Science Opportunities of Wet Extreme Mass-Ratio Inspirals

TL;DR

The paper analyzes wet EMRIs—stellar-mass BHs migrating within AGN accretion disks—as prime sources for space-based GW detectors. It updates population forecasts using a TDE-informed SMBH mass function, evaluates detectability with LISA-like observatories, and demonstrates how wet EMRIs can serve as both bright and dark sirens for cosmology. It highlights multi-messenger opportunities through potential EM counterparts such as Type II QPEs, calibration of EM BH mass/spin techniques, and tests of disk and jet physics via GW-derived inclinations and jet orientations. The work shows that wet EMRIs can yield percent-level measurements of the Hubble parameter and enable stringent tests of accretion physics, providing a compelling framework for joint GW-EM studies in the coming era. $H(z)=H_0 \,\sqrt{\Omega_{m,0}(1+z)^3+\Omega_{\Lambda,0}}$ and related cosmological inferences illustrate the potential of wet EMRIs to inform cosmology alongside traditional EM probes.

Abstract

Wet extreme mass-ratio inspirals (wet EMRIs), which arise from stellar-mass black holes inspiral into supermassive black holes (SMBHs) within the gas-rich environments of Active Galactic Nuclei (AGN), are primary sources of gravitational waves (GWs) for space-borne detectors like LISA, TianQin, and Taiji. Unlike "dry EMRIs", which form through gravitational scattering in nuclear star clusters, wet EMRIs are naturally accompanied by interactions with accretion disks, offering rich multi-messenger science opportunities. They are distinct in generating transient electromagnetic (EM) signals, such as quasi-periodic eruptions (QPEs), which serve as valuable probes of accretion disk physics and SMBH environments. Their GW signals provide an unprecedented precision of the order of $O(10^{-4}\sim 10^{-6})$ in measuring SMBH mass and spin, enabling the calibration of traditional EM techniques and offering insights into jet formation models. Additionally, wet EMRIs serve as bright and dark sirens for cosmology, facilitating percent-level precision measurements of Hubble parameter through AGN host identification or statistical association. These systems hold immense potential for advancing our understanding of black hole dynamics, accretion physics, and cosmology.

Figures (7)

• Figure 1: Histograms of $1\sigma$ parameter uncertainties from the Fisher analysis, evaluated for $\sim 2000$ EMRI events with $\mathrm{SNR} > 20$. Shown are distributions for $\Delta M_\bullet/M_\bullet$, $\Delta \mu/\mu$, $\Delta d_L/d_L$, $\Delta \iota$, $\Delta e_0$, and $\Delta a_0$. Since masses $M_\bullet$ and $\mu$ are reported in the source frame, their relative uncertainties are larger by a factor of $1+z$ compared to the detector frame.
• Figure 2: Different effects act at different radial scales. $R_{\rm warp}$ marks the warp radius of the accretion disk, within which the disk is warped by the relativistic Lense-Thirring effect (frame-dragging), and remains flat beyond. For $r < r_{\rm dec}$, Lense-Thirring precession dominates the orbital evolution of the sBH, potentially driving it out of the disk plane and causing misalignment. When $r < R_{\rm GW}$, GW emission governs the sBH’s migration (GW-dominated regime), while for $r > R_{\rm GW}$, migration is dominated by disk effects, such as gas torques (disk-dominated regime).
• Figure 3: Posterior distribution of the inclination angle $\iota$, shown for the dimensionless semi-latus rectum at $p_0 \sim 8 M_\bullet$ (left panel), and after tracing the evolution back to $p \sim 150 M_\bullet$ due to GW radiation, and further to $p = 410 M_\bullet$ using Eq. \ref{['eq:Ldot']} with $\beta$-disk model (right panel). The orange vertical lines indicate the mean value along with the $1-\sigma$ uncertainty.
• Figure 4: Relationship among the orbital angular momentum of the sBH $\hat{L}$, the SMBH spin direction $\hat{a}$, and the jet angle. The disk orientation $\hat{L}_{\rm disk}$ is inferred by tracing $\hat{L}$ backward from the LISA band ($p_0 \sim 8 M_\bullet$) to $p \sim 410 M_\bullet$ (decoupling radius), where the sBH resides within the disk.
• Figure 5: Uncertainty in the Lense-Thirring precession angle at $p \sim 150 M_\bullet$, traced back from a semi-latus rectum of $p_0 \sim 8 M_\bullet$.