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"Modelling the evolution of solar-mass stars with a range of metallicities
and P.M. Gore "
They give different results, they cannot all be right, and might all be wrong.
D.O. Gough gave this formula for the sun
L = Lsun current = [1/[1- 0.4(1- t/4.6 billion years)]
which gives a luminosity of about 0.7 4.6 billion years ago, 1 now, and
a luminosity of about 1.9 after 10 billion years.
As was mentioned before, different mass stars process nuclear fuel differently, so there's no one relationship, but
for stars between 0.75 Mass sun and 2 Mass sun, luminosity is roughly proportional to the 4.8 power of mass for stars of same metallicity, and ths formula should work for such stars, after adjusting for expected lifetime.
For example, a star with an expcted lifttime of 20 bllion years, you'd plug in
two times 4.6 billion for the denominator in Gough's formula. For a larger star you might get a lifetime of 5 billion years,in which case you'd substitute 2.3 in plase of the 4.6 in Gough's formula.