Gravitational Wave Signatures of Quasi-Periodic Eruptions: LISA Detection Prospects for RX J1301.9+2747

TL;DR

The study investigates gravitational wave signatures from quasi-periodic eruptions (QPEs) modeled as EMRIs perturbed by orbiter-disk interactions (ODIs). It computes GW signals using the Teukolsky equation in Kerr spacetime, incorporating ODI as impulsive perturbations to the orbit and updating the orbital constants via a Jacobian to quasi-Keplerian parameters. A key result is that ODI-perturbed EMRIs exhibit non-discrete GW modes and high-frequency tails, boosting power in the LISA band and enabling discrimination from vacuum EMRIs by a mismatch criterion; RX J1301.9+2747 could be detectable by LISA for $M \

Abstract

One prominent model for quasi-periodic eruptions (QPEs) is that they originate from extreme mass-ratio inspirals (EMRIs) involving stellar-mass objects orbiting around massive black holes and colliding with their accretion disks. We compute the gravitational wave signals from such a model, demonstrating that orbiter-disk interactions result in small frequency shifts and high-frequency tails due to the excitation of non-discrete modes. Interestingly, we show that QPE RX J1301.9+2747 could be detectable by future space-based gravitational wave detectors, provided a moderate eccentricity around $0.25$ and a mass exceeding $35\,M_\odot$ for the orbiter. Moreover, based on this QPE model, we show that the signal-to-noise ratio of the gravitational wave signals from QPEs, if detectable, will be sufficiently high to distinguish such systems from vacuum EMRIs and shed light on the origin of QPEs and environments around massive black holes.

Figures (6)

• Figure 1: Schematic depiction of an EMRI system where a SMO repeatedly collides with an accretion disk whilst orbiting a MBH. These collisions produce EM flares modulated by relativistic precession and orbital inclination. GWs emitted by the EMRI encode spacetime curvature perturbations, enabling multi-messenger probes of the orbital dynamics.
• Figure 2: EMRI parameters of five QPEs with data obtained from Ref. Zhou_2024b, where the $x$-axis is the MBH mass, and the $y$-axis is the orbital eccentricity. The color encodes the orbital frequency of the QPE, and the error bars are the 2-$\sigma$ confidence interval.
• Figure 3: The characteristic strain over LISA's operation time of four years for a vacuum EMRI (dashed blue line) versus an EMRI with ODIs (solid red line) using the smallest (top panel) and largest (bottom panel) inferred initial eccentricity $e_0=0.25^{+0.18}_{-0.20}$ of RX J1301.9+2747 with the noise curves of LISA (black line) and TianQin (dashed gray line). The initial parameters are $M=4.47\times 10^6M_{\odot}$, $\mu = 30 M_{\odot}$, $a=0.9$, $p_0=55.5 M(1-e_0^2)$, $x_{0}=\cos I_0=0.63$, and the luminosity distance $d_L=100\,{\rm Mpc}$.
• Figure 4: The SNR of an EMRI with ODIs for varying $\mu$ and $e_0$ (top panel), $M$ and $e_0$ (middle panel), and $M$ and $\mu$ (bottom panel), assuming fiducial values $\mu=30M_{\odot}$, $M=4.47\times 10^6M_{\odot}$, and $e_0=0.25$, respectively. The luminosity distance and the cosine of the initial orbital inclination angle are kept at $d_L=100\;\mathrm{Mpc}$ and $x_{0}=0.63$ for all sources considered, respectively. The white dashed-dotted line marks where the threshold SNR $\rho=20$ is surpassed, and the hatched region indicates the parameter space where $\rho$ is high enough to differentiate between an EMRI with ODIs and one in vacuum (cf. Eq. \ref{['ROT']}).
• Figure 5: The relative difference in orbital paramaters between a QPE EMRI perturbed by ODIs and a vacuum EMRI $(|\Delta p|/p, |\Delta e|/e, |\Delta x_I|/x_I, |\Delta\Phi_{r,\theta,\phi}|/\Phi_{r,\theta,\phi})$, where $\Delta \mathscr{O}=\mathscr{O}'-\mathscr{O}$ is the difference between the ODI perturbed orbiter parameters $\mathscr{O}'$ and vacuum orbital parameters $\mathscr{O}$. The initial conditions for the orbit are $p_0=73.5 M(1-e_0^2)$, $e_0=0.25$, $x_{I0}=0.5$, $\Phi_{r0}=\Phi_{\theta0}=\Phi_{\phi0}=0$, and the BH masses and spins are $M= 10^{6}M_{\odot}$, $\mu=30M_{\odot}$, and $a=0.9$. The gray dash-dotted lines indicate the times when ODIs occur.