Transport-driven super-Jeans fragmentation in dynamical star-forming regions

The Jeans criterion is one cornerstone in our understanding of gravitational fragmentation. A critical limitation of the Jeans criterion is that the background density is assumed to be a constant, which is often not true in dynamic conditions such as star-forming regions. For example, during the formation phase of the high-density gas filaments in a molecular cloud, a density increase rate $\dot{\rho }$ implies a mass accumulation time of $t_{\mathrm{a}\mathrm{c}\mathrm{c}}=\rho \mathrm{/}\dot{\rho }=-\rho (\mathrm{\nabla }\cdot (\rho \vec{v}){)}^{-1}$. The system is non-stationary when the mass accumulation time becomes comparable to the free-fall time $t_{\mathrm{f}\mathrm{f}}=1\mathrm{/}\sqrt{G\rho }$. We study fragmentation in non-stationary settings, and find that accretion can significantly increase in the characteristic mass of gravitational fragmentation ( ${\lambda }_{\mathrm{J}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{s},\mathrm{a}\mathrm{a}\mathrm{c}}={\lambda }_{\mathrm{J}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{s}}(1+t_{\mathrm{f}\mathrm{f}}\mathrm{/}{t}_{\mathrm{a}\mathrm{c}\mathrm{c}}{)}^{1\mathrm{/}3}$, $m_{\mathrm{J}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{s},\mathrm{a}\mathrm{c}\mathrm{c}}=m_{\mathrm{J}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{s}}(1+t_{\mathrm{f}\mathrm{f}}\mathrm{/}{t}_{\mathrm{a}\mathrm{c}\mathrm{c}})$). In massive star-forming regions, this mechanism of transport-driven super-jeans fragmentation can contribute to the formation of massive stars by causing order-of-magnitude increases in the mass of the fragments.