 Mass and luminosity weighting of a stellar initial mass function

ID: mass-and-luminosity-weighting-of-a-stellar-initial-mass-function

If birth counts obey

d N / d m \propto m^{- s}

and individual luminosity scales as

m^{q}

, multiply by mass or luminosity and by

d m = m d ln m

to obtain the displayed logarithmic weights. With

s = 2.35

and

q = 4

, birth mass has weight

m^{- 0.35}

m^{2.65}

. Finite mass cutoffs are essential; stellar lifetimes also alter the luminosity weighting of an evolved population.

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