  We investigate the internal 3D magnetic structure of dense interstellar
filaments within NGC 1333 using polarization data at $850 \mu\mathrm{m}$ from
the $B$-fields In STar-forming Region Observations survey at the James Clerk
Maxwell Telescope. Theoretical models predict that the magnetic field lines in
a filament will tend to be dragged radially inward (i.e., pinched) toward the
central axis due to the filament's self-gravity. We study the cross-sectional
profiles of the total intensity ($I$) and polarized intensity (PI) of dust
emission in four segments of filaments unaffected by local star formation that
are expected to retain a pristine magnetic field structure. We find that the
filaments' FWHM in PI are not the same as those in $I$, with two segments being
appreciably narrower in PI (FWHM ratio $\simeq 0.7-0.8$) and one segment being
wider (FWHM ratio $\simeq 1.3$). The filament profiles of the polarization
fraction ($P$) do not show a minimum at the spine of the filament, which is not
in line with an anticorrelation between $P$ and $I$ normally seen in molecular
clouds and protostellar cores. Dust grain alignment variation with density
cannot reproduce the observed $P$ distribution. We demonstrate numerically that
the $I$ and PI cross-sectional profiles of filaments in magnetohydrostatic
equilibrium will have differing relative widths depending on the viewing angle.
The observed variations of FWHM ratios in NGC 1333 are therefore consistent
with models of pinched magnetic field structures inside filaments, and
especially if they are magnetically near-critical or supercritical.

Astrophysics of Galaxies