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Observations suggest that star formation in filamentary molecular clouds occurs in a two-step process, with the formation of filaments preceding that of prestellar cores and stars. Here, we apply the gravo-turbulent fragmentation theory of Hennebelle & Chabrier (2008, 2009, 2013 to a filamentary environment, taking into account magnetic support. We discuss the induced geometrical effect on the cores, with a transition from 3D geometry at small scales to 1D at large ones. The model predicts the fragmentation behavior of a filament for a given mass per unit length (MpL) and level of magnetization. This CMF for individual filaments is then convolved with the distribution of filaments to obtain the final system CMF. The model yields two major results: (i) the filamentary geometry naturally induces a hierarchical fragmentation process, first into groups of cores, separated by a length equal to a few filament Jeans lengths, i.e. a few times the filament width. These groups then fragment into individual cores. (ii) Non-magnetized filaments with high MpL are found to fragment excessively, at odd with observations. This is resolved by taking into account the magnetic field treated simply as additional pressure support). The present theory suggests two complementary modes of star formation: while small (spherical or filamentary) structures will collapse directly into prestellar cores, according to the standard Hennebelle-Chabrier theory, the large (filamentary) ones, the dominant population according to observations, will follow the afore-described two-step process.

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“…Assuming a uniform density, the gravitational energy of an ellipsoid takes the form (Parker 1954;Neutsch 1979)…”

Section: Density Threshold To Formation Of An Unstable Corementioning

confidence: 99%

“…C. THE GRAVITATIONAL POTENTIAL ENERGY OF AN ELLIPSOID Following the calculations of Neutsch (1979), an ellipsoid with semi-axes R, R, Rη with uniform density has gravitational potential energy E g = 3 5…”

Section: Appendixmentioning

confidence: 99%

Analytical Core Mass Function (CMF) from Filaments: Under Which Circumstances Can Filament Fragmentation Reproduce the CMF?

Lee

Hennebelle

Chabrier

2017

ApJ

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“…The virial mass was calculated for a constant density sphere, but molecular cloud substructures are clearly not spheres. Generalizing from spheres, the gravitational energy of an ellipsoid can be written in closed form for various radial density profiles (Neutsch 1979), including constant density,…”

Section: Structure Analysis Result: Size-linewidth-flux Relationsmentioning

confidence: 99%

Structural and Dynamical Analysis of 0.1 pc Cores and Filaments in the 30 Doradus-10 Giant Molecular Cloud

Indebetouw

Wong

Chen

et al. 2020

ApJ

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High-resolution (<0.1 pc) ALMA observations of the 30Dor-10 molecular cloud 15 pc north of R136 are presented. The 12 CO 2-1 emission morphology contains clumps near the locations of known midinfrared massive protostars, as well as a series of parsec-long filaments oriented almost directly towards R136. There is elevated kinetic energy (linewidths at a given size scale) in 30Dor-10 compared to other LMC and Galactic star formation regions, consistent with large scale energy injection to the region. Analysis of the cloud substructures is performed by segmenting emission into disjoint approximately round "cores" using clumpfind, by considering the hierarchical structures defined by isointensity contours using dendrograms, and by segmenting into disjoint long thin "filaments" using Filfinder. Identified filaments have widths ∼0.1 pc. The inferred balance between gravity and kinematic motions depends on the segmentation method: Entire objects identified with clumpfind are consistent with free-fall collapse or virial equilibrium with moderate external pressure, whereas many dendrogramidentified parts of hierarchical structures have higher mass surface densities Σ LT E than if gravitational and kinetic energies were in balance. Filaments have line masses that vary widely compared to the critical line mass calculated assuming thermal and nonthermal support. Velocity gradients in the region do not show any strong evidence for accretion of mass along filaments. The upper end of the "core" mass distribution is consistent with a power-law with the same slope as the stellar initial mass function.

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“…To this aim, Å £ and Å should be indexed as and , respectively, and the expression of´Î µ ÔÕ should be used (see e.g., Paper I). With regard to case (c), owing to intersecting boundaries, the expressions of both´Î µ ÔÕ and Î µ ÔÕ , calculated in Paper I, lose their validity, and a generalization of the kind used by Neutsch (1979) for interactionenergy tensors is needed.…”

Section: Fig 2 As Inmentioning

confidence: 99%

On the tidal-energy tensor for two homogeneous coaxial ellipsoids

Caimmi,

Secco

2001

Astron. Nachr.

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The tidal-energy tensor for two homogeneous and coaxial ellipsoids, one lying completely within the other, is investigated in connection with the tidal action exerted by the outer ellipsoid on the inner one. Making reference to the explicit expression found in a previous paper of ours, it is shown that the generic component of the tidal-energy tensor, (i) may be expressed as the product of the corresponding component of the self-energy tensor related to the inner ellipsoid, by the density ratio, and the shape factor ratio, and (ii) equals the one due to any homogeneous, outer ellipsoid, for which the product of the density and a specified shape factor remains unchanged; in particular, the outer ellipsoid may be similar and similarly placed with respect to the inner one. In addition, an explicit expression for the Clausius-virial tensor is derived. Analogous results for the corresponding scalar quantities are also given. Further attention is paid to the particular case of spheroids.

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Cited by 21 publications

References 0 publications

Analytical Core Mass Function (CMF) from Filaments: Under Which Circumstances Can Filament Fragmentation Reproduce the CMF?

Analytical Core Mass Function (CMF) from Filaments: Under Which Circumstances Can Filament Fragmentation Reproduce the CMF?

Structural and Dynamical Analysis of 0.1 pc Cores and Filaments in the 30 Doradus-10 Giant Molecular Cloud

On the tidal-energy tensor for two homogeneous coaxial ellipsoids

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