Mass absorption coefficient (${\kappa }_{\nu }$)

The mass absorption coefficient is absorbing cross-section per unit mass. For identical spherical dust grains of radius $a$, mass $m_d$, and absorption efficiency $Q_{\nu }$, it is ${\kappa }_{\nu }=\pi a^2{Q}_{\nu }/m_d$.

For isothermal optically thin dust at distance $D$, its measured spectral flux density determines its mass through $M_d=F_{\nu }{D}^2/[{\kappa }_{\nu }{B}_{\nu }(T)]$. Temperature and opacity uncertainty commonly dominate the inferred mass uncertainty.