LISA observations of supermassive black holes: parameter estimation using full post-Newtonian inspiral waveforms

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 10^8\Ms-10^5\Ms, 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 5\times10^6\Ms, as well as a large improvement in the mass determination.Comment: Final version. Accepted for publication in Phys. Rev.

Higher harmonics increase LISA's mass reach for supermassive black holes

Current expectations on the signal to noise ratios and masses of supermassive black holes which the Laser Interferometer Space Antenna (LISA) can observe are based on using in matched filtering only the dominant harmonic of the inspiral waveform at twice the orbital frequency. Other harmonics will affect the signal-to-noise ratio of systems currently believed to be observable by LISA. More significantly, inclusion of other harmonics in our matched filters would mean that more massive systems that were previously thought to be {\it not} visible in LISA should be detectable with reasonable SNRs. Our estimates show that we should be able to significantly increase the mass reach of LISA and observe the more commonly occurring supermassive black holes of masses $\sim 10^8M_\odot.$ More specifically, with the inclusion of all known harmonics LISA will be able to observe even supermassive black hole coalescences with total mass $\sim 10^8 M_\odot (10^9M_\odot)$ (and mass-ratio 0.1) for a low frequency cut-off of $10^{-4}{\rm Hz}$ $(10^{-5}{\rm Hz})$ with an SNR up to $\sim 60$ $(\sim 30)$ at a distance of 3 Gpc. This is important from the astrophysical viewpoint since observational evidence for the existence of black holes in this mass range is quite strong and binaries containing such supermassive black holes will be inaccessible to LISA if one uses as detection templates only the dominant harmonic.Comment: minor corrections mad

Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms

We provide ready-to-use time-domain gravitational waveforms for spinning compact binaries with precession effects through 1.5PN order in amplitude and compute their mode decomposition using spin-weighted -2 spherical harmonics. In the presence of precession, the gravitational-wave modes (l,m) contain harmonics originating from combinations of the orbital frequency and precession frequencies. We find that the gravitational radiation from binary systems with large mass asymmetry and large inclination angle can be distributed among several modes. For example, during the last stages of inspiral, for some maximally spinning configurations, the amplitude of the (2,0) and (2,1) modes can be comparable to the amplitude of the (2,2) mode. If the mass ratio is not too extreme, the l=3 and l=4 modes are generally one or two orders of magnitude smaller than the l = 2 modes. Restricting ourselves to spinning, non-precessing compact binaries, we apply the stationary-phase approximation and derive the frequency-domain gravitational waveforms including spin-orbit and spin(1)- spin(2) effects through 1.5PN and 2PN order respectively in amplitude, and 2.5PN order in phase. Since spin effects in the amplitude through 2PN order affect only the first and second harmonics of the orbital phase, they do not extend the mass reach of gravitational-wave detectors. However, they can interfere with other harmonics and lower or raise the signal-to-noise ratio depending on the spin orientation. These ready-to-use waveforms could be employed in the data-analysis of the spinning, inspiraling binaries as well as in comparison studies at the interface between analytical and numerical relativity.Comment: 43 pages, 10 Postscript figures. submitted to Physical Review D. Includes corrections due to errat

Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit

The increasing sophistication and accuracy of numerical simulations of compact binaries (especially binary black holes) presents the opportunity to test the regime in which post-Newtonian (PN) predictions for the emitted gravitational waves are accurate. In order to confront numerical results with those of post-Newtonian theory, it is convenient to compare multipolar decompositions of the two waveforms. It is pointed out here that the individual modes can be computed to higher post-Newtonian order by examining the radiative multipole moments of the system, rather than by decomposing the 2.5PN polarization waveforms. In particular, the dominant (l = 2, m = 2) mode can be computed to 3PN order. Individual modes are computed to as high a post-Newtonian order as possible given previous post-Newtonian results.Comment: 15 page

Parameter estimation of coalescing supermassive black hole binaries with LISA

Laser Interferometer Space Antenna (LISA) will routinely observe coalescences of supermassive black hole (BH) binaries up to very high redshifts. LISA can measure mass parameters of such coalescences to a relative accuracy of $10^{-4}-10^{-6}$, for sources at a distance of 3 Gpc. The problem of parameter estimation of massive nonspinning binary black holes using post-Newtonian (PN) phasing formula is studied in the context of LISA. Specifically, the performance of the 3.5PN templates is contrasted against its 2PN counterpart using a waveform which is averaged over the LISA pattern functions. The improvement due to the higher order corrections to the phasing formula is examined by calculating the errors in the estimation of mass parameters at each order. The estimation of the mass parameters ${\cal M}$ and $\eta$ are significantly enhanced by using the 3.5PN waveform instead of the 2PN one. For an equal mass binary of $2\times10^6M_\odot$ at a luminosity distance of 3 Gpc, the improvement in chirp mass is $\sim 11$ and that of $\eta$ is $\sim 39$. Estimation of coalescence time $t_c$ worsens by 43%. The improvement is larger for the unequal mass binary mergers. These results are compared to the ones obtained using a non-pattern averaged waveform. The errors depend very much on the location and orientation of the source and general conclusions cannot be drawn without performing Monte Carlo simulations. Finally the effect of the choice of the lower frequency cut-off for LISA on the parameter estimation is studied.Comment: 12 pages, 5 figures (eps) significant revision, accepted for publication in Phys. Rev. D. Matches with the published versio

Matched-filter study and energy budget suggest no detectable gravitational-wave 'extended emission' from GW170817

Van Putten & Della Valle (2018) have reported a possible detection of gravitational-wave 'extended emission' from a neutron star remnant of GW170817. Starting from the time-frequency evolution and total emitted energy of their reported candidate, we show that such an emission is not compatible with the current understanding of neutron stars. We explore the additional required physical assumptions to make a full waveform model, for example, taking the optimistic emission from a spining-down neutron star with fixed quadrupolar deformation, and study whether even an ideal single-template matched-filter analysis could detect an ideal, fully phase-coherent signal. We find that even in the most optimistic case an increase in energy and extreme parameters would be required for a confident detection with LIGO sensitivity as of 2018-08-17. The argument also holds for other waveform models following a similar time-frequency track and overall energy budget. Single-template matched filtering on the LIGO data around GW170817, and on data with added simulated signals, verifies the expected sensitivity scaling and the overall statistical expectation.Comment: 9 pages, 6 figures, updated version as accepted by MNRA

Binary black hole detection rates in inspiral gravitational wave searches

The signal-to-noise ratios (SNRs) for quasi-circular binary black hole inspirals computed from restricted post-Newtonian waveforms are compared with those attained by more complete post-Newtonian signals, which are superpositions of amplitude-corrected harmonics of the orbital phase. It is shown that if one were to use the best available amplitude-corrected waveforms for detection templates, one should expect SNRs in actual searches to be significantly lower than those suggested by simulations based purely on restricted waveforms.Comment: 9 pages, 1 figur

Parameter estimation of compact binaries using the inspiral and ringdown waveforms

We analyze the problem of parameter estimation for compact binary systems that could be detected by ground-based gravitational wave detectors. So far this problem has only been dealt with for the inspiral and the ringdown phases separately. In this paper, we combine the information from both signals, and we study the improvement in parameter estimation, at a fixed signal-to-noise ratio, by including the ringdown signal without making any assumption on the merger phase. The study is performed for both initial and advanced LIGO and VIRGO detectors.Comment: matching cqg versio

Lie groups of conformal motions acting on null orbits

Space-times admitting a 3-dimensional Lie group of conformal motions $C_3$ acting on null orbits are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespectively of the matter content) and then all possible perfect fluid solutions are found, although none of these verify the weak and dominant energy conditions over the whole space-time manifold.Comment: 5 pages, Late

Spectral Line Removal in the LIGO Data Analysis System (LDAS)

High power in narrow frequency bands, spectral lines, are a feature of an interferometric gravitational wave detector's output. Some lines are coherent between interferometers, in particular, the 2 km and 4 km LIGO Hanford instruments. This is of concern to data analysis techniques, such as the stochastic background search, that use correlations between instruments to detect gravitational radiation. Several techniques of `line removal' have been proposed. Where a line is attributable to a measurable environmental disturbance, a simple linear model may be fitted to predict, and subsequently subtract away, that line. This technique has been implemented (as the command oelslr) in the LIGO Data Analysis System (LDAS). We demonstrate its application to LIGO S1 data.Comment: 11 pages, 5 figures, to be published in CQG GWDAW02 proceeding