---
title: "Galactic bars, resonances and stellar migration"
description: "Follow stars through a rotating pattern, derive orbital resonances and torque, then recalculate periodic parents and read a fixed 2026 simulation paper."
canonical_url: "https://sandboxphysics.com/stories/galactic-bar-orbits/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/galactic-bar-orbits/"
last_modified: "2026-11-05"
---

Galactic bar orbits

# Galactic bars, resonances and stellar migration

[Open the rotating-bar Lab](https://sandboxphysics.com/labs/galactic-bar-orbits/)

Sandbox Physics · 2026-11-05

Stars orbit through patterns that can rotate at a different speed. Begin with that picture, derive frequencies and angular-momentum exchange, then solve complete orbits and examine how evolving patterns move stars.

1. L1

   ## [Why stars pass through galactic spiral arms](https://sandboxphysics.com/stories/galactic-bar-orbits/why-stars-cross-spiral-arms/)

   A spiral is a changing pattern of stars and gas. Follow how differential rotation, orbital resonances and temporary arms separate a pattern from its stars.

2. L1

   ## [Differential rotation and orbital resonances](https://sandboxphysics.com/stories/galactic-bar-orbits/differential-rotation-and-orbital-resonances/)

   Derive angular and epicycle frequencies for a flat rotation curve, then locate corotation and the circular Lindblad reference radii.

3. L2

   ## [Torque and energy in a rotating bar](https://sandboxphysics.com/stories/galactic-bar-orbits/torque-energy-and-a-rotating-bar/)

   Derive the Jacobi integral from specific torque and power, then identify the extra work when a bar grows or changes its pattern speed.

4. L3

   ## [Periodic orbits and radial migration](https://sandboxphysics.com/stories/galactic-bar-orbits/periodic-orbits-and-radial-migration/)

   Shoot complete periodic parents in one fixed bar, distinguish linear stability from orbital shape, and follow how temporary waves can leave migration.

5. L3

   ## [Recalculate a bar orbit from saved states](https://sandboxphysics.com/stories/galactic-bar-orbits/replay-a-bar-orbit-from-saved-states/)

   Run independent Python integration, analyze saved angular momentum and torque, shoot six periodic parents, and reproduce the registered failure examples.

6. L4

   ## [Reading the 2026 bar-resonance tree rings](https://sandboxphysics.com/stories/galactic-bar-orbits/reading-bar-resonance-tree-rings-2026/)

   Read Chiba et al. 2604.01294v1 from its live/static-halo control to phase-space ordering, satellite tests and conditional pattern-speed recovery.

## Sources and calculation scope

1. [Dehnen (1999v1/2000), The Effect of the Outer Lindblad Resonance of the Galactic Bar on the Local Stellar Velocity Distribution](https://arxiv.org/abs/astro-ph/9911161v1)

   Fixed 14-page astro-ph/9911161v1, all text read in parameter preflight; equation 3, section 3 and original orbital figures. The own model uses a fixed bar radius 0.5 and counterclockwise convention. The paper's historical Milky Way inference is not treated as a current measurement.

2. [Sellwood & Binney (2002), Radial mixing in galactic discs, astro-ph/0203510v2](https://arxiv.org/abs/astro-ph/0203510v2)

   Fixed 13-page v2, complete original read; section 2 specific energy/action exchange and sections 3–4 transient self-gravitating waves. The paper's live-disk simulations are distinct from our prescribed external-bar release.

3. [Chiba, Fujii, Baba, Dubinski & Schönrich (2026), Tree-ring structure of Galactic bar resonance in N-body simulations, arXiv:2604.01294v1](https://arxiv.org/abs/2604.01294v1)

   Fixed 1 April 2026 v1, PDF draft dated 3 April; complete 21 pages including appendices/references actually read. Key printed pages 3/5/6/7/8/10/13/15/18 rendered and viewed. A/B live/static control, C/D satellite tests, equations 5–11 and appendices A–D; no original PDF/figure is redistributed.

4. [Sandbox Physics independent galactic-bar scientific reader v1](https://sandboxphysics.com/stories/galactic-bar-orbits/materials/galactic-bar-orbits-reader-science-v1.zip)

   Own zero-network Python integration and saved-record analysis: one full 256-tracer population, ten independent DOP853 controls, exact circle/epicycle, prescribed-growth work, six fresh periodic roots and three own synthetic figures. No App, completed orbit input, original paper or observed data.