Extraction of a second power‐law tail of the density distribution in simulated clouds

Marinkova, Lyubov; Veltchev, Todor V.; Girichidis, Ph.; Donkov, Sava

doi:10.1002/asna.202113968

Cited by 4 publications

(5 citation statements)

References 32 publications

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“…Possible processes are rotation of collapsing cores, which introduces an angular momentum barrier (Khullar et al 2021), increasing optical depth and weaker cooling, magnetic fields, geometrical effects, and protostellar feedback. Though such a flatter PLT was first found in a simulation presented by Kritsuk et al (2011), it is only recently that there are theoretical explanations for this phenomenon (Jaupart & Chabrier 2020;Donkov et al 2021). Jaupart & Chabrier (2020) develop an analytical theory of the density PDF and attribute the second PLT to free-fall collapse of a dense region in a cloud.…”

Section: Introductionmentioning

confidence: 92%

“…The slope and the DP are then derived simultaneously as averaged values as the number of bins is varied. The method was elaborated further for detection of a second PLT (Marinkova et al 2021) -this technique was also used to get the results in this paper.…”

Section: Probability Distribution Functions Of Column Density (N-pdfs)mentioning

confidence: 99%

“…In this case, there would indeed be a succession of a steep PLT and a flatter one. Donkov et al (2021) on the other hand discuss a model in which cores of an averaged representative of a whole class of molecular clouds are considered. They propose that the thermodynamic state of the gas (only turbulence and gravity included) changes from isothermal on large scales to a polytropic equation of state of the gas p ∝ ρ Γ with pressure p and density ρ and an exponent Γ larger than 1 on the sub-parsec proto-stellar core scale.…”

Section: Power Law Tail Slopesmentioning

confidence: 99%

“…Important tools for characterizing molecular clouds are probability distribution functions of density (ρ-PDF) and column density (N-PDF) because they can be directly linked to theories of the star formation process (e.g., Padoan et al 1997Padoan et al , 2002 Vázquez-lutionary state of the cloud. For example, the N-PDF is purely log-normal if the cloud structure is governed only by isothermal supersonic turbulence and develops a power law tail (PLT) under self-gravity (e.g., Klessen 2000;Vázquez-Semadeni & Garcia 2001;Dib & Burkert 2005;Kritsuk et al 2011;Collins et al 2012;Girichidis et al 2014;Ward et al 2014;Burkhart et al 2015a;Veltchev et al 2016;Mocz et al 2017;Auddy et al 2018;Veltchev et al 2019;Körtgen et al 2019;Krumholz & McKee 2020;Jaupart & Chabrier 2020;Donkov et al 2021). The slope of the PLT changes during the evolution of the cloud and can depend on the 2D projection (Ballesteros-Paredes et al 2011;Cho et al 2011;Burkhart 2018).…”

Section: Introductionmentioning

confidence: 99%

“…Jaupart & Chabrier (2020) develop an analytical theory of the density PDF and attribute the second PLT to free-fall collapse of a dense region in a cloud. Donkov et al (2021) propose that the thermodynamic state of the gas changes from isothermal on large scales to polytropic with an exponent larger than 1 on the sub-parsec proto-stellar core scale. In the hydrodynamics models of Khullar et al (2021), the second PLT appears only at much higher densities and small (sub-parsec) scales, and corresponds to rotationally supported material, for example a disc.…”

Section: Introductionmentioning

confidence: 99%

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Understanding star formation in molecular clouds

Schneider

Ossenkopf-Okada

Clarke

et al. 2022

A&A

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Probability distribution functions of the total hydrogen column density (N-PDFs) are a valuable tool for distinguishing between the various processes (turbulence, gravity, radiative feedback, magnetic fields) governing the morphological and dynamical structure of the interstellar medium. We present N-PDFs of 29 Galactic regions obtained from Herschel imaging at high angular resolution (18 ), covering diffuse and quiescent clouds, and those showing low-, intermediate-, and high-mass star formation (SF), and characterize the cloud structure using the ∆-variance tool. The N-PDFs show a large variety of morphologies. They are all double-log-normal at low column densities, and display one or two power law tails (PLTs) at higher column densities. For diffuse, quiescent, and low-mass SF clouds, we propose that the two log-normals arise from the atomic and molecular phase, respectively. For massive clouds, we suggest that the first log-normal is built up by turbulently mixed H 2 and the second one by compressed (via stellar feedback) molecular gas. Nearly all clouds have two PLTs with slopes consistent with self-gravity, where the second one can be flatter or steeper than the first one. A flatter PLT could be caused by stellar feedback or other physical processes that slow down collapse and reduce the flow of mass toward higher densities. The steeper slope could arise if the magnetic field is oriented perpendicular to the LOS column density distribution. The first deviation point (DP), where the N-PDF turns from log-normal into a PLT, shows a clustering around values of a visual extinction of A V (DP1)∼2-5. The second DP, which defines the break between the two PLTs, varies strongly. In contrast, the width of the N-PDFs is the most stable parameter, with values of σ between ∼0.5 and 0.6. Using the ∆-variance tool, we observe that the A V value, where the slope changes between the first and second PLT, increases with the characteristic size scale in the ∆variance spectrum. We conclude that at low column densities, atomic and molecular gas is turbulently mixed, while at high column densities, the gas is fully molecular and dominated by self-gravity. The best fitting model N-PDFs of molecular clouds is thus one with log-normal low column density distributions, followed by one or two PLTs.

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Section: Introductionmentioning

confidence: 92%

Section: Probability Distribution Functions Of Column Density (N-pdfs)mentioning

confidence: 99%

Section: Power Law Tail Slopesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Understanding star formation in molecular clouds

Schneider

Ossenkopf-Okada

Clarke

et al. 2022

A&A

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A new tool to derive simultaneously exponent and extremes of power-law distributions

Pezzuto,

Coletta,

Klessen

et al. 2023

Monthly Notices of the Royal Astronomical Society

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Many experimental quantities show a power-law distribution p(x) ∝ x−α. In astrophysics, examples are: size distribution of dust grains or luminosity function of galaxies. Such distributions are characterized by the exponent α and by the extremes xminxmax where the distribution extends. There are no mathematical tools that derive the three unknowns at the same time. In general, one estimates a set of α corresponding to different guesses of xminxmax. Then, the best set of values describing the observed data is selected a posteriori. In this paper, we present a tool that finds contextually the three parameters based on simple assumptions on how the observed values xi populate the unknown range between xmin and xmax for a given α. Our tool, freely downloadable, finds the best values through a non-linear least-squares fit. We compare our technique with the maximum likelihood estimators for power-law distributions, both truncated and not. Through simulated data, we show for each method the reliability of the computed parameters as a function of the number N of data in the sample. We then apply our method to observed data to derive: (i) the slope of the core mass function in the Perseus star-forming region, finding two power-law distributions: α = 2.576 between $1.06\, \mathrm{M}_{\odot }$ and $3.35\, \mathrm{M}_{\odot }$, α = 3.39 between $3.48\, \mathrm{M}_{\odot }$ and $33.4\, \mathrm{M}_{\odot }$; (ii) the slope of the γ-ray spectrum of the blazar J0011.4+0057, extracted from the Fermi-LAT archive. For the latter case, we derive α = 2.89 between 1484 MeV and 28.7 GeV; then we derive the time-resolved slopes using subsets of 200 photons each.

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Density profile of a self-gravitating polytropic turbulent fluid in a rotating disc near to the cloud core

Donkov,

Stefanov,

Veltchev

et al. 2023

Monthly Notices of the Royal Astronomical Society

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We obtain two equations (following from two different approaches) for the density profile in a self-gravitating polytropic cylindrically symmetric and rotating turbulent gas disc. The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state of the gas changes from isothermal (in the outer cloud layers) to one of ‘hard polytrope’, and the symmetry changes from spherical to cylindrical. On the assumption of steady state, as the accreting matter passes through all spatial scales, we show that the total energy per unit mass is an invariant with respect to the fluid flow. The obtained equation describes the balance of the kinetic, thermal, and gravitational energy of a fluid element. We also introduce a method for approximating density profile solutions (in a power-law form), leading to the emergence of three different regimes. We apply, as well, dynamical analysis of the motion of a fluid element. Only one of the regimes is in accordance with the two approaches (energy and force balance). It corresponds to a density profile of a slope −2, polytropic exponent 3/2, and sub-Keplerian rotation of the disc, when the gravity is balanced by the thermal pressure. It also matches with some observations and numerical works and, in particular, leads to a second power-law tail (of a slope ∼−1) of the density distribution function in dense, self-gravitating cloud regions.

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Extraction of a second power‐law tail of the density distribution in simulated clouds

Cited by 4 publications

References 32 publications

Understanding star formation in molecular clouds

Understanding star formation in molecular clouds

A new tool to derive simultaneously exponent and extremes of power-law distributions

Density profile of a self-gravitating polytropic turbulent fluid in a rotating disc near to the cloud core

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