Environmental Imprints of Dark Matter and Accretion Disks on Eccentric EMRIs around Kerr Black Holes
Abstract
Extreme-mass-ratio inspirals (EMRIs), systems in which a stellar-mass compact object spirals into a supermassive black hole (M1), are prime targets for the space-based gravitational-wave interferometers and are acutely sensitive to their astrophysical environment. We quantify the joint imprint of a dark matter (DM) spike and an accretion disk on the waveforms of eccentric, equatorial Kerr EMRIs, integrating four modular effects---DM dynamical friction, DM self-gravity, Newtonian accretion-disk torques, and disk self-gravity---into a fifth post-Newtonian (5PN) augmented analytic kludge (AAK) waveform model, and assess their measurability via a Fisher-matrix analysis. The DM dynamical-friction dephasing peaks at M1∼ 106 M⊙, reaching ∼ 102--103 rad; there the DM spike slope is measurable to sub-percent precision and both DM channels are unambiguously detectable, while omitting DM biases the intrinsic parameters significantly. At M1≳ 108 M⊙ the DM and disk self-gravity channels dominate their dissipative counterparts. The disk parameters remain degenerate across the explored parameter space, since the supersonic regime dominates the inspiral and the subsonic-to-supersonic transition only mildly weakens this degeneracy without lifting it; a combined DM+disk analysis further reveals a cross-sector degeneracy between the DM slope and the disk parameters. This physical degeneracy, reflected in the near-singular Fisher matrix, implies that independently measuring the disk parameters requires a relativistic torque model or an electromagnetic counterpart.
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BibTeX
@misc{yuan2026environmental,
title = {{Environmental Imprints of Dark Matter and Accretion Disks on Eccentric EMRIs around Kerr Black Holes}},
author = {Hai-Chao Yuan and Yong Tang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29770},
eprint = {2609.29770},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29770},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Environmental Imprints of Dark Matter and Accretion Disks on Eccentric EMRIs around Kerr Black Holes
AU - Hai-Chao Yuan
AU - Yong Tang
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29770
UR - https://arxiv.org/abs/2609.29770
AB - Extreme-mass-ratio inspirals (EMRIs), systems in which a stellar-mass compact object spirals into a supermassive black hole (M_1), are prime targets for the space-based gravitational-wave interferometers and are acutely sensitive to their astrophysical environment. We quantify the joint imprint of a dark matter (DM) spike and an accretion disk on the waveforms of eccentric, equatorial Kerr EMRIs, integrating four modular effects---DM dynamical friction, DM self-gravity, Newtonian accretion-disk torques, and disk self-gravity---into a fifth post-Newtonian (5PN) augmented analytic kludge (AAK) waveform model, and assess their measurability via a Fisher-matrix analysis. The DM dynamical-friction dephasing peaks at M_1∼ 10^6 M_⊙, reaching ∼ 10^2--10^3 rad; there the DM spike slope is measurable to sub-percent precision and both DM channels are unambiguously detectable, while omitting DM biases the intrinsic parameters significantly. At M_1≳ 10^8 M_⊙ the DM and disk self-gravity channels dominate their dissipative counterparts. The disk parameters remain degenerate across the explored parameter space, since the supersonic regime dominates the inspiral and the subsonic-to-supersonic transition only mildly weakens this degeneracy without lifting it; a combined DM+disk analysis further reveals a cross-sector degeneracy between the DM slope and the disk parameters. This physical degeneracy, reflected in the near-singular Fisher matrix, implies that independently measuring the disk parameters requires a relativistic torque model or an electromagnetic counterpart.
ER -