Gravitational Wave Measurements Research Articles

A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437–4715

We report Bayesian inference of the mass, radius, and hot X-ray emitting region properties—using data from the Neutron Star Interior Composition ExploreR (NICER)—for the brightest rotation-powered millisecond X-ray pulsar, PSR J0437−4715. Our modeling is conditional on informative tight priors on mass, distance, and binary inclination obtained from radio pulsar timing using the Parkes Pulsar Timing Array (PPTA; Reardon et al.), and we use NICER background models to constrain the nonsource background, cross-checking with data from XMM-Newton. We assume two distinct hot emitting regions and various parameterized hot region geometries that are defined in terms of overlapping circles; while simplified, these capture many of the possibilities suggested by detailed modeling of return current heating. For the preferred model identified by our analysis, we infer a mass of M = 1.418 ± 0.037 M ⊙ (largely informed by the PPTA mass prior) and an equatorial radius of R=11.36−0.63+0.95 km, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. This radius favors softer dense matter equations of state and is highly consistent with constraints derived from gravitational wave measurements of neutron star binary mergers. The hot regions are inferred to be nonantipodal and hence inconsistent with a pure centered dipole magnetic field.

Test of the Brans–Dicke theory with GW200105 and GW200115

We study whether it is possible to constrain the Brans–Dicke (BD) theory from the measurement of gravitational waves (GW) released in neutron star-black hole collisions. Considering the scalar field modifications through monopole and dipole radiations, we find additional contributions to the phase evolution in the emitted gravitational waveform. After effectively calculating such effect in the post-Newtonian order, we are in a position to measure the scalar field and give bounds on the BD coupling parameter ω BD . We derive the analytical expression for the phase modification due to the orbital eccentricity of eccentric binaries in both general relativity and BD theory. Employing the Bayesian analysis, we obtain the constraints on ω BD from the GW events, GW200105 and GW200115.

Determining the Hubble constant with AGN-assisted black hole mergers

ABSTRACT Gravitational waves from neutron star mergers have long been considered a promising way to measure the Hubble constant, H0, which describes the local expansion rate of the Universe. While black hole mergers are more abundantly observed, their expected lack of electromagnetic emission and poor gravitational-wave localization make them less well suited for measuring H0. Black hole mergers within the discs of Active Galactic Nuclei (AGN) could be an exception. Accretion from the AGN disc may produce an electromagnetic signal, pointing observers to the host galaxy. Alternatively, the low number density of AGNs could help identify the host galaxy of $1{\!-\!}5~{{\ \rm per\ cent}}$ of mergers. Here we show that black hole mergers in AGN discs may be a sensitive way to determine H0 with gravitational waves. If 1 per cent (10 per cent) of LIGO’s observations occur in AGN discs with identified host galaxies, we could measure H0 with 12 per cent (4 per cent) uncertainty in five years, possibly comparable to the sensitivity of neutron star mergers and set to considerably improve current gravitational wave measurements.

Gravitational wave measurement in the mid-band with atom interferometers

Gravitational Waves (GWs) have been detected in the ∼ 100 Hz and nHz bands, but most of the gravitational spectrum remains unobserved. A variety of detector concepts have been proposed to expand the range of observable frequencies. In this work, we study the capability of GW detectors in the “mid-band”, the ∼ 30 mHz– 10 Hz range between LISA and LIGO, to measure the signals from and constrain the properties of ∼ 1 – 100 M ⊙ compact binaries. We focus on atom-interferometer-based detectors. We describe a Fisher matrix code, AIMforGW, which we created to evaluate their capabilities, and present numerical results for two benchmarks: terrestrial km-scale detectors, and satellite-borne detectors in medium Earth orbit. Mid-band GW detectors are particularly well-suited to pinpointing the location of GW sources on the sky. We demonstrate that a satellite-borne detector could achieve sub-degree sky localization for any detectable source with chirp mass ℳ c ≲ 50 M ⊙. We also compare different detector configurations, including different locations of terrestrial detectors and various choices of the orbit of a satellite-borne detector. As we show, a network of only two terrestrial single-baseline detectors or one single-baseline satellite-borne detector would each provide close-to-uniform sky-coverage, with signal-to-noise ratios varying by less than a factor of two across the entire sky. We hope that this work contributes to the efforts of the GW community to assess the merits of different detector proposals.

Probing Supermassive Black Hole Seed Scenarios with Gravitational-wave Measurements

The process whereby the supermassive black holes (SMBHs) populating the centers of galaxies have been assembled remains to be established, with the relative importance of seeds provided by collapsed Population III stars, black holes formed in nuclear star clusters via repeated mergers, or direct collapses of protogalactic disks yet to be determined. In this paper we study the prospects for casting light on this issue by future measurements of gravitational waves emitted during the inspirals and mergers of pairs of intermediate-mass black holes (IMBHs), discussing in particular the roles of prospective measurements by LISA and the proposed atom interferometers AION and AEDGE. We find that the expected number of detectable IMBH binaries is O(100) for LISA and AEDGE and O(10) for AION in low-mass seeds scenarios and goes down to O(10) for LISA and below one for AEDGE and AION in high-mass seed scenarios. This allows all of these observatories to probe the parameters of the seed model, in particular, if at least a fraction of the SMBHs arises from a low-mass seed population. We also show that the measurement accuracy of the binary parameters is, in general, best for AEDGE, which sees very precisely the merger of the binary.

Fast and Fourier: extreme mass ratio inspiral waveforms in the frequency domain

Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future space-based gravitational wave interferometers. Measurements of EMRI gravitational waves are expected to determine the characteristics of their sources with sub-percent precision. However, their waveform generation is challenging due to the long duration of the signal and the high harmonic content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI waveform implementation in the frequency domain for use with either graphics processing units (GPUs) or central processing units (CPUs). We present the overall waveform implementation and test the accuracy and performance of the frequency domain waveforms against the time domain implementation. On GPUs, the frequency domain waveform takes in median 0.044 s to generate and is twice as fast to compute as its time domain counterpart when considering massive black hole masses ≥2×106M⊙ and initial eccentricities e0 > 0.2. On CPUs, the median waveform evaluation time is 5 s, and it is five times faster in the frequency domain than in the time domain. Using a sparser frequency array can further speed up the waveform generation, reaching up to 0.3 s. This enables us to perform, for the first time, EMRI parameter inference with fully relativistic waveforms on CPUs. Future EMRI models, which encompass wider source characteristics (particularly black hole spin and generic orbit geometries), will require significantly more harmonics. Frequency domain models will be essential analysis tools for these astrophysically realistic and important signals.

Research on constellation attitude synchronous tracking control for space gravitational wave measurement

Space based gravitational wave detectors require a precision relative attitude pointing control in science mode. Their configuration drifts sensitively under the influence of perturbations. The spacecraft and telescope optical assembly attitude control loops need to respond to this change in real time to maintain an ultra-high precision laser pointing. To implement precision gravitational wave scientific measurement, distributed detector systems need to coordinate the relative attitude pointing between spacecrafts in the constellation. This article proposes a synchronization coordination control method based on state estimation feedforward and finite frequency domain optimization. The simulation results show that the synchronization and coordination tracking of the relative attitude between satellites can be achieved under configuration perturbations, and the jitter in the ultra-low frequency range can be effectively reduced. Especially in the frequency range below 10−3 Hz, the stability of the line of sight attitude pointing is improved from 10−6 rad/Hz1/2 to 10−9 rad/Hz1/2. The absolute attitude pointing performance and stability are greatly improved.

Imprints of ultralight axions on the gravitational wave and pulsar timing measurement

Imprints of ultralight axions on the gravitational wave and pulsar timing measurement

Impact of modelling galaxy redshift uncertainties on the gravitational-wave dark standard siren measurement of the Hubble constant

ABSTRACT Gravitational wave science is a new and rapidly expanding field of observational astronomy. Multimessenger observations of the binary neutron star merger GW170817 have provided some iconic results including the first gravitational-wave standard siren measurement of the Hubble constant, opening up a new way to probe cosmology. The majority of the compact binary sources observed in gravitational waves are, however, without bright electromagnetic counterparts. In these cases, one can fall back on the ‘dark standard siren’ approach to include information statistically from potential host galaxies. For such a measurement, we need to be cautious about all possible sources of systematic errors. In this paper, we begin to study the possible errors coming from the galaxy catalogue sector, and in particular, look into the effect of galaxy redshift uncertainties for the cases where these are photometry-based. We recalculate the dark standard siren Hubble constant using the latest third Gravitational-Wave Transient Catalog (GWTC-3) events and associated galaxy catalogues, with different galaxy redshift uncertainty models, namely, the standard Gaussian, a modified Lorentzian, and no uncertainty at all. We find that not using redshift uncertainties at all can lead to a potential bias comparable with other potential systematic effects previously considered for the GWTC-3 H0 measurement (however still small compared to the overall statistical error in this measurement). The difference between different uncertainty models leads to small differences in the results for the current data; their impact is much smaller than the current statistical errors and other potential sources of systematic errors which have been considered in previous robustness studies.

Probing Accretion Physics with Gravitational Waves

Gravitational-wave observations of extreme mass ratio inspirals (EMRIs) offer the opportunity to probe the environments of active galactic nuclei (AGN) through the torques that accretion disks induce on the binary. Within a Bayesian framework, we study how well such environmental effects can be measured using gravitational wave observations from the Laser Interferometer Space Antenna (LISA). We focus on the torque induced by planetary-type migration on quasicircular inspirals, and use different prescriptions for geometrically thin and radiatively efficient disks. We find that LISA could detect migration for a wide range of disk viscosities and accretion rates, for both $\alpha$ and $\beta$ disk prescriptions. For a typical EMRI with masses $50M_\odot+10^6M_\odot$, we find that LISA could distinguish between migration in $\alpha$ and $\beta$ disks and measure the torque amplitude with $\sim 20\%$ relative precision. Provided an accurate torque model, we also show how to turn gravitational-wave measurements of the torque into constraints on the disk properties. Furthermore, we show that, if an electromagnetic counterpart is identified, the multimessenger observations of the AGN EMRI system will yield direct measurements of the disk viscosity. Finally, we investigate the impact of neglecting environmental effects in the analysis of the gravitational-wave signal, finding 3$\sigma$ biases in the primary mass and spin, and showing that ignoring such effects can lead to false detection of a deviation from general relativity. This work demonstrates the scientific potential of gravitational observations as probes of accretion-disk physics, accessible so far through electromagnetic observations only.

Probing the delay time of supermassive black hole binary mergers with gravitational waves

ABSTRACT Merging supermassive black hole binaries are expected as a consequence of galaxy mergers, yet the detailed evolution path and underlying merging mechanisms of these binaries are still subject to large theoretical uncertainties. In this work, we propose to combine the (future) gravitational wave measurements of supermassive black hole binary merger events with the galaxy merger rate distributions from galaxy surveys/cosmological simulations, to infer the delay time of binary mergers, as a function of binary mass. The delay time encodes key information about binary evolution, which can be used to test the predictions of various evolution models. With a Mock data set of supermassive black hole binary merger events, we discuss how to infer the distribution of delay time with hierarchical Bayesian inference and test evolution models with the Bayesian model selection method. The astrophysical model uncertainties are also considered in the hierarchical Bayesian inference and Bayesian model selection.

Compact Stars in the vBag Model and Its f-Mode Oscillations

Electromagnetic (EM) observations and gravitational wave (GW) measurements enable us to determine the mass and radius of neutron stars (NSs) and their tidal deformability, respectively. These parameters offer valuable insights into the properties of dense matter in NSs. In this study, the vector-interaction-enhanced bag model (vBag model) is employed to investigate strange and hybrid stars’ properties. The parameters of the vBag model are constrained using multi-messenger observations, revealing that strange stars are incompatible with current observations. In contrast, hybrid stars can exhibit a substantial mixed phase region and a thin hadronic shell. Furthermore, we present the frequencies and damping time of fundamental mode (f-mode) oscillations of hybrid stars and test their universal relations with compactness and tidal deformability. The findings indicate that the presence of mixed phase components leads to larger frequencies and shorter damping time of the f-mode oscillation of hybrid stars, and the softer equation of state (EoS) affects this behavior more significantly. The universal relations of hybrid stars in the vBag model can be described by fourth-order/seventh-order polynomials, which do not break the previous results.

Gravitational wave memory in conformally flat spacetimes

We study the gravitational wave memory effect in spacetimes related to flat space by a conformal transformation. The discussion is general but the gravitational wave length scale is assumed to be small compared with the background curvature radius. The general formulas are applied to Friedmann-Robertson-Walker metrics of all spatial curvatures. The effect of new terms stemming from spatial curvature is potentially detectable in future gravitational wave measurements.

Missing one-loop contributions in secondary gravitational waves

We find several missing one-loop-order contributions in previous considerations about secondary gravitational waves induced at nonlinear order in cosmological perturbations. We consider a consistent perturbative expansion to third order in cosmological perturbations, including higher-order interactions and iterative solutions ignored in the previous literature. Tensor fluctuations induced by the source with two scalar and one tensor perturbations are correlated with the first-order tensor fluctuation and thus give a one-loop order correction to the tensor-power spectrum. The missing loop correction is scale invariant and negative in the superhorizon region, which secondarily reduces the initial primordial tensor-power spectrum prior to the horizon reentry. Such an IR behavior is very different from the autospectrum of second-order induced tensor modes discussed in the previous literature and can be important for the actual gravitational wave measurements. For a sharp peak of scalar fluctuations with ${A}_{\ensuremath{\zeta}}={10}^{\ensuremath{-}2}$ at ${k}_{*}={10}^{5}\text{ }h/\mathrm{Mpc}$ motivated by the LIGO/Virgo events, we show that the tensor-power spectrum at the cosmic microwave background scale reduces by at most 35%. Hence, the polarization B mode might not be seen because of the reduction of the original tensor spectrum due to the secondary effect of primordial black hole formation.

Strong correlation of the neutron star core-crust transition density with the σ-meson mass via vacuum polarization

We study the neutron star core-crust transition density ρt with the inclusion of the vacuum polarization in the dielectric function in the nonlinear relativistic Hartree approach (RHAn). It is found that the strong correlation between the ρt and the scalar meson mass mσ strikingly overwhelms the uncertainty of the nuclear equation of state in the RHAn models, in contrast to the usual awareness that ρt is predominantly sensitive to the isovector nuclear potential and symmetry energy. The accurate extraction of ρt through the future gravitational wave measurements can thus provide a strong constraint on the longstanding uncertainty of mσ, which is of significance to better infer the vacuum property. As an astrophysical implication, it suggests that the correlation between ρt and mσ is very favorable to reconcile the difficulty in reproducing the large crustal moment of inertia for the pulsar glitches with the well constrained symmetry energy.

Breaking bad degeneracies with Love relations: Improving gravitational-wave measurements through universal relations

The distance-inclination degeneracy limits gravitational-wave parameter estimation of compact binary mergers. Although the degeneracy can be partially broken by including higher-order modes or precession, these effects are suppressed in binary neutron stars. In this work, we implement a new parametrization of the tidal effects in the binary neutron-star waveform, exploiting the binary Love relations, that breaks the distance-inclination degeneracy. The binary Love relations prescribe the tidal deformability of a neutron star as a function of its source-frame mass in an equation-of-state insensitive way and, thus, allows direct measurement of the redshift of the source. If the cosmological parameters are assumed to be known, the redshift can be converted to a luminosity distance, and the distance-inclination degeneracy can thus be broken. We implement this new approach, studying a range of binary neutron-star observing scenarios using Bayesian parameter estimation on synthetic data. In the era of the third-generation detectors, for observations with signal-to-noise ratios ranging from 6 to 167, we forecast up to an $\ensuremath{\sim}70%$ decrease in the 90% credible interval of the distance and inclination and up to an $\ensuremath{\sim}50%$ decrease in that of the source-frame component masses. For edge-on systems, our approach can result in moderate ($\ensuremath{\sim}50%$) improvement in the measurements of distance and inclination for binaries with a signal-to-noise ratio as low as 10. This prescription can be used to better infer the source-frame masses and, hence, refine population properties of neutron stars, such as their maximum mass, impacting nuclear astrophysics. When combined with the search for electromagnetic counterpart observations, the work presented here can be used to put improved bounds on the opening angle of jets from binary neutron-star mergers.

Constraining modifications of black hole perturbation potentials near the light ring with quasinormal modes

In modified theories of gravity, the potentials appearing in the Schr\"odinger-like equations that describe perturbations of nonrotating black holes are also modified. In this paper we ask: can these modifications be constrained with high-precision gravitational-wave measurements of the black hole's quasinormal mode frequencies? We expand the modifications in a small perturbative parameter regulating the deviation from the general-relativistic potential, and in powers of $M/r$. We compute the quasinormal modes of the modified potential up to quadratic order in the perturbative parameter. Then we use Markov-chain Monte Carlo methods to recover the coefficients in the $M/r$ expansion in an ``optimistic'' scenario where we vary them one at a time, and in a ``pessimistic'' scenario where we vary them all simultaneously. In both cases, we find that the bounds on the individual parameters are not robust. Because quasinormal mode frequencies are related to the behavior of the perturbation potential near the light ring, we propose a different strategy. Inspired by Wentzel-Kramers-Brillouin (WKB) theory, we demonstrate that the value of the potential and of its second derivative at the light ring can be robustly constrained. These constraints allow for a more direct comparison between tests based on black hole spectroscopy and observations of black hole ``shadows'' by the Event Horizon Telescope and future instruments.

Gravitational Waves from Extreme-Mass-Ratio Systems in Astrophysical Environments.

We establish a generic, fully relativistic formalism to study gravitational-wave emission by extreme-mass-ratio systems in spherically symmetric, nonvacuum black hole spacetimes. The potential applications to astrophysical setups range from black holes accreting baryonic matter to those within axionic clouds and dark matter environments, allowing one to assess the impact of the galactic potential, of accretion, gravitational drag, and halo feedback on the generation and propagation of gravitational waves. We apply our methods to a black hole within a halo of matter. We find fluid modes imparted to the gravitational-wave signal (a clear evidence of the black hole fundamental mode instability) and the tantalizing possibility to infer galactic properties from gravitational-wave measurements by sensitive, low-frequency detectors.

Systematic errors due to quasiuniversal relations in binary neutron stars and their correction for unbiased model selection

Inference of the equation of state (EOS) of dense nuclear matter in neutron-star cores is a principal science goal of x-ray and gravitational-wave observations of neutron stars. In particular, gravitational-wave observations provide an independent probe of the properties of bulk matter in neutron star cores that can then be used to compare with theoretically derived equations of state. In this paper, we quantify the systematic errors arising from the application of EOS-independent quasiuniversal relations in the estimation of neutron star tidal deformabilities and radii from gravitational-wave measurements and introduce a strategy to correct for the systematic biases in the inferred radii. We apply this method to a simulated population of events expected to be observed by future upgrades of current detectors and the next generation of ground-based observatories. We show that our approach can accurately correct for the systematic biases arising from approximate universal relations in the mass-radius curves of neutron stars. Using the posterior distributions of the mass and radius for the simulated population we infer the underlying EOS with a good degree of precision. Our method revives the possibility of using the universal relations for rapid Bayesian model selection of the dense matter EOS in gravitational-wave observations.

Population properties of spinning black holes using the gravitational-wave transient catalog 3

Binary black holes formed via different pathways are predicted to have distinct spin properties. Measuring these properties with gravitational waves provides an opportunity to unveil the origins of binary black holes. Recent work draws conflicting conclusions regarding the spin distribution observed by LIGO-Virgo-KAGRA (LVK). Some analyses suggest that a fraction of the observed black-hole spin vectors are significantly misaligned (by $>90\ifmmode^\circ\else\textdegree\fi{}$) relative to the orbital angular momentum. This has been interpreted to mean that some binaries in the LVK dataset are assembled dynamically in dense stellar environments. Other analyses find support for a subpopulation of binaries with negligible spin and no evidence for significantly misaligned spin---a result consistent with the field formation scenario. In this work, we study the spin properties of binary black holes in the third LVK gravitational-wave transient catalog. We find that there is insufficient data to resolve the existence of a subpopulation of binaries with negligible black-hole spin (the presence of this subpopulation is supported by a modest Bayes factor of 1.7). We find modest support for the existence of mergers with extreme spin tilt angles $>90\ifmmode^\circ\else\textdegree\fi{}$ (the presence of extreme-tilt binaries is favored by a Bayes factor of 10.1). Only one thing is clear based on gravitational-wave measurements of black hole spin: at least some of the LVK binaries formed in the field. At most 89% of binaries are assembled dynamically (99% credibility), though, the true branching fraction could be much lower, even negligible.