Tensor virial analysis and magnetic field perturbations of magnetized molecular cloud cores

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Franzmann, Erica
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We present a detailed analysis of the three-axis stability of molecular cloud core model geometries and the effects of three-dimensional magnetic field perturbations on simulated polarization maps. We have previously developed a molecular cloud core modelling package called “PolCat”, which generates three-dimensional models of density and magnetic field structures constrained by reduced χ2 fits to submillimetre polarization and continuum intensity data. PolCat fits provide insight into the underlying structures of cores, and by extension, the initial conditions from which stars form. The most commonly applied form of the virial theorem in an astrophysical context is the scalar form, with relatively few applications of the full tensor form. We have found through examination of the three-axis virial equilibria not only the expected families of spheroidal geometries, but also families of triaxial ellipsoid geometries. In application as a PolCat stability check, we allowed our models to be slightly out of tensor equilibrium. We performed tests with both synthetic data and data of the OMC-1 BN/KL region from the SCUPOL Legacy Catalogue and BISTRO survey. We found that the virial criterion eliminated models with unrealistic geometries. Additionally, magnetic field strength estimates from the virial fits were in good agreement with independent measurements of the region. A common method to estimate magnetic field strengths from polarization is the Chandrasekhar-Fermi method, where deflections of B-field polarization vectors from an assumed large-scale structure are assumed to directly equate to Alfvénic perturbations in the underlying magnetic field. However, a limitation of this method is that polarization maps are two-dimensional projections of three-dimensional structures, and the traced large-scale field may not be truly representative of the underlying structure. To examine the how three-dimensional perturbations would affect the polarization maps, we developed a method to propagate Alfvén waves along PolCat models’ curved magnetic field lines and compared the perturbed and unperturbed maps. After perturbing our models with both individual and cumulative single-mode Alfvén waves, we find that patterns of deflection are highly dependent on the inclination of the magnetic field to the line of sight, and each model geometry has a characteristic pattern of deflection.
Molecular Clouds, Astrophysics, Modelling, Stability, virial theorem, Alfvén waves, Star formation, Submillimetre polarization, MHD, magnetohydrodynamics, ISM, tensor virial theorem, Alfvén wave propagation