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In this study, the detailed magnetic field structure of the dense protostellar core Barnard 335 (B335) was revealed based on near-infrared polarimetric observations of background stars to measure dichroically polarized light produced by magnetically aligned dust grains in the core. Magnetic fields pervading B335 were mapped using 24 stars after subtracting unrelated ambient polarization components, for the first time revealing that they have an axisymmetrically distorted hourglass-shaped structure toward the protostellar core. On the basis of simple two- and three-dimensional magnetic field modeling, magnetic inclination angles in the plane-of-sky and line-of-sight directions were determined to be $90^{circ} pm 7^{circ}$ and $50^{circ} pm 10^{circ}$, respectively. The total magnetic field strength of B335 was determined to be $30.2 pm 17.7$ $mu {rm G}$. The critical mass of B335, evaluated using both magnetic and thermal/turbulent support against collapse, was determined to be $M_{rm cr} = 3.37 pm 0.94$ ${rm M}_{odot}$, which is identical to the observed core mass of $M_{rm core}=3.67$ M$_{odot}$. We thus concluded that B335 started its contraction from a condition near equilibrium. We found a linear relationship in the polarization versus extinction diagram, up to $A_V sim 15$ mag toward the stars with the greatest obscuration, which verified that our observations and analysis provide an accurate depiction of the core.
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The magnetic field structure, kinematical stability, and evolutionary status of the starless dense core Barnard 68 (B68) are revealed based on the near-infrared polarimetric observations of background stars, measuring the dichroically polarized light produced by aligned dust grains in the core. After subtracting unrelated ambient polarization components, the magnetic fields pervading B68 are mapped using 38 stars and axisymmetrically distorted hourglass-like magnetic fields are obtained, although the evidence for the hourglass field is not very strong. On the basis of simple 2D and 3D magnetic field modeling, the magnetic inclination angles on the plane-of-sky and in the line-of-sight direction are determined to be $47^{circ} pm 5^{circ}$ and $20^{circ} pm 10^{circ}$, respectively. The total magnetic field strength of B68 is obtained to be $26.1 pm 8.7$ $mu {rm G}$. The critical mass of B68, evaluated using both magnetic and thermal/turbulent support, is $M_{rm cr} = 2.30 pm 0.20$ ${rm M}_{odot}$, which is consistent with the observed core mass of $M_{rm core}=2.1$ M$_{odot}$, suggesting nearly critical state. We found a relatively linear relationship between polarization and extinction up to $A_V sim 30$ mag toward the stars with deepest obscuration. Further theoretical and observational studies are required to explain the dust alignment in cold and dense regions in the core.
The magnetic field structure of a star-forming Bok globule BHR 71 was determined based on near-infrared polarimetric observations of background stars. The magnetic field in BHR 71 was mapped from 25 stars. By using a simple 2D parabolic function, the plane-of-sky magnetic axis of the core was found to be $theta_{rm mag} = 125^{circ} pm 11^{circ}$. The plane-of-sky mean magnetic field strength of BHR 71 was found to be $B_{rm pos} = 8.8 - 15.0$ $mu$G, indicating that the BHR 71 core is magnetically supercritical with $lambda = 1.44 - 2.43$. Taking into account the effect of thermal/turbulent pressure and the plane-of-sky magnetic field component, the critical mass of BHR 71 was $M_{rm cr} = 14.5-18.7$ M$_{odot}$, which is consistent with the observed core mass of $M_{rm core} approx 14.7$ M$_{odot}$ (Yang et al. 2017). We conclude that BHR 71 is in a condition close to a kinematically critical state, and the magnetic field direction lies close to the plane of sky. Since BHR 71 is a star-forming core, a significantly subcritical condition (i.e., the magnetic field direction deviating from the plane of sky) is unlikely, and collapsed from a condition close to a kinematically critical state. There are two possible scenarios to explain the curved magnetic fields of BHR 71, one is an hourglass-like field structure due to mass accumulation and the other is the Inoue & Fukui (2013) mechanism, which proposes the interaction of the core with a shock wave to create curved magnetic fields wrapping around the core.
Three dimensional (3D) magnetic field information on molecular clouds and cores is important for revealing their kinematical stability (magnetic support) against gravity which is fundamental for studying the initial conditions of star formation. In the present study, the 3D magnetic field structure of the dense starless core FeSt 1-457 is determined based on the near-infrared polarimetric observations of the dichroic polarization of background stars and simple 3D modeling. With an obtained angle of line-of-sight magnetic inclination axis $theta_{rm inc}$ of $45^{circ}pm10^{circ}$ and previously determined plane-of-sky magnetic field strength $B_{rm pol}$ of $23.8pm12.1$ $mu{rm G}$, the total magnetic field strength for FeSt 1-457 is derived to be $33.7pm18.0$ $mu{rm G}$. The critical mass of FeSt 1-457, evaluated using both magnetic and thermal/turbulent support is ${M}_{rm cr} = 3.70pm0.92$ ${rm M}_{odot}$, which is identical to the observed core mass, $M_{rm core}=3.55pm0.75$ ${rm M}_{odot}$. We thus conclude that the stability of FeSt 1-457 is in a condition close to the critical state. Without infalling gas motion and no associated young stars, the core is regarded to be in the earliest stage of star formation, i.e., the stage just before the onset of dynamical collapse following the attainment of a supercritical condition. These properties would make FeSt 1-457 one of the best starless cores for future studies of the initial conditions of star formation.
The detailed magnetic field structure of the starless dense core CB81 (L1774, Pipe 42) in the Pipe Nebula was determined based on near-infrared polarimetric observations of background stars to measure dichroically polarized light produced by magnetically aligned dust grains in the core. The magnetic fields pervading CB81 were mapped using 147 stars and axisymmetrically distorted hourglass-like fields were identified. On the basis of simple 2D and 3D magnetic field modeling, the magnetic inclination angles in the plane-of-sky and line-of-sight directions were determined to be $4^{circ} pm 8^{circ}$ and $20^{circ} pm 20^{circ}$, respectively. The total magnetic field strength of CB81 was found to be $7.2 pm 2.3$ $mu{rm G}$. Taking into account the effects of thermal/turbulent pressure and magnetic fields, the critical mass of CB81 was calculated to be $M_{rm cr}=4.03 pm 0.40$ M$_{odot}$, which is close to the observed core mass of $M_{rm core}=3.37 pm 0.51$ M$_{odot}$. We thus conclude that CB81 is in a condition close to the critical state. In addition, a spatial offset of $92$ was found between the center of magnetic field geometry and the dust extinction distribution; this offset structure could not have been produced by self-gravity. The data also indicate a linear relationship between polarization and extinction up to $A_V sim 30$ mag going toward the core center. This result confirms that near-infrared polarization can accurately trace the overall magnetic field structure of the core.
The relationship between dust polarization and extinction was determined for the cold dense starless molecular cloud core FeSt 1-457 based on the background star polarimetry of dichroic extinction at near-infrared wavelengths. Owing to the known (three-dimensional) magnetic field structure, the observed polarizations from the core were corrected by considering (a) the subtraction of the ambient polarization component, (b) the depolarization effect of inclined distorted magnetic fields, and (c) the magnetic inclination angle of the core. After these corrections, a linear relationship between polarization and extinction was obtained for the core in the range up to $A_V approx 20$ mag. The initial polarization vs. extinction diagram changed dramatically after the corrections of (a) to (c), with the correlation coefficient being refined from 0.71 to 0.79. These corrections should affect the theoretical interpretation of the observational data. The slope of the finally obtained polarization--extinction relationship is $P_H / E_{H-K_s} = 11.00 pm 0.72$ $%$ ${rm mag}^{-1}$, which is close to the statistically estimated upper limit of the interstellar polarization efficiency (Jones 1989). This consistency suggests that the upper limit of interstellar polarization efficiency might be determined by the observational viewing angle toward polarized astronomical objects.
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