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Register a new userDistortion of Magnetic Fields in a Starless Core IV: Magnetic Field Scaling on Density and Mass-to-flux Ratio Distribution in FeSt 1-457
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In the present study, the magnetic field scaling on density, $|B| propto rho^{kappa}$, was revealed in a single starless core for the first time. The $kappa$ index of $0.78 pm 0.10$ was obtained toward the starless dense core FeSt 1-457 based on the analysis of the radial distribution of the polarization angle dispersion of background stars measured at the near-infrared wavelengths. The result prefers $kappa = 2/3$ for the case of isotropic contraction, and the difference of the observed value from $kappa = 1/2$ is 2.8 sigma. The distribution of the ratio of mass to magnetic flux was evaluated. FeSt 1-457 was found to be magnetically supercritical near the center ($lambda approx 2$), whereas nearly critical or slightly subcritical at the core boundary ($lambda approx 0.98$). Ambipolar-diffusion-regulated star formation models for the case of moderate magnetic field strength may explain the physical status of FeSt 1-457. The mass-to-flux ratio distribution for typical dense cores (critical Bonnor--Ebert sphere with central $lambda=2$ and $kappa=1/2$--$2/3$) was calculated and found to be magnetically critical/subcritical at the core edge, which indicates that typical dense cores are embedded in and evolve from magnetically critical/subcritical diffuse surrounding medium.
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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 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.
Observational data for the hourglass-like magnetic field toward the starless dense core FeSt 1-457 were compared with a flux freezing magnetic field model (Myers et al. 2018). Fitting of the observed plane-of-sky magnetic field using the flux freezing model gave a residual angle dispersion comparable with the results based on a simple three-dimensional parabolic model. The best-fit parameters for the flux freezing model were a line-of-sight magnetic inclination angle of $gamma_{rm mag} = 35^{circ} pm 15^{circ}$ and a core center to ambient (background) density contrast of $rho_{rm c} / rho_{rm bkg} = 75$. The initial density for core formation ($rho_0$) was estimated to be $rho_{rm c} / 75 = 4670$ cm$^{-3}$, which is about one order of magnitude higher than the expected density ($sim 300$ cm$^{-3}$) for the inter-clump medium of the Pipe Nebula. FeSt 1-457 is likely to have been formed from the accumulation of relatively dense gas, and the relatively dense background column density of $A_V simeq 5$ mag supports this scenario. The initial radius (core formation radius) $R_0$ and the initial magnetic field strength $B_0$ were obtained to be 0.15 pc ($1.64 R$) and $10.8-14.6$ $mu$G, respectively. We found that the initial density $rho_0$ is consistent with the mean density of the nearly critical magnetized filament with magnetic field strength $B_0$ and radius $R_0$. The relatively dense initial condition for core formation can be naturally understood if the origin of the core is the fragmentation of magnetized filaments.
The relationship between submillimeter (submm) dust emission polarization and near-infrared (NIR) $H$-band polarization produced by dust dichroic extinction was studied for the cold starless dense core FeSt 1-457. The distribution of polarization angles ($90^{circ}$-rotated for submm) and degrees were found to be very different between at submm and NIR wavelengths. The mean polarization angles for FeSt 1-457 at submm and NIR wavelengths are $132.1^{circ} pm 22.0^{circ}$ and $2.7^{circ} pm 16.2^{circ}$, respectively. The correlation between $P_H$ and $A_V$ was found to be linear from outermost regions to relatively dense line of sight of $A_V approx 25$ mag, indicating that NIR polarization reflects overall polarization (magnetic field) structure of the core at least in this density range. The flat $P_H/A_V$ versus $A_V$ correlations were confirmed, and the polarization efficiency was found to be comparable to the observational upper limit (Jones 1989). On the other hand, as reported by Alves et al., submm polarization degrees show clear linearly decreasing trend against $A_V$ from $A_V approx 20$ mag to the densest center ($A_V approx 41$ mag), appearing as polarization hole structure. The power law index for the $P_{rm submm}$ versus $A_V$ relationship was obtained to be $approx -1$, indicating that the alignment for the submm sensitive dust is lost. These very different polarization distributions at submm and NIR wavelengths suggest that (1) there is different radiation environment at these wavelengths or (2) submm-sensitive dust is localized or the combination of them.
High resolution molecular line observations of CS, HCO+, C18O and N2H+ were obtained toward the starless globule FeSt 1-457 in order to investigate its kinematics and chemistry. The HCO+ and CS spectra show clear self-reversed and asymmetric profiles across the face of the globule. The sense of the observed asymmetry is indicative of the global presence of expansion motions in the outer layers of the globule. These motions appear to be subsonic and significantly below the escape velocity of the globule. Comparison of our observations with near-infrared extinction data indicate that the globule is gravitationally bound. Taken together these considerations lead us to suggest that the observed expansion has its origin in an oscillatory motion of the outer layers of the globule which itself is likely in a quasi-stable state near hydrostatic equilibrium. Analysis of the observed linewidths of CO and N2H+ confirm that thermal pressure is the dominant component of the clouds internal support. A simple calculation suggests that the dominant mode of pulsation would be an l = 2 mode with a period of 0.3 Myr. Deformation of the globule due to the large amplitude l = 2 oscillation may be responsible for the double-peaked structure of the core detected in high resolution extinction maps. Detailed comparison of the molecular-line observations and extinction data provides evidence for significant depletion of C18O and perhaps HCO+ while N2H+ may be undepleted to a cloud depth of about 40 magnitudes of visual extinction.
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