The opacity limit

Understand

The opacity limit is an important concept in star formation: isothermal collapse cannot proceed without limit, because eventually cooling radiation is trapped and the temperature rises quasi-adiabatically, setting a minimum Jeans mass $M_{\rm J}^{\rm min}$.

• Various works have considered this scenario and derived expressions for $M_{\rm J}^{\rm min}$, generally $\sim 10^{-3}-10^{-2}M_\odot$ in normal star-forming conditions, but with conflicting results about the scaling with ambient conditions and material properties.
• We derive expressions for the thermal evolution of dust-cooled collapsing gas clumps in various limiting cases, given a general ambient radiation field ($u_{\rm rad}$, $T_{\rm rad}$) and a general power-law dust opacity law $\sigma_{\rm d} = A_{\rm d} T^{\beta}$.
• By accounting for temperature evolution self-consistently we rule out a previously-proposed regime in which the adiabatic transition occurs while the core is still optically-thin.