Magnetohydrostatic Equilibrium Structure and Mass of Polytropic Filamentary Cloud Threaded by Lateral Magnetic Field

Abstract

Filamentary structures are recognized as a fundamental component of interstellar molecular clouds in observations by the Herschel satellite. These filaments, especially massive filaments, often extend in a direction perpendicular to the interstellar magnetic field. Furthermore, the filaments sometimes have an apparently negative temperature gradient, that is, their temperature decreases towards the center. In this paper, we study the magnetohydrostatic equilibrium state of negative-indexed polytropic gas with the magnetic field running perpendicular to the axis of the filament. The model is controlled by four parameters: center-to-surface density ratio (${\rho }_c/{\rho }_s$), plasma $\beta$ of the surrounding gas, radius of the parent cloud $R_0^{\prime }$ normalized by the scale height, and the polytropic index $N$. The steepness of the temperature gradient is represented by $N$. We found that the envelope of the column density profile becomes shallow when the temperature gradient is large. This reconciles the inconsistency between the observed profiles and those expected from the isothermal models. We compared the maximum line-mass (mass per unit length), above which there is no equilibrium, with that of the isothermal non-magnetized filament. We obtained an empirical formula to express the maximum line-mass of a magnetized polytropic filament as ${\lambda }_{max}\simeq {\left[{\left({\lambda }_{0,max}(N)/M_{\odot }\mathrm{p}{\mathrm{c}}^{-1}\right)}^2+{\left[5.9(1.0+1.2/N{)}^{1/2}({\Phi }_{cl}/1\mu \mathrm{G}\mathrm{pc})\right]}^2\right]}^{1/2}{M}_{\odot }\mathrm{p}{\mathrm{c}}^{-1}$, where ${\lambda }_{0,max}(N)$ represents the maximum line-mass of the non-magnetized filament and ${\Phi }_{cl}$ indicates one-half of the magnetic flux threading the filament per unit length. Although the negative-indexed polytrope makes the maximum line-mass decrease compared with that of the isothermal model, a magnetic field threading the filament increases the line-mass.

arXiv comment40 pages, 12 figures, accepted for publication in ApJ

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Cited by in corpus (9)

• Mapping the magnetic field in the Taurus/B211 filamentary cloud with SOFIA HAWC+ and comparing with simulation
• Witnessing the fragmentation of a filament into prestellar cores in Orion B/NGC 2024
• The JCMT BISTRO Survey: Evidence for Pinched Magnetic Fields in Quiescent Filaments of NGC 1333
• The origin of a universal filament width in molecular clouds
• The Role of Magnetic Fields in the Stability and Fragmentation of Filamentary Molecular Clouds: Two Case Studies at OMC-3 and OMC-4
• Filaments in the OMC-3 cloud and uncertainties in estimates of filament profiles
• Simulation of Head-on Collisions Between Filamentary Molecular Clouds Threaded by a Lateral Magnetic Field and Subsequent Evolution
• Instability and Evolution of Shocked Clouds Formed by Orthogonal Collisions between Magnetized Filamentary Molecular Clouds
• Evolution of compressed clouds formed by filament coalescence. I. Oblique collisions