The Formation of Population I Stars: Part I. Gravitational Contraction

McCrea, W. H.

doi:10.1093/mnras/117.5.562

Cited by 82 publications

(48 citation statements)

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“…Spheres have a well-known critically stable configuration with an overpressure above which the sphere becomes gravitationally unstable under compression (Ebert 1955;Bonnor 1956;McCrea 1957;Curry & McKee 2000;Fischera & Dopita 2008;Fischera 2011;Fischera & Martin 2012b; see Appendix A.1.1). The critically stable configuration is characterized through an overpressure of p c /p ext ∼ 14.04 at θ crit = 6.451.…”

Section: Bonnor-ebert Spherementioning

confidence: 99%

On the probability distribution function of the mass surface density of molecular clouds. II.

Fischera

2014

A&A

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The probability distribution function (PDF) of the mass surface density of molecular clouds provides essential information about the structure of molecular cloud gas and condensed structures out of which stars may form. In general, the PDF shows two basic components: a broad distribution around the maximum with resemblance to a log-normal function, and a tail at high mass surface densities attributed to turbulence and self-gravity. In a previous paper, the PDF of condensed structures has been analyzed and an analytical formula presented based on a truncated radial density profile, ρ(r) = ρ c /(1 + (r/r 0 ) 2 ) n/2 with central density ρ c and inner radius r 0 , widely used in astrophysics as a generalization of physical density profiles. In this paper, the results are applied to analyze the PDF of self-gravitating, isothermal, pressurized, spherical (Bonnor-Ebert spheres) and cylindrical condensed structures with emphasis on the dependence of the PDF on the external pressure p ext and on the overpressure q −1 = p c /p ext , where p c is the central pressure.Apart from individual clouds, we also consider ensembles of spheres or cylinders, where effects caused by a variation of pressure ratio, a distribution of condensed cores within a turbulent gas, and (in case of cylinders) a distribution of inclination angles on the mean PDF are analyzed. The probability distribution of pressure ratios q −1 is assumed to be given by P(q −1 ) ∝ q −k 1 /(1 + (q 0 /q) γ ) (k 1 +k 2 )/γ , where k 1 , γ, k 2 , and q 0 are fixed parameters. The PDF of individual spheres with overpressures below ∼100 is well represented by the PDF of a sphere with an analytical density profile with n = 3. At higher pressure ratios, the PDF at mass surface densities Σ Σ(0), where Σ(0) is the central mass surface density, asymptotically approaches the PDF of a sphere with n = 2. Consequently, the power-law asymptote at mass surface densities above the peak steepens from P sph (Σ) ∝ Σ −2 to P sph (Σ) ∝ Σ −3 . The corresponding asymptote of the PDF of cylinders for the large q −1 is approximately given by P cyl (Σ) ∝ Σ −4/3 (1 − (Σ/Σ(0)) 2/3 ) −1/2 . The distribution of overpressures q −1 produces a power-law asymptote at high mass surface densities given by P sph (Σ) ∝ Σ −2k 2 −1 (spheres) or P cyl (Σ) ∝ Σ −2k 2 (cylinders).

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Section: Bonnor-ebert Spherementioning

confidence: 99%

On the probability distribution function of the mass surface density of molecular clouds. II.

Fischera

2014

A&A

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“…An isothermal gas sphere embedded in an external medium of given pressure p ext has a critical Bonnor-Ebert mass above which no state of equilibrium can exist (Ebert 1955;Bonnor 1956;McCrea 1957),…”

Section: Theoretical Backgroundmentioning

confidence: 99%

The structure and stability of molecular cloud cores in external radiation fields

Galli

Walmsley

Gonçalves

2002

A&A

146

170

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Abstract.We have considered the thermal equilibrium in pre-protostellar cores in the approximation where the dust temperature is independent of interactions with the gas and where the gas is heated both by collisions with dust grains and ionization by cosmic rays. We have then used these results to study the stability of cores in hydrostatic equilibrium in the limit where thermal pressure dominates over magnetic field and turbulence. We compare the density distribution derived in this manner with results obtained in the isothermal case. We find that for cores with characteristics similar to those observed in nearby molecular clouds, the gas and dust temperatures are coupled in the core interior with densities above ∼3×10 4 cm −3 . As a consequence, one expects that the gas temperature like the dust temperature decreases towards the center of these objects. However, the regime where gas and dust temperatures are coupled coincides approximately with that in which CO and many other molecular species deplete onto dust grain surfaces. At larger radii and lower densities, the gas and dust temperatures decouple and the gas temperature tends to the value expected for cosmic ray heating alone. The density structure which one computes taking into account such deviations from isothermality are not greatly different from that expected for an isothermal Bonnor-Ebert sphere. It is impossible in the framework of these models to have a stable equilibrium core with mass above ∼5 M and column density compatible with observed values (N H > 2 × 10 22 cm −2 or A V > 10 mag). We conclude from this that observed high mass cores are either supported by magnetic field or turbulence or are already in a state of collapse. Lower mass cores on the other hand have stable states where thermal pressure alone provides support against gravitation and we conclude that the much studied object B68 may be in a state of stable equilibrium if the internal gas temperature is computed in self-consistent fashion. Finally we note that in molecular clouds such as Ophiuchus and Orion with high radiation fields and pressures, gas and dust temperatures are expected to be well coupled and hence in the absence of an internal heat source, one expects temperatures to decrease towards core centers and to be relatively high as compared to low pressure clouds like Taurus.

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“…Using the virial theorem, we can infer the basic properties of an isothermal, self-gravitating cloud [59] [101]. Setting M = 0 in equation (24) and evaluating P G with the aid of equation (23), we find…”

Section: Isothermal Cloudsmentioning

confidence: 99%

The Dynamical Structure and Evolution of Giant Molecular Clouds

McKee

1999

The Origin of Stars and Planetary Systems

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The Formation of Population I Stars: Part I. Gravitational Contraction

Cited by 82 publications

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On the probability distribution function of the mass surface density of molecular clouds. II.

On the probability distribution function of the mass surface density of molecular clouds. II.

The structure and stability of molecular cloud cores in external radiation fields

The Dynamical Structure and Evolution of Giant Molecular Clouds

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