We use the statistical tool known as the “ Spectral Correlation Function ” [ SCF ] to intercompare simulations and observations of the atomic interstellar medium .
The simulations considered , which mimic three distinct sets of physical conditions , are each calculated for a 300 pc ^ { 3 } box centered at the Galactic plane .
Run “ ISM ” is intended to represent a mixture of cool and warm atomic gas , and includes self-gravity and magnetic fields in the calculations .
Run “ ISM-IT ” is more representative of molecular clouds , where 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 ( for 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 which are intercompared , both with each other , and with observations , using the SCF .
For runs where the separation of velocty 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 sub-thermal velocity sub-structure in observed spectra .
So , simulated spectra for runs where 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 here for comparison are of the North Celestial Pole Loop , a region chosen to minimize line-of-sight confusion on scales > 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 understandble , but one is particularly curious : the most realistic “ simulation ” comes from artifically expanding the velocity axis of run ISM by a factor of six .
Without rescaling , the high temperature associated with much of the gas in run ISM causes almost all of the spectra to appear as virtually identical gaussians whose width is deterimined solely by the temperature–all velocity structure is smeared out by thermal broadening .
However , if the velocity axis is expanded \times 6 , the SCF distributions of run ISM an the NCP Loop match up fairly well .
This means that the ratio of thermal to turbulent pressure in run ISM is much too large in the simulation as it stands , and that either the temperature is much ( \sim 36 times ) lower , and/or that the turbulent energy in the simulation is much too small .
Run ISM does not include the effects of supernovae , which means that the turbulent energy ( and hence velocity scale ) is likely to be dramatically underestimated .

The paper concludes that the SCF is a useful tool for understanding and fine-tuning simulations of interstellar gas , and in particular that a realistic simulation of the atomic ISM needs to include the effects of energetic stellar winds ( e.g .
supernovae ) before the ratio of thermal-to-turbulent pressure will give spectra representative of the observed interstellar medium in our Galaxy .