  Filaments are considered to be basic structures and molecular clouds consist
of filaments. Filaments are often observed as extending in the direction
perpendicular to the interstellar magnetic field. The structure of filaments
has been studied based on a magnetohydrostatic equilibrium model (Tomisaka
2014). Here, we simulate the expected polarization pattern for isothermal
magnetohydrostatic filaments. The filament exhibits a polarization pattern in
which the magnetic field is apparently perpendicular to the filament when
observed from the direction perpendicular to the magnetic field. When the
line-of-sight is parallel to the global magnetic field, the observed
polarization pattern is dependent on the center-to-surface density ratio for
the filament and the concentration of the gas mass toward the central magnetic
flux tube. Filaments with low center-to-surface density ratios have an
insignificant degree of polarization when observed from the direction parallel
to the global magnetic field. However, models with a large center-to-surface
density ratio have polarization patterns that indicate the filament is
perpendicularly threaded by the magnetic field. When mass is heavily
concentrated at the central magnetic flux tube, which can be realized by the
ambipolar diffusion process, the polarization pattern is similar to that
expected for a low center-to-surface density contrast.
