Probing scalar field with generic extreme mass-ratio inspirals around Kerr black holes

Abstract

The future space-based gravitational wave observatories are expected to provide unprecedented opportunities to explore intricate characteristics of black hole binaries, particularly for extreme mass-ratio inspirals (EMRIs), in which a stellar-mass compact object slowly inspirals into a supermassive black hole. These systems are very prominent sources for testing gravity in the strong gravity fields and for probing potential deviations from general relativity, including those arising from the presence of fundamental scalar fields. In this work, we examine the impact of a scalar charge carried by the inspiraling object within the context of EMRIs. We focus on generic orbits that present both eccentricity and inclination to evaluate how these parameters affect the modifications induced by the scalar charge to the gravitational wave signal. Our results demonstrate that the inclusion of orbital inclination, in particular, enhances the detectability of scalar field effects by introducing richer waveform features that deviate from the purely general relativistic case. The interplay among scalar charge, eccentricity and inclination provides a more complete sampling of the black hole spacetime, suggesting that EMRIs with such generic orbits represent compelling systems for stringently constraining or discovering new fundamental fields through future gravitational wave observations.

Figures (8)

• Figure 1: Ratios between the gravitational and scalar fluxes, relative ratio of changing rates of energy and Carter constant $[\log_{10}(\dot{E}_S/\dot{E}_G), \log_{10}(\dot{Q}_S/\dot{Q}_G)]$, are plotted for different orbital parameter settings and a fixed spinning MBH with $a=0.6$. The top panels show the fluxes ratio of the energy and Carter constant for a fixed eccentricity $e=0.3$, distinct orbital inclination $x\in[0.1,0.3,0.5,0.7]~(I\in[0.47,0.4,0.33,0.24]\pi)$. The bottom panels are also the fluxes ratio for a fixed orbital inclination $x=0.1$ and the changing eccentricity $e\in[0.1,0.3,0.5,0.7]$. The other parameters are set as follows: the mass-ratio of the binary $q=10^{-5}$, the scalar charge $q_s=0.05$.
• Figure 2: Interpolation error of scalar energy and Carter fluxes as the function of orbital parameters $(p,e)$ for the rotating MBH with a dimensionless spin $a=0.3$ is plotted, setting orbital inclination $x=0.1$. These are the difference of fluxes from the relativistic and interpolation methods over the sampling grids. The other parameters are set as follows: the mass-ratio of the binary $q=10^{-5}$, the scalar charge $q_s=0.05$.
• Figure 3: Maximum value of accumulated phase error induced by the imprecision of interpolated gravitational energy flux as function of orbital inclination is plotted, including the inspiral of two-year and three cases of eccentricities $e_0\in\{0.1,0.3,0.5\}$.
• Figure 4: Azimuthal, radial and polar dephasing as a function of observation time for two eccentricities $e=(0.3,0.5)$ and a fixed MBH spin $a=0.3$ is plotted, including six scalar charges $q_s=(10^{-7},10^{-6},10^{-4},10^{-3},10^{-2},10^{-1})$, where the observation time is set for two years. The horizontal black dashed line is the detection threshold distinguished LISA, which is about $0.1$ rad. The orbital initial eccentricity and inclination is $p=12$ and $x=0.5~ (I\sim0.33\pi)$, initial orbital phases are taken as follows $\Phi_{r,0} =\Phi_{\theta,0} =\Phi_{\phi,0}=1.0$ and the mass-ratio of binary system is $10^{-5}$.
• Figure 5: Mismatch of EMRI waveforms $(h^{q_s=0}, h^{q_s\neq0})$ with and without the correction of scalar charge as a contour of different parameters setting is plotted, incorporating the dependent relations of $(q_s, e)$ in the top-left panel, $(x, e)$ in the top-right panel, $(\log_{10}(\mu/M_\odot), e)$ in the bottom-left panel and $(q_s, \log_{10}(\mu/M_\odot))$ in the bottom-right panel. The other parameters are set as follows: the initial semi-latus rectum $p=10$, MBH spin $a=0.3$, the initial orbital inclination $x=0.3$ (top-left panel), scalar charge $q_s=0.004$ (top-right panel), initial parameters $e=0.3, x=0.3$ and scalar charge $q_s=0.005$ (bottom-left panel), initial eccentricity $e=0.3$ and inclination $x=0.3$ (bottom-right panel). The mass-ratio in three panels is fixed as $q=10^{-5}$, except the bottom-left panel.