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Register a new userThe Density Variance Mach Number Relation in the Taurus Molecular Cloud
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Chris Brunt
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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 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 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 sigma^{2}_{rho/rho_{0}}. We find b ~ 0.48, 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. We also report a break in the Taurus column density power spectrum at a scale of ~1pc, 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. [ abridged ]
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It is widely accepted that supersonic, magnetised turbulence plays a fundamental role for star formation in molecular clouds. It produces the initial dense gas seeds out of which new stars can form. However, the exact relation between gas compression, turbulent Mach number, and magnetic field strength is still poorly understood. Here, we introduce and test an analytical prediction for the relation between the density variance and the root-mean-square Mach number in supersonic, isothermal, magnetised turbulent flows. We approximate the density and velocity structure of the interstellar medium as a superposition of shock waves. We obtain the density contrast considering the momentum equation for a single magnetised shock and extrapolate this result to the entire cloud. Depending on the field geometry, we then make three different assumptions based on observational and theoretical constraints: B independent of density, B proportional to the root square of the density and B proportional to the density. We test the analytically derived density variance--Mach number relation with numerical simulations, and find that for B proportional to the root square of the density, the variance in the logarithmic density contrast, $sigma_{ln rho/rho_0}^2=ln[1+b^2mathscr{M}^2beta_0/(beta_0+1)]$, fits very well to simulated data with turbulent forcing parameter b=0.4, when the gas is super-Alfvenic. However, this result breaks down when the turbulence becomes trans-Alfvenic or sub-Alfvenic, because in this regime the turbulence becomes highly anisotropic. Our density variance--Mach number relations simplify to the purely hydrodynamic relation as the ratio of thermal to magnetic pressure $beta_0$ approaches infinite.
Measuring the mass distribution of infrared dark clouds (IRDCs) over the wide dynamic range of their column densities is a fundamental obstacle in determining the initial conditions of high-mass star formation and star cluster formation. We present a new technique to derive high-dynamic-range, arcsecond-scale resolution column density data for IRDCs and demonstrate the potential of such data in measuring the density variance - sonic Mach number relation in molecular clouds. We combine near-infrared data from the UKIDSS/Galactic Plane Survey with mid-infrared data from the Spitzer/GLIMPSE survey to derive dust extinction maps for a sample of ten IRDCs. We then examine the linewidths of the IRDCs using 13CO line emission data from the FCRAO/Galactic Ring Survey and derive a column density - sonic Mach number relation for them. For comparison, we also examine the relation in a sample of nearby molecular clouds. The presented column density mapping technique provides a very capable, temperature independent tool for mapping IRDCs over the column density range equivalent to A_V=1-100 mag at a resolution of 2. Using the data provided by the technique, we present the first direct measurement of the relationship between the column density dispersion, sigma_{N/<N>}, and sonic Mach number, M_s, in molecular clouds. We detect correlation between the variables with about 3-sigma confidence. We derive the relation sigma_{N/<N>} = (0.047 pm 0.016) Ms, which is suggestive of the correlation coefficient between the volume density and sonic Mach number, sigma_{rho/<rho>} = (0.20^{+0.37}_{-0.22}) Ms, in which the quoted uncertainties indicate the 3-sigma range. When coupled with the results of recent numerical works, the existence of the correlation supports the picture of weak correlation between the magnetic field strength and density in molecular clouds (i.e., B ~ rho^{0.5}).
We study four lines of sight that probe the transition from diffuse molecular gas to molecular cloud material in Taurus. Measurements of atomic and molecular absorption are used to infer the distribution of species and the physical conditions toward stars behind the Taurus Molecular Cloud (TMC). New high-resolution spectra at visible and near infrared wavelengths of interstellar Ca II, Ca I, K I, CH, CH^+, C2, CN, and CO toward HD28975 and HD29647 are combined with data at visible wavelengths and published CO results from ultraviolet measurements for HD27778 and HD30122. Gas densities and temperatures are inferred from C2, CN, and CO excitation and CN chemistry. Our results for HD29647 are noteworthy because the CO column density is 10^{18} cm^{-2} while C2 and CO excitation reveals a temperature of 10 K and density about 1000 cm^{-3}, more like conditions found in dark molecular clouds. Similar results arise from our chemical analysis for CN through reactions involving observations of CH, C2, and NH. Enhanced potassium depletion and a reduced CH/H2 column density ratio also suggest the presence of a dark cloud. The directions toward HD27778 and HD30122 probe molecule-rich diffuse clouds, which can be considered CO-dark gas, while the sight line toward HD28975 represents an intermediate case. Maps of dust temperature help refine the description of the material along the four sight lines and provide an estimate of the distance between HD29647 and a clump in the TMC. An Appendix provides results for the direction toward HD26571; this star also probes diffuse molecular gas.
We present the results of mapping observations toward a nearby starless filamentary cloud, the Taurus Molecular Cloud 1 (TMC-1), in the CCS(JN=43-32, 45.379033 GHz) emission line, using the Nobeyama 45-m telescope. The map shows that the TMC-1 filament has a diameter of ~0.1 pc and a length of ~0.5 pc at a distance of 140 pc. The position-velocity diagrams of CCS clearly indicate the existence of velocity-coherent substructures in the filament. We identify 21 substructures that are coherent in the position-position-velocity space by eye. Most of the substructures are elongated along the major axis of the TMC-1 filament. The line densities of the subfilaments are close to the critical line density for the equilibrium (~17 Mo/pc for the excitation temperature of 10 K), suggesting that self-gravity should play an important role in the dynamics of the subfilaments.
Optical stellar polarimetry in the Perseus molecular cloud direction is known to show a fully mixed bi-modal distribution of position angles across the cloud (Goodman et al. 1990). We study the Gaia trigonometric distances to each of these stars and reveal that the two components in position angles trace two different dust clouds along the line of sight. One component, which shows a polarization angle of -37.6 deg +/- 35.2 deg and a higher polarization fraction of 2.0 +/- 1.7%, primarily traces the Perseus molecular cloud at a distance of 300 pc. The other component, which shows a polarization angle of +66.8 deg +/- 19.1 deg and a lower polarization fraction of 0.8 +/- 0.6%, traces a foreground cloud at a distance of 150 pc. The foreground cloud is faint, with a maximum visual extinction of < 1 mag. We identify that foreground cloud as the outer edge of the Taurus molecular cloud. Between the Perseus and Taurus molecular clouds, we identify a lower-density ellipsoidal dust cavity with a size of 100 -- 160 pc. This dust cavity locates at l = 170 deg, b = -20 deg, and d = 240 pc, which corresponds to an HI shell generally associated with the Per OB2 association. The two-component polarization signature observed toward the Perseus molecular cloud can therefore be explained by a combination of the plane-of-sky orientations of the magnetic field both at the front and at the back of this dust cavity.
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