Hub Formation and Filament-Filament Collision: An Analytical Model

TL;DR

This paper develops an analytical model to understand how filament-filament collisions in the galaxy lead to hub formation and massive star formation, deriving physical properties and mass functions based on filament geometry and collision dynamics.

Contribution

It introduces a simple cylindrical filament collision model and derives hub mass functions, linking filament collisions to the formation of massive hubs in star-forming regions.

Findings

Collision cross section depends on filament orientation and size.

Hub mass function follows a power law with exponent ~ -3.

Global hub mass function mirrors the filament line-mass distribution.

Abstract

Filaments are ubiquitous throughout the Galaxy. Massive star formation is often observed in hub-filament systems, where multiple filaments appear to be interconnected and merging. Filament-filament collisions are therefore a likely triggering mechanism for massive star formation. We derive basic physical properties of filament-filament collisions, such as the collision cross section (CCS), the hub mass, and its mass function, based on a simple cylindrical filament model. We assume a cylindrical filament with length $2p$, full width $2q$, and line-mass $\lambda_0$, and consider the CCS between two identical filaments. The collision is specified by three vectors: the directions of the colliding filaments ($n_1$ and $n_2$) and the direction of the relative velocity between the two filaments ($n_v=v/|v|$). For the thin filament, $p\gg q$, the CCS is expressed as $S=4p^2|n'_1\times n'_2|$, where $n'_1$ and $n'_2$ represent the directional vectors projected onto a plane perpendicular to the relative velocity $n_v$. As the angle between $n'_1$ and $n'_2$ becomes smaller, the cross section proportional to $p\cdot q$ becomes relatively important. We propose a simple model in which the hub mass is estimated by the overlapping portion of the two colliding filaments. The hub mass function is derived using the CCSs and the geometrically estimated overlapping mass. When the directions and relative velocities of the filaments are isotropically distributed, the mass function expected from a single species of filaments fits well to a power law and the power exponent is $\gamma_M\simeq -2.96$ ~ $-3.78$. The power exponent of the global hub mass function is the same as that of the line-mass distribution function, $\gamma_\lambda\simeq -1.5$. This means that a massive hub is formed by the collision of two massive filaments.