Extreme Mass Ratio Inspirals Research Articles

Erratum: Extreme mass-ratio inspirals into black holes surrounded by scalar clouds [Phys. Rev. D 108 , 084019 (2023)

Erratum: Extreme mass-ratio inspirals into black holes surrounded by scalar clouds [Phys. Rev. D <b>108</b> , 084019 (2023)

Prograde and retrograde stars in nuclear cluster merger. Evolution of the supermassive black hole binary and the host galactic nucleus

Nuclear star cluster (NSC) mergers, involving the fusion of dense stellar clusters near the centres of galaxies, play a pivotal role in shaping galactic structures. The distribution of stellar orbits has significant effects on the formation and characteristics of extreme mass ratio inspirals (EMRIs). In this study, we address the orbital distribution of stars in merging NSCs and the subsequent effects on supermassive black hole binary (SMBHB) evolution. We ran dedicated direct-summation $N$-body simulations with different initial conditions to do a detailed study of the resulting NSC after their progenitors had merged. Our findings reveal that prograde stars form a flattened structure, while retrograde stars have a more spherical distribution. The axial ratios of the prograde component vary based on the presence and mass ratio of the SMBHs. The fraction of prograde and retrograde stars depends on the merger orbital properties and the SMBH mass ratio. The interactions of retrograde stars with the SMBHB affect the eccentricity and separation evolution of the binary. Our analysis reveals a strong correlation between the angular momentum and eccentricity of the SMBH binary. This relationship could serve as a means to infer information about the stellar dynamics surrounding the binary. We find that prograde orbits are particularly close to the binary of SMBHs, a promising fact regarding EMRI production. Moreover, prograde and retrograde stars have different kinematic structures, with the prograde stars typically rotating faster than the retrograde ones. The line-of-sight velocity and velocity dispersion, as well as the velocity anisotropy of each NSC, depend on the initial merger orbital properties and SMBH mass ratios. The prograde and retrograde stars always show different behaviours. The distribution of stellar orbits and the dynamical properties of each kinematic population can potentially be used as a way to tell the properties of the parent nuclei apart, and has an important impact on expected rates of EMRIs, which will be detected by future gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA).

Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes

Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes

Concept study of a storage ring-based gravitational wave observatory: Gravitational wave strain and synchrotron radiation noise

This work for the first time addresses the feasibility of measuring millihertz gravitational waves (mHz GWs) with a storage ring-based detector. While this overall challenge consists of several partial problems, here we focus solely on quantifying design limitations imposed by the kinetic energy and radiated power of circulating ions at relativistic velocities. We propose an experiment based on the measurement of the time-of-flight signal of an ion chain. One of the dominant noise sources inherent to the measurement principle for such a GW detector is the shot noise of the emitted synchrotron radiation. We compute the noise amplitude of arrival time signals obtained by analytical estimates and simulations of ions with different masses and velocities circulating in a storage ring with the circumference of the Large Hadron Collider. Thereby, we show that our experiment design could reduce the noise amplitude due to the synchrotron radiation in the frequency range 10−4–10−2 Hz to one or two orders of magnitude below the expected GW signals from of astrophysical sources, such as supermassive binary black holes or extreme mass-ratio inspirals. Other key requirements for building a working storage ring-based GW detector include the generation and acceleration of heavy ion chains with the required energy resolution, their injection and continued storage, as well as the detection method to be used for the determination of the particle arrival time. However, these are not the focus of the work presented here, in which we instead concentrate on the definition of a working principle in terms of ion type, kinetic energy, and ring design, which will later serve as a starting point when addressing a more complete experimental setup. Published by the American Physical Society 2024

Enhanced Extreme Mass Ratio Inspiral Rates and Intermediate Mass Black Holes.

Extreme mass ratio inspirals (EMRIs) occur when stellar-mass compact objects begin a gravitational wave (GW) driven inspiral into massive black holes. EMRI waveforms can precisely map the surrounding spacetime, making them a key target for future space-based GW interferometers such as LISA, but their event rates and parameters are massively uncertain. One of the largest uncertainties is the ratio of true EMRIs (which spend at least thousands of orbits in the LISA band) and direct plunges, which are in-band for at most a handful of orbits and are not detectable in practice. In this Letter, we show that the traditional dichotomy between EMRIs and plunges-EMRIs originate from small semimajor axes, plunges from large-does not hold for intermediate-mass black holes with masses M_{•}≲10^{5}M_{⊙}. In this low-mass regime, a plunge always has an O(1) probability of failing and transitioning into a novel "cliffhanger" EMRI. Cliffhanger EMRIs are more easily produced for larger stellar-mass compact objects, and are less likely for smaller ones. This new EMRI production channel can dominate volumetric EMRI rates n[over ˙]_{EMRI} if intermediate-mass black holes are common in dwarf galactic nuclei, potentially increasing n[over ˙]_{EMRI} by an order of magnitude.

Detecting the tidal heating with the generic extreme mass-ratio inspirals

The horizon of a classical black hole (BH), functioning as a one-way membrane, plays a vital role in the dynamic evolution of binary BHs, capable of absorbing fluxes entirely.Tidal heating, stemming from this phenomenon, exerts a notable influence on the production of gravitational waves (GWs). If at least one member of a binary is an exotic compact object (ECO) instead of a BH, the absorption of fluxes is expected to be incomplete and the tidal heating would be different. Thus, tidal heating can be utilized for model-independent investigations into the nature of compact object. In this paper, assuming that the extreme mass-ratio inspiral (EMRI) contains a stellar-mass compact object orbiting around a massive ECO with a reflective surface, we compute the GWs from the generic EMRI orbits. Using the accurate and analytic flux formulas in the black hole spacetime, we adapted these formulas in the vicinity of the ECO surface by incorporating a reflectivity parameter.Under the adiabatic approximation, we can evolve the orbital parameters and compute the EMRI waveforms. The effect of tidal heating for the spinning and non-spinning objects can be used to constrain the reflectivity of the surface at the level of 𝒪(10-6) by computing the mismatch and fisher information matrix.

Exploring waveforms with non-GR deviations for extreme mass-ratio inspirals

The fundamental process of detecting and examining the polarization modes of gravitational waves plays a pivotal role in enhancing our grasp on the precise mechanisms behind their generation. A thorough investigation is essential for delving deeper into the essence of gravitational waves and rigorously evaluating and validating the range of modified gravity theories. In this line of interest, a general description of black holes in theories beyond general relativity can serve a meaningful purpose where distinct deviation parameters can be mapped to solutions representing distinct theories. Employing a refined version of the deformed Kerr geometry, which is free from pathological behaviours such as unphysical divergences in the metric, we explore an extreme mass-ratio inspiral system, wherein a stellar-mass object perturbs a supermassive black hole. We compute the effects of deformation parameters on the rate of change of orbital energy and angular momentum, orbital evolution and phase dynamics with leading order post-Newtonian corrections. With the waveform analysis, we assess the plausibility of detecting deviations from general relativity through observations facilitated by the Laser Interferometer Space Antenna (LISA), simultaneously constraining the extent of these deviations. Therefore, this analysis provides an understanding while highlighting the essential role of observations in advancing gravitational phenomena beyond general relativity.

Gravitational waves for eccentric extreme mass ratio inspirals of self-dual spacetime

In this paper, we calculate the frequencies of geodesic orbits in self-dual spacetime on the equatorial plane and obtain the leading-order effects of loop quantum parameters P on the energy flux and angular momentum flux in eccentric extreme mass ratio inspirals. The gravitational waveform under different eccentricity is carried out by improved “analytic-kludge” method. We calculate the waveform mismatches for the LISA detector and the measurement error on loop quantum parameters. The constraint capability on P will be improved by a factor of 3 to 10, compared to the weak field experiments in the solar system.

Coupled Disk-star Evolution in Galactic Nuclei and the Lifetimes of QPE Sources

A modest fraction of the stars in galactic nuclei fed toward the central supermassive black hole (SMBH) approach on low-eccentricity orbits driven by gravitational-wave radiation (extreme mass ratio inspiral (EMRI)). In the likely event that a gaseous accretion disk is created in the nucleus during this slow inspiral (e.g., via an independent tidal disruption event (TDE)), star–disk collisions generate regular short-lived flares consistent with the observed quasiperiodic eruption (QPE) sources. We present a model for the coupled star-disk evolution, which self-consistently accounts for mass and thermal energy injected into the disk from stellar collisions and associated mass ablation. For weak collision/ablation heating, the disk is thermally unstable and undergoes limit-cycle oscillations, which modulate its properties and lead to accretion-powered outbursts on timescales of years to decades, with a time-averaged accretion rate ∼0.1Ṁ Edd. Stronger collision/ablation heating acts to stabilize the disk, enabling roughly steady accretion at the EMRI-stripping rate. In either case, the stellar destruction time through ablation, and hence the maximum QPE lifetime, is ∼102–103 yr, far longer than fallback accretion after a TDE. The quiescent accretion disks in QPE sources may at the present epoch be self-sustaining and fed primarily by EMRI ablation. Indeed, the observed range of secular variability broadly matches those predicted for collision-fed disks. Changes in the QPE recurrence pattern following such outbursts, similar to that observed in GSN 069, could arise from temporary misalignment between the EMRI-fed disk and the SMBH equatorial plane as the former regrows its mass after a state transition.

Fast inspirals and the treatment of orbital resonances

Abstract Extreme mass ratio inspirals (EMRIs), where a compact object orbits a massive black hole, are a key source of gravitational waves for the future Laser Interferometer Space Antenna (LISA). Due to their small mass ratio, ε ~ 10-4 -- 10-7 , the binary evolves slowly and EMRI signals will be in-band for years. Additionally, astrophysical EMRIs are expected to have complex dynamics featuring both spin-precession and eccentricity. A standard approach to modelling these inspirals is via the method of osculating geodesics (OG) which we employ along with a toy model for the gravitational self-force. Using this method requires resolving tens of thousands radial and polar orbital librations over the long duration of the signal which makes the inspiral trajectory expensive to compute.In this work we accelerate these calculations by employing Near-Identity (averaging) Transformations. &amp;#xD;However, this averaging technique breaks down at orbital resonances where the radial and polar frequencies are an integer ratio of each other. Thus, we switch to a partial averaging transformation in the vicinity of the resonance where the dynamics are characterised by the slow evolution of the so-called ``resonant phase". Additionally, we develop an optimal switching criterion to minimise the computation time while maximising accuracy. We find the error in the waveform phase is improved from O(ε-1/2) in the fully averaged scheme to O(ε4/7) in the switching scheme. At the same time, this scheme improves the scaling of the computation time from being inversely proportional to ε using OG, to a very weak scaling with ε. This results in a speed-up of at least two orders of magnitude for LISA EMRIs with room for further optimisation.

Mono- and oligochromatic extreme-mass-ratio inspirals

The gravitational capture of a stellar-mass object by a supermassive black hole represents a unique probe of warped spacetime. The small object, typically a stellar-mass black hole, describes a very large number of cycles before crossing the event horizon. Because of the mass difference, we call these captures extreme-mass-ratio inspirals (EMRIs). Their merger event rate at the Galactic Center is negligible, but the amount of time spent in the early inspiral is not. Early EMRIs (E-EMRIs) spend hundreds of thousands of years in band during this phase. At very early stages, the peak of the frequency will not change during an observational time. At later stages in the evolution, it will change a bit and finally the EMRI explores a wide range of them when it is close to merger. We distinguish between “monocromatic” E-EMRIs, which do not change their (peak) frequency, oligochromatic E-EMRIs, which explore a short range and polychromatic ones, and the EMRIs which have been discussed so far in the literature. We derive the number of E-EMRIs at the Galactic Center, and we also calculate their signal-to-noise ratios (SNR) and perform a study of parameter extraction. We show that parameters such as the spin and the mass can be extracted with an error which can be as small as 10−11 and 10−5M⊙. There are between hundreds and thousands of E-EMRIs in their monochromatic stage at the Galactic Centre (GC), and tens in their oligochromatic phase. The SNR ranges from a minimum of 10 (larger likelihood) to a maximum of 106 (smaller likelihood). Moreover, we derive the contribution signal corresponding to the incoherent sum of continuous sources of oligochromatic E-EMRIs with two representatives masses, 10M⊙ and 40M⊙, and show that their curves will cover a significant part of Laser Interferometer Space Antennas (LISAs) sensitivity curve. Depending on their level of circularization, they might be detected as individual sources or form a foreground population. Published by the American Physical Society 2024

Exploring dark forces with multimessenger studies of extreme mass ratio inspirals

The exploration of dark sector interactions via gravitational waves (GWs) from binary inspirals has been a subject of recent interest. We study dark forces using extreme mass ratio inspirals (EMRIs), pointing out two issues of interest. Firstly, the innermost stable circular orbit (ISCO) of the EMRI, which sets the characteristic length scale of the system and hence the dark force range to which it exhibits enhanced sensitivity, probes force mediator masses that complement those studied with supermassive black hole (SMBH) or neutron star binaries. The LISA mission (the proposed μAres detector) will probe mediators with masses m V ∼ 10-16 eV (m V ∼ 10-18 eV), corresponding to ISCOs of 106 M ⊙ (108 M ⊙) central SMBHs. Secondly, while the sensitivity to dark couplings is typically limited by the uncertainty in the binary component masses, independent mass measurements of the central SMBH through reverberation mapping campaigns or the motion of dynamical tracers enable one to break this degeneracy. Our results therefore highlight the necessity for coordinated studies, loosely referred to as “multimessenger”, between future μHz- mHz GW observatories and ongoing and forthcoming SMBH mass measurement campaigns, including OzDES-RM, SDSS-RM, and SDSS-V Black Hole Mapper.

Extreme mass-ratio inspiral around the horizonless massive object

In this paper, we calculated the extreme mass-ratio inspiral (EMRI) waveform radiated from a binary composed of a massive horizonless object (MHO) and a compact object (CO), where CO is spiraling on a circular equatorial orbit around the MHO. Due to the absent of horizon, there exist the ingoing and outgoing waves near the reflective surface of MHO, which have significantly influence on the evolution of orbital parameters. We observe that there indeed exist the differences of EMRI trajectories between the massive Kerr black hole and MHO cases. By calculating the mismatch of gravitational wave (GW) waveforms from massive black hole (MBH) and MHO, our result indicates that the space-borne gravitational wave detector could distinguish the modified effect of reflectivities from the BH case, which allows to put an upper constraint on the reflectivity R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {R}}$$\\end{document} of MHO, at the level of R≳10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {R}} > rsim 10^{-4}$$\\end{document}.

Constraining the EdGB theory with extreme mass-ratio inspirals

The Einstein-dilaton-Gauss–Bonnet (EdGB) theory is a modified theory of gravity which include a scalar field to couple with the higher order curvature terms. It has already been constrained with various observations include the gravitational wave (GW) with LIGO, Virgo and KAGRA (LVK) Collaboration. In this work, we study the capability for space-borne GW detectors to constrain the EdGB theory using the signal of Extreme Mass-Ratio Inspiral (EMRIs). We use the “numerical kludge (NK)” method to construct the waveform of EMRI in the EdGB theory, focusing on the case when the central black hole is spinless. We then study how a future space-borne gravitational wave detector, TianQin, for example, can place constraints on the EdGB theory through the detection of EMRIs. With the analysis using mismatch and Fisher Information Matrix (FIM), we find that the EdGB parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\\alpha }$$\\end{document} is expected to be constrained to the level of ∼O(0.1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim \\mathcal {O}(0.1)$$\\end{document} km.

Improving Cosmological Constraints by Inferring the Formation Channel of Extreme-mass-ratio Inspirals

Extreme-mass-ratio inspirals (EMRIs) could be detected by space-borne gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA), TianQin, and Taiji. Localizing EMRIs by GW detectors can help us select candidate host galaxies, which can be used to infer the cosmic expansion history. In this paper, we demonstrate that the localization information can also be used to infer the formation channel of EMRIs, and can hence allow us to extract more precisely the redshift probability distributions. By conducting mock observations of the EMRIs that can be detected by TianQin and LISA, as well as the galaxies that can be provided by the future Chinese Space Station Telescope, we find that TianQin can constrain the Hubble–Lemaître constant H 0 to a precision of ∼3%–8% and the dark energy equation-of-state parameter w 0 to ∼10%–40%. The TianQin+LISA network, by increasing the localization accuracy, can improve the precisions of H 0 and w 0 to ∼0.4%–7% and ∼4%–20%, respectively. Then, considering an illustrative case in which all EMRIs originate in active galactic nuclei (AGNs), and combining the mock EMRI observation with a mock AGN catalog, we show that TianQin can recognize the EMRI–AGN correlation with ∼1300 detections. The TianQin+LISA network can reduce this required number to ∼30. Additionally, we propose a statistical method to directly estimate the fraction of EMRIs produced in AGNs, f agn, and show that observationally deriving this value could significantly improve the constraints on the cosmological parameters. These results demonstrate the potentials of using EMRIs as well as galaxy and AGN surveys to improve the constraints on cosmological parameters and the formation channel of EMRIs.

Tidal heating as a discriminator for horizons in equatorial eccentric extreme mass ratio inspirals

Tidal heating in a binary black hole system is driven by the absorption of energy and angular momentum by the black hole’s horizon. Previous works have shown that this phenomenon becomes particularly significant during the late stages of an extreme mass ratio inspiral (EMRI) into a rapidly spinning massive black hole, a key focus for future low-frequency gravitational-wave observations by (for instance) the Laser Interferometer Space Antenna mission. Past analyses have largely focused on quasicircular inspiral geometry, with some of the most detailed studies looking at equatorial cases. Though useful for illustrating the physical principles, this limit is not very realistic astrophysically, since the population of EMRI events is expected to arise from compact objects scattered onto relativistic orbits in galactic centers through many-body events. In this work, we extend those results by studying the importance of tidal heating in equatorial EMRIs with generic eccentricities. Our results suggest that accurate modeling of tidal heating is crucial to prevent significant dephasing and systematic errors in EMRI parameter estimation. We examine a phenomenological model for EMRIs around exotic compact objects by parametrizing deviations from the black hole (BH) picture in terms of the fraction of radiation absorbed compared to the BH case. Based on a mismatch calculation, we find that reflectivities as small as |R|2∼O(10−5) are distinguishable from the BH case, irrespective of the value of the eccentricity. We stress, however, that this finding should be corroborated by future parameter estimation studies. Published by the American Physical Society 2024

Viscous torque in turbulent magnetized active galactic nucleus accretion disks and its effects on the gravitational waves of extreme mass ratio inspirals

The merger of supermassive black holes produces millihertz gravitational waves (GWs), which are potentially detectable by the future Laser Interferometer Space Antenna (LISA). Such binary systems are usually embedded in an accretion disk environment at the center of an active galactic nucleus (AGN). Recent studies suggest the plasma environment imposes measurable imprints on the GW signal if the mass ratio of the binary is around q ∼ 10−4 − 10−3. The effect of the gaseous environment on the GW signal is strongly dependent on the disk’s parameters; therefore, it is believed that future low-frequency GW detections will provide us with precious information about the physics of AGN accretion disks. We investigated this effect by measuring the viscous torque via modeling of the evolution of magnetized tori around the primary massive black hole. Using the general relativistic magnetohydrodynamic HARM-COOL code, we performed 2D and 3D simulations of weakly magnetized, thin accretion disks, with a possible truncation and transition to advection-dominated accretion flow. We studied the angular momentum transport and turbulence generated by the magnetorotational instability. We quantified the disk’s effective alpha viscosity and its evolution over time. We applied our numerical results to quantify the relativistic viscous torque on a hypothetical low-mass secondary black hole via a 1D analytical approach, and we estimated the GW phase shift due to the gas environment.

Repeating nuclear transients as candidate electromagnetic counterparts of LISA extreme mass ratio inspirals

ABSTRACT Extreme mass ratio inspirals (EMRIs) are one of the primary targets for the recently adopted millihertz gravitational-wave observatory LISA. Some previous studies have argued that a fraction of all EMRIs form in matter-rich environments, and can potentially explain the dozens of soft X-ray band ($\sim 10^{-1}\,\rm keV$), low-frequency ($\sim 0.1$ mHz) periodic phenomena known as quasi-periodic eruptions (QPEs) and quasi-periodic oscillations (QPOs). Here, using a representative EMRI population retrofitted with cutoffs on LISA-band SNRs and luminosity distances to account for the sensitivity of current instruments, we estimate the mean frequency band in which QPEs and QPOs originating from detectable LISA EMRIs may be emitting an X-ray signal ‘today’ (i.e. in 2024) to be $0.46 \pm 0.22$ mHz. We also model the well-known QPO source, RE J1034+396, which falls in this frequency band, as an EMRI assuming its primary black hole mass to be $10^6{-}10^7 \,{\rm M}_\odot$. Through a prior-predictive analysis, we estimate the orbiting compact object’s mass to be $46^{+ 10}_{-40} \,{\rm M}_\odot$ and the source’s LISA-band SNR as $\approx 14$, highlighting it as a candidate multimessenger EMRI target. We also highlight the role of current and near-future X-ray and UV observatories in enabling multimessenger observations of EMRIs in conjunction with LISA, and conclude with a discussion of caveats of the current analysis, such as the exclusion of eccentricity and inclination from the model, and the measurability of subsolar mass compact object EMRIs.

Discovering Love numbers through resonance excitation during extreme mass ratio inspirals

General Relativity predicts that black holes (BHs) do not possess an internal structure and consequently cannot be excited. This leads to a specific prediction about the waveform of gravitational waves (GWs) which they emit during a binary BH inspiral and to the vanishing of their Love numbers. However, if astrophysical BHs do possess an internal structure, their Love numbers would no longer vanish, and they could be excited during an inspiral by the transfer of orbital energy. This would affect the orbital period and lead to an observable imprint on the emitted GWs waveform. The effect is enhanced if one of the binary companions is resonantly excited. We discuss the conditions for resonant excitation of a hypothetical internal structure of BHs and calculate the phase change of the GWs waveform that is induced due to such resonant excitation during intermediate- and extreme-mass-ratio inspirals. We then relate the phase change to the electric quadrupolar Love number of the larger companion, which is resonantly excited by its smaller companion. We discuss the statistical error on measuring the Love number by LISA and show that, because of this phase change, the statistical error is small even for values of the Love number as small as 10−4 for moderate values of the spin parameter. Our results indicate that, for extreme-mass-ratio inspirals with moderate spin parameter, the Love number could be detected by LISA with an accuracy which is higher by up to two orders of magnitude than what can be achieved via tidal deformation effects. Thus, our results indicate that resonant excitation of the central BH during an extreme- or intermediate-mass-ratio inspirals is the most promising effect for putting bounds on, or detecting, non-vanishing tidal Love numbers of BHs.

Measurable parameter combinations of environmentally-dephased EMRI gravitational-wave signals

The future space-borne Laser Interferometer Space Antenna (LISA) is expected to detect gravitational waves (GW) from Extreme Mass Ratio Inspiral (EMRI) binaries which may live in nontrivial environments such as accretion disks. In this work, we apply the Fisher matrix Principal Component Analysis (PCA) method to assess how well LISA observations can jointly constrain the source parameters and environmental densities around EMRIs. Specifically, we calculate the Fisher matrix from the post-Newtonian parameters of an EMRI binary embedded in a fluid with a constant density profile. We determine that the most dominant measurable parameter combination is dominated by contributions from environmental effects, namely, gravitational drag, accretion, and gravitational pull (in order of contribution). The proposed reparameterization of the PN parameters can be used to improve the power and efficiency of future detection and parameter estimation methods.