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.
