TY - JOUR
T1 - The density variance-mach number relation in supersonic, isothermal turbulence
AU - Price, Daniel
AU - Federrath, Christoph
AU - Brunt, Chris
PY - 2011
Y1 - 2011
N2 - We examine the relation between the density variance and the
mean-square Mach number in supersonic, isothermal turbulence, assumed
in several recent analytic models of the star formation process. From
a series of calculations of supersonic, hydrodynamic turbulence driven
using purely solenoidal Fourier modes, we find that the standard
relationship between the variance in the log of density and the Mach
number squared, i.e., sigma(2)(ln rho/(rho) over bar) = ln (1 +
b(2)M(2)), with b = 1/3, is a good fit to the numerical results in the
supersonic regime up to at least Mach 20, similar to previous
determinations at lower Mach numbers. While direct measurements of the
variance in linear density are found to be severely underestimated by
finite resolution effects, it is possible to infer the linear density
variance via the assumption of log-normality in the probability
distribution function. The inferred relationship with Mach number,
consistent with sigma(rho/rho) approximate to bM with b = 1/3, is,
however, significantly shallower than observational determinations of
the relationship in the Taurus Molecular Cloud and IC5146 (both
consistent with b approximate to 0.5), implying that additional
physics such as gravity is important in these clouds and/or that
turbulent driving in the interstellar medium contains a significant
compressive component. Magnetic fields are not found to change this
picture significantly, in general reducing the measured variances and
thus worsening the discrepancy with observations
AB - We examine the relation between the density variance and the
mean-square Mach number in supersonic, isothermal turbulence, assumed
in several recent analytic models of the star formation process. From
a series of calculations of supersonic, hydrodynamic turbulence driven
using purely solenoidal Fourier modes, we find that the standard
relationship between the variance in the log of density and the Mach
number squared, i.e., sigma(2)(ln rho/(rho) over bar) = ln (1 +
b(2)M(2)), with b = 1/3, is a good fit to the numerical results in the
supersonic regime up to at least Mach 20, similar to previous
determinations at lower Mach numbers. While direct measurements of the
variance in linear density are found to be severely underestimated by
finite resolution effects, it is possible to infer the linear density
variance via the assumption of log-normality in the probability
distribution function. The inferred relationship with Mach number,
consistent with sigma(rho/rho) approximate to bM with b = 1/3, is,
however, significantly shallower than observational determinations of
the relationship in the Taurus Molecular Cloud and IC5146 (both
consistent with b approximate to 0.5), implying that additional
physics such as gravity is important in these clouds and/or that
turbulent driving in the interstellar medium contains a significant
compressive component. Magnetic fields are not found to change this
picture significantly, in general reducing the measured variances and
thus worsening the discrepancy with observations
UR - http://adsabs.harvard.edu/abs/2011ApJ...727L..21P
U2 - 10.1088/2041-8205/727/1/L21
DO - 10.1088/2041-8205/727/1/L21
M3 - Article
SN - 2041-8205
VL - 727
SP - 1
EP - 5
JO - The Astrophysical Journal Letters
JF - The Astrophysical Journal Letters
IS - 1
ER -