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

Abstract

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).

Dense gas in a giant molecular filament

“…Following the method described in Appendix D of Schneider et al (2016), we correlate the slope of the power-law tail s and the exponent α of a spherical (for clumps and cores, ρ(r) ∝ r −α c ) and a cylindrical (for filaments, ρ(r) ∝ r −α f ) density distribution via α c = 1 + 2/s and α f = 1 + 1/s, respectively (see also Appendx C). Similar calculations are also discussed by Federrath & Klessen (2013), Fischera (2014), and Myers (2015). The power-law indices s * for the dense gas are all around 2, thus the radial density profile α c is around 2 and α f around 1.5.…”

“…and α c = 1 + 2/s. Similar calculations are also discussed by Federrath & Klessen (2013), Fischera (2014), and Myers (2015).…”

Dense Gas in a Giant Molecular Filament

“…Assuming a singular polytropic cylinder, ρ(r) ∝ r −α f , then α f = 1 + 1/α. Similar calculations are also discussed by Federrath & Klessen (2013), Fischera (2014), andMyers (2015). For the power-law indices we derived from the dense gas, the radial density profile α c is estimated to be between 1.2 and 1.5, which is consistent with the self-gravitating filament model (e.g., Myers 2015).…”

Shocked Interstellar Clouds and Dust Grain Destruction in the LMC Supernova Remnant N132D

“…Using the images from Figure 3 and the preshock densities from Table 5, we obtain masses in the range 0.1 − 20 M with a mean of ∼ 4 M . Thus we infer these clouds initially represented typical ISM selfgravitating Bonnor-Ebert spheres such as those recently investigated on a theoretical basis by Sipilä et al (2011), Fischera (2014 and Sipilä et al (2017). Given that the shock which moves into them following the passage of the supernova blast-wave is strongly compressive, and that such Bonnor-Ebert spheres can be marginally stable against collapse, it is tempting to imagine that the supernova shock may later induce formation of ∼ 1.0M stars within the cores of those clouds.…”