Introduction to Cosmology Ryden · Problem 9.3

Nucleosynthesis and the Early Universe

Physics — Astrophysics · stellar-helium-production-galaxy

Problem

The total luminosity of the stars in our galaxy is L≈3×1010 L⊙L \approx 3 \times 10^{10}\,L_\odot. Suppose that the luminosity of our galaxy has been constant for the past 10 Gyr. How much energy has our galaxy emitted in the form of starlight during that time? Most stars are powered by the fusion of H into 4^4He, with the release of 28.4 MeV for every helium nucleus formed. How many helium nuclei have been created within stars in our galaxy over the course of the past 10 Gyr, assuming that the fusion of H into 4^4He is the only significant energy source? If the baryonic mass of our galaxy is M≈1011 M⊙M \approx 10^{11}\,M_\odot, by what amount has the helium fraction YY of our galaxy been increased over its primordial value Y4=0.24Y_4 = 0.24?
Intuitive explanation

The key is connecting a galaxy's total light output over time to the nuclear fuel it must have burned. You'll convert luminosity and time into total energy radiated, then use the energy per helium nucleus to count how many fusion reactions occurred. Finally, compare that helium mass to the galaxy's total baryonic mass to find how much the helium fraction has grown from its primordial value. This ties together stellar evolution, nuclear physics, and galactic composition.

Intuitive explanation

The key is connecting a galaxy's total light output over time to the nuclear fuel it must have burned. You'll convert luminosity and time into total energy radiated, then use the energy per helium nucleus to count how many fusion reactions occurred. Finally, compare that helium mass to the galaxy's total baryonic mass to find how much the helium fraction has grown from its primordial value. This ties together stellar evolution, nuclear physics, and galactic composition.

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