How do velocity structure functions trace gas dynamics in simulated molecular clouds?

Abstract

Context. Supersonic disordered flows accompany the formation and evolution of molecular clouds (MCs). It has been argued that this is turbulence that can support against gravitational collapse and form hierarchical sub-structures. Aims. We investigate the time evolution of simulated MCs to investigate: What physical process dominates the driving of turbulent flows? How can these flows be characterised? Are they consistent with uniform turbulence or gravitational collapse? Do the simulated flows agree with observations? Methods. We analyse three MCs that have formed self-consistently within kiloparsec-scale numerical simulations of the interstellar medium (ISM). The simulated ISM evolves under the influence of physical processes including self-gravity, stratification, magnetic fields, supernova-driven turbulence, and radiative heating and cooling. We characterise the flows using velocity structure functions (VSFs) with and without density weighting or a density cutoff, and computed in one or three dimensions. However, we do not include optical depth effects that can hide motions in the densest gas, limiting comparison of our results with observations. Results. In regions with sufficient resolution, the density-weighted VSFs initially appear to follow the expectations for uniform turbulence, with a first-order power-law exponent consistent with Larson's size-velocity relationship. SN blast wave impacts on MCs produce short-lived coherent motions at large scales, increasing the scaling exponents for a crossing time. Gravitational contraction drives small-scale motions, producing scaling coefficients that drop or even turn negative as small scales become dominant. Removing the density weighting eliminates this effect as that emphasises the diffuse ISM. Conclusions. We conclude that two different effects coincidentally reproduce Larson's size velocity relationship. Initially, uniform turbulence dominates, so the energy cascade produces VSFs consistent with Larson's relationship. Later, contraction dominates, the density-weighted VSFs become much shallower or even inverted, but the relationship of the global average velocity dispersion of the MCs to their radius follows Larson's relationship, reflecting virial equilibrium or free-fall collapse. The injection of energy by shocks is visible in the VSFs, but decays within a crossing time.

Dynamical cloud formation traced by atomic and molecular gas

“…Important information about the kinematics of the gas are encoded in the slopes of the velocity structure functions. The overall regimes of derived slopes between 0.29 and 0.68 is well within the regime of other observational studies (see, e.g., the compilation in Table 1 of Chira et al 2019). However, while the slopes are similar for 13 CO(1-0), [CI], and 13 CO(3-2) (values between 0.52 and 0.68), the slope of the HISA velocity structure function is flatter with a value of 0.29.…”

“…Comparing the slopes of observational velocity structure functions (compiled from the literature) with their simulations, Chira et al (2019) conclude that the observed clouds are consistent with an intermediate evolutionary stage that are A44, page 9 of 13 neither purely turbulence dominated (e.g., driven by supernova remnants) nor gravitationally collapsing, but where the gas flows are dominated by the formation of hierarchical structures and cores. The cloud we are observing here around the infrared dark cloud G28.3 appears to be in a similar evolutionary stage.…”

“…A different way to investigate the kinematics of molecular clouds is the analysis of velocity structure functions (e.g., Miesch & Bally 1994;Ossenkopf & Mac Low 2002;Esquivel & Lazarian 2005;Heyer & Dame 2015;Chira et al 2019;Henshaw et al in prep.). Velocity structure functions are essentially a measure of how much the velocity measured between pixels separated by a given distance varies as a function of spatial scale.…”

“…where l is known as the spatial lag and represents the separation between pairs of points where S p is calculated for. As outlined for example in Chira et al (2019), the slope of the structure function can be used to infer whether turbulence and/or gravity play an important role in shaping the gas dynamics of the cloud. Chira et al (2019) show in their simulations that purely turbulence-dominated structure functions are steeper than those where gravity becomes more important because gravity increases the velocity on small scales so that the structure function becomes shallower.…”

The “Maggie” filament: Physical properties of a giant atomic cloud

“…Systematic studies of more homogeneous samples of molecular clouds traced in CO found velocity scaling exponents in a range between 0.24 and 0.79 (see Table 2 in Izquierdo et al (2021), which summarizes more than 40 years of observational work). Izquierdo et al (2021) find in their simulations that the scaling exponents lean toward lower values when molecular clouds are dominated by the influence of the Galactic potential rather than the effects of clustered SN feedback and self-gravity (see also Chira et al 2019). This suggests that low velocity scaling exponents are associated with diffuse regions of low star forming activity (e.g.…”