Reflex instabilities I: Boundaries makes grid-based disc simulations frame-dependent
Abstract
If the mass distribution within an accretion disc is asymmetric, it will exert a gravitational pull on its central object. The central object must then move away from the origin of the reference frame, resulting in atypical gravitational pulls on the disc. The goal of the present series of papers is to investigate the stability of this feedback loop. In this first paper, we report a surprising finding: the choice of reference frame affects the number and nature of the waves and instabilities contained in the analytical equations. To show this, we use a simple example: the modes discovered by Sanchez et al. (2025, Appendix A.3). We provide the first analytical description of those modes, we explain their physical mechanism, and propose to call them 'bracket modes' because they arise from the bracket side of an integration by parts. We show that the same disc can be stable in the stellocentric reference frame but unstable in the barycentric reference frame. This is because the boundaries of the simulation domain are frame-dependent. To avoid this, one must model the entire disc all the way from the central cavity to the outer edge. But this is prohibitively expensive, and some discs do not have a central cavity anyway. Our results suggest that extreme caution is required when interpreting simulations of asymmetric discs, and that our community may not have the tools to model the reflex motion of the central object yet.
Related
- Reflex instabilities II: The reflex motion of the central object drives at least seven instabilities in accretion discs
- Hydrodynamic instabilities in long-term three-dimensional simulations of neutrino-driven supernovae of 13 red supergiant progenitors
- Spectral Properties of Solar Wind Charge Exchange from Earth's Magnetospheric Boundaries: MHD and Test Particle Simulations
- Time-dependent Simulations of Solar Wind Evolution from Subsonic to Supersonic Flow with Different Coronal-base Outflow Speeds
- Galaxy morphology dependent (black hole mass)-(velocity dispersion) relations: implications for gravitational wave forecasts and cosmological simulations
BibTeX
@misc{magnan2026reflex,
title = {{Reflex instabilities I: Boundaries makes grid-based disc simulations frame-dependent}},
author = {Nathan Magnan and Michel Tagger and Clément Baruteau and Aurélien Crida and Jean-François Gonzalez and Héloïse Méheut},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08471},
eprint = {2610.08471},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05842221v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reflex instabilities I: Boundaries makes grid-based disc simulations frame-dependent
AU - Nathan Magnan
AU - Michel Tagger
AU - Clément Baruteau
AU - Aurélien Crida
AU - Jean-François Gonzalez
AU - Héloïse Méheut
PY - 2026
DA - 2026/10/06
PB - HAL
DO - 10.48550/arxiv.2610.08471
UR - https://hal.science/hal-05842221v1
AB - If the mass distribution within an accretion disc is asymmetric, it will exert a gravitational pull on its central object. The central object must then move away from the origin of the reference frame, resulting in atypical gravitational pulls on the disc. The goal of the present series of papers is to investigate the stability of this feedback loop. In this first paper, we report a surprising finding: the choice of reference frame affects the number and nature of the waves and instabilities contained in the analytical equations. To show this, we use a simple example: the modes discovered by Sanchez et al. (2025, Appendix A.3). We provide the first analytical description of those modes, we explain their physical mechanism, and propose to call them 'bracket modes' because they arise from the bracket side of an integration by parts. We show that the same disc can be stable in the stellocentric reference frame but unstable in the barycentric reference frame. This is because the boundaries of the simulation domain are frame-dependent. To avoid this, one must model the entire disc all the way from the central cavity to the outer edge. But this is prohibitively expensive, and some discs do not have a central cavity anyway. Our results suggest that extreme caution is required when interpreting simulations of asymmetric discs, and that our community may not have the tools to model the reflex motion of the central object yet.
ER -