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Filamentary structures are recognized as a fundamental component ofinterstellar molecular clouds in observations by the Herschel satellite. Thesefilaments, especially massive filaments, often extend in a directionperpendicular to the interstellar magnetic field. Furthermore, the filamentssometimes have an apparently negative temperature gradient, that is, theirtemperature decreases towards the center. In this paper, we study themagnetohydrostatic equilibrium state of negative-indexed polytropic gas withthe magnetic field running perpendicular to the axis of the filament. The modelis controlled by four parameters: center-to-surface density ratio($\rho_c/\rho_s$), plasma $\beta$ of the surrounding gas, radius of the parentcloud $R'_0$ normalized by the scale height, and the polytropic index $N$. Thesteepness of the temperature gradient is represented by $N$. We found that theenvelope of the column density profile becomes shallow when the temperaturegradient is large. This reconciles the inconsistency between the observedprofiles and those expected from the isothermal models. We compared the maximumline-mass (mass per unit length), above which there is no equilibrium, withthat of the isothermal non-magnetized filament. We obtained an empiricalformula to express the maximum line-mass of a magnetized polytropic filament as$\lambda_{max}\simeq\left[{\left(\lambda_{0,max}(N)/M_\odot{\rmpc^{-1}}\right)^2+\left[5.9(1.0+1.2/N)^{1/2}({\Phi_{cl}}/{1\mu {\rmG\,pc}})\right]^2}\right]^{1/2}M_\odot {\rm pc^{-1}}$, where$\lambda_{0,max}(N)$ represents the maximum line-mass of the non-magnetizedfilament and $\Phi_{cl}$ indicates one-half of the magnetic flux threading thefilament per unit length. Although the negative-indexed polytrope makes themaximum line-mass decrease compared with that of the isothermal model, amagnetic field threading the filament increases the line-mass.

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