Distortion of Magnetic Fields in a Starless Core VI: Application of Flux Freezing Model and Core Formation of FeSt 1-457

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.