Differential and integral scaling laws of the mass density of molecular clouds
Abstract
In this work we investigate the mass density - size scaling law in molecular clouds (MCs). This relation reflects the fractal nature of MCs and plays a key role for understanding the physics, structure and evolution of these objects. We make use of the notion "ensemble of MCs", introduced in our previous work (Donkov, Veltchev \& Klessen, 2017), in which all MCs with the same probability density function (PDF) of mass density and effective size are represented by an abstract spherical cloud with the same PDF and size. In this spirit, the model is built on the base of abstract scales of the clouds' substructures (which are simply the radii of the spherical object). We consider two forms of the mass density - size scaling law: differential and integral, which in turn reveal the local and the global fractal clouds' structure. Both scaling functions are characterized by their scaling exponents, which can be explicitly expressed by the PDF of mass density, in the general case. Moreover, we derive a first order linear differential equation connecting the two scaling exponents and obtain its exact solution. As examples we apply this abstract construction to two PDFs: the so called power-law tail and the log-normal. Both have great importance for MC structure and evolution, as the latter corresponds to the earlier stages of clouds' evolution, when supersonic turbulence dominates the physical processes, while the former describes the latest stages of evolution, when star-formation takes place. The obtained results for the scaling exponents in both examples are qualitatively and numerically consistent with respective observations and simulations of MCs.
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BibTeX
@misc{donkov2026differential,
title = {{Differential and integral scaling laws of the mass density of molecular clouds}},
author = {Sava Donkov and Valentin Kopchev and Ivan Z. Stefanov and Todor V. Veltchev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32344},
eprint = {2610.32344},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32344},
}
RIS
TY - UNPB
TI - Differential and integral scaling laws of the mass density of molecular clouds
AU - Sava Donkov
AU - Valentin Kopchev
AU - Ivan Z. Stefanov
AU - Todor V. Veltchev
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32344
UR - https://arxiv.org/abs/2610.32344
AB - In this work we investigate the mass density - size scaling law in molecular clouds (MCs). This relation reflects the fractal nature of MCs and plays a key role for understanding the physics, structure and evolution of these objects. We make use of the notion "ensemble of MCs", introduced in our previous work (Donkov, Veltchev \& Klessen, 2017), in which all MCs with the same probability density function (PDF) of mass density and effective size are represented by an abstract spherical cloud with the same PDF and size. In this spirit, the model is built on the base of abstract scales of the clouds' substructures (which are simply the radii of the spherical object). We consider two forms of the mass density - size scaling law: differential and integral, which in turn reveal the local and the global fractal clouds' structure. Both scaling functions are characterized by their scaling exponents, which can be explicitly expressed by the PDF of mass density, in the general case. Moreover, we derive a first order linear differential equation connecting the two scaling exponents and obtain its exact solution. As examples we apply this abstract construction to two PDFs: the so called power-law tail and the log-normal. Both have great importance for MC structure and evolution, as the latter corresponds to the earlier stages of clouds' evolution, when supersonic turbulence dominates the physical processes, while the former describes the latest stages of evolution, when star-formation takes place. The obtained results for the scaling exponents in both examples are qualitatively and numerically consistent with respective observations and simulations of MCs.
ER -