Ultracompact binary pulsars as continuous dual-line gravitational wave sources

A spinning neutron star (NS) that is asymmetric with respect to its spin axis can emit continuous gravitational wave (GW) signals. The spin frequencies and their distribution of radio millisecond pulsars (MSPs) and accreting MSPs provide some evidences of GW radiation, and MSPs are ideal probes detecting high frequency GW signals. It is generally thought that MSPs originate from the recycled process, in which the NS accretes the material and angular momentum from the donor star. The accreted matter would be confined at the polar cap zone by an equatorial belt of compressed magnetic field fixed in the deep crust of the NS, and yields "magnetic mountain". Based on an assumption that the spin-down rates of three transitional MSPs including PSR J1023+0038 are the combinational contribution of the accretion torque, the propeller torque, and the GW radiation torque, in this work we attempt to constrain the ellipticities of MSPs with observed spin-down rates. Assuming some canonical parameters of NSs, the ellipticities of three transitional MSPs and ten redbacks are estimated to be $\epsilon=(0.9-23.4)\times 10^{-9}$. The electrical resistivities of three transitional MSPs are also derived to be in the range $\eta=(1.2-15.3)\times 10^{-31}~\rm s$, which display an ideal power law relation with the accretion rate. The characteristic strains ($h_{\rm c}=(0.6-2.5)\times10^{-27}$) of GW signals emitting by these sources are obviously beyond the sensitivity scope of the aLIGO. We expect that the third-generation GW detectors like the Einstein Telescope can seize the GW signals from these sources in the future.

The Einstein Telescope is a third-generation gravitational wave detector which is expected to be an order of magnitude more sensitive than the current detectors. While the current detectors enabled various measurements which were first of their kind (such as the strong field test of general relativity, an independent measurement of the Hubble constant, probing the dense nuclear matter inside the neutron stars, and many more), the proposed third-generation detectors may not only bring about unprecedented accuracy and precision to these measurements but also enable new first-of-their-kind measurements which may be outside the reach of current detectors (the detection of primordial black holes or phase transitions in the neutron star matter, for example). While the improvement in the sensitivity is desirable, it also makes it more difficult to extract physics-related insights from data. Of particular concern are transient, instrumental noise sources (also known as glitches) overlapping with the gravitational wave signal(s). For the third-generation detectors, we expect many more glitches to overlap with the signals compared to the current scenario, making it crucial to develop a methodology which can reliably “de-glitch” the data without corrupting the underlying signal. To address this challenge, we develop a novel framework which can accurately remove glitches overlapping with gravitational wave signals. The framework is unique to the triangular geometry of the Einstein Telescope, i.e., it cannot be realised for other proposed geometries such as the two distant, mis-aligned L-shaped detectors. Exploiting the triangular geometry, our framework outperforms the traditional methodology of de-glitching the signals used for L-shaped detector networks, showcasing a clear edge of the triangle geometry over the geometries. In this context, our work stands to play an important role in the design studies related to the Einstein Telescope, underway at the time of writing of this thesis. Bayesian parameter inference plays a key role in the measurements of the source parameters (such as masses, spins, sky-location, and distance) of a gravitational wave signal. Increasing costs of Bayesian parameter inference is another challenge posed by the improved sensitivity of the detectors. To address this challenge, we develop a relative-binning based framework to reduce the cost of Bayesian inferences. We benchmark our methodology on a large number of real as well as simulated signals for the current and next generation detectors. We also test the validity of our rapid inference framework on overlapping signals and lensed gravitational wave signals. In addition, we perform simulation to demonstrate how gravitational lensing can help constrain gravitational wave propagation beyond general relativity.

Third-generation gravitational wave detectors, such as the Einstein Telescope and Cosmic Explorer, will detect a bunch of gravitational-wave (GW) signals originating from the coalescence of binary neutron star (BNS) and binary black hole (BBH) systems out to higher redshifts, $z\ensuremath{\sim}5--10$. There is a potential concern that some of the GW signals detected at a high statistical significance eventually overlap with each other, and the parameter estimation of such an overlapping system can differ from the one expected from a single event. Also, there are certainly overlapping systems in which one of the overlapping events has a low signal-to-noise ratio $\ensuremath{\lesssim}4$, and is thus unable to be clearly detected. Those systems will potentially be misidentified with a single GW event, and the estimated parameters of binary GWs can be biased. We estimate the occurrence rate of those overlapping events. We find that the numbers of overlapping events are $\ensuremath{\sim}200$ per day for BNSs and a few per hour for BBHs. Then we study the statistical impacts of these overlapping GWs on a parameter estimation based on the Fisher matrix analysis. Our finding is that the overlapping signals produce neither large statistical errors nor serious systematic biases on the parameters of binary systems, unless the coalescence time and the redshifted chirp masses of the two overlapping GWs are very close to each other, i.e., $|{\mathcal{M}}_{z1}\ensuremath{-}{\mathcal{M}}_{z2}|\ensuremath{\lesssim}{10}^{\ensuremath{-}4}({10}^{\ensuremath{-}1})\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and $|{t}_{\mathrm{c}1}\ensuremath{-}{t}_{\mathrm{c}2}|\ensuremath{\lesssim}{10}^{\ensuremath{-}2}({10}^{\ensuremath{-}1})\text{ }\text{ }\mathrm{s}$ for BNSs (BBHs). The occurrence rate of such a closely overlapping event is shown to be much smaller than one per year with the third-generation detectors.

Lensed gravitational-wave (GW) events are expected to be powerful new probes of cosmology, contingent on redshift measurement by electromagnetic observations. Host galaxy identification is thus crucial but challenging due to poor localization by GW signal alone. In this Letter, we show that the third-generation ground-based GW detectors will detect a population of lensed events with three or more detectable images (including the central one), each arriving at distinct times and Earth locations in space, forming an effective network that reduces the typical localization area to ∼0.01 deg 2 . For at least 90% (or 50%) of these events, the localization improves by more than a factor of 10 (or 30) compared with unlensed cases. Such precise localization and multiple-image detections enable robust host-galaxy identification and, through lens modeling, further yield subarcsecond position. As dark lensed sirens, these events become powerful probes of cosmological parameters. Using simulated lensed compact-binary mergers, we show that 2 yr or longer observations with third-generation GW detectors can measure the Hubble constant to ≲1% precision via “dark lensed sirens” (even when relying solely on lensed stellar-mass binary black hole events) while simultaneously constraining other cosmological parameters. This approach will provide an independent, complementary avenue for measuring cosmological parameters.

As gravitational wave astronomy prepares for the first detections of gravitational waves from compact-object binary inspirals, theoretical work is required on the study of (i) gravitational-wave sources, (ii) the signals emitted by those sources, and (iii) the searches for those signals in detector data. This thesis describes work on all three fronts. (i) We discuss intermediate-mass-ratio inspirals (IMRIs) of black holes or neutron stars into intermediate-mass black holes (IMBHs) that could be detected with Advanced LIGO. We analyze different mechanisms of IMRI formation and compute IMRI event rates of up to tens of events per year for Advanced LIGO. We study the spin evolution of IMBHs that grow through a series of minor mergers. We explore how a deviation of an IMRI's central body from a Kerr black hole influences geodesics, including the possibility of chaotic orbital dynamics. We also address the scientific consequences of extreme-mass-ratio inspiral (EMRI) detections by LISA for astrophysics and general relativity, and the difficulties associated with detecting and analyzing EMRI signals. (ii) We study the periodic standing-wave approximation (PSWA), which can potentially provide accurate waveforms in the last inspiral cycles of a comparable-mass black-hole binary. Using a simple model, we find that the solution to Einstein's equations for inspiraling black holes can be recovered to a high accuracy by the addition a perturbative radiation-reaction field to the standing-wave, noninspiraling solution. (iii) We demonstrate the utility of searching for and analyzing tracks in time-frequency spectrograms of a gravitational-wave signal as a means of estimating the parameters of a massive black-hole binary inspiral, as observed by LISA.

The observation of low-frequency gravitational waves with the Laser Interferometer Space Antenna will allow the study of new sources of gravitational radiation that are not accessible by ground-based instruments. Gravitational wave sources provide invaluable information both about their astrophysics, as well as the nature of the gravitational interaction in their neighborhoods. One low frequency source that has not received much attention regarding the latter are galactic binaries composed of two white dwarves or a white dwarf and a neutron star. We here show that, contrary to the common lore, such gravitational wave sources can indeed be used to constrain an important feature of the gravitational interaction: the absence of pre-Newtonian, dipolar dissipation. We propose a model-independent framework to carry out a null test for the presence of this feature in the data that is very much analogous to tests of general relativity with radio-observations of binary pulsars. We then go one step further and specialize this test to scalar–tensor theories to derive projected constraints on spontaneous scalarization. We find that these constraints can be comparable to current bounds with binary pulsars, and in some optimistic cases, they can be even stronger.

Pulsar timing arrays (PTAs) are anticipated to detect continuous gravitational waves (GWs) from individual supermassive black hole binaries (SMBHBs) in the near future. To identify the host galaxy of a GW source, PTAs require significantly improved angular resolution beyond the typical range of 100–1000 square degrees achieved by recent continuous GW searches. In this study, we investigate how precise pulsar distance measurements can enhance the localization of a single GW source. Accurate distance information, comparable to or better than the GW wavelength (typically 1 pc) can refine GW source localization. In the near future, with the advent of Square Kilometre Array (SKA), such high-precision distance measurements will be feasible for a few nearby pulsars. We focus on the relatively nearby pulsars J0437-4715 (156 pc) and J 0030 + 0451 (331 pc), incorporating their actual distance uncertainties based on current very long baseline interferometry measurements and the anticipated precision of the SKA-era. By simulating 87 pulsars with the GW signal and Gaussian white noise in the timing residuals, we assess the impact of the pulsar distance information on GW source localization. Our results show that without precise distance information, localization remains insufficient to identify host galaxies under 10 ns noise. However, incorporating SKA-era distance precision for nearby pulsars J0437-4715 and J 0030 + 0451 can reduce localization uncertainties to the required level of 10 − 3 deg 2 under 10 ns noise. Localization accuracy strongly depends on the geometric configuration of pulsars with well-measured distances and improves notably near and between such pulsars. The improvement of the localization will greatly aid in identifying the host galaxy of a GW source and constructing an SMBHB catalog. It will further enable follow-up electromagnetic observations to investigate the SMBHB in greater detail.

In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for ground-based detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies, lens environments, and magnification bias. We find that in certain GW source rate scenarios, we should be able to observe strongly lensed GW events once per year ($\sim1~\text{yr}^{-1}$) in the aLIGO survey at its design sensitivity; for the proposed ET survey, the rate could be as high as $\sim80~\text{yr}^{-1}$. These results depend on the estimate of GW source abundance, and hence can be correspondingly modified with an improvement in our understanding of the merger rate of stellar binary black holes. We also compute the fraction of four-image lens systems in each survey, predicting it to be $\sim30$ per cent for the aLIGO survey and $\sim6$ per cent for the ET survey. Finally, we evaluate the possibility of missing some images due to the finite survey duration, by presenting the probability distribution of lensing time delays. We predict that this selection bias will be insignificant in future GW surveys, as most of the lens systems ($\sim90$ per cent) will have time delays less than $\sim1$ month, which will be far shorter than survey durations.

The field of gravitational wave astronomy is still in its early stages, with published detections of compact binary coalescences numbering 14 and the most recent observing run (O3) providing 50 more candidates. Another possible source of gravitational waves is rapidly rotating neutron stars which can emit gravitational waves if they have some asymmetry around their rotation axis. These are predicted to emit long duration quasi-sinusoidal signals known as continuous gravitational waves. All-sky and wide parameter space searches for continuous gravitational waves are generally template-matching schemes which test a bank of signal waveforms against data from a gravitational wave detector. Often these searches are highly-tuned to specific signal types and are computationally expensive. We have developed a search method (entitled SOAP) based on the Viterbi algorithm which is model-agnostic and has a computational cost several orders of magnitude lower than template methods and with a comparable sensitivity. In particular, this method can search for signals which have an unknown frequency evolution. We test the algorithm on three simulated and real data sets: gapless Gaussian noise, Gaussian noise with gaps and real data from the final run of initial LIGO (S6). We show that at 95% efficiency, with a 1% false alarm rate, the algorithm achieves a sensitivity of 60, 72 and 74 in the optimal coherent signal to noise ratio in each of these datasets. We discuss the use of this algorithm for detecting a wide range of quasi-monochromatic gravitational wave signals and instrumental artefacts, and demonstrate that it can also identify shorter duration signals such as compact binary coalescences. Many continuous gravitational wave searches are affected by instrumental lines as the long duration narrowband nature of a line can appear to be very similar to a real continuous gravitational wave signal. This has led to the development of techniques to try and limit the effect of instrumental lines, which mostly involve developing a statistic to penalise signals that appear in only a single detector. Whilst these statistics limit the effect of instrumental lines, in the SOAP search described above, many lines still contaminate the statistics and have to be manually removed by investigating other search outputs. We have developed a method using convolutional neural networks to reduce the impact of instrumental artefacts on the SOAP search described above. This has the ability to identify features in each of the detectors spectrograms such that a frequency band can be classified into a signal or noise class. This limits the amount of manual investigation of frequency bands and allowed the SOAP search to be fully automated without a reduction in the sensitivity. Once a continuous gravitational wave is detected, we would want to extract some parameters associated with the source to help understand more about its structure and evolution. We describe a Bayesian method which extracts the sky location, frequency, frequency derivative and signal to noise ratio of a source associated with the frequency evolution returned by the SOAP algorithm. This has the aim of limiting the size of the parameter space for a more sensitive fully coherent follow up search. We tested this approach on 200 simulations in Gaussian noise, generating posterior distributions for the parameters described above. In 90% of these simulations we limit the sky area to 45 deg^2 with a 95% confidence contour. However, we find that this contour contains the true parameter only 42% of the time. We present these results and describe the features and shortcomings of our approach. As mentioned above, we limit the effect of instrumental lines on the SOAP search using machine learning, however we can also identify and mitigate these lines separately before a search is run. We demonstrate how we can use SOAP in a simple configuration to identify instrumental lines. We compare this method to existing line identification tools used in the LIGO collaboration, and find that using the Viterbi statistic SOAP identifies 37% of the same lines as these methods, where for many of the lines which were not identified, other SOAP outputs do show evidence of a line. With further investigation, we expect to identify many more lines in common with existing methods. As well as these common lines, the SOAP algorithm returned 150 more 0.1 Hz wide bands which potentially contain an instrumental line and did not appear on LIGO line-lists.

The gigaelectronvolt γ -ray excess observed towards the Galactic centre remains unexplained. While dark matter annihilation has long been considered a leading explanation, an alternative scenario involving a large population of millisecond pulsars remains viable. Testing this hypothesis with electromagnetic observations is difficult, as pulsar searches in the bulge are strongly affected by interstellar scattering, high sky temperature, and source confusion. We investigate whether gravitational-wave observations with the Laser Interferometer Space Antenna (LISA) could provide an independent probe of the millisecond pulsar binary population in the Galactic bulge in the future. We constructed synthetic populations of detached millisecond pulsar–white dwarf binaries under two illustrative formation scenarios: an accreted scenario, in which systems are deposited by disrupted globular clusters, and an in situ scenario, in which binaries form through isolated binary evolution. In both cases, only 10 −5 –10 −4 of the underlying bulge population is detectable by LISA. Still, even a few detections would imply tens to hundreds of thousands of unseen systems. Accreted binaries are expected to have lower chirp masses (∼0.4 M ⊙ ), while in situ binaries produce more massive companions (∼0.9 M ⊙ ), though part of this contrast reflects our modelling assumptions. LISA will measure binary frequencies with high precision, but chirp masses can only be determined for the most massive or highest-frequency systems. Thus, identifying millisecond-pulsar binaries among the far more numerous double white dwarfs will be challenging, as their gravitational-wave signals alone are indistinguishable. However, coordinated follow-up with the Square Kilometre Array of LISA-selected targets could directly test the millisecond-pulsar explanation of the γ -ray excess.

The detection of gravitational waves (GW) by the LIGO and Virgo collaborations offers a whole new range of possible tests and opens up a new window which may shed light on the nature of dark energy and dark matter. In the present work we investigate how future gravitational waves data could help to constrain different dynamical dark energy models. In particular, we perform cosmological forecastings of a class of well known and most used dynamical dark energy models using the third-generation gravitational wave detector, the Einstein Telescope. We have considered 1000 simulated GW events in order to constrain the parameter space of the dynamical dark energy models. Our analyses show that the inclusion of the GW data from the Einstein Telescope, significantly improves the parameter space of the dynamical dark energy models compared to their constraints extracted from the standard cosmological probes, namely, the cosmic microwave observations, baryon acoustic oscillations distance measurements, Supernove type Ia, and the Hubble parameter measurements.

Quickly localizing the identified white dwarf (WD) binaries is the basic requirement for the space-based gravitational wave (GW) detection. In fact, the amplitude of GW signals are modulated by the periodic motion of GW detectors on the solar orbit. The intensity of the observed signals is enhanced according to the observation time beyond a year to enhance a high signal to noise ratio (SNR). As data gap exists, the completeness of the data observed for a long time depends on filling gaps in the data. Actually, in a year period, the GW sources have a best observation orbit position of GW detectors, where the intensity of GW is maximum. Thus, the best positions can be searched for the verified GW sources of the sky map to enhance SNR too, which avoids filling data gaps. For the three arms response intensity of the GW signals changing more clearly with the location of the GW sources relative to the detector, the noises and the suppression of noise by time delay interferometer are ignored. As a verification case, the four WD binaries are chosen, whose best observation orbit positions of the GW detectors are related to the direction of WD binaries perpendicular to the detection arms. The two verification binaries: J0806 and V407 Vul are observed at the best orbit positions by TAIJI for the short time of 2 and 3 days respectively. The corresponding intensities of GWs are above the values of the TAIJI sensitivity curve, significantly. Location parameter estimation of the verification WD binaries are performed using the Metropolis–Hastings MCMC method. The confidence level of the parameters obtained in the best position is significantly several times higher than that in the worst position where the direction of WD binaries are almost parallel to the detection arms. Compared with a single detector, the network of two detectors improve slightly the accuracy of location of the verification binaries. These results imply that the searching of GW signals and parameter estimation of GW sources from the experimental data of the space-based mission do not ignore the orbit positions relevant to GW sources.

We present a search for gravitational waves from 116 known millisecond and young pulsars using data from the fifth science run of the LIGO detectors. For this search ephemerides overlapping the run period were obtained for all pulsars using radio and X-ray observations. We demonstrate an updated search method that allows for small uncertainties in the pulsar phase parameters to be included in the search. We report no signal detection from any of the targets and therefore interpret our results as upper limits on the gravitational wave signal strength. The most interesting limits are those for young pulsars. We present updated limits on gravitational radiation from the Crab pulsar, where the measured limit is now a factor of seven below the spin-down limit. This limits the power radiated via gravitational waves to be less than ~2% of the available spin-down power. For the X-ray pulsar J0537-6910 we reach the spin-down limit under the assumption that any gravitational wave signal from it stays phase locked to the X-ray pulses over timing glitches, and for pulsars J1913+1011 and J1952+3252 we are only a factor of a few above the spin-down limit. Of the recycled millisecond pulsars several of the measured upper limits are only about an order of magnitude above their spin-down limits. For these our best (lowest) upper limit on gravitational wave amplitude is 2.3x10^-26 for J1603-7202 and our best (lowest) limit on the inferred pulsar ellipticity is 7.0x10^-8 for J2124-3358.

The proposed TianQin gravitational wave observatory is aiming to detect gravitational wave signals in the millihertz frequency band, through the method of space-borne laser interferometry. In total, three satellites will be launched, each following a geocentric orbit, with an orbital altitude of about one hundred thousand kilometers. They form into an equilateral triangle formation, with an orbital period of <sc>3.6 d.</sc> The orbital plane of TianQin is fixed almost constant, towards one specific gravitational wave source, RXJ0806.3+1527, so that TianQins response to this source is maximized, and this source can be used to calibrate and assess the facilities performance. It is widely anticipated that in the millihertz frequency band, there lurks a wide variety of gravitational wave sources, ranging from massive black hole binary mergers, extreme mass ratio inspirals, Galactic binary white dwarves, stellar mass binary compact objects inspirals, as well as stochastic gravitational wave background. Meanwhile, the expected source number in such frequency band would also be huge. The successful implementation of the TianQin project would pave the way towards exciting prospects of future gravitational wave research. By successfully performing gravitational wave observation, the TianQin gravitational wave observatory can open a new window for the study of gravitational wave astronomy, gravitational wave cosmology as well as gravitational wave physics. The science prospect of TianQin gravitational wave observation can be further enhanced through a combination with multi-band gravitational wave detection and multi-messenger astronomical observations, by collaboration with gravitational wave detectors operating in different frequency bands as well as with other probes focusing on different messengers like electro-magnetic signals, neutrinos or cosmic rays. The TianQin project will also greatly promote the construction of a high-precision space-time reference system, ultra-long-range laser interferometry, high-precision satellite platform, etc. The development of cutting-edge space technologies has important applications in the national economy as well as the national strategic needs. Currently, the TianQin project has made important progress in the precision gravity measurement facility, the payload research base, the laser ranging station, the simulation facility for space-borne gravitation wave detection on ground, and the series test satellite for the TianQin project. Based on the long-term accumulation of relevant technology, the TianQin project team proposed the goal of achieving gravitational wave detection in the 2030s, and a 0123 plan roadmap is formulated, aiming to perform, step by step, lunar or relay satellite laser ranging, testing key technology like space-borne laser interferometry and drag-free control, verifying high precision space-borne laser interferometry technology, and ultimately detecting gravitational wave. By the 2030s, the scientific cooperation between scientists from all over the world and the use of various means to jointly conduct exploration and research on the Universe will face great development. So far, the TianQin project has held many international seminars and received extensive international attention and active participation. Currently, the TianQin Collaboration Group has been formally established, with a collaboration group advisory committee also established, consisting of scientists with significant influence in the field of gravitational wave detection all over the world. The TianQin project will establish a collaborative research or comprehensive cooperation agreement with foreign universities or research organizations, and vigorously promote the China-led space-borne gravitational wave detection business. Through extensive international cooperation, the TianQin project will unite domestic and foreign strengths and strive to take the lead in realizing the gravitational wave detection in the window of millihertz band.

We present a systematic study of the evolution of intermediate- and low-mass X-ray binaries. Our calculations suggest that millisecond binary pulsars in wide orbits might have neutron stars born massive, or been formed through mass transfer driven by planet/brown dwarf-involved common envelope evolution.