Velocity Structure of the Interstellar Medium as Seen by the Spectral Correlation Function

Abstract

We use the statistical tool known as the ``spectral correlation function'' (SCF) to intercompare simulations and observations of the atomic interstellar medium (ISM). The simulations considered, which mimic three distinct sets of physical conditions, are each calculated for a 300 pc3 box centered at the Galactic plane. The ``ISM'' run is intended to represent a mixture of cool and warm atomic gas and includes self-gravity and magnetic fields in the calculations. The ``ISM-IT'' run is more representative of molecular clouds, in which the gas is presumed isothermal. The third run ``IT'' is for purely isothermal gas, with zero magnetic field and no self-gravity. Forcing in the three cases is accomplished by including simulated effects of stellar heating (ISM), stellar winds (ISM-IT), or random compressible fluctuations (IT). For each simulation, H I spectral line maps are simulated, and it is these maps that are intercompared, both with each other and with observations, using the SCF. For runs where the separation of velocity features is much greater than the ``thermal'' width of a line, density-weighted velocity histograms are decent estimates of H I spectra. When thermal broadening is large in comparison with fine-scale turbulent velocity structure, this broadening masks subthermal velocity substructure in observed spectra. So, simulated spectra for runs in which thermal broadening is important must be calculated by convolving density-weighted histograms with Gaussians whose width represents the thermal broadening. The H I observations we use for comparison are of the north celestial pole (NCP) loop, a region chosen to minimize line-of-sight confusion on scales greater than 100 pc. None of the simulations match the NCP loop data very well, for a variety of reasons described in the paper. Most of the reasons for simulation/observation discrepancy are predictable and understandable, but one is particularly interesting: the most realistic sets of line profiles and SCF statistics come from artificially expanding the velocity axis of the ISM run by a factor of 6. Without rescaling, the low-velocity dispersion associated with much of the gas in the ISM run causes almost all of the spectra to appear as virtually identical Gaussians whose width is determined solely by temperature-all velocity structure is smeared out by thermal broadening. However, if the velocity axis is expanded by a factor of 6,the SCF distributions of the ISM run and the NCP loop match up fairly well. This means that the ratio of thermal to turbulent pressure in the ISM simulation is much too large as it stands, and that the simulation is deficient in turbulent energy. This is a consequence of the ISM run not including the effects of supernovae. This paper concludes that the SCF is a useful tool for understanding and fine-tuning simulations of interstellar gas, and in particular that realistic simulations of the atomic ISM need to include the effects of energetic stellar winds (e.g., supernovae) in order for the ratio of thermal-to-turbulent pressure to give spectra representative of the observed ISM in our Galaxy.