main-Sequence Lifetimes are NOT so bad as we can see by comparison to the more accurate results given in the image. However, NOT surprisingly our results become poorer as stellar mass increases well above 1 solar mass. They are also expected to be poorer as stellar mass decreases well below 1 solar mass, but the accurate results in the image do NOT give values for comparison in this case.