The density variance – Mach number relation in the Taurus molecular cloud

Astrophysics Group, School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK e-mail: brunt@astro.ex.ac.uk

Received: 20 October 2009
Accepted: 2 February 2010

Abstract

Supersonic turbulence in molecular clouds is a key agent in generating density enhancements that may subsequently go on to form stars. The stronger the turbulence – the higher the Mach number – the more extreme the density fluctuations are expected to be. Numerical models predict an increase in density variance, , with rms Mach number, M of the form: = , where b is a numerically-estimated parameter, and this prediction forms the basis of a large number of analytic models of star formation. We provide an estimate of the parameter b from ¹³CO J = 1-0 spectral line imaging observations and extinction mapping of the Taurus molecular cloud, using a recently developed technique that needs information contained solely in the projected column density field to calculate . When this is combined with a measurement of the rms Mach number, M, we are able to estimate b. We find , which is consistent with typical numerical estimates, and is characteristic of turbulent driving that includes a mixture of solenoidal and compressive modes. More conservatively, we constrain b to lie in the range 0.3-0.8, depending on the influence of sub-resolution structure and the role of diffuse atomic material in the column density budget (accounting for sub-resolution variance results in higher values of b, while inclusion of more low column density material results in lower values of b; the value b = 0.48 applies to material which is predominantly molecular, with no correction for sub-resolution variance). We also report a break in the Taurus column density power spectrum at a scale of ~1 pc, and find that the break is associated with anisotropy in the power spectrum. The break is observed in both ¹³CO and dust extinction power spectra, which, remarkably, are effectively identical despite detailed spatial differences between the ¹³CO and dust extinction maps.