Strong Magnetic Fields Play Important Role in the Filamentary Infrared Dark Cloud G11.11-0.12

We report on the near-infrared polarimetric observations of G11.11--0.12 with the 1.4 m IRSF telescope. The starlight polarization of the background stars reveals the magnetic fields in the envelope of G11.11--0.12, which are consistent in orientation with the magnetic fields obtained from submillimeter dust polarization. The magnetic fields in G11.11--0.12 are perpendicular to the filament in a large column density range, independent of the relative orientations of G11.11--0.12. The field strength on the plane of the sky in G11.11--0.12 has a typical value of $152\pm 17\mu$G. The analyses of the magnetic fields and gas velocity dispersion indicate that the envelope of G11.11--0.12 is supersonic and sub-Alfv{\'e}nic to trans-Alfv{\'e}nic. The mass-to-flux ratio in the outer part of the envelope is $\lesssim 1$ and slightly increases to $\gtrsim 1$ closer to the filament. The weights on the relative importance of magnetic fields, turbulence and gravity indicate that gravity has been dominating the dynamical state of G11.11--0.12, with significant contribution from magnetic fields. The field strength increases slower than the gas density from the envelope to the spine of G11.11--0.12, characterized by the relation $B\propto n^{0.2}$. The observed strength and orientation of magnetic fields in G11.11--0.12 imply that supersonic gas flow is channelled by sub-Alfv{\'e}nic magnetic fields and is assembled into filaments perpendicular to the magnetic fields. The formation of low-mass stars is enhanced in the filaments with high column density, in agreement with the excess in numbers of low-mass protostars detected in one of the densest part of G11.11--0.12.