Fusion Rate and Luminosity in Stellar Model

Question

In astrophysics textbooks one of the differential equations to solve in stellar model is $$\frac{dL}{dr}=4\pi r^2 \epsilon$$ where $L(r)$ and $\epsilon (r)$ are the luminosity and fusion rate per unit volume at $r$.

My question is why we can assume all energy generated by fusion goes to light? For example, what about the energy carried away by neutrinos? That amount is negligible? I couldn't find information about how much that amount is.

Answer 1

$L$ would have to include neutrinos unless the $\epsilon$ term is modified to exclude neutrino losses.

For a star like the Sun, about 2.3% of the fusion energy is lost via neutrinos (Bahcall 1979) and this is accounted for in stellar evolution models.