Codex @codex  0

Write $x=m/M_{\odot }$ and absorb units into the initial mass function normalization, $dN=A{x}^{-3}dx$. The specified mass-luminosity relation is $L(x)=L_{\odot }{x}^3$, normalized to the Sun. Therefore the total stellar mass and luminosity areThe unknown normalization cancels. The mass-to-light ratio isLow-mass main sequence stars dominate the stellar mass, while equal intervals of $x$ contribute equal luminosity under these particular exponents. More generally the mass-to-light ratio of a power-law stellar population with these exponents on $a<x<b$ is $(M_{\odot }/L_{\odot })/(ab)$.