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Register a new userLISA observations of supermassive black holes: parameter estimation using full post-Newtonian inspiral waveforms
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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.
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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.
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 $a = 0.998$.
One of the most exciting potential sources of gravitational waves for the Laser Interferometer Space Antenna (LISA) are the inspirals of approximately solar mass compact objects into massive black holes in the centres of galaxies - extreme mass ratio inspirals (EMRIs). LISA should observe between a few tens and a few hundred EMRIs over the mission lifetime, mostly at low redshifts (z < 1). Each observation will provide a measurement of the parameters of the host system to unprecendented precision. LISA EMRI observations will thus offer a new and unique way to probe black holes at low redshift. In this article we provide a description of the population of EMRI events that LISA is likely to observe, and describe how the numbers of events vary with changes in the underlying assumptions about the black hole population. We also provide fitting functions that characterise LISAs ability to detect EMRIs and which will allow LISA event rates to be computed for arbitrary population models. We finish with a discussion of an ongoing programme that will use these results to assess what constraints LISA observations could place on galaxy evolution models.
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.
The planned Laser Interferometer Space Antenna (LISA) is expected to detect the inspiral and merger of massive black hole binaries (MBHBs) at z <~ 5 with signal-to-noise ratios (SNRs) of hundreds to thousands. Because of these high SNRs, and because these SNRs accrete over periods of weeks to months, it should be possible to extract the physical parameters of these systems with high accuracy; for instance, for a ~ 10^6 Msun MBHBs at z = 1 it should be possible to determine the two masses to ~ 0.1% and the sky location to ~ 1 degree. However, those are just the errors due to noise: there will be additional theoretical errors due to inaccuracies in our best model waveforms, which are still only approximate. The goal of this paper is to estimate the typical magnitude of these theoretical errors. We develop mathematical tools for this purpose, and apply them to a somewhat simplified version of the MBHB problem, in which we consider just the inspiral part of the waveform and neglect spin-induced precession, eccentricity, and PN amplitude corrections. For this simplified version, we estimate that theoretical uncertainties in sky position will typically be ~ 1 degree, i.e., comparable to the statistical uncertainty. For the mass and spin parameters, our results suggest that while theoretical errors will be rather small absolutely, they could still dominate over statistical errors (by roughly an order of magnitude) for the strongest sources. The tools developed here should be useful for estimating the magnitude of theoretical errors in many other problems in gravitational-wave astronomy.
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