Coupled Map Lattice for Astronomical Object Formation: A Scenario for Evolution from Star to Disk, Arms, and Companions

TL;DR

The paper introduces Astro CML, a coupled map lattice framework that dynamically forms a central star, Keplerian disk, spiral arms, and diverse companions in protoplanetary-like systems. It employs a minimal two-procedure model with Eulerian gravitational interaction and Lagrangian viscoelastic advection acting on gas clumps containing a small dust fraction, evolving mass and momentum on a 2D lattice. The results reveal five evolutionary stages—central star formation, disk/arm formation, maturation, companion formation via arm crossing, and companion maturation—demonstrating an arm-crossing mechanism that yields planetary to stellar companions and can sustain spiral arms around companions; these findings align with observed mass ratios and suggest a route to overcome radial drift and angular momentum challenges. By linking chaotic gas ejection around a central star to the emergence of protoplanetary architecture, the work provides a dynamic, CI-inspired perspective that complements traditional core accretion and disk-instability theories. The Astro CML thus offers a unified, computationally efficient framework to study how complex structures can arise from simple local rules in astrophysical disks.

Abstract

We present a new dynamic formation model of a star, a disk, arms, and companions using a coupled map lattice (CML), a complex systems approach. This CML simulates the viscoelastic and chaotic dynamics and evolution of gas clumps containing a little dust with a minimal set of one Eulerian procedure for the flow formation of gas clumps due to gravitational interaction, and one Lagrangian procedure for the collision and mixture of gas clumps due to viscoelastic advection. Despite its simplicity, this CML successfully obtains four typical astronomical objects consistent with protoplanetary disk observations: a central star, Keplerian disk, spiral arms, and even stellar, substellar, and planetary companions. All these formation processes are truly dynamic, with the central star "starring" in them, and they are not based on the conventional disk gravitational instability but on the central star gravitational instability with high-dimensional chaotic gas ejection, namely the chaotic itinerancy. Of particular note is the process in which diverse companions are formed due to the rapid density increase caused by the intersection of spiral arms. This suggests a novel companion formation scenario that should be called "arm-crossing companion formation" with a view to planet formation, which may overcome the radial drift barrier and angular momentum problem.

Figures (1)

• Figure S1: Two complementary pictures of field variables, the gas clump mass $m_{ij}^{t}$ and velocity $\hbox{\boldmath $v$}_{ij}^{t}$ at lattice point $ij$. (a) Lattice picture. The black dot denotes lattice point $ij$. The filled circle represents the mass of the gas clump, and the black arrow represents its velocity. In the circle, the blue part shows the gas mass $(1-\alpha)m_{ij}^{t}$, and the red part shows the dust mass $\alpha m_{ij}^{t}$ in the gas clump. (b) Particle picture. The black dotted square denotes the cell with size one, which is centered at lattice point $ij$. The set of the filled small circles represents the total mass of virtual particles made from gas and dust, and the set of the black arrows represents their flow. In each circle, the blue part shows the gas mass proportional to $(1-\alpha)m_{ij}^{t}$, and the red part shows the dust mass proportional to $\alpha m_{ij}^{t}$. The mixing coefficient (the dust mass fraction in gas clumps) is actually very small, but the figure is drawn with a value of 0.25 for visual clarity.