Statistical Analysis on the Turbulent Multi-scale Interstellar Medium

Abstract

Turbulence is ubiquitous in the interstellar medium (ISM) and plays a crucial role in the evolution of the ISM over a large range of scales from AU to kpc. To understand the multi-scale nature of interstellar turbulence, the study of the statistical properties of the interstellar turbulence is required not only for observations but also for numerical simulations. Numerical simulation is the only way to understand the dynamics of interstellar turbulence and is essential for understanding the evolution of turbulent ISM in a variety of different scales and environments. Observational studies also provide a glimpse of nature of interstellar turbulence occurring at various scales based on statistical studies. In this paper, I have conducted statistical analyses of turbulence with observational and numerical studies on the evolution of interstellar turbulence on molecular cloud scale and galactic scale. To do this, I used two well-known statistical methods, the probability density function (PDF) and the power spectrum (PS). In an isothermal or incompressible ideal environment, a typical distribution of the log-normal distribution for PDF and the Kolmogorov power spectrum for PS can be expected.

In the first chapter, I discuss the star formation rate quantitatively in the molecular cloud affected by turbulence and self-gravity. For numerical experiments involving self-gravity, turbulent supersonic flow, and magnetic field, I obtain the density PDF. The density structure of interstellar turbulence deviates from the log-normal distribution by self-gravity. With the investigation of the core formation rate per free fall time, the core formation rate shows a sharp increase with self-gravity. When 100 times of the initial average density is considered as the critical density of the core formation, the core formation rate under the influence of self-gravity is 49 times higher than that of assuming the log-normal distribution. Therefore, the previous study, which assumes the log-normal distribution and has obtained the star formation rate, should be modified to account for self-gravity.

In the second chapter, I present statistical analyses of the stratified and turbulent ISM of numerical models performed on the galactic scale at different vertical distances from the galactic plane. Near the galactic plane, the density PDF shows a double-peaked distribution, indicating a deviation from the log-normal distribution. This double-peaked distribution is due to cold and warm gas components in the ISM. The density PDF of each gas is compared to a log-normal distribution since the gas is assumed to be quasi-mass-conserving with the normalized height by a density-weighted scale height. At higher positions from the galactic plane, warm gas is the majority whose density PDF fits well into the log-normal distribution. The density PS steepens to $ -5 / 3 $, and as the velocity PS flattens from $ -5 / 3 $ as the positions where I investigated go higher. When the velocity field is divided into compressible and incompressible components, the PS of the incompressible component is flatter compared to the PS of the compressible component. In this study, I devised a new method to visualize the degree of compressibility of the velocity field, which could be calculated in real space with the divergence and curl of the velocity field. It has been expected that powerful explosive phenomena such as supernovae will cause only strong compressive turbulence around. But from the way of visualizing compressibility, it can be shown that incompressible components are caused by curved shock waves near supernova remnants.

In the third chapter, I present a study on the turbulent interstellar medium from neutral hydrogen distributed in the Outer spiral arm using I-GALFA HI 21 cm survey data. The slope of PS is steeper ($ \ alpha \ sim $ - 2) at lower latitudes than at higher latitudes ($ \ alpha \ sim $ -1.8). Near the galactic plane, the slope gradually increases with the thickness of the velocity channel and falls (-1.97) as the thickness reaches the thermal velocity of the medium. To understand this change in slope, I compare the I-GALFA observations with numerical models. I synthesized a position-position-velocity cube from a numerical model with similar surface density. From the cube, I found that the effect of young supernova remnants can be one possibility to cause a change in the slope of the PS for the integrated brightness temperature. The PDFs of the integrated brightness temperature do not fit log-normal distribution. Near the galactic plane, it was skewed to the low-density region and skewed toward the higher-density region. And these PDFs are well divided into two log-normal distributions, each representing cold and warm components of neutral hydrogen.