On the role of gravity, turbulence, and the magnetic field in angular momentum transfer within molecular clouds

TL;DR

This work investigates the origin of the observed $j \propto R^{3/2}$ scaling in molecular clouds by systematically turning on turbulence, gravity, and magnetic fields in SPH simulations. By defining dense clumps across six density thresholds and analyzing both full and reduced (filament-excluded) samples, the authors show that gravity expands the dynamic range of clump sizes, while turbulence sets the angular-momentum magnitude and redistributes it via hydrodynamic torques, with magnetic fields suppressing turbulence and reducing scatter. The torques measured—predominantly hydrodynamic, followed by gravitational, then magnetic and pressure-gradient—support a turbulence-driven angular-momentum transfer mechanism enhanced by gravity, and they reveal that filamentary geometry can bias $j$ measurements unless accounted for. Gravity appears essential for hub-filament formation, and the inclusion of magnetic fields can align the full clump population with the observed $j$-$R$ relation by reducing turbulent fragmentation, though filaments complicate the interpretation of $j$ in observational-like measurements. Overall, the results suggest a two-stage picture: gravity enables clump growth and filamentary structure, while turbulence and inertial motions redistribute angular momentum, with magnetic fields modulating the efficiency of this transfer. $j$-$\sigma$ relations and $j/\Sigma$ trends broadly reflect this interplay, though deviations in filamentary regimes indicate the need for axis-based angular-momentum diagnostics in elongated structures.

Abstract

Observations of molecular structures on scales of $\sim 0.1-50$ pc show that the specific angular momentum ($j$) scales with radius ($R$) as $j\sim R^{3/2}$. We study the effects of turbulence, gravity, and the magnetic field in shaping this scaling, by measuring clump size and specific angular momentum in three SPH simulations of the formation of giant molecular clouds, progressively adding these three ingredients. In each simulation, we define ``full'' and ``reduced'' clump samples, the latter restricted to aspect ratios $A<3$. We find that, in the non-magnetic runs, elongated clumps deviate the most from the \jR\ relation, which is best reproduced by the reduced sample in the gravity+turbulence run. In the purely hydrodynamic case, no dense elongated structures form, suggesting that turbulence alone is insufficient to generate dense filaments, although clumps have $j$ magnitudes consistent with observations. In the gravity+turbulence+magnetic field run, most of the clumps are filamentary, yet the full sample appears to follow the observed \jR\ relation. This result, rather than being a real trend, could be the combination of the increase in $j$ by the filamentary geometry, and its reduction by turbulence inhibition by the magnetic field. Finally, we measure the gravitational, magnetic, pressure-gradient, and hydrodynamic torques (which involve turbulent viscosity) in our clump samples. We find that, in magnitude, the hydrodynamic torques tend to be larger than the rest. This result is consistent with our previous work, where we proposed that gravity drives cloud formation and contraction, while turbulence redistributes angular momentum through fluid-parcel exchanges.

Figures (13)

• Figure 1: Evolution of runs HD3 ( top panels), HDG3 ( middle panels) and MHDG3 ( bottom panels). The columns show increasing times from left to right, as indicated by the labels at the top. The color bar shows the column density along the z-axis of the entire numerical box, with the same range of values for the three simulations. Sinks are represented by white dots. Sink formation is noticeably delayed in the magnetic simulation and completely nonexistent in the simulation without gravity. The HD3 and HDG3 simulations appear significantly more fragmented than MHDG3, which looks smoother and more filamentary.
• Figure 2: Representative round (left column) and elongated (right column) clumps of each numerical sample in the HD3 (top row), HDG3 (middle row) and MHDG3 (bottom row) simulations. The color code represents the density in units of cm${}^{-3}$. The most elongated clumps are recovered in the HDG3 and MHDG3 simulations, the latter having the most defined and narrow filaments. Densities around $10^5\, {\rm cm}^{-3}$ are only reached in the HDG3 and MHDG3 simulations.
• Figure 3: Left column: plots of the $j$-$R$ relation for the three full numerical clump samples corresponding to each simulation. Right column: plots of the $j$-$R$ relation for the three reduced numerical clump samples, i.e., after removing structures with aspect ratios $>3$. The density thresholds is represented by the color code. The solid black line represents the fitting to the observational sample compiled in Figure 1 of Arroyo-Chavez.Vazquez-Semadeni2022, while the dashed red line represents the fitting to the numerical clump samples for the three simulations. The shaded gray region represents a variation in fitting parameters of 1$\sigma$. The $j$-$R$ relation is most closely reproduced for the reduced sample of the HDG3 simulation.
• Figure 4: Histogram of aspect ratios obtained as the ratio between the largest and shorted principal axis of inertia for the full sample of clumps in simulations HD3, HDG3, and MHDG3. Color represents the density threshold used to define the clumps samples, following a similar color patter as in Figure \ref{['fig:com_jR']}.
• Figure 5: Left column: $j$-$R$ relation for the full samples in each simulation (as in the left column of Figure \ref{['fig:com_jR']}), where the color now represents the value of the 3D velocity dispersion, $\sigma_{v}$. Middle column: $j$ as a function of the velocity dispersion, $\sigma_{v}$, for the full samples. Right column: same as in the middle column for the reduced samples. Clumps with larger $j$ values that deviate further from the observational trend in the HD3 and HDG3 simulations, are those with a higher velocity dispersion, and at the same time, are the structures with larger aspect ratios. A clear correlation in the $j$-$\sigma_{v}$ plots can be observed for all three simulations, which also seems to have a dependence on the density threshold, and the slope becomes steeper as gravity and magnetic field are added.