A Bayesian approach to multi-messenger astronomy: Identification of gravitational-wave host galaxies

We present a general framework for incorporating astrophysical information into Bayesian parameter estimation techniques used by gravitational wave data analysis to facilitate multi-messenger astronomy. Since the progenitors of transient gravitational wave events, such as compact binary coalescences, are likely to be associated with a host galaxy, improvements to the source sky location estimates through the use of host galaxy information are explored. To demonstrate how host galaxy properties can be included, we simulate a population of compact binary coalescences and show that for ~8.5% of simulations with in 200Mpc, the top ten most likely galaxies account for a ~50% of the total probability of hosting a gravitational wave source. The true gravitational wave source host galaxy is in the top ten galaxy candidates ~10% of the time. Furthermore, we show that by including host galaxy information, a better estimate of the inclination angle of a compact binary gravitational wave source can be obtained. We also demonstrate the flexibility of our method by incorporating the use of either B or K band into our analysis.Comment: 22 pages, 8 figures, accepted for publication in the Ap

Probing intrinsic properties of short gamma-ray bursts with gravitational waves

Progenitors of short gamma-ray bursts are thought to be neutron stars coalescing with their companion black hole or neutron star, which are one of the main gravitational wave sources. We have devised a Bayesian framework for combining gamma-ray burst and gravitational wave information that allows us to probe short gamma-ray burst luminosities. We show that combined short gamma-ray burst and gravitational wave observations not only improve progenitor distance and inclination angle estimates, they also allow the isotropic luminosities of short gamma-ray bursts to be determined without the need for host galaxy or light-curve information. We characterise our approach by simulating 1000 joint short gamma-ray burst and gravitational wave detections by Advanced LIGO and Advanced Virgo. We show that ${\sim}90\%$ of the simulations have uncertainties on short gamma-ray burst isotropic luminosity estimates that are within a factor of 2 of the ideal scenario, where the distance is known exactly. Therefore, isotropic luminosities can be confidently determined for short gamma-ray bursts observed jointly with gravitational wave detected by Advanced LIGO and Advanced Virgo. Planned enhancements to Advanced LIGO will extend its range and likely produce several joint detections of short gamma-ray bursts and gravitational waves. Third-generation gravitational wave detectors will allow for isotropic luminosity estimates for the majority of the short gamma-ray burst population within a redshift of $z{\sim}1$

Cosmological inference using only gravitational wave observations of binary neutron stars

Gravitational waves emitted during the coalescence of binary neutron star systems are self-calibrating signals. As such, they can provide a direct measurement of the luminosity distance to a source without the need for a cross-calibrated cosmic distance-scale ladder. In general, however, the corresponding redshift measurement needs to be obtained via electromagnetic observations since it is totally degenerate with the total mass of the system. Nevertheless, Fisher matrix studies have shown that, if information about the equation of state of the neutron stars is available, it is possible to extract redshift information from the gravitational wave signal alone. Therefore, measuring the cosmological parameters in pure gravitational-wave fashion is possible. Furthermore, the huge number of sources potentially observable by the Einstein Telescope has led to speculations that the gravitational wave measurement is potentially competitive with traditional methods. The Einstein Telescope is a conceptual study for a third generation gravitational wave detector which is designed to yield 103–107 detections of binary neutron star systems per year. This study presents the first Bayesian investigation of the accuracy with which the cosmological parameters can be measured using information coming only from the gravitational wave observations of binary neutron star systems by the Einstein Telescope. We find, by direct simulation of 103 detections of binary neutron stars, that, within our simplifying assumptions, H0, Ωm, ΩΛ, w0 and w1 can be measured at the 95% level with an accuracy of ∼8%, 65%, 39%, 80% and 90%, respectively. We also find, by extrapolation, that a measurement accuracy comparable with current measurements by Planck is possible if the number of gravitational wave events observed is Oð106–7Þ. We conclude that, while not competitive with electromagnetic missions in terms of significant digits, gravitational waves alone are capable of providing a complementary determination of the dynamics of the Universe

Implementation of the frequency-modulated sideband search method for gravitational waves from low mass X-ray binaries

We describe the practical implementation of the sideband search, a search for periodic gravitational waves from neutron stars in binary systems. The orbital motion of the source in its binary system causes frequency-modulation in the combination of matched filters known as the $\mathcal{F}$-statistic. The sideband search is based on the incoherent summation of these frequency-modulated $\mathcal{F}$-statistic sidebands. It provides a new detection statistic for sources in binary systems, called the $\mathcal{C}$-statistic. The search is well suited to low-mass X-ray binaries, the brightest of which, called Sco X-1, is an ideal target candidate. For sources like Sco X-1, with well constrained orbital parameters, a slight variation on the search is possible. The extra orbital information can be used to approximately demodulate the data from the binary orbital motion in the coherent stage, before incoherently summing the now reduced number of sidebands. We investigate this approach and show that it improves the sensitivity of the standard Sco X-1 directed sideband search. Prior information on the neutron star inclination and gravitational wave polarization can also be used to improve upper limit sensitivity. We estimate the sensitivity of a Sco X-1 directed sideband search on 10 days of LIGO data and show that it can beat previous upper limits in current LIGO data, with a possibility of constraining theoretical upper limits using future advanced instruments.Comment: 20 pages, 5 figure

Method to detect gravitational waves from an ensemble of known pulsars

Combining information from weak sources, such as known pulsars, for gravitational wave detection, is an attractive approach to improve detection efficiency. We propose an optimal statistic for a general ensemble of signals and apply it to an ensemble of known pulsars. Our method combines F-statistic values from individual pulsars using weights proportional to each pulsar’s expected optimal signal-to-noise ratio to improve the detection efficiency. We also point out that to detect at least one pulsar within an ensemble, different thresholds should be designed for each source based on the expected signal strength. The performance of our proposed detection statistic is demonstrated using simulated sources, with the assumption that all pulsar ellipticities belong to a common (yet unknown) distribution. Comparing with an equal-weight strategy and with individual source approaches, we show that the weighted combination of all known pulsars, where weights are assigned based on the pulsars’ known information, such as sky location, frequency and distance, as well as the detector sensitivity, always provides a more sensitive detection statistic

Cosmological Inference using Gravitational Waves and Normalising Flows

We present a machine learning approach using normalising flows for inferring cosmological parameters from gravitational wave events. Our methodology is general to any type of compact binary coalescence event and cosmological model and relies on the generation of training data representing distributions of gravitational wave event parameters. These parameters are conditional on the underlying cosmology and incorporate prior information from galaxy catalogues. We provide an example analysis inferring the Hubble constant using binary black holes detected during the O1, O2, and O3 observational runs conducted by the advanced LIGO/VIRGO gravitational wave detectors. We obtain a Bayesian posterior on the Hubble constant from which we derive an estimate and 1$\sigma$ confidence bounds of $H_{0} = 74.51^{+14.80}_{-13.63} \: \text{km} \:\text{s}^{-1} \text{Mpc}^{-1}$. We are able to compute this result in $\mathcal{O}(1)$ s using our trained Normalising Flow model.Comment: 5 pages, 2 figures, to be submitted to Physics Review Letters (PRL

Astrophysical calibration of gravitational-wave detectors

We investigate a method to assess the validity of gravitational-wave detector calibration through the use of gamma-ray bursts as standard sirens. Such signals, as measured via gravitational-wave observations, provide an estimated luminosity distance that is subject to uncertainties in the calibration of the data. If a host galaxy is identified for a given source then its redshift can be combined with current knowledge of the cosmological parameters yielding the true luminosity distance. This will then allow a direct comparison with the estimated value and can validate the accuracy of the original calibration. We use simulations of individual detectable gravitational-wave signals from binary neutron star (BNS) or neutron star-black hole systems, which we assume to be found in coincidence with short gamma-ray bursts, to estimate any discrepancy in the overall scaling of the calibration for detectors in the Advanced LIGO and Advanced Virgo network. We find that the amplitude scaling of the calibration for the LIGO instruments could on average be confirmed to within ∼10% for a BNS source within 100 Mpc. This result is largely independent of the current detector calibration method and gives an uncertainty that is competitive with that expected in the current calibration procedure. Confirmation of the calibration accuracy to within ∼20% can be found with BNS sources out to ∼500 Mpc

Method to detect gravitational waves from an ensemble of known pulsars

Combining information from weak sources, such as known pulsars, for gravitational wave detection, is an attractive approach to improve detection efficiency. We propose an optimal statistic for a general ensemble of signals and apply it to an ensemble of known pulsars. Our method combines ℱ-statistic values from individual pulsars using weights proportional to each pulsar’s expected optimal signal-to-noise ratio to improve the detection efficiency. We also point out that to detect at least one pulsar within an ensemble, different thresholds should be designed for each source based on the expected signal strength. The performance of our proposed detection statistic is demonstrated using simulated sources, with the assumption that all pulsar ellipticities belong to a common (yet unknown) distribution. Comparing with an equal-weight strategy and with individual source approaches, we show that the weighted combination of all known pulsars, where weights are assigned based on the pulsars’ known information, such as sky location, frequency and distance, as well as the detector sensitivity, always provides a more sensitive detection statistic

Robust machine learning algorithm to search for continuous gravitational waves

Many continuous gravitational wave searches are affected by instrumental spectral lines that could be confused with a continuous astrophysical signal. Several techniques have been developed to limit the effect of these lines by penalizing signals that appear in only a single detector. We have developed a general method, using a convolutional neural network, to reduce the impact of instrumental artifacts on searches that use the SOAP algorithm Bayley et al. [Phys. Rev. D 100, 023006 (2019)]. The method can identify features in corresponding frequency bands of each detector and classify these bands as containing a signal, an instrumental line, or noise. We tested the method against four different datasets: Gaussian noise with time gaps, data from the final run of Initial LIGO (S6) with signals added, the reference S6 mock data challenge dataset Walsh et al. [Phys. Rev. D 94, 124010 (2016)] and signals injected into data from the second advanced LIGO observing run (O2). Using the S6 mock data challenge dataset and at a 1% false alarm probability we showed that at 95% efficiency a fully automated SOAP search has a sensitivity corresponding to a coherent signal-to-noise ratio of 110, equivalent to a sensitivity depth of 10  Hz−1/2, making this automated search competitive with other searches requiring significantly more computing resources and human intervention