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Register a new userOn the relation between the column density structures and the magnetic field orientation in the Vela C molecular complex
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We statistically evaluate the relative orientation between gas column density structures, inferred from Herschel submillimetre observations, and the magnetic field projected on the plane of sky, inferred from polarized thermal emission of Galactic dust observed by BLASTPol at 250, 350, and 500 micron, towards the Vela C molecular complex. First, we find very good agreement between the polarization orientations in the three wavelength-bands, suggesting that, at the considered common angular resolution of 3.0 arcminutes that corresponds to a physical scale of approximately 0.61 pc, the inferred magnetic field orientation is not significantly affected by temperature or dust grain alignment effects. Second, we find that the relative orientation between gas column density structures and the magnetic field changes progressively with increasing gas column density, from mostly parallel or having no preferred orientation at low column densities to mostly perpendicular at the highest column densities. This observation is in agreement with previous studies by the Planck collaboration towards more nearby molecular clouds. Finally, we find a correspondence between the trends in relative orientation and the shape of the column density probability distribution functions. In the sub-regions of Vela C dominated by one clear filamentary structure, or ridges, we find a sharp transition from preferentially parallel or having no preferred relative orientation at low column densities to preferentially perpendicular at highest column densities. In the sub-regions of Vela C dominated by several filamentary structures with multiple orientations, or nests, such a transition is also present, but it is clearly less sharp than in the ridge-like sub-regions. Both of these results suggest that the magnetic field is dynamically important for the formation of density structures in this region.
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We compare the magnetic field orientation for the young giant molecular cloud Vela C inferred from 500-$mu$m polarization maps made with the BLASTPol balloon-borne polarimeter to the orientation of structures in the integrated line emission maps from Mopra observations. Averaging over the entire cloud we find that elongated structures in integrated line-intensity, or zeroth-moment maps, for low density tracers such as $^{12}$CO and $^{13}$CO $J$ $rightarrow$ 1 - 0 are statistically more likely to align parallel to the magnetic field, while intermediate or high density tracers show (on average) a tendency for alignment perpendicular to the magnetic field. This observation agrees with previous studies of the change in relative orientation with column density in Vela C, and supports a model where the magnetic field is strong enough to have influenced the formation of dense gas structures within Vela C. The transition from parallel to no preferred/perpendicular orientation appears to happen between the densities traced by $^{13}$CO and by C$^{18}$O $J$ $rightarrow$ 1 - 0. Using RADEX radiative transfer models to estimate the characteristic number density traced by each molecular line we find that the transition occurs at a molecular hydrogen number density of approximately $10^3$ cm$^{-3}$. We also see that the Centre-Ridge (the highest column density and most active star-forming region within Vela C) appears to have a transition at a lower number density, suggesting that this may depend on the evolutionary state of the cloud.
We present results for Vela C obtained during the 2012 flight of the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry (BLASTPol). We mapped polarized intensity across almost the entire extent of this giant molecular cloud, in bands centered at 250, 350, and 500 {mu}m. In this initial paper, we show our 500 {mu}m data smoothed to a resolution of 2.5 arcminutes (approximately 0.5 pc). We show that the mean level of the fractional polarization p and most of its spatial variations can be accounted for using an empirical three-parameter power-law fit, p = p_0 N^(-0.4) S^(-0.6), where N is the hydrogen column density and S is the polarization-angle dispersion on 0.5 pc scales. The decrease of p with increasing S is expected because changes in the magnetic field direction within the cloud volume sampled by each measurement will lead to cancellation of polarization signals. The decrease of p with increasing N might be caused by the same effect, if magnetic field disorder increases for high column density sightlines. Alternatively, the intrinsic polarization efficiency of the dust grain population might be lower for material along higher density sightlines. We find no significant correlation between N and S. Comparison of observed submillimeter polarization maps with synthetic polarization maps derived from numerical simulations provides a promising method for testing star formation theories. Realistic simulations should allow for the possibility of variable intrinsic polarization efficiency. The measured levels of correlation among p, N, and S provide points of comparison between observations and simulations.
The role of the magnetic field in the formation of the filamentary structures observed in the interstellar medium (ISM) is a debated topic. The Planck all-sky maps of linearly polarized emission from dust at 353GHz provide the required combination of imaging and statistics to study the correlation between the structures of the Galactic magnetic field and of interstellar matter, both in the diffuse ISM and in molecular clouds. The data reveal structures, or ridges, in the intensity map with counterparts in the Stokes Q and/or U maps. We focus on structures at intermediate and high Galactic latitudes with column density from $10^{20}$ to $10^{22}$ cm$^{-2}$. We measure the magnetic field orientation on the plane of the sky from the polarization data, and present an algorithm to estimate the orientation of the ridges from the dust intensity map. We use analytical models to account for projection effects. Comparing polarization angles on and off the structures, we estimate the mean ratio between the strengths of the turbulent and mean components of the magnetic field to be between 0.6 and 1.0, with a preferred value of 0.8. We find that the ridges are preferentially aligned with the magnetic field measured on the structures. This trend becomes more striking for increasing polarization fraction and decreasing column density. We interpret the increase of alignment with polarization fraction as a consequence of projections effects. The decrease of alignment for high column density is not due to a loss of correlation between the structures and the geometry of the magnetic field. In molecular complexes, we observe structures perpendicular to the magnetic field, which cannot be accounted for by projection effects. We discuss our results in the context of models and MHD simulations, which describe the formation of structures in the magnetized ISM.
Simulations generally show that non-self-gravitating clouds have a lognormal column density ($Sigma$) probability distribution function (PDF), while self-gravitating clouds with active star formation develop a distinct power-law tail at high column density. Although the growth of the power law can be attributed to gravitational contraction leading to the formation of condensed cores, it is often debated if an observed lognormal shape is a direct consequence of supersonic turbulence alone, or even if it is really observed in molecular clouds. In this paper we run three-dimensional magnetohydrodynamic simulations including ambipolar diffusion with different initial conditions to see the effect of strong magnetic fields and nonlinear initial velocity perturbations on the evolution of the column density PDFs. Our simulations show that column density PDFs of clouds with supercritical mass-to-flux ratio, with either linear perturbations or nonlinear turbulence, quickly develop a power-law tail such that $dN/d log Sigma propto Sigma^{-alpha}$ with index $alpha simeq 2$. Interestingly, clouds with subcritical mass-to-flux ratio also proceed directly to a power-law PDF, but with a much steeper index $alpha simeq 4$. This is a result of gravitationally-driven ambipolar diffusion. However, for nonlinear perturbations with a turbulent spectrum ($v_{k}^{2} propto k^{-4}$), the column density PDFs of subcritical clouds do retain a lognormal shape for a major part of the cloud evolution, and only develop a distinct power-law tail with index $alpha simeq 2$ at greater column density when supercritical pockets are formed.
Both observational and theoretical research over the past decade has demonstrated that the probability distribution function (PDF) of the gas density in turbulent molecular clouds is a key ingredient for understanding star formation. It has recently been argued that the PDF of molecular clouds is a pure power-law distribution. It has been claimed that the log-normal part is ruled out when using only the part of the PDF up/down to which it is complete, that is where the column density contours are still closed. By using the results from high-resolution magnetohydrodynamical simulations of molecular cloud formation and evolution, we find that the column density PDF is indeed composed of a log-normal and, if including self-gravity, a power-law part. We show that insufficient sampling of a molecular cloud results in closed contours that cut off the log-normal part. In contrast, systematically increasing the field of view and sampling the entire cloud yields a completeness limit at the lower column densities, which also recovers the log-normal part. This demonstrates that the field of view must be sufficiently large for the PDF to be complete down to its log-normal part, which has important implications for predictions of star-formation activity based on the PDF.
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