LISA Mission Research Articles

Waterfall stiff period can generate observable primordial gravitational waves

A toy-model is studied, which considers two flat directions meeting at an enhanced symmetry point such that they realise the usual hybrid inflation mechanism. The kinetic term of the waterfall field features a pole at its Planckian vacuum expectation value (VEV), as with α-attractors. Consequently, after the phase transition which terminates hybrid inflation, the waterfall field never rolls to its VEV. Instead, it drives a stiff period, where the barotropic parameter of the Universe w ≈ 1/2 results in a peak in the spectrum of primordial gravitational waves, which will be observable by the forthcoming LISA mission as well as by Advanced LIGO.

Measuring the propagation speed of gravitational waves with LISA

The propagation speed of gravitational waves, cT , has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent cT . Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of cT from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ansätze for cT (f), and study their impact upon the gravitational waveforms of massive black hole binary mergers detectable by the LISA mission. We forecast the constraints on cT (f) obtainable from individual systems and a population of sources, from both inspiral and a full inspiral-merger-ringdown waveform. We show that LISA will enable us to place stringent independent bounds on departures from General Relativity in unexplored low-frequency regimes, even in the absence of an electromagnetic counterpart.

Time delay interferometry combinations as instrument noise monitors for LISA

The LISA mission will likely be a signal dominated detector, such that one challenge is the separation of the different astrophysical sources, and to distinguish between them and the instrumental noise. One of the goals of LISA is to probe the early Universe by detecting stochastic GW backgrounds. As correlation with other detectors is not possible for LISA, discrimination of such a GW background from the instrumental noise requires a good estimate of the latter. To this purpose we have revisited Time Delay Interferometry (TDI) to look for new TDI signal combinations that fulfill the laser frequency noise suppression requirements. We illustrate that it is possible to do a linear combination of these TDI channels to find special null-combinations that suppress gravitational waves and mainly carry information about instrumental noise. We find that there exist many null-combinations that show different sensitivities to gravitational waves, some of which seem more suitable than the traditional T combination for estimating test-mass acceleration noise. In an idealised LISA configuration, they are all sensitive to a particular linear combination of the six test-masses acceleration, similar to a rigid rotation of the LISA triangle. In the following article, we illustrate what are the noise properties that can be extracted by monitoring these interferometry signals and discuss the implication of these findings for the detection of stochastic GW backgrounds.

The effect of mission duration on LISA science objectives

The science objectives of the LISA mission have been defined under the implicit assumption of a 4-years continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of approx 0.75, which would reduce the effective span of usable data to 3 years. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 years of mission operations is recommended.

Alternative LISA-TAIJI networks: Detectability of the isotropic stochastic gravitational wave background

In previous work [1], three TAIJI orbital deployments have been proposed to compose alternative LISA-TAIJI networks, TAIJIm (leading the Earth by $20^\circ$ and $-60^\circ$ inclined with respect to ecliptic plane), TAIJIp (leading the Earth by $20^\circ$ and $+60^\circ$ inclined), TAIJIc (colocated and coplanar with LISA) with respect to the LISA mission (trailing the Earth by $20^\circ$ and $+60^\circ$ inclined). And the LISA-TAIJIm network has been identified as the most capable configuration for massive black hole binary observation. In this work, we examine the performance of three networks to the stochastic gravitational wave background (SGWB) especially for the comparison of two eligible configurations, LISA-TAIJIm and LISA-TAIJIp. This investigation shows that the detectability of LISA-TAIJIm is competitive with the LISA-TAIJIp network for some specific SGWB spectral shapes. And the capability of LISA-TAIJIm is also identical to LISA-TAIJIp to separate the SGWB components by determining the parameters of signals. Considering the performances on SGWB and massive black hole binaries observations, the TAIJIm could be recognized as an optimal option to fulfill joint observations with LISA.

Sensitivity functions of space-borne gravitational wave detectors for arbitrary time-delay interferometry combinations regarding nontensorial polarizations

Direct observation of gravitational waves offers us numerous novel possibilities to further explore the Universe. In practice, the efficiency of the experimental facility for a given gravitational wave source can be measured in terms of the sensitivity function of the instrument. The latter essentially indicates the least incident amplitude required in order to achieve the desired level of the signal-to-noise ratio. Among others, the resultant sensitivity function depends on the specific polarization state of the incident gravitational wave as well as the spatial layout of the detector and its orientation to the wave source. Theoretically, Einstein's general relativity predicts two tensor polarization modes, from a total of six possible modes arising from an arbitrary perturbation of the spacetime metric. Therefore, in this context, the feasibility of measuring nontensorial polarization states provides access to an alternative theory of gravity. In the present study, we analytically evaluate the response functions for arbitrary time-delay interferometry combinations while enumerating all possible polarization modes. The derivation is accomplished by separating the average on the all-sky solid angle from the remaining expression, which, in turn, gives rise to a few factors independent of the time-delay interferometry combination in question. Moreover, we applied the obtained results to the LISA and TianQin missions, and the asymptotic behavior of the resultant sensitivity functions is analyzed and discussed. Among others, it is observed that, for Sagnac combinations, the averaged response function of the breathing mode attains zero at specific discrete frequencies. Such a frequency value corresponds to a multiple of the reciprocal of the one-way light propagation time along the detector arm, irrelevant to the orientation of the wave source. For all six polarization modes, the present findings can be readily applied to an arbitrary time-delay interferometry combination with improved efficiency and accuracy.

LION: laser interferometer on the moon

Gravitational wave astronomy has now left its infancy and has become an important tool for probing the most violent phenomena in our Universe. The LIGO/Virgo-KAGRA collaboration operates ground based detectors which cover the frequency band from 10 Hz to the kHz regime. Meanwhile, the pulsar timing array and the soon to launch LISA mission will cover frequencies below 0.1 Hz, leaving a gap in detectable gravitational wave frequencies. Here we show how a laser interferometer on the moon (LION) gravitational wave detector would be sensitive to frequencies from sub Hz to kHz. We find that the sensitivity curve is such that LION can measure compact binaries with masses between 10 and 100M ⊙ at cosmological distances, with redshifts as high as z = 100 and beyond, depending on the spin and the mass ratio of the binaries. LION can detect binaries of compact objects with higher-masses, with very large signal-to-noise ratios (SNRs), help us to understand how supermassive black holes got their colossal masses on the cosmological landscape, and it can observe in detail intermediate-mass ratio inspirals at distances as large as at least 100 Gpc. Compact binaries that never reach the LIGO/Virgo sensitivity band can spend significant amounts of time in the LION band, while sources present in the LISA band can be picked up by the detector and observed until their final merger. Since LION covers the deci-Hertz regime with such large SNRs, it truly achieves the dream of multi messenger astronomy.

Investigation of the in-flight anomalies of the LISA Pathfinder Test Mass release mechanism

The LISA Pathfinder mission was flown to test some key technologies for the in-flight detection of gravitational waves. The mechanism developed to initialise the science phase, releasing the test mass into a geodesic trajectory, produced unexpected test mass states, requiring dedicated in-flight and on-ground test campaigns. Due to the limited information available from the telemetry, the analysis of the results required a combination of experimental and analytical approaches. A dynamic model of the release mechanism, integrated by an impact model, is developed to explain the in-flight test results. The proposed interpretation of the mechanism anomalies may provide useful guidelines for the design and development of the flight units for the forthcoming LISA mission.

Bremsstrahlung of Light through Spontaneous Emission of Gravitational Waves

Zero-point fluctuations are a universal consequence of quantum theory. Vacuum fluctuations of electromagnetic field have provided crucial evidence and guidance for QED as a successful quantum field theory with a defining gauge symmetry through the Lamb shift, Casimir effect, and spontaneous emission. In an accelerated frame, the thermalisation of the zero-point electromagnetic field gives rise to the Unruh effect linked to the Hawking effect of a black hole via the equivalence principle. This principle is the basis of general covariance, the symmetry of general relativity as the classical theory of gravity. If quantum gravity exists, the quantum vacuum fluctuations of the gravitational field should also lead to the quantum decoherence and dissertation of general forms of energy and matter. Here we present a novel theoretical effect involving the spontaneous emission of soft gravitons by photons as they bend around a heavy mass and discuss its observational prospects. Our analytic and numerical investigations suggest that the gravitational bending of starlight predicted by classical general relativity should also be accompanied by the emission of gravitational waves. This in turn redshifts the light causing a loss of its energy somewhat analogous to the bremsstrahlung of electrons by a heavier charged particle. It is suggested that this new effect may be important for a combined astronomical source of intense gravity and high-frequency radiation such as X-ray binaries and that the proposed LISA mission may be potentially sensitive to the resulting sub-Hz stochastic gravitational waves.

Measuring the primordial gravitational wave background in the presence of other stochastic signals

Standard methodologies for the extraction of the stochastic gravitational wave background (SGWB) from auto- or cross-correlation of interferometric signals often involve the use of a filter function.The standard optimal filter maximizes the signal-to-noise ratio (SNR) between the total SGWB and the noise.We derive expressions for the optimal filter and SNR in the presence of a target SGWB plus other unwanted components. We also generalize the methodology to the case of template-free reconstruction.The formalism allows to easily perform analyses and forecasts that marginalize over foreground signals, such as the typical ΩGW∝ f2/3 background arising from binary coalescence.We demonstrate the methodology with the LISA mission and discuss possible extensions and domains of application.

Gravitational tuning forks and hierarchical triple systems

We study gravitational wave (GW) emission in the strong-field regime by a hierarchical triple system composed of a binary system placed in the vicinity of a supermassive black hole (SMBH). The LIGO-Virgo collaboration recently reported evidence for coalescences with this dynamical origin. These systems are common in galactic centers and thus are a target for the space-based LISA mission as well as other advanced detectors. Doppler shifts, aberration, lensing and strong amplitude modulations are features present in the GW signal from these systems, built into our framework and with no need for phenomenological patches. We find that the binary can resonantly excite the quasinormal modes of the SMBH, as in the resonant excitation of two tuning forks with matching frequencies. The flux of energy crossing the SMBH horizon can be significant, when compared with that from standard extreme-mass-ratio inspirals. Therefore, these triple systems are an outstanding probe of strong-field physics and of the BH nature of compact objects.

Observing gravitational wave polarizations with the LISA-TAIJI network

Two polarizations of the gravitational waves, the plus and cross modes, are derived from general relativity. However, alternative theories of gravity can yield the gravitational waves with up to six polarizations. Searching for the polarizations beyond plus and cross is an important test of general relativity. In principle, one spaceborne detector, like LISA, could measure the gravitational wave polarizations from a long time observation with its orbital motion. With comparable sensitivities, the joint LISA and TAIJI missions will improve the observations on the polarization predictions of theories beyond general relativity. In this work, a class of parametrized post-Einsteinian waveforms is employed to describe the alternative polarizations, and six parametrized post-Einsteinian parameters quantifying the deviation from the general relativity waveforms are examined by using the LISA-TAIJI network. Our results show that the measurements on amplitudes of alternative polarizations from joint LISA-TAIJI observation could be improved by more than 10 times compared to LISA single mission in an optimal scenario.

Probing primordial features with the stochastic gravitational wave background

The stochastic gravitational wave background (SGWB) offers a new opportunity to observe signals of primordial features from inflationary models. We study their detectability with future space-based gravitational waves experiments, focusing our analysis on the frequency range of the LISA mission. We compute gravitational wave spectra from primordial features by exploring the parameter space of a two-field inflation model capable of generating different classes of features. Fine-tuning in scales and amplitudes is necessary for these signals to fall in the observational windows. In some cases the scalar power spectrum can significantly exceed the ns=5 limit in single-field inflation and grow as fast as ns=9.1. Once they show up, several classes of frequency-dependent oscillatory signals, characteristic of different underlying inflationary physics, may be distinguished and the SGWB provides a window on dynamics of the primordial universe independent of cosmic microwave background and large-scale structure. To connect with future experimental data, we discuss two approaches of how the results may be applied to data analyses. First, we discuss the possibility of reconstructing the signal with LISA, which requires a high signal-to-noise ratio. The second more sensitive approach is to apply templates representing the spectra as estimators. For the latter purpose, we construct templates that can accurately capture the spectral features of several classes of feature signals and compare them with the SGWB produced by other physical mechanisms.

Rapid Generation of Fully Relativistic Extreme-Mass-Ratio-Inspiral Waveform Templates for LISA Data Analysis.

The future space mission LISA will observe a wealth of gravitational-wave sources at millihertz frequencies. Of these, the extreme-mass-ratio inspirals of compact objects into massive black holes are the only sources that combine the challenges of strong-field complexity with that of long-lived signals. Such signals are found and characterized by comparing them against a large number of accurate waveform templates during data analysis, but the rapid generation of templates is hindered by computing the ∼10^{3}-10^{5} harmonic modes in a fully relativistic waveform. We use order-reduction and deep-learning techniques to derive a global fit for the ≈4000 modes in the special case of an eccentric Schwarzschild orbit, and implement the fit in a complete waveform framework with hardware acceleration. Our high-fidelity waveforms can be generated in under 1s, and achieve a mismatch of ≲5×10^{-4} against reference waveforms that take ≳10^{4} times longer. This marks the first time that analysis-length waveforms with full harmonic content can be produced on timescales useful for direct implementation in LISA analysis algorithms.

Distinguishing Fuzzballs from Black Holes through Their Multipolar Structure.

Within general relativity, the unique stationary solution of an isolated black hole is the Kerr spacetime, which has a peculiar multipolar structure depending only on its mass and spin. We develop a general method to extract the multipole moments of arbitrary stationary spacetimes and apply it to a large family of horizonless microstate geometries. The latter can break the axial and equatorial symmetry of the Kerr metric and have a much richer multipolar structure, which provides a portal to constrain fuzzball models phenomenologically. We find numerical evidence that all multipole moments are typically larger (in absolute value) than those of a Kerr black hole with the same mass and spin. Current measurements of the quadrupole moment of black-hole candidates could place only mild constraints on fuzzballs, while future gravitational-wave detections of extreme mass-ratio inspirals with the space mission LISA will improve these bounds by orders of magnitude.

Gravitational wave background from extreme mass ratio inspirals

Extreme mass ratio inspirals (EMRIs), i.e. binary systems comprised by a compact stellar-mass object orbiting a massive black hole, are expected to be among the primary gravitational wave (GW) sources for the forthcoming LISA mission. The astrophysical processes leading to the formation of such systems still remain poorly understood, resulting into large uncertainties in the predicted cosmic rate of these sources, spanning at least three orders of magnitude. As LISA can individually resolve mostly EMRIs up to $z\gtrsim1$, the ensemble of signals below its detection threshold will add up incoherently forming an unresolved confusion noise, which can be formally described as a stochastic background. We perform an extensive study of this background by considering a collection of astrophysically motivated EMRI formation scenarios, spanning current uncertainties. We find that, for most astrophysical models, this signal is easily detectable by LISA, with signal to noise ratios of several hundreds. In fiducial EMRI models -- predicting hundreds of EMRI detections during mission operations -- the background level is comparable to the LISA noise, affecting the performance of the instrument around 3 mHz. In extreme cases, this background can even "erase" the whole LISA sensitivity bucket in the 2-10 mHz frequency range. This points to the need of a better understanding of EMRIs' astrophysics for a full assessment of the LISA mission potential.

Reissner-Nordström perturbation framework with gravitational wave applications

We present a new convenient framework for modeling Reissner-Nordstr\"om black hole perturbations from charged distributions of matter. Using this framework, we quantify how gravitational wave observations of compact binary systems would be affected if one or both components were charged. Our approach streamlines the (linearized) Einstein-Maxwell equations through convenient master functions that we designed to ameliorate certain disadvantages of prior strategies. By solving our improved master equations with a point source, we are able to quantify the rate of orbital energy dissipation via electromagnetic and gravitational radiation. Through adiabatic and quasicircular approximations, we apply our dissipative calculations to determine trajectories for intermediate and extreme mass-ratio inspirals. By comparing trajectories and waveforms with varied charges to those with neutral components, we explore the potential effect of electric charge on gravitational wave signals. We observe that the case of opposite charge-to-mass ratios has the most dramatic impact. Our findings are largely interpreted through the lens of the upcoming LISA mission.

LISA sources from young massive and open stellar clusters

I study the potential role of young massive (YMCs) and open star clusters (OCs) in assembling stellar-mass binary black holes (BBHs) which would be detectable as persistent gravitational-wave (GW) sources by the forthcoming LISA mission. The energetic dynamical interactions inside star clusters make them factories of assembling BBHs and other types of double-compact binaries that undergo general-relativistic (GR) inspiral and merger. The initial phase of such inspirals would, typically, sweep through the LISA GW band. Here, such LISA sources are studied from a set of evolutionary models of star clusters with masses ranging over $10^4M_\odot-10^5M_\odot$ that represent YMCs and intermediate-aged OCs in metal-rich and metal-poor environments of the Local Universe. These models are evolved with long-term, direct, relativistic many-body computations incorporating state-of-the-art stellar-evolutionary and remnant-formation models. Based on models of Local Universe constructed with such model clusters, it is shown that YMCs and intermediate-aged OCs would yield several 10s to 100s of LISA BBH sources at the current cosmic epoch with GW frequency within $10^{-3}{\rm~Hz} - 10^{-1}{\rm~Hz}$ and signal-to-noise-ratio (S/N) $>5$, assuming a mission lifetime of 5 or 10 years. Such LISA BBHs would have a bimodal distribution in total mass, be generally eccentric ($\lesssim0.7$), and typically have similar component masses although mass-asymmetric systems are possible. Intrinsically, there would be 1000s of present-day, LISA-detectable BBHs from YMCs and OCs. That way, YMCs and OCs would provide a significant and the dominant contribution to the stellar-mass BBH population detectable by LISA. A small fraction, $<5$%, of these BBHs would undergo GR inspiral to make it to LIGO-Virgo GW frequency band and merge, within the mission timespan; $<15$% would do so within twice the timespan.

The LISA DFACS: A nonlinear model for the spacecraft dynamics

In the last few years, the observation of gravitational waves by means of LIGO and Virgo interferometers and the success of LISA Pathfinder, gave a significant boost to the development of space-based gravitational wave observatories. The European Space Agency confirmed LISA as the third large class mission of the Cosmic Vision program. The present work is part of the Drag Free and Attitude Control System (DFACS) preliminary prototyping study, which aims at the development of mathematical models and advanced controllers for the science phases of the LISA mission. Nonlinear modelling is a fundamental step for the derivation of linearized and decoupled models as well as for the development of suitable linear and nonlinear controllers. In this paper, an analytical nonlinear model is derived, which describes all the relevant dynamics of a LISA spacecraft, representing an effective compromise between accuracy and complexity. The model is extensively validated through linearization analysis and Monte Carlo simulations.

Model independent tests of the Kerr bound with extreme mass ratio inspirals

An outstanding prediction of general relativity is the fact that the angular momentum S of an isolated black hole with mass μ is limited by the Kerr bound, S≤Gμ2/c. Testing this cornerstone is challenging due to the difficulty in modeling spinning compact objects that violate this bound. We argue that precise, model-independent tests can be achieved by measuring gravitational waves from an extreme mass ratio inspiral around a supermassive object, one of the main targets of the future LISA mission. In the extreme mass ratio limit, the dynamics of the small compact object depends only on its multipole moments, which are free parameters. At variance with the comparable-mass case, accurate waveforms are valid also when the spin of the small object greatly exceeds the Kerr bound. By computing the orbital dephasing and the gravitational-wave signal emitted by a spinning point particle in circular, nonprecessing, equatorial motion around a Kerr black hole, we estimate that LISA will be able to measure the spin of the small compact object at the level of 10%. Together with mass measurements, this will allow for theory-agnostic, unprecedented constraints on string-theory inspired objects such as “superspinars”, almost in their entire parameter space.