Gravitational wave (GW) detector LISA will observe near-coalescence extreme mass ratio inspirals (EMRIs), which typically form in galactic central accretion disks. Gas torques on EMRI will alter its GW-driven inspiral trajectory from the vacuum expectation, leading to potentially LISA-observable GW dephasing (Δψ_ gas). Most studies compute Δψ_ gas for a thin, laminar disk, with negligible flow turbulence, where the disk exerts a fairly well-understood linear torque (T_ lin). However, these disks must be turbulent due to magneto-rotational instability in the inner regions. Hence, we present a proof-of-concept general, agnostic prescription for the turbulent torque (T_ turb) acting on an EMRI by modeling it as a Gaussian distribution around T_ lin, based on recent advances from a global hydrodynamical (HD) study. We compute Δψ_ gas for the “golden” circular EMRI with total source mass M=10^6 M_⊙ and mass ratio q=5×10^-5 in its final four-year evolution at redshift z=0.276 and signal-to-noise ratio (SNR) =50 by varying Eddington ratio f_ Edd, turbulence normalization C (= 360 in the aforementioned HD study), disk aspect ratio h_0, and turbo-viscous coefficient α in a reasonable parameters space. We find that for f_ Edd≳0.3, C≳300, h_0≳0.03, and α≳0.1, gas-induced dephasings are unobservable if only considering T_ lin but could become detectable (Δψ_ gas>8/SNR) if EMRIs exhibit chaotic migration due to turbulent gas flow. Hence, this work motivates running MHD simulations of accretion disks with embedded LISA EMRIs in the early in-spiral phase over long enough timescales to understand the evolution of their orbital elements and the imprint of the turbulent environment on their gravitational waveforms.

We perform 3D hydrodynamics simulations of an equal-mass quasi-circular live 10^6 M_⊙ massive black hole binary (MBHB) embedded in a prograde, locally isothermal circumbinary disk (CBD) with 0.1 aspect ratio. The binary evolution is driven by the gaseous torques and its dynamics is described with 2.5 post-Newtonian corrections. This approach allows us to track the influence of the CBD on a gravitational-wave (GW) driven MBHB inspiral from 55 to 46 Schwarzschild radii, i.e., at its early evolution in the LISA band at redshift z∼1. For the first time for the 0.1 aspect ratio disk, we report the measurement of gravitational and accretion torques with and without concurrent GW emission. We also report how the morphology of the accretion time series onto the MBHB modestly alters when GW emission is the dominant binary evolutionary mechanism. Lastly, we find that the gas-induced orbital phase-shift is 0.12 rad over 600 orbital cycles, which LISA should detect at z=1. Our results have implications for multi-messenger astronomy, since observation of accretion rate modulation by LSST/Roman surveys and phase-shift by LISA will provide crucial information on the complex environment surrounding MBHBs.

Upcoming space-based gravitational wave detectors such as LISA, the Laser Interferometer Space Antenna, will be sensitive to extreme- and intermediate-mass-ratio inspirals (EMRIs and IMRIs). These binaries are comprised of a supermassive black hole and a stellar-mass object or intermediate-mass black hole. Their detection will probe the structure of galactic nuclei and enable tests of general relativity. As these events will be observed over thousands of orbital cycles, they will be extremely sensitive to both the underlying spacetime and astrophysical environment, demanding exquisite theoretical models on both fronts to avoid biased or even erroneous results. In particular, many (E/)IMRIs are expected to occur within accretion discs around supermassive black holes, and the nonlinearities present when modeling these systems require numerical simulations. In preparation for future modeling of LISA sources, we have conducted a comparison between eight different hydrodynamical codes and applied them to the problem of a q = 10^-4 mass ratio binary interacting with an accretion disc. Thicker discs appear more lenient, and all codes at sufficiently high resolutions are in good agreement with each other and analytical predictions. For thinner discs, beyond the reach of analytical models, we find substantial disagreement between 2D and 3D simulations and between different codes, including both the magnitude and sign of the torque. With time and energy efficiency in mind, codes that leverage moving meshes or grid-based Lagrangian remapping seem preferable, as do codes that can leverage graphical processing units and other energy-efficient hardware.

The opening of the gravitational wave window has significantly enhanced our capacity to explore the Universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our Universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them.

We investigate the effect of dynamically coupling gas torques with gravitational wave (GW) emission during the orbital evolution of an equal-mass massive black hole binary (MBHB). We perform hydrodynamical simulations of eccentric MBHBs with total mass M = 10 ^6 M _⊙ embedded in a prograde locally isothermal circumbinary disk (CBD). We evolve the binary from 55 to 49 Schwarzschild radii separations using up to 2.5 post-Newtonian corrections to the binary dynamics, which allow us to follow the GW-driven inspiral. For the first time, we report the measurement of gas torques onto a live binary a few years before the merger, with and without concurrent GW radiation. We also report the gas-induced orbital dephasing δϕ _orb ∼ −0.007 rad over 278 orbital cycles that is likely driven mainly by disk-induced precession, and LISA should be able to detect it at redshift z = 1. Our results show how GWs alone can be used to probe the astrophysical properties of CBDs and have important implications for multimessenger strategies aimed at studying the environments of MBHBs.

ABSTRACT We explore the eccentricity measurement threshold of Laser Interferometer Space Antenna (LISA) for gravitational waves radiated by massive black hole binaries (MBHBs) with redshifted BH masses Mz in the range 104.5–107.5 M⊙ at redshift z = 1. The eccentricity can be an important tracer of the environment where MBHBs evolve to reach the merger phase. To consider LISA’s motion and apply the time delay interferometry, we employ the lisabeta software and produce year-long eccentric waveforms using the inspiral-only post-Newtonian model taylorf2ecc. We study the minimum measurable eccentricity (emin, defined one year before the merger) analytically by computing matches and Fisher matrices, and numerically via Bayesian inference by varying both intrinsic and extrinsic parameters. We find that emin strongly depends on Mz and weakly on mass ratio and extrinsic parameters. Match-based signal-to-noise ratio criterion suggest that LISA will be able to detect emin ∼ 10−2.5 for lighter systems (Mz ≲ 105.5 M⊙) and ∼10−1.5 for heavier MBHBs with a 90 per cent confidence. Bayesian inference with Fisher initialization and a zero noise realization pushes this limit to emin ∼ 10−2.75 for lower-mass binaries, assuming a <50 per cent relative error. Bayesian inference can recover injected eccentricities of 0.1 and 10−2.75 for a 105 M⊙ system with an ∼10−2 per cent and an ∼10 per cent relative errors, respectively. Stringent Bayesian odds criterion ($\ln {\mathcal {B}}\gt 8$) provides nearly the same inference. Both analytical and numerical methodologies provide almost consistent results for our systems of interest. LISA will launch in a decade, making this study valuable and timely for unlocking the mysteries of the MBHB evolution.

ABSTRACT We assess the possibility of detecting both eccentricity and gas effects (migration and accretion) in the gravitational wave (GW) signal from LISA massive black hole binaries at redshift $z=1$. Gas induces a phase correction to the GW signal with an effective amplitude ($C_{\rm g}$) and a semimajor axis dependence (assumed to follow a power-law with slope $n_{\rm g}$). We use a complete model of the LISA response and employ a gas-corrected post-Newtonian inspiral-only waveform model TaylorF2Ecc. By using the Fisher formalism and Bayesian inference, we constrain $C_{\rm g}$ together with the initial eccentricity $e_0$, the total redshifted mass $M_z$, the primary-to-secondary mass ratio q, the dimensionless spins $\chi _{1,2}$ of both component BHs, and the time of coalescence $t_c$. We find that simultaneously constraining $C_{\rm g}$ and $e_0$ leads to worse constraints on both parameters with respect to when considered individually. For a standard thin viscous accretion disc around $M_z=10^5~{\rm M}_{\odot }$, $q=8$, $\chi _{1,2}=0.9$, and $t_c=4$ years MBHB, we can confidently measure (with a relative error of $\lt 50$ per cent) an Eddington ratio ${\rm f}_{\rm Edd}\sim 0.1$ for a circular binary and ${\rm f}_{\rm Edd}\sim 1$ for an eccentric system assuming $\mathcal {O}(10)$ stronger gas torque near-merger than at the currently explored much-wider binary separations. The minimum measurable eccentricity is $e_0\gtrsim 10^{-2.75}$ in vacuum and $e_0\gtrsim 10^{-2}$ in gas. A weak environmental perturbation (${\rm f}_{\rm Edd}\lesssim 1$) to a circular binary can be mimicked by an orbital eccentricity during inspiral, implying that an electromagnetic counterpart would be required to confirm the presence of an accretion disc.

We examine expected effective spin (chi(eff,1yr)) and orbital eccentricity (e(1yr)) correlations for a population of observable equal-mass massive black hole binaries (MBHBs) with total redshifted mass M-z similar to[10(4.5),10(7.5)] M circle dot embedded in a circumbinary disc (CBD) at redshifts z=1 and z=2, 1 yr before merging in the Laser Interferometer Space Antenna (LISA) band. We find a strong correlation between measurable eccentricity and negative effective spin for MBHBs that are carried to merger by retrograde accretion. This is due to the well-established eccentricity pumping of retrograde accretion and less-well-established formation of retrograde mini-discs coupled with a stable retrograde CBD throughout the binary evolution from the self-gravitating radius. Conversely, prograde accretion channels result in positive chi eff,1yr and non-measurable e(1yr) except for almost unity Eddington ratio and M-z less than or similar to 10(5) M-circle dot MBHBs at z=1. This clear contrast between the two CBD orientations - and particularly the unique signature of retrograde configurations - provides a promising way to unlock the mysteries of MBHB formation channels in the LISA era.

Our current understanding is that an environment - mainly consisting of gas or stars - is required to bring massive black hole binaries (MBHBs) with total redshifted mass M-z similar to[10(4), 10(7)] M-circle dot to the LISA band from parsec separation. Even in the gravitational wave (GW) dominated final inspiral, realistic environments can non-negligibly speed up or slow down the binary evolution, or leave residual, measurable eccentricity in the LISA band. Despite this fact, most of the literature does not consider environmental effects or orbital eccentricity in modelling GWs from near-equal mass MBHBs. Considering either a circular MBHB embedded in a circumbinary disc or a vacuum eccentric binary, we explore if ignoring either secular gas effects (migration and accretion) or eccentric corrections to the GW waveform can mimic a failure of general relativity (GR). We use inspiral-only aligned-spin 3.5 post-Newtonian (PN) waveforms, a complete LISA response model, and Bayesian inference to perform a parameterized test of GR. For a 4-yr LISA observation of an MBHB with M-z = 10(5) M-circle dot, primary-to-secondary mass ratio q = 8, and component BHs' dimensionless spins chi(1,2) = 0.9 at redshift z = 1, even a moderate gas-disc imprint (Eddington ratio f(Edd )similar to 0.1) or low initial eccentricity (e(0 )similar to 10(-2.5)) causes a false violation of GR in several PN orders. However, correctly modelling either effect can mitigate systematics while avoiding significant biases in vacuum circular systems. The adoption of LISA makes it urgent to consider gas imprints and eccentricity in waveform models to ensure accurate inference for MBHBs.

We analyse the effect of stochastic torque fluctuations on the orbital evolution and the gravitational wave (GW)emission of gas-embedded sources with intermediate and extreme mass ratios. We show that gas-driven fluctuations imprint additional harmonic content in the GWs of the binary system, which we dub dirty waveforms(DWs). We find three interesting observational prospects for DWs, provided that torque fluctuations do indeed persist beyond the resolution limit of current hydrodynamical simulations. Firstly, DWs can produce a significant stochastic GW background, comparable to other GW noise sources. Secondly, the energy flux implied by the additional harmonics can cause a detectable secular phase shift in Laser Interferometer Space Antenna (LISA) sources, even if the net torque fluctuations vanish when averaged over orbital time-scales. Lastly, the DWs of moderate-redshift nHz supermassive binaries detectable by pulsar timing arrays (PTAs) could be detectable in the mHz range, producing a new type of PTA-LISA multiband gravitational source. Our results suggest that searching for DWs and their effects can potentially be a novel way to probe the heaviest of black holes and the physics of the accretion discs surrounding them. We find these results to be a further confirmation of the many exciting prospects of actively searching for environmental effects within the data stream of future GW detectors.

ABSTRACT We study the effect of torques on circular inspirals of intermediate-mass black hole binaries (IMBHBs) embedded in gas discs, wherein both BH masses are in the range 102–105 M⊙, up to redshift z = 10. We focus on how torques impact the detected gravitational wave (GW) waveform in the LISA frequency band when the binary separation is within a few hundred Schwarzschild radii. For a sub-Eddington accretion disc with a viscosity coefficient α = 0.01, surface density Σ ≈ 105 g cm−2, and Mach number $\mathcal {M}_{\rm {a}}\approx 80$, a gap, or a cavity, opens when the binary is in the LISA band. Depending on the torque’s strength, LISA will observe dephasing in the IMBHB’s GW signal up to either z ∼ 5 for high mass ratios (q ≈ 0.1) or to z ∼ 7 for q ≈ 10−3. We study the dependence of the measurable dephasing on variations of BH masses, redshift, and accretion rates. Our results suggest that phase shift is detectable even in high-redshift (z = 10) binaries if they experience super-Eddington accretion episodes. We investigate if the disc-driven torques can result in an observable ‘time-dependent’ chirp mass with a simplified Fisher formalism, finding that, at the expected signal-to-noise ratio, the gas-induced variation of the chirp mass is too small to be detected. This work shows how gas-induced perturbations of vacuum waveforms should be strong enough to be detected by LISA for the IMBHB in the early inspiral phase. These perturbations encode precious information on accretion discs and galactic nuclei astrophysics. High-accuracy waveform models which incorporate these effects will be needed to extract such information.

General Relativity enjoys the freedom of different geometrical interpretations in terms of curvature, torsion or non-metricity. Within this geometrical trinity, a simpler geometrical formulation of General Relativity manifests itself in the latter, where gravity is entirely attributed to non-metricity. In this Letter, we consider non-linear extensions of Coincident General Relativity f(Q˚) for phenomenological applications on both cosmological as well as galactic scales. The theory not only delivers dark energy on large scales but also recovers MOND on galactic scales, together with implications for the early universe cosmology. To the best of our knowledge, this represents the first relativistic, covariant, and ghost-free hybrid-formulation of MOND which recovers both, General Relativity and MOND in the appropriate limits and reconciles expected cosmological behavior. We further illustrate that previous bimetric formulations of MOND generically suffer from ghost instabilities and f(Q˚) crystalizes as a unique ghost-free theory.

We consider a simpler geometrical formulation of General Relativity based on non-metricity, known as Coincident General Relativity. We study the ADM formulation of the theory and perform a detailed Hamiltonian analysis. We explicitly show the propagation of two physical degrees of freedom, as it should, even though the role of boundary terms and gauge conditions is significantly altered. This might represent an alternative promising new route for numerical relativity and canonical quantum gravity. We also give an outlook on the number of propagating degrees of freedom in non-linear extension of non-metricity scalar.