Hierarchical Structure of Magnetohydrodynamic Turbulence In Position-Position-Velocity Space

TL;DR

This paper uses dendrograms to analyze hierarchical structures in magnetohydrodynamic turbulence within the interstellar medium, revealing how physical parameters influence the observed structures in synthetic PPV data.

Contribution

It introduces a novel application of dendrograms to characterize hierarchical structures in MHD turbulence and links these structures to physical parameters like Mach numbers and self-gravity.

Findings

Hierarchical structures increase with higher Alfvenic Mach number and self-gravity.

Dendrogram moments correlate with sonic and Alfvenic Mach numbers.

PPV and PPP emission contours are related in supersonic gas.

Abstract

Magnetohydrodynamic turbulence is able to create hierarchical structures in the interstellar medium that are correlated on a wide range of scales via the energy cascade. We use hierarchical tree diagrams known as dendrograms to characterize structures in synthetic Position-Position-Velocity (PPV) emission cubes of optically thin isothermal magnetohydrodynamic turbulence. We show that the structures and degree of hierarchy observed in PPV space are related to the physics of the gas, i.e. self-gravity and the global sonic and Alfvenic Mach number. Simulations with higher Alfvenic Mach number, self-gravity and supersonic flows display enhanced hierarchical structure. We observed a strong sonic and Alfvenic dependency when we apply the the statistical moments (i.e. mean, variance, skewness, kurtosis) to the dendrogram distribution. Larger magnetic field and sonic Mach number correspond to larger values of the moments. Application of the dendrogram to 3D density cubes, also known as Position-Position-Position cubes (PPP), reveals that the dominant emission contours in PPP and PPV are related for supersonic gas but not for subsonic. We also explore the effects of smoothing, thermal broadening and velocity resolution on the dendrograms in order to make our study more applicable to observational data. These results all point to hierarchical tree diagrams as being a promising additional tool for studying ISM turbulence and star forming regions in the direction of obtaining information on the degree of self-gravity, the Mach numbers and the complicated relationship between PPV and PPP.