Time-delay interferometry (TDI) is the data processing technique that cancels the large laser phase fluctuations affecting the one-way Doppler measurements made by unequal-arm space-based gravitational wave interferometers. By taking finite linear combinations of properly time-shifted Doppler measurements, laser phase fluctuations are removed at any time t and gravitational wave signals can be studied at a requisite level of precision. In this article we show the delay operators used in TDI can be represented as matrices acting on arrays associated with the laser noises and Doppler measurements. The matrix formulation is nothing but the group theoretic representation (ring homomorphism) of the earlier approach involving time-delay operators and so in principle is the same. It is shown that the homomorphism is valid generally and we cover all situations of interest. To understand the potential advantages the matrix representation brings, care must be taken by the data analyst to account for the light travel times when linearly relating the one-way Doppler measurements to the laser noises. This is especially important in view of the future gravitational wave projects envisaged. We show that the matrix formulation of TDI results in the cancellation of the laser noises at an arbitrary time t by only linearly combining a finite number of samples of the one-way Doppler data measured at and around time t.

We present results of an all-sky search for continuous gravitational waves which can be produced by spinning neutron stars with an asymmetry around their rotation axis, using data from the third observing run of the Advanced LIGO and Advanced Virgo detectors. Four different analysis methods are used to search in a gravitational-wave frequency band from 10 to 2048 Hz and a first frequency derivative from −10 −8 to 10 −9 Hz/s. No statistically-significant periodic gravitational-wave signal is observed by any of the four searches. As a result, upper limits on the gravitational-wave strain amplitude h0 are calculated. The best upper limits are obtained in the frequency range of 100 to 200 Hz and they are ∼1.1 × 10 −25 at 95% confidence-level. The minimum upper limit of 1.10 × 10 −25 is achieved at a frequency 111.5 Hz. We also place constraints on the rates and abundances of nearby planetary-and asteroid-mass primordial black holes that could give rise to continuous gravitationalwave signals.

We present the results of a model-based search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1 using LIGO detector data from the third observing run of Advanced LIGO and Advanced Virgo. This is a semicoherent search that uses details of the signal model to coherently combine data separated by less than a specified coherence time, which can be adjusted to balance sensitivity with computing cost. The search covered a range of gravitational-wave frequencies from 25 to 1600 Hz, as well as ranges in orbital speed, frequency, and phase determined from observational constraints. No significant detection candidates were found, and upper limits were set as a function of frequency. The most stringent limits, between 100 and 200 Hz, correspond to an amplitude h 0 of about 10−25 when marginalized isotropically over the unknown inclination angle of the neutron star’s rotation axis, or less than 4 × 10−26 assuming the optimal orientation. The sensitivity of this search is now probing amplitudes predicted by models of torque balance equilibrium. For the usual conservative model assuming accretion at the surface of the neutron star, our isotropically marginalized upper limits are close to the predicted amplitude from about 70 to 100 Hz; the limits assuming that the neutron star spin is aligned with the most likely orbital angular momentum are below the conservative torque balance predictions from 40 to 200 Hz. Assuming a broader range of accretion models, our direct limits on gravitational-wave amplitude delve into the relevant parameter space over a wide range of frequencies, to 500 Hz or more.

We present a targeted search for continuous gravitational waves (GWs) from 236 pulsars using data from the third observing run of LIGO and Virgo (O3) combined with data from the second observing run (O2). Searches were for emission from the l = m = 2 mass quadrupole mode with a frequency at only twice the pulsar rotation frequency (single harmonic) and the l = 2, m = 1, 2 modes with a frequency of both once and twice the rotation frequency (dual harmonic). No evidence of GWs was found, so we present 95% credible upper limits on the strain amplitudes h 0 for the single-harmonic search along with limits on the pulsars’ mass quadrupole moments Q 22 and ellipticities ε. Of the pulsars studied, 23 have strain amplitudes that are lower than the limits calculated from their electromagnetically measured spin-down rates. These pulsars include the millisecond pulsars J0437−4715 and J0711−6830, which have spin-down ratios of 0.87 and 0.57, respectively. For nine pulsars, their spin-down limits have been surpassed for the first time. For the Crab and Vela pulsars, our limits are factors of ∼100 and ∼20 more constraining than their spin-down limits, respectively. For the dual-harmonic searches, new limits are placed on the strain amplitudes C 21 and C 22. For 23 pulsars, we also present limits on the emission amplitude assuming dipole radiation as predicted by Brans-Dicke theory.

The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org. The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages.