Preliminary forecasting constraint on scalar charge with LISA in non-vacuum environments

TL;DR

This work investigates how a scalar charge on the stellar-mass component of an EMRI can be constrained by LISA when the system is embedded in realistic beyond-vacuum environments. It develops a beyond-vacuum model with a Schwarzschild MBH surrounded by an accretion disk and a DM minispike, allowing the secondary to carry a scalar charge $q_s$ and computing combined fluxes from gravitational, scalar, and dynamical-friction processes. Waveforms are generated using a hybrid augmented analytical-kludge (AAK) approach that incorporates environment-corrected trajectories, and parameter estimation is performed with a Fisher information matrix to forecast uncertainties on $q_s$ and other parameters. The results indicate that, under favorable conditions, LISA can distinguish scalar-charge effects from vacuum signals and constrain $q_s$ with a typical absolute precision of $\sim 10^{-2}$ and a relative precision of $\sim 0.1$, though degeneracies with environmental parameters can arise, especially in a DM+disk environment. This study underscores the importance of accurately modeling environmental influences to test fundamental physics with EMRIs in space-based gravitational-wave observations.

Abstract

We compute the gravitational wave signal from eccentric extreme-mass-ratio inspirals (EMRIs) embedded within beyond-vacuum environments, where the secondary object carries a scalar charge and evolves in the presence of both an accretion disk and a dark matter halo. The waveform modification is derived by incorporating the scalar charge correcting the fluxes and orbital trajectories of the secondary. Our results indicate that, under suitable parameter configurations, the influence of the scalar charge on EMRIs waveform in such environments can be distinguished from that in vacuum spacetime. For the EMRIs signal modified by the astrophysical environments, the future space-borne detector can determine the relative error of scalar charge constrained by LISA at the level of $\sim0.1$, providing a preliminary prediction of detecting scalar charge in the beyond-vacuum spacetime.

Figures (8)

• Figure 1: Comparison of the plus polarization $h_{+}(t)$ for four EMRI waveforms in the time domain, illustrating the impact of different physical effects. The mass-ratio of binary objects is fixed to $\eta=10^{-5}$ and the initial orbital parameters are $(p_0,e_0)=(12,0.3)$. The environmental parameters are chosen as $\Sigma_p = 3/2$, $h_0 = 0.02$, $\Sigma_0 = 5.25\times10^3\,{\rm g\,cm^{-3}}$, $\alpha_{\rm DM}=1.8$, and scalar charge $q_s=0.1$. The black curve corresponds to the EMRI evolution including only the correction due to scalar emission. The red curve shows the waveform when the accretion-disk effect is added on top of the vacuum GR case. The cyan curve isolates the contribution from a DM minispike, while the purple curve represents the combined impact of both environmental effects, namely the accretion disk and the DM minispike.
• Figure 2: Comparison of the plus polarization $h_{+}(t)$ for five EMRI waveforms in the time domain, highlighting the impact of different physical effects. The mass-ratio of binary objects is fixed to $\eta = 10^{-5}$, and the initial orbital parameters are $(p_0,e_0) = (12,0.3)$. The cyan curve shows the EMRI waveform in a vacuum Schwarzschild spacetime, while the remaining curves correspond to the same environmental configurations as in Fig. \ref{['Fig:wave1']}.
• Figure 3: Maximum deviations in the evolution of the orbital parameters $(p(t),e(t))$ induced by various environmental effects on EMRI dynamics, shown as functions of the orbital semi-latus rectum and eccentricity. The quantities $(\delta p)_{\rm max}$ and $(\delta e)_{\rm max}$ indicated above the color bars denote the maximum deviations in the evolution of $p(t)$ and $e(t)$ over the full duration of the eccentric inspirals. Black dashed curves indicate contours of constant maximum deviation in all four panels. The left panels display the maximum deviations between the vacuum spacetime and the accretion-disk case, while the right panels compare the vacuum spacetime with the DM environment. All remaining parameters associated with the environmental effects and the scalar charge are identical to those in Fig. \ref{['Fig:wave1']}.
• Figure 4: Azimuthal and radial dephasing are shown as functions of the orbital semi-latus rectum and eccentricity, comparing scalar emission in vacuum with that in nonvacuum environments including dark-matter dynamical friction and an accretion disk. All remaining EMRI, environmental, and scalar-charge parameters are identical to those adopted in Fig. \ref{['Fig:wave1']}.
• Figure 5: Mismatches between EMRI signals with scalar emission and those including environmental effects from DM dynamical friction or accretion-disk interactions are shown as functions of the orbital eccentricity $e$ and the relevant environmental parameters. Four representative cases are considered with initial semi-latus rectum $p_0 = 12$, scalar charge $q = 0.01$, and all remaining parameters identical to those in Fig. \ref{['Fig:wave1']}. The labels $h^{\rm scalar}$ and $h^{\rm DM}$ above the color bars denote EMRI waveforms corrected by scalar emission and by DM friction, respectively. The waveform $h^{\rm disk}$ corresponds to an EMRI embedded in an accretion disk, while $h^{\rm env}$ describes an EMRI evolving in a combined environment consisting of both a DM minispike and an accretion disk. The black dashed curves indicate contours of constant mismatch; in particular, the contour at $\mathcal{M} \simeq 10^{-3}$ marks the typical threshold for distinguishability adopted for LISA-like detectors. The remaining environmental parameters are chosen as $\alpha_{\rm disk}=0.04$, $h_0=0.05$ (top left panel), $\alpha_{\rm DM}=1.65$, $h_0=0.05$ (top right panel), $\alpha_{\rm DM}=1.65$, $\alpha_{\rm disk}=0.04$ (bottom left panel), and $\alpha_{\rm disk}=0.04$, $\alpha_{\rm DM}=1.65$ (bottom right panel).