An Origin of Radially Aligned Filaments in Hub-Filament Systems

Abstract

Recent observations have identified hub-filament systems (HFSs) as the primary formation sites of massive stars and star clusters. Some HFSs are characterized by multiple filaments aligned radially toward a central high-density hub. However, the physical origin of radially aligned filaments remains unknown. Here, we propose a new formation mechanism of HFSs driven by the interaction of a fast magnetohydrodynamic shock with a molecular cloud characterized by an hourglass-shaped magnetic field and density inhomogeneity. Our three-dimensional magnetohydrodynamic simulations show that the shock propagation leads to the formation of radially aligned filamentary structures with line masses slightly above the thermally critical line mass and lengths of $1$-$3\,\rm{pc}$, and widths of $0.06$-$0.08\,\rm{pc}$. High-density filamentary gas ($n_{\rm{H_2}} \sim 10^4 \, \rm{cm^{-3}}$) selectively exhibits inward velocities of $1-4\, \rm{km \, s^{-1}}$ that increase toward the hub center, while the ambient low-density inter-filament gas retains low velocities regardless of the radius. Mass accretion onto the hub is channeled through dense filaments. The filament formation is driven by oblique shocks generated at the bent magnetic field lines. The resulting post-shock amplification of the tangential magnetic field induces a magnetically guided inflow. The shock-interface interaction amplifies density perturbations, resembling Richtmyer--Meshkov instability modes, which promotes the fragmentation of the shocked layer into multiple filaments. The process studied in this Letter explains both the morphology of radially aligned filaments and the selective mass accretion observed in HFSs. In our simulation, the resulting star formation efficiency is $\sim4\%$, suggesting that the shock-driven evolution limits the SFE to only a few percent.

Figures (5)

• Figure 1: $\mathrm{H_2}$ column density maps in the $x$--$y$ plane at $t=0.5\,\mathrm{Myr}$ after the shock sweeps the cloud for different inclination angles $\psi$ between the shock propagation direction and the magnetic-field axis. The panels show $\psi=0^\circ$, $15^\circ$, and $30^\circ$. The color scale represents the $\mathrm{H_2}$ column density integrated along the $z$-axis. The box size is $5.0\,\mathrm{pc}$ on each side. Small inset schematics in each panel illustrate the definition of the inclination angle $\psi$ (between the shock propagation direction and the magnetic-field axis) and the corresponding initial cloud--field geometry; the gray shape, magenta line, and blue arrow indicate the initial cloud density profile, magnetic-field direction, and shock propagation direction, respectively.
• Figure 2: (a) $\mathrm{H_2}$ column density map from the left panel of Figure \ref{['hf']}, overlaid with filament skeletons identified using DisPerSEsousbie2011asousbie2011b. The lines labeled R1 and R2 denote cuts parallel and perpendicular to the filaments, respectively (see Figure \ref{['v_b']} for details). The white circle (diameter of $4.5\,\mathrm{pc}$) indicates the region centered on the density peak. (b)--(c) Radial profiles of the mean angle $\langle\Delta\theta\rangle$ (b) and the RMS angle (c) of the filaments relative to the radial vector from the hub center. The hub center is defined as the column density peak, distinct from the geometric center of the simulation box. The angle $\Delta\theta$ ranges from $-90^\circ$ to $90^\circ$, where $0^\circ$ corresponds to the radial direction. The plots cover the region within the white circle in (a). Error bars represent the standard errors.
• Figure 3: Velocity structure of the HFS $0.5\,\mathrm{Myr}$ after the shock impact. (a) Radial velocity $V_r$ plotted as a function of the cylindrical radius $r$ from the hub center. $V_r$ and $r$ are defined in a cylindrical coordinate system aligned with the $z$-axis. The color of each point corresponds to the $\mathrm{H_2}$ number density. Only cells within a cylindrical radius of $r=2.25\,\mathrm{pc}$ are plotted. (b) Median of the density-weighted velocity dispersion $\sigma_{v_z}$ along the $z$-axis as a function of $r$. Error bars indicate the $95\%$ confidence intervals. Note that in both panels, the hub center is defined as the position of the peak gas density at this epoch and does not coincide with the origin of the computational domain. (c) Observationally motivated kinematic maps constructed from the same snapshot as in the left panel of Figure \ref{['hf']}. (c1) Column-density-selected line-of-sight velocity map. Only regions with $N_{\mathrm{H_2}} > 8\times10^{21}\,\mathrm{cm^{-2}}$, corresponding approximately to the mean column density of the identified filaments, are included. The line-of-sight velocity components are measured along the $z$-axis from an observer located at $z=-\infty$ and are shown in the laboratory frame. (c2) Position--velocity (PV) diagram showing the line-of-sight velocity $V_\mathrm{los, z-}$ as a function of the projected $x$-coordinate, weighted by the column density.
• Figure 4: Distributions of density, velocity, and magnetic fields in slices along the filament axis (R1) and across the filament width (R2). The positions of these cuts are indicated by white lines in Figure \ref{['filfinder']} (a). Magenta bars and blue arrows denote the magnetic field and velocity vectors, respectively. The velocity vectors are presented in the shock rest frame ($v_{\mathrm{shock}}=-5\,\mathrm{km\,s^{-1}}$). The grayscale represents the $\mathrm{H_2}$ number density. The horizontal axis $d$ corresponds to the distance along the cut, where the white circle with a gray outline in Figure \ref{['filfinder']} (a) marks the starting points ($d=0$). The vertical axis $z$ represents the vertical position within the slice.
• Figure 5: Schematic illustration of a fast-mode shock propagating through a self-gravitating molecular cloud with hourglass-shaped magnetic field lines. The upper panels show a two-dimensional slice in the $x$--$z$ plane, in which the cloud is flattened along the $z$-direction. The grayscale shading represents the gas density. The blue arrows indicate the velocity field, the magenta curves show the magnetic field lines, and the orange line represents the shock front. (a) Longitudinal slice of the filament, corresponding to cut R1 in Figure \ref{['v_b']}. (b) Nearly perpendicular slice of the filament, corresponding to cut R2. The velocity $v^{*}$ denotes the velocity in the shock rest frame.