Question

The first major star formation in the universe occurred in “proto-galaxies” soon after the Big Bang, ∼13 billion years ago. Could any of those stars still be surviving on the Main Sequence today, i.e., still burning H into He in their cores? If yes, approximately what range of Main Sequence spectral types and stellar masses should still be surviving? Express the stellar masses relative to the Sun’s mass. Hint: In class we noted that stellar lifetimes scale with mass due to the luminosities scaling with mass roughly as L ∝ M3.5 . Also note that the lifetime of the Sun is t ∼ 1010 years. Refer to Appendix G in your text for information on the masses and luminosities of stars with different spectral types.

Answer 1

The lifetime t is proportional to M/L.

M = mass, L =luminosity.

and L ∝ M^3.5

So,

Hence we for two stars we can write

Let M₁ = M_o (mass of sun) and t₁ = 10¹⁰ yrs (lifetime of sun)

To find critical mass below which star has a lifetime greater than the age of universe put t₂=13x10⁹ yrs (age of the universe).

So

So stars from early universe having a mass less than 0.9M_o still be surviving in the main sequence today.