Extreme-mass-ratio Inspirals Signals Research Articles

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. 
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.

Search for Extreme Mass Ratio Inspirals Using Particle Swarm Optimization and Reduced Dimensionality Likelihoods

Extreme-mass-ratio inspirals (EMRIs) are significant observational targets for spaceborne gravitational wave detectors, namely, LISA, Taiji, and Tianqin, which involve the inspiral of stellar-mass compact objects into massive black holes (MBHs) with a mass range of approximately 104∼107M⊙. EMRIs are estimated to produce long-lived gravitational wave signals with more than 105 cycles before plunge, making them an ideal laboratory for exploring the strong-gravity properties of the spacetimes around the MBHs, stellar dynamics in galactic nuclei, and properties of the MBHs itself. However, the complexity of the waveform model, which involves the superposition of multiple harmonics, as well as the high-dimensional and large-volume parameter space, make the fully coherent search challenging. In our previous work, we proposed a 10-dimensional search using Particle Swarm Optimization (PSO) with local maximization over the three initial angles. In this study, we extend the search to an 8-dimensional PSO with local maximization over both the three initial angles and the angles of spin direction of the MBH, where the latter contribute a time-independent amplitude to the waveforms. Additionally, we propose a 7-dimensional PSO search by using a fiducial value for the initial orbital frequency and shifting the corresponding 8-dimensional Time Delay Interferometry responses until a certain lag returns the corresponding 8-dimensional log-likelihood ratio’s maximum. The reduced dimensionality likelihoods enable us to successfully search for EMRI signals with a duration of 0.5 years and signal-to-noise ratio of 50 within a wider search range than our previous study. However, the ranges used by both the LISA Data Challenge (LDC) and Mock LISA Data Challenge (MLDC) to generate their simulated signals are still wider than the those we currently employ in our direct searches. Consequently, we discuss further developments, such as using a hierarchical search to narrow down the search ranges of certain parameters and applying Graphics Processing Units to speed up the code. These advances aim to improve the efficiency, accuracy, and generality of the EMRI search algorithm.

Fast Radio Bursts: Electromagnetic Counterparts to Extreme Mass-ratio Inspirals

Recent observations discovered that some repeating fast radio bursts (FRBs) show a large value and complex variations of Faraday rotation measures (RMs). The binary systems containing a supermassive black hole and a neutron star can be used to explain such RM variations. Meanwhile, such systems produce low-frequency gravitational-wave (GW) signals, which are one of the primary interests of three proposed space-based GW detectors: the Laser Interferometer Space Antenna (LISA), Tianqin, and Taiji. These signals are known as extreme mass-ratio inspirals (EMRIs). Therefore, FRBs can serve as candidates of electromagnetic counterparts for EMRI signals. In this Letter, we study the EMRI signals in this binary system, which can be detected up to z ∼ 0.04 by LISA and Tianqin for the most optimistic case. Assuming the cosmic comb model for FRB production, the total event rate can be as high as ∼1 Gpc−3 yr−1. EMRI signals associated with FRBs can be used to reveal the progenitor of FRBs. It is also a new type of standard siren, which can be used as an independent cosmological probe.

Rapid determination of LISA sensitivity to extreme mass ratio inspirals with machine learning

ABSTRACT Gravitational wave observations of the inspiral of stellar-mass compact objects into massive black holes (MBHs), extreme mass ratio inspirals (EMRIs), enable precision measurements of parameters such as the MBH mass and spin. The Laser Interferometer Space Antenna is expected to detect sufficient EMRIs to probe the underlying source population, testing theories of the formation and evolution of MBHs and their environments. Population studies are subject to selection effects that vary across the EMRI parameter space, which bias inference results if unaccounted for. This bias can be corrected, but evaluating the detectability of many EMRI signals is computationally expensive. We mitigate this cost by (i) constructing a rapid and accurate neural network interpolator capable of predicting the signal-to-noise ratio of an EMRI from its parameters, and (ii) further accelerating detectability estimation with a neural network that learns the selection function, leveraging our first neural network for data generation. The resulting framework rapidly estimates the selection function, enabling a full treatment of EMRI detectability in population inference analyses. We apply our method to an astrophysically motivated EMRI population model, demonstrating the potential selection biases and subsequently correcting for them. Accounting for selection effects, we predict that with 116 EMRI detections LISA will measure the MBH mass function slope to a precision of 8.8 per cent, the CO mass function slope to a precision of 4.6 per cent, the width of the MBH spin magnitude distribution to a precision of 10 per cent, and the event rate to a precision of 12 per cent with EMRIs at redshifts below z = 6.

Modeling transient resonances in extreme-mass-ratio inspirals

Extreme-mass-ratio inspirals are one of the most exciting and promising target sources for space-based interferometers (such as LISA, TianQin). The observation of their emitted gravitational waves will offer stringent tests on general theory of relativity, and provide a wealth of information about the dense environment in galactic centers. To unlock such potential, it is necessary to correctly characterize EMRI signals. However, resonances are a phenomena that occurs in EMRI systems and can impact parameter inference, and therefore the science outcome, if not properly modeled. Here, we explore how to model resonances and develop an efficient implementation. Our previous work has demonstrated that tidal resonances induced by the tidal field of a nearby astrophysical object alters the orbital evolution, leading to a significant dephasing across observable parameter space. Here, we extensively explore a more generic model for the tidal perturber with additional resonance combinations, to study the dependence of resonance strength on the intrinsic orbital and tidal parameters. To analyze the resonant signals, accurate templates that correctly incorporate the effects of the tidal field are required. The evolution through resonances is obtained using a step function, whose amplitude is calculated using an analytic interpolation of the resonance jumps. We benchmark this procedure by comparing our approximate method to a numerical evolution. We find that there is no significant error caused by this simplified prescription, as far as the astronomically reasonable range in the parameter space is concerned. Further, we use Fisher matrices to study both the measurement precision of parameters and the systematic bias due to inaccurate modeling. Modeling of self-force resonances can also be carried out using the implementation presented in this study, which will be crucial for EMRI waveform modeling.

Detecting gravitational waves from extreme mass ratio inspirals using convolutional neural networks

Extreme mass ratio inspirals (EMRIs) are among the most interesting gravitational wave (GW) sources for space-borne GW detectors. However, successful GW data analysis remains challenging due to many issues, ranging from the difficulty of modeling accurate waveforms, to the impractically large template bank required by the traditional matched filtering search method. In this work, we introduce a proof-of-principle approach for EMRI detection based on convolutional neural networks (CNNs). We demonstrate the performance with simulated EMRI signals buried in Gaussian noise. We show that over a wide range of physical parameters, the network is effective for EMRI systems with a signal-to-noise ratio larger than 50, and the performance is most strongly related to the signal-to-noise ratio. The method also shows good generalization ability towards different waveform models. Our study reveals the potential applicability of machine learning technology like CNNs towards more realistic EMRI data analysis.

Gravitational waves from extreme-mass-ratio inspirals using general parametrized metrics

Future space-borne interferometers will be able to detect gravitational waves at $10^{-3}$ to $10^{-1}$ Hz. At this band extreme-mass-ratio inspirals (EMRIs) can be promising gravitational wave sources. In this paper, we investigate possibility of testing Kerr hypothesis against a parametrized non-Kerr metric by matching EMRI signals. However, EMRIs from either equatorial orbits or inclined orbits suffer from the "confusion problem". Our results show that, within the time scale before radiation flux plays an important role, small and moderate deviations from the Kerr spacetime($|\delta_i|<1$) can be discerned only when spin parameter is high. In most cases, the EMRI waveforms related with a non-Kerr metric can be mimicked by the waveform templates produced with a Kerr black hole.

Testing general relativity using binary extreme-mass-ratio inspirals

Abstract It is known that massive black holes (MBHs) of $10^{5-7}\, \mathrm{ M}_\odot$ could capture small compact objects to form extreme-mass-ratio inspirals (EMRIs). Such systems emit gravitational waves (GWs) in the band of the Laser Interferometer Space Antenna (LISA) and are ideal probes of the space–time geometry of MBHs. Recently, we have shown that MBHs could also capture stellar-mass binary black holes (about $10\, \mathrm{ M}_\odot$) to form binary-EMRIs (b-EMRIs) and, interestingly, a large fraction of the binaries coalesce due to the tidal perturbation by the MBHs. Here we further show that the coalescence could be detected by LISA as glitches in EMRI signals. We propose an experiment to use the multiband (102 and 10−3 Hz) glitch signals to test gravity theories. Our simulations suggest that the experiment could measure the mass and linear momentum lost via GW radiation, as well as constrain the mass of gravitons, to a precision that is one order of magnitude better than the current limit.

Bayesian inference on EMRI signals using low frequency approximations

Extreme mass ratio inspirals (EMRIs) are thought to be one of the most exciting gravitational wave sources to be detected with LISA. Due to their complicated nature and weak amplitudes the detection and parameter estimation of such sources is a challenging task. In this paper we present a statistical methodology based on Bayesian inference in which the estimation of parameters is carried out by advanced Markov chain Monte Carlo (MCMC) algorithms such as parallel tempering MCMC. We analysed high and medium mass EMRI systems that fall well inside the low frequency range of LISA. In the context of the Mock LISA Data Challenges, our investigation and results are also the first instance in which a fully Markovian algorithm is applied for EMRI searches. Results show that our algorithm worked well in recovering EMRI signals from different (simulated) LISA data sets having single and multiple EMRI sources and holds great promise for posterior computation under more realistic conditions. The search and estimation methods presented in this paper are general in their nature, and can be applied in any other scenario such as AdLIGO, AdVIRGO and Einstein Telescope with their respective response functions.

Testing Chern-Simons modified gravity with observations of extreme-mass-ratio binaries

Extreme-Mass-Ratio Inspirals (EMRIs) are one of the most promising sources of gravitational waves (GWs) for space-based detectors like the Laser Interferometer Space Antenna (LISA). EMRIs consist of a compact stellar object orbiting around a massive black hole (MBH). Since EMRI signals are expected to be long lasting (containing of the order of hundred thousand cycles), they will encode the structure of the MBH gravitational potential in a precise way such that features depending on the theory of gravity governing the system may be distinguished. That is, EMRI signals may be used to test gravity and the geometry of black holes. However, the development of a practical methodology for computing the generation and propagation of GWs from EMRIs in theories of gravity different than General Relativity (GR) has only recently begun. In this paper, we present a parameter estimation study of EMRIs in a particular modification of GR, which is described by a four-dimensional Chern-Simons (CS) gravitational term. We focus on determining to what extent a space-based GW observatory like LISA could distinguish between GR and CS gravity through the detection of GWs from EMRIs.

Detection strategies for extreme mass ratio inspirals

The capture of compact stellar remnants by galactic black holes provides a unique laboratory for exploring the near-horizon geometry of the Kerr spacetime, or possible departures from general relativity if the central cores prove not to be black holes. The gravitational radiation produced by these extreme mass ratio inspirals (EMRIs) encodes a detailed map of the black hole geometry, and the detection and characterization of these signals is a major scientific goal for the LISA mission. The waveforms produced are very complex, and the signals need to be coherently tracked for tens of thousands of cycles to produce a detection, making EMRI signals one of the most challenging data analysis problems in all of gravitational wave astronomy. Estimates for the number of templates required to perform an exhaustive grid-based matched-filter search for these signals are astronomically large, and far out of reach of current computational resources. Here I describe an alternative approach that employs a hybrid between genetic algorithms and Markov chain Monte Carlo techniques, along with several time-saving techniques for computing the likelihood function. This approach has proven effective at the blind extraction of relatively weak EMRI signals from simulated LISA data sets.

Simulations of extreme-mass-ratio inspirals using pseudospectral methods

Extreme-mass-ratio inspirals (EMRIs), stellar-mass compact objects (SCOs) inspiralling into a massive black hole, are one of the main sources of gravitational waves expected for the Laser Interferometer Space Antenna (LISA). To extract the EMRI signals from the expected LISA data stream, which will also contain the instrumental noise as well as other signals, we need very accurate theoretical templates of the gravitational waves that they produce. In order to construct those templates we need to account for the gravitational backreaction, that is, how the gravitational field of the SCO affects its own trajectory. In general relativity, the backreaction can be described in terms of a local self-force, and the foundations to compute it have been laid recently. Due to its complexity, some parts of the calculation of the self-force have to be performed numerically. Here, we report on an ongoing effort towards the computation of the self-force based on time-domain multi-grid pseudospectral methods.

Improved time–frequency analysis of extreme-mass-ratio inspiral signals in mock LISA data

The planned Laser Interferometer Space Antenna (LISA) is expected to detect gravitational wave signals from ∼100 extreme-mass-ratio inspirals (EMRIs) of stellar-mass compact objects into massive black holes. The long duration and large parameter space of EMRI signals make data analysis for these signals a challenging problem. One approach to EMRI data analysis is to use time–frequency methods. This consists of two steps: (i) searching for tracks from EMRI sources in a time–frequency spectrogram and (ii) extracting parameter estimates from the tracks. In this paper we discuss the results of applying these techniques to the latest round of the Mock LISA Data Challenge, Round 1B. This analysis included three new techniques not used in previous analyses: (i) a new chirp-based algorithm for track search for track detection; (ii) estimation of the inclination of the source to the line of sight; (iii) a Metropolis–Hastings Monte Carlo over the parameter space in order to find the best fit to the tracks.

Time-frequency analysis of extreme-mass-ratio inspiral signals in mock LISA data

Extreme-mass-ratio inspirals (EMRIs) of compact objects with mass m ∼ 1–10 M⊙ into massive black holes with mass M ∼ 106 M⊙ can serve as excellent probes of strong-field general relativity. The Laser Interferometer Space Antenna (LISA) is expected to detect gravitational wave signals from ∼ 100 EMRIs per year, but the data analysis of EMRI signals poses a unique set of challenges due to their long duration and the extensive parameter space of possible signals. One possible approach is to carry out a search for EMRI tracks in the time-frequency domain. We have applied a time-frequency search to the data from the Mock LISA Data Challenge (MLDC) with promising results. Our analysis used the Hierarchical Algorithm for Clusters and Ridges to identify tracks in the time-frequency spectrogram corresponding to EMRI sources. We then estimated the EMRI source parameters from these tracks. In these proceedings, we discuss the results of this analysis of the MLDC round 1.3 data.

Gaussianity of LISA’s confusion backgrounds

Data analysis for the proposed Laser Interferometer Space Antenna (LISA) will be complicated by the huge number of sources in the LISA band. In the frequency band ~10-^4 - 2×10^-3 Hz, galactic white dwarf binaries (GWDBs) are sufficiently dense in frequency space that it will be impossible to resolve most of them, and “confusion noise” from the unresolved Galactic binaries will dominate over instrumental noise in determining LISA's sensitivity to other sources in that band. Confusion noise from unresolved extreme-mass-ratio inspirals (EMRIs) could also contribute significantly to LISA's total noise curve. To date, estimates of the effect of LISA's confusion noise on matched-filter searches and their detection thresholds have generally approximated the noise as Gaussian, based on the central limit theorem. However in matched-filter searches, the appropriate detection threshold for a given class of signals may be located rather far out on the tail of the signal-to-noise probability distribution, where a priori it is unclear whether the Gaussian approximation is reliable. Using the Edgeworth expansion and the theory of large deviations, we investigate the probability distribution of the usual matched-filter detection statistic, far out on the tail of the distribution. We apply these tools to four somewhat idealized versions of LISA data searches: searches for EMRI signals buried in GWDB confusion noise, and searches for massive black hole binary signals buried in (i) GWDB noise, (ii) EMRI noise, and (iii) a sum of EMRI noise and Gaussian noise. Assuming reasonable short-distance cutoffs in the populations of confusion sources (since the very closest and hence strongest sources will be individually resolvable), modifications to the appropriate detection threshold, due to the non-Gaussianity of the confusion noise, turn out to be quite small for realistic cases. The smallness of the correction is partly due to the fact that these three types of sources evolve on quite different time scales, so no single background source closely resembles any search template. We also briefly discuss other types of LISA searches where the non-Gaussianity of LISA's confusion backgrounds could perhaps have a much greater impact on search reliability and efficacy.