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

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Volume 571 (November 2014)

A&A, 571 (2014) A95

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Table 2

Location of the PDF maxima.


	Sphere						Cylinder
	BE	n = 3	n = 2	BE	n = 3	n = 2	n = 4	n = 4
	linear PDF			logarithmic PDF			lin.	log.


[ y_n ] _max ^a	–	0.155	0.211	–	0.414	0.478	0.141	0.497
[ X_n ] _max ^a	–	0.465	0.537	–	1.099	1.057	0.461	1.797


onset for maxima with [ x ] _max> 0
[ θ_cl ] _0,max	1.287	1.257	0.731	2.568	2.470	1.353	1.147	2.811
[ Σ ] _0,max ^b	1.343	1.311	0.760	2.961	2.824	1.494	1.208	3.605
[ q^-1 ] _0,max	1.291	1.287	1.267	2.319	2.230	1.916	1.356	3.952


critically stable cloud^c
[ x ] _max	0.9014	0.9012	—	0.7114	0.7049	–	–	–
[ Σ ] _max ^b	0.8800	0.8863	–	2.0402	2.0928	–	–	–


maxima in the limit q → 0
[ x ] _max	0.888	0.919	0.888	0.722	0.765	0.722	0.927	0.709
[ Σ ] _max ^b	0.760	0.000	0.760	1.494	0.000	1.494	0.000	0.000

Notes.

^(a)

Maxima values with x> 0 for clouds with an analytical density profile as given in Eq. (1). The values for cylinders refer to the asymptotic PDF without a pole (Eq. (43)).

^(c)

Critical stability in this paper is defined as critically stable under compression where dp(r_cl)/dr_cl = 0.

^(b)

Mass surface density in units of with λ = 1 for cylinders and λ = 0 for spheres.

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