TY  - EJOUR
AU  - Jiang, Qiqi
AU  - Li, Guang-Xing
AU  - Singh, Chandra B.
TI  - Dispersion relation for the linear theory of relativistic Rayleigh–Taylor instability in a magnetized medium revisited
IS  - arXiv:2411.03347
M1  - PUBDB-2026-00114
M1  - arXiv:2411.03347
M1  - DESY-24-008
PY  - 2026
AB  - The Rayleigh–Taylor instability (RTI) arises at the interface between two fluids of different densities, notably when a heavier fluid lies above a lighter one in an effective gravitational field. In astrophysical systems with high velocities, relativistic corrections are necessary. We investigate the linear theory of the relativistic Rayleigh-Taylor instability (R-RTI) in a magnetized medium, where fluids can move with relativistic velocities. We chose an ïntermediate frame" in which the fluids on each side of the interface move in opposite directions with identical Lorentz factors γ<sub>*</sub> and derive the new dispersion relation of the R-RTI. This symmetry facilitates analytical derivations and the study of relativistic effects on the dynamics of instabilities. We find that the instability is activated when the Atwood number <i>A</i> = (ρ<sub>1</sub> h<sub>1</sub> − ρ<sub>2</sub> h<sub>2</sub>) / (ρ<sub>1</sub> h<sub>1</sub> + ρ<sub>2</sub> h<sub>2</sub>)  > 0, where ρ<sub>1</sub> and ρ<sub>2</sub> are densities measured in the rest of the fluids. The relativistic effect is mostly contained in the Lorentz transformation of the effective acceleration g′ = g γ<sub>*</sub><sup>−2</sup>, which, combined with time dilation, leads to a much slower growth of instability (ω′=γ<sub>*</sub><sup>−1</sup> ω<sub>0</sub>), and a slightly elongated length of the unstable patch, due to weaker g in the intermediate frame. Taking time dilation into account, when viewed in the rest frame of the medium, we expect the instability to grow at a much reduced rate. The analytical results should guide further explorations of instability in systems such as microquasars (μQSOs), Active galactic nuclei (AGNs),  gamma-ray bursts (GRBs), and radio pulsars (PSRs), where the apparent stability of the jet can be attributed to either the intrinsic stability (e.g. the Atwood number) or the much prolonged duration through which R-RTI can grow.
KW  - Instabilities (autogen)
KW  - Magnetohydrodynamics (autogen)
KW  - Relativistic process (autogen)
KW  - Jets (autogen)
LB  - PUB:(DE-HGF)25
DO  - DOI:10.3204/PUBDB-2026-00114
UR  - https://bib-pubdb1.desy.de/record/643308
ER  -