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Correlations in Parameter Estimation of Low-Mass Eccentric Binaries: GW151226 & GW170608

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Correlations in Parameter Estimation of Low-Mass Eccentric Binaries: GW151226 & GW170608 Correlations in parameter estimation of low-mass eccentric binaries: GW151226 & GW170608 Eamonn O'Shea1, ∗ and Prayush Kumar1, 2 1Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca, New York 14853, USA 2International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India (Dated: July 19, 2021) 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 ≈ 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. I. INTRODUCTION interactions can produce multiple generations of merg- ers. Such formation channels lead to binaries with higher As of 2021, the Laser Interferometer Gravitatonal-wave mass [24, 25] that can lie in the supernova pair-instability Observatory (LIGO) and the Virgo observatory have de- mass gap [26, 27], isotropic spins [18, 28], and eccentric- tected gravitational wave (GW) signals from dozens of ity [29{31]. In such cases the eccentricity of a binary can binary black hole (BBH) mergers during their first three be driven to non-zero values through the Lidov-Kozai ef- observing runs [1]. As the field of gravitational wave fect [32, 33]. By performing Monte Carlo simulations of astronomy moves forward, the network of Earth-based such dense clusters, it has been shown [34, 35] that on detectors will be joined by KAGRA [2] and LIGO In- the order of 5% of mergers in globular clusters can have dia [3] in the coming few years, and possibly followed eccentricity > 0:1 when the frequency of their orbits en- up by third-generation instruments such as the Cosmic ters the sensitivity band of terrestrial GW detectors at Explorer (CE) [4] and the Einstein Telescope (ET) [5]. 10 Hz. Interactions within AGN disks can also lead to Expanding the network to include more geographical lo- binaries with measurable eccentricity [36, 37]. Orbital cations will improve the sky localization of events, and eccentricity is therefore striking evidence that can con- the increased sensitivity of future detectors (CE and ET) clusively establish dense clusters as breeding grounds for will increase our detection rates, particularly at lower fre- compact binary mergers. quencies. The presence of eccentricity in any of the gravitational The mechanisms of formation and merging of these waveforms seen thus far has yet to be conclusively estab- binary systems are the subject of active research [6{9]. lished. Direct searches for eccentric neutron-star candi- One possibility is that of isolated binary formation, either dates in LIGO's O2 data have yielded no detections [38{ through formation of a common envelope phase [10{12], 40]. There have also been studies [41, 42] to measure or- or through chemically homogeneous evolution [13, 14]. bital eccentricities of merger events in GWTC-1, and the arXiv:2107.07981v1 [astro-ph.HE] 16 Jul 2021 This formation channel generally results in black holes eccentricities of the two neutron star events [43]. While < with lower masses, ∼ 50 M , and aligned spins [15]. they agree that most observed GW signals are sourced Another possible formation channel that can account from quasi-circular binary mergers, one of the studies for the rate of mergers seen is that of dynamical binary finds evidence of residual orbital eccentricity in a couple evolution in dense globular clusters [16{20] or in AGN of events [42]. There is statistical evidence that at least disks [21{23]. In the case of dense environments, bi- one merger in GWTC-2 is the result of hierarchical merg- nary black holes merge after undergoing many interac- ers [9] and that GW190521 is favoured to have formed tions with third bodies or other binaries. Dynamical from the merger of second generation black holes [44], or possibly through dynamical capture [45]. There is some evidence that it could be the result of an eccentric merger [46], although it could be indistinguishable from ∗ [email protected] a precessing, quasi-circular binary merger [47] given the 2 short length of the signal. related with the measured masses and spins implies that Our ability to accurately determine the eccentricity of non-spinning eccentric approximants may be insufficient mergers such as GW190521 [39] should increase as the for the measurement of eccentricities of binary black network of detectors expands to include deciHertz de- holes, especially if the objects are spinning. tectors [48, 49]. It has been shown that the addition In Section II we describe our methods, including a de- of detectors such as Cosmic Explorer and the Einstein scription of the waveform models we use in II A. In Sec- Telescope will increase signal-to-noise ratio (SNR) of ec- tion II B we describe the setup for our parameter esti- centric signals, in some cases to higher SNRs than similar mation runs using BILBY. Section III C details the eccen- quasi-circular systems [50]. tric simulated signals and results of their recovery with There has been previous work to investigate the effect quasi-circular templates. In section III B we employ a that eccentric signals can have on the detectability of full IMR, eccentric waveform to perform parameter esti- eccentric signals when the quasi-circular template banks mation on the two GW events described above, with and that LIGO/Virgo currently employs are used [51, 52]. without spins included in our prior. We follow up our Mildly eccentric systems can still be detected by the studies on real events in Section III C by simulating the pipelines, but with a loss of SNR. However, moderately best fit quasi-circular parameters for these events, and performing inference with the same eccentric IMR model eccentric (e0 > 0:275) systems would likely be missed by search pipelines [53]. Once detected, ignoring eccentric- to determine how their parameters would be recovered if ity could still lead us to infer with biases other intrinsic they were truly non-eccentric. parameters of the source. Throughout, we refer to mass as measured in the de- In this paper we pursue two related goals. The first tector frame. We denote eccentricity as e0, meaning ec- is to understand how our lack of inclusion of orbital centricity at a particular reference frequency. eccentricity in waveform templates alters our inference on the source parameters of GW signals. To this end we simulate a set of eccentric inspiral-merger-ringdown II. METHODS (IMR) signals and perform Bayesian parameter estima- tion on them using waveform templates that represent A. Waveform models binary mergers on quasi-circular orbits. We find that as we increase the orbital eccentricity of GW sources, our Detection and characterization of the source properties quasi-circular templates furnish larger chirp mass values of eccentric signals require accurate and efficient wave- and less asymmetric mass ratios than the those simu- form models. Some of the existing waveform models use lated. Although eccentricity alters the rate of inspiral in a post-Newtonian description and only predict the inspi- the same way a larger chirp mass does [54], it also intro- ral portion of the signal, such as the EccentricFD [58] duces modulations in the orbital frequency as a function and EccentricTD [59], which are both implemented in of time to make the phase evolution qualitatively very LALsuite [60]. Recently, models have been developed different from what a shift in binary masses does. This to produce full inspiral-merger-ringdown (IMR) wave- bias is therefore not obvious, especially when considering form for eccentric binaries, by hybridizing eccentric inspi- the full inspiral-merger-ringdown. We quantify the bias ral signals with a quasi-circular merger-ringdown portion to find an O(10%) drift in chirp mass measurement alone (ENIGMA) [53], through an effective one-body (EOB) for- in the case of low-mass binaries with moderate SNRs (20- malism [61, 62], or by surrogate modelling of numerical 30), which is significant given that the measurement pre- relativity waveforms [63]. cision on the chirp mass is smaller than O(1%). We also The first eccentric model we use is the inspiral portion find a similarly significant bias in the measurement of bi- of ENIGMA [53]. ENIGMA is a time-domain model designed nary mass ratio. Our quantitative findings are consistent to produce full inspiral-merger-ringdown waveforms up with previous results [43, 55]. to moderate eccentricities. ENIGMA incorporates correc- Our second goal is to investigate whether this bias ap- tions for the energy flux of quasi-circular binaries and pears with real GW events [56]. To this end, we show that gravitational self-force corrections to the binding energy GW151226 and GW170608 are possibly eccentric binary of compact binaries up to 6PN order.
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