= Euclidean magnitude-limited source count
For identical <luminosities>, uniform spatial density, and no extinction, the <inverse-square law> gives limiting distance $r\propto F_{\min}^{-1/2}$. The number in the enclosed volume is therefore $N\propto F_{\min}^{-3/2}\propto10^{0.6m_{\lim}}$. Increasing the sample by a factor $b$ needs a magnitude-limit increase $(5/3)\log_{10}b$. This relation need not hold with evolving source populations, dust, or cosmological distance effects.
Back to article page
