Solution (source code)

= Solution

The result is in the broad range expected for an old, relatively faint <stellar population>, but is high compared with many observed stellar <mass-to-light ratios> of a few solar units in optical bands. The comparison must specify the band and whether the measured <mass> includes <dark matter>: for example, https://arxiv.org/abs/astro-ph/0505042[early-type galaxy dynamical measurements] find an $I$-band normalization near $3.8$ solar units at <velocity dispersion> $200\,\mathrm{km\,s^{-1}}$, including a contribution from <dark matter>. That is an illustrative observational comparison, not a direct equality with a bolometric stellar calculation.

For an old <stellar population>, an upper surviving <main sequence> mass near $M_\odot$ is reasonable because more massive stars have shorter lifetimes; low-mass <main sequence> stars also contain much of the surviving stellar <mass>. However, <red giants> and other evolved stars can contribute a large fraction of the light despite their small numbers, so omitting them generally makes this calculated <mass-to-light ratio> too large. Omitting <stellar remnants> has the opposite effect on the inferred <mass>, and a single cubic <mass-luminosity relation> is only approximate across the stated range. Finally, a single $m^{-3}$ <initial mass function> down to $0.1M_\odot$ is steeper and more low-mass-heavy than commonly adopted distributions, which flatten at low <mass>. \b[Ten solar units is a useful toy-model estimate, not a precision stellar-population prediction.]