Space-based Gravitational Wave Detectors Research Articles

Classifying Lensed Gravitational Waves in the Geometrical Optics Limit with Machine Learning

Gravitational waves are theorized to be gravitationally lensed when they propagate near massive objects. Such lensing effects cause potentially detectable repeated gravitational wave patterns in ground- and space-based gravitational wave detectors. These effects are difficult to discriminate when the lens is small and the repeated patterns superpose. Traditionally, matched filtering techniques are used to identify gravitational-wave signals, but we instead aim to utilize machine learning techniques to achieve this. In this work, we implement supervised machine learning classifiers (support vector machine, random forest, multi-layer perceptron) to discriminate such lensing patterns in gravitational wave data. We train classifiers with spectrograms of both lensed and unlensed waves using both point-mass and singular isothermal sphere lens models. As the result, classifiers return F1 scores ranging from 0:852 to 0:996, with precisions from 0:917 to 0:992 and recalls ranging from 0:796 to 1:000 depending on the type of classifier and lensing model used. This supports the idea that machine learning classifiers are able to correctly determine lensed gravitational wave signals. This also suggests that in the future, machine learning classifiers may be used as a possible alternative to identify lensed gravitational wave events and to allow us to study gravitational wave sources and massive astronomical objects through further analysis. KEYWORDS: Gravitational Waves; Gravitational Lensing; Geometrical Optics; Machine Learning; Classification; Support Vector Machine; Random Tree Forest; Multi-layer Perceptron

Exploring the Local Black Hole Mass Function below 106 Solar Masses

Abstract The local black hole mass function (BHMF) is of great interest to a variety of astrophysical problems, ranging from black hole binary merger rates to an indirect census of the dominant seeding mechanism of supermassive black holes. In this Letter, we combine the latest galaxy stellar mass function from the Galaxy And Mass Assembly survey with X-ray-based constraints to the local black hole occupation fraction to probe the BHMF below 106 M ⊙. Notwithstanding the large uncertainties inherent to the choice of a reliable observational proxy for black hole mass, the resulting range of BHMFs yields a combined normalization uncertainty of ≲1 dex over the [105–106] M ⊙ range, where upcoming, space-based gravitational wave detectors are designed to be most sensitive.

Frequency response of time-delay interferometry for space-based gravitational wave antenna

Space-based gravitational wave detectors cannot keep rigid structures and precise arm length equality, so the precise equality of detector arms which is required in a ground-based interferometer to cancel the overwhelming laser noise is impossible. The time-delay interferometry method is applied to unequal arm lengths to cancel the laser frequency noise. We give analytical formulas of the averaged response functions for tensor, vector, breathing and longitudinal polarizations in different TDI combinations, and obtain their asymptotic behaviors. At low frequencies, $f\ll f_*$, the averaged response functions of all TDI combinations increase as $f^2$ for all six polarizations. The one exception is the averaged response functions of $\zeta$ for all six polarizations increase as $f^4$ in the equilateral-triangle case. At high frequencies, $f\gg f_*$, the averaged response functions of all TDI combinations for the tensor and breathing modes fall off as $1/f^2$, the averaged response functions of all TDI combinations for the vector mode fall off as $\ln(f)/f^2$ , and the averaged response functions of all TDI combinations for the longitudinal mode fall as $1/f$. We also give LISA and TianQin sensitivity curves in different TDI combinations for tensor, vector, breathing and longitudinal polarizations.

Probing boson stars with extreme mass ratio inspirals

We propose to use gravitational waves from extreme mass ratio inspirals (EMRI), composed of a boson star and a supermassive black hole in the center of galaxies, as a new method to search for boson stars. Gravitational waves from EMRI have the advantage of being long-lasting within the frequency band of future space-based interferometer gravitational wave detectors and can accumulate large signal-to-noise ratio (SNR) for very sub-solar mass boson stars. Compared to gravitational waves from boson star binaries, which fall within the LIGO band, we find that much larger ranges of the mass and compactness of boson stars, as well as the underlying particle physics parameter space, can be probed by EMRI. We take tidal disruption of the boson stars into account and distinguish those which dissolve before the inner-most-stable-circular-orbit (ISCO) and those which dissolve after it. Due to the large number of cycles recorded, EMRIs can lead to a very precise mass determination of the boson star and distinguish it from standard astrophysical compact objects in the event of a signal. Tidal effects in inspiralling binary systems, as well as possible correlated electromagnetic signals, can also serve as potential discriminants.

Dark matter minispike: A significant enhancement of eccentricity for intermediate-mass-ratio inspirals

When a stellar massive compact object, such as a black hole (BH), inspirals into an intermediate massive black hole (IMBH), an intermediate-mass-ratio-inspiral (IMRI) system forms. Such kind of systems are important sources for space-based gravitational wave detectors including LISA, Taiji and Tianqin. Dark matter (DM) minispikes may form around IMBHs. We study the effect of dynamical friction against DM minispike on the evolution of eccentric IMRI. For such investigation we construct the dynamical equations which describes the evolution of eccentric IMRI under the effect of dynamical friction. As dynamical friction is large for small velocity, the dissipation of energy near apastron is more than that near periastron. This will greatly enhance the eccentricity. For instance, with an initial semi-latus rectum of $1\rm AU$, even a moderate DM minispike can make the eccentricity grow from $0.3$ to $0.85$. In the extremal case the eccentricity could be enhanced to near $1$. We also study a specific case which corresponds to an IMRI in the center of a globular cluster (GC) and find the eccentricity can keep its value above $0.95$ until the IMRI enters LISA band. These gravitational wave with enhanced eccentricity by DM minispikes can be easly distinguished from that without DM at $10^{-3}\rm Hz$ due to the eccentricity difference. These anticipations can be tested by future space-based GW detectors such as LISA.

Space-Based Gravitational-Wave Detectors: Development of Ground-Breaking Technologies for Future Space-Based Gravitational Gradiometers

An analysis of modern developments in the area of space-based gravitational-wave detectors is presented, and possible applications of key technologies for future space-based measurements of the gradient of the Earth’s gravitational field are considered. The structure of a space-based gradiometer based on free masses is presented, together with proposals for the reduction and calibration of measurements from such a device.

Binary radial velocity measurements with space-based gravitational-wave detectors

ABSTRACT Unlike traditional electromagnetic measurements, gravitational-wave observations are not affected by crowding and extinction. For this reason, compact object binaries orbiting around a massive black hole can be used as probes of the inner environment of the black hole in regions inaccessible to traditional astronomical measurements. The orbit of the binary’s barycentre around the massive black hole will cause a Doppler shift in the gravitational waveform, which is in principle measurable by future space-based gravitational-wave interferometers, such as the Laser Interferometer Space Antenna (LISA). We investigate the conditions under which these Doppler shifts are observable by LISA. Our results imply that Doppler shift observations can be used to study the central region of globular clusters in the Milky Way, as well the central environment of extragalactic massive black holes.

Gaia Data Release 2 catalogue of extremely low-mass white dwarf candidates

ABSTRACT Extremely low-mass white dwarf stars (ELMs) are M < 0.3 M⊙ helium-core white dwarfs born either as a result of a common-envelope phase or after a stable Roche lobe overflow episode in a multiple system. The Universe is not old enough for ELMs to have formed through single-star evolution channels. As remnants of binary evolution, ELMs can shed light onto the poorly understood phase of common-envelope evolution and provide constraints to the physics of mass accretion. Most known ELMs will merge in less than a Hubble time, providing an important contribution to the signal to be detected by upcoming space-based gravitational wave detectors. There are currently less than 150 known ELMs; most were selected by colour, focusing on hot objects, in a magnitude-limited survey of the Northern hemisphere only. Recent theoretical models have predicted a much larger space density for ELMs than estimated observationally based on this limited sample. In order to perform meaningful comparisons with theoretical models and test their predictions, a larger well-defined sample is required. In this work, we present a catalogue of ELM candidates selected from the second data release of Gaia (DR2). We have used predictions from theoretical models and analysed the properties of the known sample to map the space spanned by ELMs in the Gaia Hertzsprung–Russell diagram. Defining a set of colour cuts and quality flags, we have obtained a final sample of 5762 ELM candidates down to Teff ≈ 5000 K.

Weighing water from space

By monitoring tiny changes to the Earth’s gravitational field, the GRACE satellites have been pinpointing the distribution of fresh water on our planet for almost two decades. But as Marric Stephens explains, a new follow-on mission is also helping with plans for a space-based gravitational-wave detector

Tests of General Relativity and Fundamental Physics with Space-based Gravitational Wave Detectors

Low-frequency gravitational-wave astronomy can perform precision tests of general relativity and probe fundamental physics in a regime previously inaccessible. A space-based detector will be a formidable tool to explore gravity's role in the cosmos, potentially telling us if and where Einstein's theory fails and providing clues about some of the greatest mysteries in physics and astronomy, such as dark matter and the origin of the Universe.

Space-based gravitational wave detection and how LISA Pathfinder successfully paved the way

In 2016 and 2017, the LISA Pathfinder mission successfully proved that the technologies for the space-based gravitational wave detector LISA are ready. LISA is now scheduled to launch in the early 2030s, to open a so far unexploited scientific field.

Coupling of wavefront errors and pointing jitter in the LISA interferometer: misalignment of the interfering wavefronts

The laser interferometer space antenna is a foreseen space-based gravitational wave detector, which aims to detect 10−20 strains in the frequency range from 0.1 mHz to 1 Hz. It is a triangular constellation of three spacecraft, with equal sides of m, where every spacecraft hosts a pair of telescopes that simultaneously transmit and receive laser beams measuring the constellation arms by heterodyning the received wavefronts with local references. Due to the spacecraft and constellation jitters, the interfering (received and local) wavefronts become misaligned. We investigate analytically the coupling between misalignments and aberrations of the interfering wavefronts and estimate the relevant contribution to the noise of the heterodyne signal.

Probing the Universe through the stochastic gravitational wave background

Stochastic gravitational wave backgrounds, predicted in many models of the early universe and also generated by various astrophysical processes, are a powerful probe of the Universe. The spectral shape is key information to distinguish the origin of the background since different production mechanisms predict different shapes of the spectrum. In this paper, we investigate how precisely future gravitational wave detectors can determine the spectral shape using single and broken power-law templates. We consider the detector network of Advanced-LIGO, Advanced-Virgo and KAGRA and the space-based gravitational-wave detector DECIGO, and estimate the parameter space which could be explored by these detectors. We find that, when the spectrum changes its slope in the frequency range of the sensitivity, the broken power-law templates dramatically improve the χ2 fit compared with the single power-law templates and help to measure the shape with a good precision.

Limits on primordial magnetic fields from direct detection experiments of gravitational wave background

Primordial magnetic fields (PMFs) can source gravitational wave background (GWB). In this paper, we investigate the possible constraints on small-scale PMF considering the ongoing and forthcoming direct detection observations of GWB. In contrast to the conventional cosmological probes, e.g., cosmic microwave background anisotropies, which are useful to investigate large-scale PMFs ($>1\text{ }\text{ }\mathrm{Mpc}$), the direct detection experiments of GWB can explore small-scale PMFs whose scales correspond to the observed frequencies of GWB. We show that future ground-based or space-based interferometric gravitational wave detectors give a strong constraint of about $1{0}^{2}\text{ }\text{ }\mathrm{nG}$ on much smaller scales of about $k\ensuremath{\approx}{10}^{12}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. We also demonstrate that pulsar timing arrays have a potential to strongly constrain PMFs. The current limits on GWB from pulsar timing arrays can put the tight constraint on the amplitude of the PMFs of about 30 nG whose coherent length is about $k\ensuremath{\approx}{10}^{6}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. The future experiments for the direct detection of GWB by the Square Kilometre Array could give much tighter constraints on the amplitude of PMFs of about 5 nG on $k\ensuremath{\approx}{10}^{6}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, on which scales it is difficult to reach by using the cosmological observations.

Searching for Dark Photon Dark Matter with Gravitational-Wave Detectors.

If dark matter stems from the background of a very light gauge boson, this gauge boson could exert forces on test masses in gravitational wave detectors, resulting in displacements with a characteristic frequency set by the gauge boson mass. We outline a novel search strategy for such dark matter, assuming the dark photon is the gauge boson of U(1)_{B} or U(1)_{B-L}. We show that both ground-based and future space-based gravitational wave detectors have the capability to make a 5σ discovery in unexplored parameter regimes.

Gravitational-wave standard siren and cosmology

The discoveries of gravitational-wave (GW) event GW170817, caused by the coalescence of binary neutron-star, as well as the electromagnetic counterparts in multi-frequency bands, mark the coming of multimessenger GW astronomy. By observing the GW waveform of compact binary coalescence, one can independently determine its luminosity distance, which indicates that this kind of GW sources can be treated as “standard sirens to study the expansion history of the Universe. This provides a novel method for the research of cosmology. In this article, we introduce the basic principle of GW sources as “standard sirens, and focus on various methods to determine the distance and redshift of GW events. We also discuss the detection capabilities of constraining cosmological parameters for (second-generation and third-generation) ground-based GW detectors and space-based GW detectors. In particular, we investigate the potential constraints on the Hubble constant and equation-of-state of dark energy.

Towards a framework for testing general relativity with extreme-mass-ratio-inspiral observations

Extreme-mass-ratio-inspiral observations from future space-based gravitational-wave detectors such as LISA will enable strong-field tests of general relativity with unprecedented precision, but at prohibitive computational cost if existing statistical techniques are used. In one such test that is currently employed for LIGO black-hole binary mergers, generic deviations from relativity are represented by $N$ deformation parameters in a generalised waveform model; the Bayesian evidence for each of its $2^N$ combinatorial submodels is then combined into a posterior odds ratio for modified gravity over relativity in a null-hypothesis test. We adapt and apply this test to a generalised model for extreme-mass-ratio inspirals constructed on deformed black-hole spacetimes, and focus our investigation on how computational efficiency can be increased through an evidence-free method of model selection. This method is akin to the algorithm known as product-space Markov chain Monte Carlo, but uses nested sampling and improved error estimates from a rethreading technique. We perform benchmarking and robustness checks for the method, and find order-of-magnitude computational gains over regular nested sampling in the case of synthetic data generated from the null model.

Non-linear quantization error reduction for the temperature measurement subsystem on-board LISA Pathfinder.

Laser Interferometer Space Antenna (LISA) Pathfinder is a mission to test the technology enabling gravitational wave detection in space and to demonstrate that sub-femto-g free fall levels are possible. To do so, the distance between two free falling test masses is measured to unprecedented sensitivity by means of laser interferometry. Temperature fluctuations are one of the noise sources limiting the free fall accuracy and the interferometer performance and need to be known at the ∼10 μK Hz-1/2 level in the sub-millihertz frequency range in order to validate the noise models for the future space-based gravitational wave detector LISA. The temperature measurement subsystem on LISA Pathfinder is in charge of monitoring the thermal environment at key locations with noise levels of 7.5 μK Hz-1/2 at the sub-millihertz. However, its performance worsens by one to two orders of magnitude when slowly changing temperatures are measured due to errors introduced by analog-to-digital converter non-linearities. In this paper, we present a method to reduce this effect by data post-processing. The method is applied to experimental data available from on-ground validation tests to demonstrate its performance and the potential benefit for in-flight data. The analog-to-digital converter effects are reduced by a factor between three and six in the frequencies where the errors play an important role. An average 2.7 fold noise reduction is demonstrated in the 0.3 mHz-2 mHz band.

Fundamentals of the orbit and response for TianQin

TianQin is a space-based laser interferometric gravitational wave detector aimed at detecting gravitational waves at low frequencies (0.1 mHz–1 Hz). It is formed by three identical drag-free spacecrafts in an equilateral triangular constellation orbiting around the Earth. The distance between each pair of spacecrafts is approximately . The spacecrafts are interconnected by infrared laser beams forming up to three Michelson-type interferometers. The detailed mission design and the study of science objectives for the TianQin project depend crucially on the orbit and the response of the detector. In this paper, we provide the analytic expressions for the coordinates of the orbit for each spacecraft in the heliocentric-ecliptic coordinate system to the leading orders. This enables a sufficiently accurate study of science objectives and data analysis, and serves as a first step to further orbit design and optimization. We calculate the response of a single Michelson detector to plane gravitational waves in arbitrary waveform which is valid in the full range of the sensitive frequencies. It is then used to generate the more realistic sensitivity curve of TianQin. We apply this model on a reference white-dwarf binary as a proof of principle.

Constraining the mass of dark photons and axion-like particles through black-hole superradiance

Ultralight bosons and axion-like particles appear naturally in different scenarios and could solve some long-standing puzzles. Their detection is challenging, and all direct methods hinge on unknown couplings to the Standard Model of particle physics. However, the universal coupling to gravity provides model-independent signatures for these fields. We explore here the superradiant instability of spinning black holes triggered in the presence of such fields. The instability taps angular momentum from and limits the maximum spin of astrophysical black holes. We compute, for the first time, the spectrum of the most unstable modes of a massive vector (Proca) field for generic black-hole spin and Proca mass. The observed stability of the inner disk of stellar-mass black holes can be used to derive direct constraints on the mass of dark photons in the mass range 10−13 eV≲ mV ≲ 3× 10−12 eV. By including also higher azimuthal modes, similar constraints apply to axion-like particles in the mass range 6×10−13 eV≲ mALP ≲ 10−11 eV. Likewise, mass and spin distributions of supermassive BHs—as measured through continuum fitting, Kα iron line, or with the future space-based gravitational-wave detector LISA – imply indirect bounds in the mass range approximately 10−19 eV≲ mV, mALP ≲ 10−13 eV, for both axion-like particles and dark photons. Overall, superradiance allows to explore a region of approximately 8 orders of magnitude in the mass of ultralight bosons.