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We study parameter estimation of supermassive black holes in the range $10^5-10^8Ms$ by LISA using the inspiral full post-Newtonian gravitational waveforms, and we compare the results with those arising from the commonly used restricted post-Newtonian approximation. The analysis shows that for observations of the last year before merger, the inclusion of the higher harmonics clearly improves the parameter estimation. We pay special attention to the source location errors and we study the improvement on the percentage of sources for which we could potentially identify electromagnetic counterparts. We also show how the additional harmonics can help to mitigate the impact of losing laser links during the mission.
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We study parameter estimation of supermassive black hole binary systems in the final stage of inspiral using the full post-Newtonian gravitational waveforms. We restrict our analysis to systems in circular orbit with negligible spins, in the mass range $10^8Ms-10^5Ms$, and compare the results with those arising from the commonly used restricted post-Newtonian approximation. The conclusions of this work are particularly important with regard to the astrophysical reach of future LISA measurements. Our analysis clearly shows that modeling the inspiral with the full post-Newtonian waveform, not only extends the reach to higher mass systems, but also improves in general the parameter estimation. In particular, there are remarkable improvements in angular resolution and distance measurement for systems with a total mass higher than $5times10^6Ms$, as well as a large improvement in the mass determination.
Stellar-mass black hole binaries (SBHBs), like those currently being detected with the ground-based gravitational-wave (GW) observatories LIGO and Virgo, are also an anticipated GW source for LISA. LISA will observe them during the early inspiral stage of evolution; some of them will chirp through the LISA band and reappear some time later in the band of $3^{rd}$ generation ground-based detectors. SBHBs could serve as laboratories for testing the theory of General Relativity and inferring the astrophysical properties of the underlying population. In this study, we assess LISAs ability to infer the parameters of those systems, a crucial first step in understanding and interpreting the observation of those binaries and their use in fundamental physics and astrophysics. We simulate LISA observations for several fiducial sources and perform a full Bayesian analysis. We demonstrate and explain degeneracies in the parameters of some systems. We show that the redshifted chirp mass and the sky location are always very well determined, with typical errors below $10^{-4}$ (fractional) and $0.4 {rm deg^2}$. The luminosity distance to the source is typically measured within $40-60%$, resulting in a measurement of the chirp mass in the source frame of $mathcal{O}(1 %)$. The error on the time to coalescence improves from $mathcal{O}(1 {rm day})$ to $mathcal{O}(30 {rm s})$ as we observe the systems closer to their merger. We introduce an augmented Fisher-matrix analysis which gives reliable predictions for the intrinsic parameters compared to the full Bayesian analysis. Finally, we show that combining the use of the long-wavelength approximation for the LISA instrumental response together with the introduction of a degradation function at high frequencies yields reliable results for the posterior distribution when used self-consistently, but not in the analysis of real LISA data.
We describe a model that generates first order adiabatic EMRI waveforms for quasi-circular equatorial inspirals of compact objects into rapidly rotating (near-extremal) black holes. Using our model, we show that LISA could measure the spin parameter of near-extremal black holes (for $a gtrsim 0.9999$) with extraordinary precision, $sim$ 3-4 orders of magnitude better than for moderate spins, $a sim 0.9$. Such spin measurements would be one of the tightest measurements of an astrophysical parameter within a gravitational wave context. Our results are primarily based off a Fisher matrix analysis, but are verified using both frequentest and Bayesian techniques. We present analytical arguments that explain these high spin precision measurements. The high precision arises from the spin dependence of the radial inspiral evolution, which is dominated by geodesic properties of the secondary orbit, rather than radiation reaction. High precision measurements are only possible if we observe the exponential damping of the signal that is characteristic of the near-horizon regime of near-extremal inspirals. Our results demonstrate that, if such black holes exist, LISA would be able to successfully identify rapidly rotating black holes up to $a = 1-10^{-9}$ , far past the Thorne limit of $a = 0.998$.
The Laser Interferometer Space Antenna (LISA) is slated for launch in the early 2030s. A main target of the mission is massive black hole binaries that have an expected detection rate of $sim20$ yr$^{-1}$. We present a parameter estimation analysis for a variety of massive black hole binaries. This analysis is performed with a graphics processing unit (GPU) implementation comprising the phenomhm waveform with higher-order harmonic modes and aligned spins; a fast frequency-domain LISA detector response function; and a GPU-native likelihood computation. The computational performance achieved with the GPU is shown to be 500 times greater than with a similar CPU implementation, which allows us to analyze full noise-infused injections at a realistic Fourier bin width for the LISA mission in a tractable and efficient amount of time. With these fast likelihood computations, we study the effect of adding aligned spins to an analysis with higher-order modes by testing different configurations of spins in the injection, as well as the effect of varied and fixed spins during sampling. Within these tests, we examine three different binaries with varying mass ratios, redshifts, sky locations, and detector-frame total masses ranging over three orders of magnitude. We discuss varied correlations between the total masses and mass ratios; unique spin posteriors for the larger mass binaries; and the constraints on parameters when fixing spins during sampling, allowing us to compare to previous analyses that did not include aligned spins.
We investigate the precision with which the parameters describing the characteristics and location of nonspinning black hole binaries can be measured with the Laser Interferometer Space Antenna (LISA). By using complete waveforms including the inspiral, merger and ringdown portions of the signals, we find that LISA will have far greater precision than previous estimates for nonspinning mergers that ignored the merger and ringdown. Our analysis covers nonspinning waveforms with moderate mass ratios, q >= 1/10, and total masses 10^5 < M/M_{Sun} < 10^7. We compare the parameter uncertainties using the Fisher matrix formalism, and establish the significance of mass asymmetry and higher-order content to the predicted parameter uncertainties resulting from inclusion of the merger. In real-time observations, the later parts of the signal lead to significant improvements in sky-position precision in the last hours and even the final minutes of observation. For comparable mass systems with total mass M/M_{Sun} = ~10^6, we find that the increased precision resulting from including the merger is comparable to the increase in signal-to-noise ratio. For the most precise systems under investigation, half can be localized to within O(10 arcmin), and 10% can be localized to within O(1 arcmin).
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