Laser Interferometer Space Antenna Band Research Articles

Impacts of gravitational-wave background from supermassive black hole binaries on the detection of compact binaries by LISA* *Supported by the NSFC (12250010, 11991052) and Key Research Program of Frontier Sciences, CAS, (ZDBS-LY-7009)

In the frequency band of the Laser Interferometer Space Antenna (LISA), extensive research has been conducted on the impact of foreground confusion noise generated by galactic binaries within the Milky Way Galaxy. Additionally, recent evidence of a stochastic signal, announced by the NANOGrav, EPTA, PPTA, CPTA, and InPTA, indicates that the stochastic gravitational-wave background (SGWB) generated by supermassive black hole binaries (SMBHBs) can contribute strong background noise within the LISA band. Given the presence of such strong noise, it is expected to have significant impacts on LISA's scientific missions. In this study, we investigate the impacts of the SGWB generated by SMBHBs on the detection of individual massive black hole binaries, verified galactic binaries, and extreme mass ratio inspirals in the context of LISA. We find it essential to resolve and eliminate the excess noise from the SGWB to guarantee the success of LISA's missions.

The Enhanced Population of Extreme Mass-ratio Inspirals in the LISA Band from Supermassive Black Hole Binaries

Extreme mass-ratio inspirals (EMRIs) take place when a stellar-mass black hole (BH) merges with a supermassive BH (SMBH). The gravitational-wave emission from such an event is expected to be detectable by the future Laser Interferometer Space Antenna (LISA) and other millihertz detectors. It was recently suggested that the EMRI rate in SMBH binary systems is orders of magnitude higher than the EMRI rate around a single SMBH with the same total mass. Here we show that this high rate can produce thousands of SMBH–BH sources at a redshift of unity. We predict that LISA may detect a few hundred of these EMRIs with signal-to-noise ratio above S/N ≥8 within a 4 yr mission lifetime. The remaining subthreshold sources will contribute to a large confusion noise, which is approximately an order of magnitude above LISA’s sensitivity level. Finally, we suggest that the individually detectable systems, as well as the background noise from the subthreshold EMRIs, can be used to constrain the SMBH binary fraction in the low-redshift Universe.

Identifying LISA verification binaries among the Galactic population of double white dwarfs

ABSTRACT Double white dwarfs (DWDs) will be the most numerous gravitational-wave (GW) sources for the Laser Interferometer Space Antenna (LISA). Most of the Galactic DWDs will be unresolved and will superpose to form a confusion noise foreground, the dominant LISA noise source around ${\sim} 0.5\!-\!3\, \mathrm{mHz}$ . A small fraction of these sources will stand out from the background and be individually detectable. Uniquely among GW sources, a handful of these binaries will be known in advance from electromagnetic (EM) observations and will be guaranteed sources of detectable GWs in the LISA band; these are known as verification binaries (VBs). High-cadence photometric surveys are continuously discovering new VB systems, and their number will continue to grow ahead of the launch of LISA. We analyse, in a fully Bayesian framework, all the currently known VB candidates with the latest design requirements for the LISA mission and find that 25 of the considered sources can be detected within a 4 yr observation time. We explore what can be expected from GW observations, both alone and in combination with EM observations, and estimate the VB’s time to detection in the early months of LISA operations. We also show how VBs can be analysed in the case where their GW signals compete with many other unknown binary signals (both resolved and unresolved) from a realistic Galactic population of DWDs.

Milli-Hertz Gravitational-wave Background Produced by Quasiperiodic Eruptions

Extreme-mass-ratio inspirals (EMRIs) are important targets for future space-borne gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA). Recent works suggest that EMRIs may reside in a population of newly discovered X-ray transients called “quasiperiodic eruptions” (QPEs). Here, we follow this scenario and investigate whether LISA could in the future detect the QPEs. We consider two specific models, in which the QPEs are made of either stellar-mass objects moving on circular orbits around massive black holes (MBHs) or white dwarfs (WDs) on eccentric orbits around MBHs. We find that in either case the five QPEs detected so far are too weak to be resolvable by LISA. However, if QPEs are made of eccentric WD–MBH binaries, they radiate GWs over a wide range of frequencies. The broad spectra overlap to form a background that peaks in the milli-Hertz band and has a signal-to-noise ratio of 9–17 even in the most pessimistic scenario. The presence of this GW background in the LISA band could impact future searches for seed black holes at high redshift as well as stellar-mass binary black holes in the local universe.

Enhanced frequency noise suppression for LISA by combining cavity and arm locking control systems

This paper presents a novel method for laser frequency stabilization in the Laser Interferometer Space Antenna (LISA) mission by locking a laser to two stable length references-the arms of the interferometer and an on-board optical cavity. The two references are digitally fused using carefully designed control systems, attempting minimal or no changes to the baseline LISA mission hardware. The interferometer arm(s) provides the most stable reference available in the LISA science band (0.1 mHz--1 Hz), while the cavity sensor's wideband and linear readout enables additional control system gain below and above the LISA band. The main technical issue with this dual sensor approach is the undesirable slow laser frequency pulling which couples into the control system with the imperfect knowledge of the Doppler shift of the light due to relative spacecraft motion along the LISA arm. This paper outlines requirements on the Doppler shift knowledge to maintain the cavity well within the resonance when activating the fused control system. Two Doppler shift estimation methods are presented that use the already on-board measurements, the inter-spacecraft interferometer link (the main science measurement), and the absolute inter-spacecraft laser ranging system. Both methods reach the required precision after a few thousand seconds of measurement integration. The paper demonstrates an approach to initialize and engage the proposed laser stabilization system, starting from free-running laser and ending with the dual sensor frequency control system. The results show that the technique lowers the residual laser frequency noise in the LISA science band by over 3 orders of magnitude: from $30\text{ }\text{ }\mathrm{Hz}/\sqrt{\mathrm{Hz}}$ to as low as $7\text{ }\text{ }\mathrm{mHz}/\sqrt{\mathrm{Hz}}$, potentially allowing the requirements on Time Delay Interferometry (TDI) to be relaxed---possibly to the point where first-generation TDI may be sufficient.

Revised event rates for extreme and extremely large mass-ratio inspirals

ABSTRACT One of the main targets of the Laser Interferometer Space Antenna (LISA) is the detection of extreme mass-ratio inspirals (EMRIs) and extremely large mass-ratio inspirals (X-MRIs). Their orbits are expected to be highly eccentric and relativistic when entering the LISA band. Under these circumstances, the inspiral time-scale given by Peters’ formula loses precision and the shift of the last-stable orbit (LSO) caused by the massive black hole spin could influence the event rates estimate. We re-derive EMRIs and X-MRIs event rates by implementing two different versions of a Kerr loss-cone angle that includes the shift in the LSO, and a corrected version of Peters’ time-scale that accounts for eccentricity evolution, 1.5 post-Newtonian hereditary fluxes, and spin-orbit coupling. The main findings of our study are summarized as follows: (1) implementing a Kerr loss-cone changes the event rates by a factor ranging between 0.9 and 1.1; (2) the high-eccentricity limit of Peters’ formula offers a reliable inspiral time-scale for EMRIs and X-MRIs, resulting in an event-rate estimate that deviates by a factor of about 0.9–3 when compared to event rates computed with the corrected version of Peters’ time-scale and the usual loss-cone definition. (3) Event-rate estimates for systems with a wide range of eccentricities should be revised. Peters’ formula overestimates the inspiral rates of highly eccentric systems by a factor of about 8–30 compared to the corrected values. Besides, for e0 ≲ 0.8, implementing the corrected version of Peters’ formula is necessary to obtain accurate estimates.

Characterization of the stochastic signal originating from compact binary populations as measured by LISA

The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the early 2030s, is a gravitational wave observatory in space designed to detect sources emitting in the milli-Hertz band. In contrast to the present ground based detectors, the LISA data are expected to be a signaldominated, with strong and weak gravitational wave signals overlapping in time and in frequency. Astrophysical population models predict a sufficient number of signals in the LISA band to blend together and form an irresolvable foreground noise. In this work, we present a generic method for characterizing the foreground signals originating from a given astrophysical population of coalescing compact binaries. Assuming idealized detector conditions and perfect data analysis technique capable of identifying and removing the bright sources, we apply an iterative procedure which allows us to predict the different levels of foreground noise.

Gravitational-wave Signatures from Compact Object Binaries in the Galactic Center

Abstract Almost every galaxy has a supermassive black hole (SMBH) residing at its center, the Milky Way included. Recent studies suggest that these unique places are expected to host a high abundance of stellar and compact object binaries. These binaries form hierarchical triple systems with the SMBH and undergo the eccentric Kozai–Lidov (EKL) mechanism. Here we estimate the detectability of potential gravitational-wave emission from these compact objects within the frequency band of the Laser Interferometer Space Antenna (LISA) and Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo detectors. We generate a post-EKL population of stars at the onset of Roche limit crossing and follow their evolution to compact object binaries. As a proof of concept, we adopt two metallicities, solar metallicity (Z = 0.02) and 15% of it (Z = 0.003). We demonstrate that over the observation timescale of LISA, black hole (BH) binaries (BH–BH) and white dwarf (WD) binaries provide the most prominent GW sources via the EKL-assisted merger channel. Systems involving neutron stars (NSs) are less observable but possibly abundant through different merger channels. Our population synthesis of BH–BH with Z = 0.02 (Z = 0.003) translates to ∼4 (24) events per year with LIGO within a 1 Gpc3 sphere. We also estimated the number of binaries visible in the LISA band within the inner parsec of our Galactic center (and possibly other galaxies) to be about 14–150 WD–WD, 0–2 NS–BH, 0.2–4 NS–NS, and 0.3–20 BH–BH.

Improved gravitational radiation time-scales II: Spin–orbit contributions and environmental perturbations

ABSTRACT Peters’ formula is an analytical estimate of the time-scale of gravitational wave (GW)-induced coalescence of binary systems. It is used in countless applications, where the convenience of a simple formula outweighs the need for precision. However, many promising sources of the Laser Interferometer Space Antenna (LISA), such as supermassive black hole binaries and extreme mass-ratio inspirals (EMRIs), are expected to enter the LISA band with highly eccentric (e ≳ 0.9) and highly relativistic orbits. These are exactly the two limits in which Peters’ estimate performs the worst. In this work, we expand upon previous results and give simple analytical fits to quantify how the inspiral time-scale is affected by the relative 1.5 post-Newtonian (PN) hereditary fluxes and spin–orbit couplings. We discuss several cases that demand a more accurate GW time-scale. We show how this can have a major influence on quantities that are relevant for LISA event-rate estimates, such as the EMRI critical semimajor axis. We further discuss two types of environmental perturbations that can play a role in the inspiral phase: the gravitational interaction with a third massive body and the energy loss due to dynamical friction and torques from a surrounding gas medium ubiquitous in galactic nuclei. With the aid of PN corrections to the time-scale in vacuum, we find simple analytical expressions for the regions of phase space in which environmental perturbations are of comparable strength to the effects of any particular PN order, being able to qualitatively reproduce the results of much more sophisticated analyses.

Dynamical Formation Scenarios for GW190521 and Prospects for Decihertz Gravitational-wave Astronomy with GW190521-like Binaries

Abstract The gravitational-wave (GW) detection of GW190521 has provided new insights on the mass distribution of black holes and new constraints for astrophysical formation channels. With independent claims of GW190521 having significant premerger eccentricity, we investigate what this implies for GW190521-like binaries that form dynamically. The Laser Interferometer Space Antenna (LISA) will also be sensitive to GW190521-like binaries if they are circular from an isolated formation channel. However, GW190521-like binaries that form dynamically may skip the LISA band entirely. To this end, we simulate GW190521 analogs that dynamically form via post-Newtonian binary–single scattering. From these scattering experiments, we find that GW190521-like binaries may enter the LIGO-Virgo band with significant eccentricity as suggested by recent studies, though well below an eccentricity of e 10 Hz ≲ 0.7. Eccentric GW190521-like binaries further motivate the astrophysical science case for a decihertz GW observatory, such as the kilometer-scale version of the Midband Atomic Gravitational-wave Interferometric Sensor. We carry out a Fisher analysis to estimate how well the eccentricity of GW190521-like binaries can be constrained with such a decihertz detector. These eccentricity constraints would also provide additional insights into the possible environments that GW190521-like binaries form in.

Gravitational-wave Detection and Parameter Estimation for Accreting Black-hole Binaries and Their Electromagnetic Counterpart

Abstract We study the impact of gas accretion on the orbital evolution of black-hole binaries initially at large separation in the band of the planned Laser Interferometer Space Antenna (LISA). We focus on two sources: (i) stellar-origin black-hole binaries (SOBHBs) that can migrate from the LISA band to the band of ground-based gravitational-wave (GW) observatories within weeks/months; and (ii) intermediate-mass black-hole binaries (IMBHBs) in the LISA band only. Because of the large number of observable GW cycles, the phase evolution of these systems needs to be modeled to great accuracy to avoid biasing the estimation of the source parameters. Accretion affects the GW phase at negative (−4) post-Newtonian order, being thus dominant for binaries at large separations. Accretion at the Eddington or at super-Eddington rate will leave a detectable imprint on the dynamics of SOBHBs. For super-Eddington rates and a 10 yr mission, a multiwavelength strategy with LISA and a ground-based interferometer can detect about 10 (a few) SOBHB events for which the accretion rate can be measured at 50% (10%) level. In all cases, the sky position can be identified within much less than 0.4 deg2 uncertainty. Likewise, accretion at ≳100% of the Eddington rate can be measured in IMBHBs up to redshift z ≈ 0.1, and the position of these sources can be identified within less than uncertainty. Altogether, a detection of SOBHBs or IMBHBs would allow for targeted searches of electromagnetic counterparts to black-hole mergers in gas-rich environments with future X-ray detectors (such as Athena) and/or radio observatories (such as SKA).

Impact of a Spinning Supermassive Black Hole on the Orbit and Gravitational Waves of a Nearby Compact Binary

Abstract Recent theoretical studies suggest that stellar-mass binary black holes (BBHs) would merge more efficiently due to the Kozai–Lidov (K–L) mechanism if these binaries form in the vicinity of supermassive black holes (SMBHs). Since SMBHs are likely rotating rapidly, we continue our earlier study on the generalization of the K–L formalism to include the spin of the SMBH and study the evolution of a nearby BBH. We find that the eccentricity and orbital inclination of the BBH are significantly affected, because the spin (i) forces the orbital plane of the center-of-mass of the BBH around the SMBH to precess (the Lense–Thirring effect) and (ii) imposes an additional gravitomagnetic force on the BBH. As a result, the merger time of the BBH could be significantly different. We calculate the waveform from the BBH in one representative example and study its detectability with a milli-Hertz gravitational-wave detector, such as the Laser Interferometer Space Antenna (LISA). We find that the signal is distinguishable from that in the case without spin. Our results imply that the BBHs in the LISA band could potentially be used to probe the spin of the SMBHs in galaxy centers.

A Bright Electromagnetic Counterpart to Extreme Mass Ratio Inspirals

Abstract The extreme mass ratio inspiral (EMRI), defined as a stellar-mass compact object inspiraling into a supermassive black hole (SMBH), has been widely argued to be a low-frequency gravitational-wave (GW) source. Providing accurate measurements of the black hole mass and spin of EMRIs is one of the primary interests for the Laser Interferometer Space Antenna (LISA). However, it is currently understood that there are no electromagnetic (EM) counterparts to EMRIs. Here we show a new formation channel of EMRIs with tidal disruption flares as EM counterparts. In this scenario, flares can be produced from the tidal stripping of the helium (He) envelope of a massive star by an SMBH. The remaining compact core of the massive star then evolves into an EMRI. We find that, under a certain initial eccentricity and semimajor axis, the GW frequency of the inspiral can enter the LISA band within 10 ∼ 20 yr, which makes the tidal disruption flare an EM precursor to an EMRI. Although the event rate is just 2 × 10 − 4 Gpc − 3 yr − 1 , this association not only improves the localization accuracy of LISA and helps us to find the host galaxy of EMRI, but it also serves as a new GW standard siren for cosmology.

Merger Rate of Stellar Black Hole Binaries above the Pair-instability Mass Gap

Abstract In current stellar evolutionary models, the occurrence of pair-instability supernovae implies a lack of stellar black holes (BHs) with masses between about [60, 120] M⊙, resulting in the presence of an upper-mass gap in the BH mass distribution. In this Letter, we propose a simple approach to describe BHs beyond the pair-instability gap by convolving the initial mass function and star formation rate with the metallicity evolution across cosmic time. Under the ansatz that the underlying physics of binary formation does not change beyond the gap, we then construct the cosmic population of merging BH binaries. The detection rate of BH binaries with both mass components above the gap is found to range between ≃[0.4, 7] yr−1 for LIGO/Virgo at design sensitivity and [10, 460] yr−1 for third-generation ground-based detectors, considering the most pessimistic and optimistic scenarios. The Laser Interferometer Space Antenna (LISA) can individually detect these binaries up to thousands of years from coalescence. The number of events merging in less than four years, which enable multiband observation in sequence, is expected to be in the range [1, 20]. While ET will detect all these events, LIGO/Virgo is expected to detect ≲50% of them. Finally, we estimate that the gravitational-wave background from unresolved sources in the LISA band may in principle be detected with a signal-to-noise ratio between ≃2.5 and ≃80.

Multi-axis heterodyne interferometry at MHz frequencies: a short-arm measurement demonstration for LISA with off-the-shelf hardware.

We report the design, construction, and operation of a multi-axis heterodyne interferometry (MAHI) system operating at MHz heterodyne frequencies, which provides a testbed for technologies to be used in the Laser Interferometer Space Antenna (LISA) space-based gravitational wave mission. The system was calibrated for measurement of the piston, pitch, and yaw of a three-axis piezo-actuated mirror, giving measured calibration values that closely match those predicted by a simulation based on Gaussian beam tracing. The piston sensitivity of the MAHI system in the LISA band was measured to be below 10 pm Hz-1/2 for frequencies above 4 mHz and below 1 pm Hz-1/2 for frequencies above 35 mHz. The sensitivity is limited above 2 Hz by the mechanical vibrations of the apparatus and below 1 mHz by dimensional changes caused by temperature fluctuations. Evidence points towards scattered light as the limiting noise source at intermediate frequencies. The angular sensitivity of the MAHI system was measured to be close to or below 10 nrad Hz-1/2 for frequencies above 4 mHz and below 1 nrad Hz-1/2 for frequencies above 100 mHz. Noise budgets for both length and angle were determined, indicating the areas in which improvements must be made in order to reach increased sensitivity. The current operating sensitivity already provides a useful testbed for LISA technologies and a potential blueprint for future ground segment equipment.

Post-Newtonian phase accuracy requirements for stellar black hole binaries with LISA

The Laser Interferometer Space Antenna (LISA) will observe black hole binaries of stellar origin during their gravitational wave inspiral, months to years before coalescence. Due to the long duration of the signal in the LISA band, a faithful waveform is necessary in order to keep track of the binary phase. This is crucial to extract the signal from the data and to perform an unbiased estimation of the source parameters. We consider Post-Newtonian (PN) waveforms, and analyze the PN order needed to keep the bias caused by the PN approximation negligible relative to the statistical parameter estimation error, as a function of the source parameters. By considering realistic population models, we conclude that for $\sim 90\%$ of the stellar black hole binaries detectable by LISA, waveforms at low Post-Newtonian (PN) order (PN $\le 2$) are sufficiently accurate for an unbiased recovery of the source parameters. Our results provide a first estimate of the trade-off between waveform accuracy and information recovery for this class of LISA sources.

Impact of galactic foreground characterization on a global analysis for the LISA gravitational wave observatory

The Laser Interferometer Space Antenna (LISA) will explore the source-rich milli-Hertz band of the gravitational wave spectrum. In contrast to ground based detectors, where typical signals are short-lived and discrete, LISA signals are typically long-lived and over-lapping, thus requiring a global data analysis solution that is very different to the source-by-source analysis that has been developed for ground based gravitational wave astronomy. Across the LISA band, gravitational waves are both signals and noise. The dominant contribution to this so-called confusion noise (better termed unresolved signal noise) is expected to come from short period galactic white dwarf binaries, but all sources, including massive black hole binaries and extreme mass ratio captures will also contribute. Previous estimates for the galactic confusion noise have assumed perfect signal subtraction. Here we provide analytic estimates for the signal subtraction residuals and the impact they have on parameter estimation while for the first time incorporating the effects of noise modeling. The analytic estimates are found using a maximum likelihood approximation to the full global Bayesian analysis. We find that while the confusion noise is lowered in the global analysis, the waveform errors for individual sources are increased relative to estimates for isolated signals. We provide estimates for how parameter estimation errors are inflated from various parts of a global analysis.

Multi-band gravitational wave astronomy: science with joint space- and ground-based observations of black hole binaries

Soon after the observation of the first black hole binary (BHB) by advanced LIGO (aLIGO), GW150914, it was realised that such a massive system would have been observable in the milli-Hz (mHz) band few years prior to coalescence. Operating in the frequency range 0.1-100 mHz, the Laser Interferometer Space Antenna (LISA) can potentially detect up to thousands inspiralling BHBs, based on the coalescence rates inferred from the aLIGO first observing run (O1). The vast majority of them (those emitting at f < 10 mHz) will experience only a minor frequency drift during LISA lifetime, resulting in signals similar to those emitted by galactic white dwarf binaries. At f > 10 mHz however, several of them will sweep through the LISA band, eventually producing loud coalescences in the audio-band probed by aLIGO. This contribution reviews the scientific potential of these new class of LISA sources which, in the past few months, has been investigated in several contexts, including multi-messenger and multi-band gravitational wave astronomy, BHB astrophysics, tests of alternative theories of gravity and cosmography.

Characterizing spinning black hole binaries in eccentric orbits with LISA

The Laser Interferometer Space Antenna (LISA) is designed to detect gravitational wave signals from astrophysical sources, including those from coalescing binary systems of compact objects such as black holes. Colliding galaxies have central black holes that sink to the center of the merged galaxy and begin to orbit one another and emit gravitational waves. Some galaxy evolution models predict that the binary black hole system will enter the LISA band with significant orbital eccentricity, while other models suggest that the orbits will already have circularized. Using a full 17 parameter waveform model that includes the effects of orbital eccentricity, spin precession, and higher harmonics, we investigate how well the source parameters can be inferred from simulated LISA data. Defining the reference eccentricity as the value one year before merger, we find that for typical LISA sources, it will be possible to measure the eccentricity to an accuracy of parts in a thousand. The accuracy with which the eccentricity can be measured depends only very weakly on the eccentricity, making it possible to distinguish circular orbits from those with very small eccentricities. LISA measurements of the orbital eccentricity can help constraints theories of galaxy mergers in the early universe. Failing to account for the eccentricity in the waveform modeling can lead to a loss of signal power and bias the estimation of parameters such as the black hole masses and spins.

GRAVITATIONAL WAVE SIGNAL FROM ASSEMBLING THE LIGHTEST SUPERMASSIVE BLACK HOLES

We calculate the gravitational wave signal from the growth of 10 million solar mass supermassive black holes (SMBH) from the remnants of Population III stars. The assembly of these lower mass black holes is particularly important because observing SMBHs in this mass range is one of the primary science goals for the Laser Interferometer Space Antenna (LISA), a planned NASA/ESA mission to detect gravitational waves. We use high resolution cosmological N-body simulations to track the merger history of the host dark matter halos, and model the growth of the SMBHs with a semi-analytic approach that combines dynamical friction, gas accretion, and feedback. We find that the most common source in the LISA band from our volume consists of mergers between intermediate mass black holes and SMBHs at redshifts less than 2. This type of high mass ratio merger has not been widely considered in the gravitational wave community; detection and characterization of this signal will likely require a different technique than is used for SMBH mergers or extreme mass ratio inspirals. We find that the event rate of this new LISA source depends on prescriptions for gas accretion onto the black hole as well as an accurate model of the dynamics on a galaxy scale; our best estimate yields about 40 sources with a signal-to-noise ratio greater than 30 occur within a volume like the Local Group during SMBH assembly -- extrapolated over the volume of the universe yields roughly 500 observed events over 10 years, although the accuracy of this rate is affected by cosmic variance.