Eccentric extreme-mass-ratio inspirals: a new window into ultra-light vector fields

TL;DR

Problem: test GR and constrain ultra-light vector fields using EMRIs in the LISA band. Approach: develop a perturbative Einstein–Proca framework on a Schwarzschild background, compute Proca and GR fluxes for eccentric equatorial orbits, evolve the system adiabatically with a FEW-based waveform, and forecast Proca-mass constraints with a Fisher information matrix; key results show that increasing eccentricity enhances sensitivity to the vector mass, enabling detectable dephasing for $\mu$ in the range $\sim 10^{-4}$ to $5\times10^{-5}$ in their units, with strong parameter correlations guiding precision improvements. Significance: demonstrates that eccentric EMRIs offer a robust observational window to massive vector-field extensions of GR in the strong-field regime and informs future waveform modeling and data-analysis strategies for LISA.

Abstract

Space-based gravitational-wave detectors, such as the Laser Interferometer Space Antenna (LISA), provide a platform to probe new fundamental fields through extreme-mass-ratio inspirals (EMRIs), where a compact secondary object carrying scalar or vector charges inspirals into a massive primary. In a theory-agnostic framework, we compute the ultra-light vector and gravitational radiation emitted by eccentric EMRIs and determine the corresponding inspiral trajectories. We evaluate the impact of a massive vector (Proca) field on EMRIs waveform through dephasing and mismatches with predictions by general relativity. Using a Fisher information matrix analysis, we further assess LISA's capability to constrain the Proca mass from future EMRIs observations. We find that orbital eccentricity can improve estimation accuracy of parameters, making the vector mass $μ$ become detectable for the case of $μ=0.02$ . Correlation analysis further reveals strong positive dependencies between the Proca mass and intrinsic source parameters, indicating that improved measurement of these parameters directly tightens constraints on vector mass. These results demonstrate that high-eccentricity EMRIs observed by LISA offer a powerful channel to detect or constrain massive vector-field extensions of GR in the strong-field regime.

Figures (9)

• Figure 1: Fluxes errors on the retangular grid between the interpolation method and the Proca or gravitational flux obtained over summing index $(l,m,n)$, as the functions of two orbital parameters $(p,e)$ are plotted, assuming the Proca mass $\mu=0.001$. The symbol $\dot{E}^{\mathcal{G}}_{\rm Error}$ is the error of the gravitational energy fluxes computed with two methods, $\dot{J}^{\mathcal{G}}_{\rm Error}$ is the error for the gravitational angular momentum fluxes, and the quantity with a subscript $\mathcal{P}$ denotes to the Proca flux error. These energy fluxes have an unit of mass-ratio $m^2_p/M^2$ and the angular momentum fluxes possess an unit of $m^2_p/M$.
• Figure 2: Ratios of the Proca to gravitational fluxes as functions of the orbital semi-latus rectum $p$ for different initial eccentricities $e$. The left panels correspond to a Proca mass $\mu = 0.001$, and the right panels to $\mu = 0.02$. The energy fluxes are expressed in units of $m_p^2/M^2$, while the angular-momentum fluxes are expressed in units of $m_p^2/M$, where the primary mass is $10^6 M_\odot$ and the secondary mass is $10 M_\odot$.
• Figure 3: Comparison of five waveforms from a total mass $10^6M_\odot+10M_\odot$ EMRIs system with the effect of the vector mass $\mu\in\{0.0,10^{-4},10^{-3},0.018,0.02\}$ are plotted for the initial eccentricity $e_0\in\{0.3,0.5\}$ and semi-latus rectum $p_0=12$.
• Figure 4: Azimuthal (top panels) and radial (bottom) dephasing as a function of observation time for initial orbital eccentricity $e_0 =0.2$ and orbital semi-latus rectum $p_0=12.0$ is plotted, the other parameters are setting as following: $\mu \in\{10^{-6}, 10^{-5}, 5\times10^{-5}, 10^{-4}, 10^{-3},0.018,0.024\}$, vector charge $q=0.1$. The dephasing plots consider two cases: contribution of Proca flux and massless vector flux on the evolution of radial or azimuthal frequency (left panels); contribution of Proca flux and standand GR flux on the evolution of radial or azimuthal frequency (right panels). The horizontal black dashed line in four figures denotes to the threshold distinguished by LISA, where the SNR of EMRIs signal is 30 Bonga:2019ycj, other parameters keep same with Fig. \ref{['Fig:Fluxes']}.
• Figure 5: Azimuthal (top panels) and radial (bottom panels) dephasing as a function of observation time for initial orbital eccentricities $e_0 =0.6$ are plotted, the configuration of other parameters keeps same with Fig. \ref{['Fig:dephaing1']}.