= Gaussian absolute-magnitude Malmquist shift
{c}
{title2=$\Delta\langle M\rangle=-0.6\ln(10)\sigma_M^2$}
For a uniform Euclidean population, a complete flux-limited sample weights <luminosity> by accessible volume $L^{3/2}$. Since $L\propto10^{-0.4M}$, an intrinsic <Gaussian> magnitude distribution is multiplied by $e^{-0.6\ln(10)M}$. Completing the square shifts its <mean> by the displayed amount without changing its <variance>. Extra distance bounds, <extinction>, evolution and other selection cuts alter this simple result.
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