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

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, sigma(2)(rho/rho 0), with rms Mach number, M of the form: sigma(2)(rho/rho 0) = b(2)M(2), 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 (CO)-C-13 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 sigma(2)(rho/rho 0). When this is combined with a measurement of the rms Mach number, M, we are able to estimate b. We find b = 0.48(-0.11)(+0.15), 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 similar to 1 pc, and find that the break is associated with anisotropy in the power spectrum. The break is observed in both (CO)-C-13 and dust extinction power spectra, which, remarkably, are effectively identical despite detailed spatial differences between the (CO)-C-13 and dust extinction maps.