Scales of Stability and Turbulence in the Molecular ISM

Abstract

We re-analyze the data of the BU-FCRAO $^{13}{\rm CO}$ Galactic Ring Survey (GRS) to understand the dynamics of the turbulent molecular interstellar medium. We define molecular clouds by their spatial half-power contours of $^{13}{\rm CO}$ integrated intensity, independent of a boundary based on thresholding or tiling. We find properties of hydrostatic equilibrium (HE) and virial equilibrium (VE), the former independent and the latter dependent on time and spatial scales. We suggest that HE is a stationary property of the turbulence and that molecular clouds are high-density regions of a fluctuating component. The gravitational and turbulent kinetic energies within clouds are continuously evolving toward a time-dependent VE with the fluctuating, external, turbulent pressure energy (PE) that can be treated parametrically owing to the shorter time scale for virialization. The average PE is comparable to the pressure of the multiphase ISM at the Galactic mid-plane. Larson's scaling relations analyzed by different statistical methods are not significant. The non-dimensional variances of size, line width, and column density are of comparable magnitude, ruling out the inference of constant column density. Previously unrecognized autocorrelations may have contributed to the apparent validity of the inference.

Figures (10)

• Figure 1: Thirty individual azimuthally-averaged radial profiles of $^{13}$CO integrated intensity (K km s$^{-1}$ pixel$^{-1}$). Top to bottom show ten profiles each for clouds that have small, medium, and large sizes with respect to each other. The vertical, dotted and long-dashed lines indicate the HWHM and the length scale of the cloud defined as 2 HWHM. The red line shows the column density of hydrostatic equilibrium (§\ref{['Hydrostatic']}), same as in figure \ref{['coadded_profiles']} ( right, blue, long-dashed line).
• Figure 2: Histograms showing the log normal distributions of radius, column density, line width. Means and standard deviations are listed in table \ref{['table_lognormals']}.
• Figure 3: ( Left) The $^{13}$CO integrated intensity (K km s$^{-1}$ pixel$^{-1}$) and ( right) line width (km s$^{-1}$) with a color bar indicating the values in these units, respectively. From top to bottom, the clouds shown are clumps 54, 64, 70 from the clumps catalog of Rathborne_2009. The single contour ( left) is drawn at the half-power level of the peak integrated intensity within the contour. The cloud length scale is twice the circularly averaged HWHM.
• Figure 4: Left: Average non-dimensional line width profile of 3683 clouds (§\ref{['Co-addition']}). Right: Average non-dimensional column density profile. In both figures, the vertical dashed line indicates $\rm HWHM = 1$. The observed profile of column density is shown right as a red line. Two profiles of the column density in hydrostatic equilibrium are also shown ( right) in blue with the dotted line for a non-dimensional isothermal temperature and the long-dashed line for a non-dimensional temperature proportional to the square of the line width ( left).
• Figure 5: A 2-D histogram of the GRS clouds binned according to their gravitational potential (GE) and kinetic (KE) energies per unit mass with colors representing the number of clouds per bin of size (0.05 $\rm km^2 s^{-2})^2$. The ellipse shows the standard deviations of the distribution from a 2-D Gaussian fit (table \ref{['table_pve_energy']} ) with the mean marked with a cross. Constant pressure appears as a straight line in this space. The solid line identifies the average external pressure consistent with the three term virial theorem (equation \ref{['ve1']}) and the mean GE and KE. The line of zero pressure is shown dashed.