Collapse in Self-gravitating Turbulent Fluids

Daniel W. Murray, Philip Chang, Norman W. Murray, John Pittman

Published 2015-09-19Version 1

We perform simulations of star formation in self-gravitating turbulently driven gas. We find that star formation is not a self-similar process; two length scales enter, the radius of the rotationally supported disk $r_d$, and the radius $r_*$ of the sphere of influence of the nascent star, where the enclosed gas mass exceeds the stellar mass. The character of the flow changes at these two scales. We do not see any examples of inside-out collapse. Rather, the accretion of mass starts at large scales where we see large infall velocities $|u_r(r)| \approx (1/3) v_{ff} \sim (1/3)\sqrt{GM(r)/r}\gtrsim c_s$ out to $r \sim 1 \, \rm{pc}$ hundreds of thousands of years before a star forms. The density evolves to a fixed attractor, $\rho(r,t ) \rightarrow \rho(r)$, for $r_d<r<r_*$; mass flows through this structure onto a sporadically gravitationally unstable disk, and from thence onto the star. In the bulk of the molecular cloud, we find that the turbulent velocity $v_T \sim r^p$ with $p \sim 0.5$, in agreement with Larson's size-linewidth relation. But in the vicinity of star forming regions we find $ p \sim 0.2-0.3$, as seen in observations of massive star forming regions. For $r<r_*$, $v_T$ increases inward, with $p=-1/2$, i.e., it increases with increasing density, as seen in observations of massive star forming regions. The acceleration due to the turbulent pressure gradient is comparable to that due to gravity at all $r>r_d$ and rotational support becomes important for $r<r_d$. As a result, the infall velocity is substantially smaller than the free fall velocity; for $r_d<r<r_*$, we find $|u_r| \approx (1/3) v_{ff}$. Finally, we find the forming stars acquire mass from much larger radii than a typical hydrostatic core and the star forming efficiency is nonlinear with time, i.e., $M_*(t)\sim t^2$.