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Register a new userGravitational-wave parameter estimation with gaps in LISA: a Bayesian data augmentation method
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By listening to gravity in the low frequency band, between 0.1 mHz and 1 Hz, the future space-based gravitational-wave observatory LISA will be able to detect tens of thousands of astrophysical sources from cosmic dawn to the present. The detection and characterization of all resolvable sources is a challenge in itself, but LISA data analysis will be further complicated by interruptions occurring in the interferometric measurements. These interruptions will be due to various causes occurring at various rates, such as laser frequency switches, high-gain antenna re-pointing, orbit corrections, or even unplanned random events. Extracting long-lasting gravitational-wave signals from gapped data raises problems such as noise leakage and increased computational complexity. We address these issues by using Bayesian data augmentation, a method that reintroduces the missing data as auxiliary variables in the sampling of the posterior distribution of astrophysical parameters. This provides a statistically consistent way to handle gaps while improving the sampling efficiency and mitigating leakage effects. We apply the method to the estimation of galactic binaries parameters with different gap patterns, and we compare the results to the case of complete data.
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One of the main bottlenecks in gravitational wave (GW) astronomy is the high cost of performing parameter estimation and GW searches on the fly. We propose a novel technique based on Reduced Order Quadratures (ROQs), an application and data-specific quadrature rule, to perform fast and accurate likelihood evaluations. These are the dominant cost in Markov chain Monte Carlo (MCMC) algorithms, which are widely employed in parameter estimation studies, and so ROQs offer a new way to accelerate GW parameter estimation. We illustrate our approach using a four dimensional GW burst model embedded in noise. We build an ROQ for this model, and perform four dimensional MCMC searches with both the standard and ROQs quadrature rules, showing that, for this model, the ROQ approach is around 25 times faster than the standard approach with essentially no loss of accuracy. The speed-up from using ROQs is expected to increase for more complex GW signal models and therefore has significant potential to accelerate parameter estimation of GW sources such as compact binary coalescences.
LISA and Taiji are expected to form a space-based gravitational-wave (GW) detection network in the future. In this work, we make a forecast for the cosmological parameter estimation with the standard siren observation from the LISA-Taiji network. We simulate the standard siren data based on a scenario with configuration angle of $40^{circ}$ between LISA and Taiji. Three models for the population of massive black hole binary (MBHB), i.e., pop III, Q3d, and Q3nod, are considered to predict the events of MBHB mergers. We find that, based on the LISA-Taiji network, the number of electromagnetic (EM) counterparts detected is almost doubled compared with the case of single Taiji mission. Therefore, the LISA-Taiji networks standard siren observation could provide much tighter constraints on cosmological parameters. For example, solely using the standard sirens from the LISA-Taiji network, the constraint precision of $H_0$ could reach $1.3%$. Moreover, combined with the CMB data, the GW-EM observation based on the LISA-Taiji network could also tightly constrain the equation of state of dark energy, e.g., the constraint precision of $w$ reaches about $4%$, which is comparable with the result of CMB+BAO+SN. It is concluded that the GW standard sirens from the LISA-Taiji network will become a useful cosmological probe in understanding the nature of dark energy in the future.
Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution constructed using Gaussian process regression (GPR). As an example, we apply this technique to the measurement of chirp mass using (simulated) gravitational-wave signals from binary black holes that could be observed using advanced-era gravitational-wave detectors. Unless properly accounted for, uncertainty in the gravitational-wave templates could be the dominant source of error in studies of these systems. We explain our approach in detail and provide proofs of various features of the method, including the limiting behavior for high signal-to-noise, where systematic model uncertainties dominate over noise errors. We find that the marginalized likelihood constructed via GPR offers a significant improvement in parameter estimation over the standard, uncorrected likelihood both in our simple one-dimensional study, and theoretically in general. We also examine the dependence of the method on the size of training set used in the GPR; on the form of covariance function adopted for the GPR, and on changes to the detector noise power spectral density.
Reliable low-latency gravitational wave parameter estimation is essential to target limited electromagnetic followup facilities toward astrophysically interesting and electromagnetically relevant sources of gravitational waves. In this study, we examine the tradeoff between speed and accuracy. Specifically, we estimate the astrophysical relevance of systematic errors in the posterior parameter distributions derived using a fast-but-approximate waveform model, SpinTaylorF2 (STF2), in parameter estimation with lalinference_mcmc. Though efficient, the STF2 approximation to compact binary inspiral employs approximate kinematics (e.g., a single spin) and an approximate waveform (e.g., frequency domain versus time domain). More broadly, using a large astrophysically-motivated population of generic compact binary merger signals, we report on the effectualness and limitations of this single-spin approximation as a method to infer parameters of generic compact binary sources. For most low-mass compact binary sources, we find that the STF2 approximation estimates compact binary parameters with biases comparable to systematic uncertainties in the waveform. We illustrate by example the effect these systematic errors have on posterior probabilities most relevant to low-latency electromagnetic followup: whether the secondary is has a mass consistent with a neutron star; whether the masses, spins, and orbit are consistent with that neutron stars tidal disruption; and whether the binarys angular momentum axis is oriented along the line of sight.
Massive black hole binaries are expected to provide the strongest gravitational wave signals for the Laser Interferometer Space Antenna (LISA), a space mission targeting $sim,$mHz frequencies. As a result of the technological challenges inherent in the missions design, implementation and long duration (4 yr nominal), the LISA data stream is expected to be affected by relatively long gaps where no data is collected (either because of hardware failures, or because of scheduled maintenance operations, such as re-pointing of the antennas toward the Earth). Depending on their mass, massive black hole binary signals may range from quasi-transient to very long lived, and it is unclear how data gaps will impact detection and parameter estimation of these sources. Here, we will explore this question by using state-of-the-art astrophysical models for the population of massive black hole binaries. We will investigate the potential detectability of MBHB signals by observing the effect of gaps on their signal-to-noise ratios. We will also assess the effect of the gaps on parameter estimation for these sources, using the Fisher Information Matrix formalism as well as full Bayesian analyses. Overall, we find that the effect of data gaps due to regular maintenance of the spacecraft is negligible, except for systems that coalesce within such a gap. The effect of unscheduled gaps, however, will probably be more significant than that of scheduled ones.
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