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Register a new userCorrelations in parameter estimation of low-mass eccentric binaries: GW151226 & GW170608
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The eccentricity of binary black hole mergers is predicted to be an indicator of the history of their formation. In particular, eccentricity is a strong signature of dynamical formation rather than formation by stellar evolution in isolated stellar systems. It has been shown that searches for eccentric signals with quasi-circular templates can lead to loss of SNR, and some signals could be missed by such a pipeline. We investigate the efficacy of the existing quasi-circular parameter estimation pipelines to determine the source parameters of such eccentric systems. We create a set of simulated signals with eccentricity up to 0.3 and find that as the eccentricity increases, the recovered mass parameters are consistent with those of a binary with up to a $approx 10%$ higher chirp mass and mass ratio closer to unity. We also employ a full inspiral-merger-ringdown waveform model to perform parameter estimation on two gravitational wave events, GW151226 and GW170608, to investigate this bias on real data. We find that the correlation between the masses and eccentricity persists in real data, but that there is also a correlation between the measured eccentricity and effective spin. In particular, using a non-spinning prior results in a spurious eccentricity measurement for GW151226. Performing parameter estimation with an aligned spin, eccentric model, we constrain the eccentricities of GW151226 and GW170608 to be $<0.15$ and $<0.12$ respectively.
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On June 8, 2017 at 02:01:16.49 UTC, a gravitational-wave signal from the merger of two stellar-mass black holes was observed by the two Advanced LIGO detectors with a network signal-to-noise ratio of 13. This system is the lightest black hole binary so far observed, with component masses $12^{+7}_{-2},M_odot$ and $7^{+2}_{-2},M_odot$ (90% credible intervals). These lie in the range of measured black hole masses in low-mass X-ray binaries, thus allowing us to compare black holes detected through gravitational waves with electromagnetic observations. The sources luminosity distance is $340^{+140}_{-140}$ Mpc, corresponding to redshift $0.07^{+0.03}_{-0.03}$. We verify that the signal waveform is consistent with the predictions of general relativity.
We study the impact of gas accretion on the orbital evolution of black-hole binaries initially at large separation in the band of the planned Laser Interferometer Space Antenna (LISA). We focus on two sources: (i)~stellar-origin black-hole binaries~(SOBHBs) that can migrate from the LISA band to the band of ground-based gravitational-wave observatories within weeks/months; and (ii) intermediate-mass black-hole binaries~(IMBHBs) in the LISA band only. Because of the large number of observable gravitational-wave cycles, the phase evolution of these systems needs to be modeled to great accuracy to avoid biasing the estimation of the source parameters. Accretion affects the gravitational-wave phase at negative ($-4$) post-Newtonian order, and is therefore dominant for binaries at large separations. If accretion takes place at the Eddington or at super-Eddington rate, it will leave a detectable imprint on the dynamics of SOBHBs. In optimistic astrophysical scenarios, a multiwavelength strategy with LISA and a ground-based interferometer can detect about $10$ (a few) SOBHB events for which the accretion rate can be measured at $50%$ ($10%$) level. In all cases the sky position can be identified within much less than $0.4,{rm deg}^2$ uncertainty. Likewise, accretion at $gtrsim 10%$ ($gtrsim 100%$) of the Eddington rate can be measured in IMBHBs up to redshift $zapprox 0.1$ ($zapprox 0.5$), and the position of these sources can be identified within less than $0.01,{rm deg}^2$ uncertainty. Altogether, a detection of SOBHBs or IMBHBs would allow for targeted searches of electromagnetic counterparts to black-hole mergers in gas-rich environments with future X-ray detectors (such as Athena) and radio observatories (such as SKA).
Among the most eagerly anticipated opportunities made possible by Advanced LIGO/Virgo are multimessenger observations of compact mergers. Optical counterparts may be short-lived so rapid characterization of gravitational wave (GW) events is paramount for discovering electromagnetic signatures. One way to meet the demand for rapid GW parameter estimation is to trade off accuracy for speed, using waveform models with simplified treatment of the compact objects spin. We report on the systematic errors in GW parameter estimation suffered when using different spin approximations to recover generic signals. Component mass measurements can be biased by $>5sigma$ using simple-precession waveforms and in excess of $20sigma$ when non-spinning templates are employed. This suggests that electromagnetic observing campaigns should not take a strict approach to selecting which LIGO/Virgo candidates warrant follow-up observations based on low-latency mass estimates. For sky localization, we find searched areas are up to a factor of ${sim}$2 larger for non-spinning analyses, and are systematically larger for any of the simplified waveforms considered in our analysis. Distance biases for the non-precessing waveforms can be in excess of 100% and are largest when the spin angular momenta are in the orbital plane of the binary. We confirm that spin-aligned waveforms should be used for low-latency parameter estimation at the minimum. Including simple precession, though more computationally costly, mitigates biases except for signals with extreme precession effects. Our results shine a spotlight on the critical need for development of computationally inexpensive precessing waveforms and/or massively parallel algorithms for parameter estimation.
We present a Bayesian parameter-estimation pipeline to measure the properties of inspiralling stellar-mass black hole binaries with LISA. Our strategy (i) is based on the coherent analysis of the three noise-orthogonal LISA data streams, (ii) employs accurate and computationally efficient post-Newtonian waveforms accounting for both spin-precession and orbital eccentricity, and (iii) relies on a nested sampling algorithm for the computation of model evidences and posterior probability density functions of the full 17 parameters describing a binary. We demonstrate the performance of this approach by analyzing the LISA Data Challenge (LDC-1) dataset, consisting of 66 quasi-circular, spin-aligned binaries with signal-to-noise ratios ranging from 3 to 14 and times to merger ranging from 3000 to 2 years. We recover 22 binaries with signal-to-noise ratio higher than 8. Their chirp masses are typically measured to better than $0.02 M_odot$ at $90%$ confidence, while the sky-location accuracy ranges from 1 to 100 square degrees. The mass ratio and the spin parameters can only be constrained for sources that merge during the mission lifetime. In addition, we report on the successful recovery of an eccentric, spin-precessing source at signal-to-noise ratio 15 for which we can measure an eccentricity of $3times 10^{-3}$.
Eccentricity has emerged as a potentially useful tool for helping to identify the origin of black hole mergers. However, owing to the large number of harmonics required to compute the amplitude of an eccentric signal, eccentric templates can be computationally very expensive, making statistical analyses to distinguish distributions from different formation channels very challenging. In this paper, we outline a method for estimating the signal-to-noise ratio for inspiraling binaries at lower frequencies such as those proposed for LISA and DECIGO. Our approximation can be useful more generally for any quasi-periodic sources. We argue that surprisingly, the signal-to-noise ratio evaluated at or near the peak frequency (of the power) is well approximated by using a constant noise curve, even if in reality the noise strain has power law dependence. We furthermore improve this initial estimate over our previous calculation to allow for frequency-dependence in the noise to expand the range of eccentricity and frequency over which our approximation applies. We show how to apply this method to get an answer accurate to within a factor of two over almost the entire projected observable frequency range. We emphasize this method is not a replacement for detailed signal processing. The utility lies chiefly in identifying theoretically useful discriminators among different populations and providing fairly accurate estimates for how well they should work. This approximation can furthermore be useful for narrowing down parameter ranges in a computationally economical way when events are observed. We furthermore show a distinctive way to identify events with extremely high eccentricity where the signal is enhanced relative to naive expectations on the high frequency end.
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