Pattern dark matter and galaxy scaling relations

TL;DR

This paper proposes a novel explanation for galaxy scaling relations by modeling dark matter as an emergent pattern formation phenomenon resulting from symmetry breaking, unifying galaxy features and rotation curves.

Contribution

It introduces a simple Lagrangian model combining matter and pattern formation, suggesting dark matter as an emergent, collective phenomenon rather than a particle.

Findings

Reproduces features of elliptic and disk galaxies including rotation curves.

Derives scaling relations for elliptical galaxy central dispersions.

Supports dark matter as an emergent phenomenon rather than a particle.

Abstract

We argue that a natural explanation for a variety of robust galaxy scaling relations comes from the perspective of pattern formation and self-organization as a result of symmetry breaking. We propose a simple Lagrangian model that combines a conventional model for normal matter in a galaxy with a conventional model for stripe pattern formation in systems that break continuous translation invariance. We show that the energy stored in the pattern field acts as an effective dark matter. Our theory reproduces the gross features of elliptic galaxies as well as disk galaxies (HSB and LSB) including their detailed rotation curves, the radial acceleration relation (RAR), and the Freeman law. We investigate the stability of disk galaxies in the context of our model and obtain scaling relations for the central dispersion for elliptical galaxies. A natural interpretation of our results is that (1) `dark matter' is potentially a collective, emergent phenomenon and not necessarily an as yet undiscovered particle, and (2) MOND is an effective theory for the description of a self-organized complex system rather than a fundamental description of nature that modifies Newton's second law.