Binary Black Hole inspirals cannot hide their eccentricity

Abstract

The events detected by the LIGO Virgo KAGRA collaboration over a period of 10 years have yielded a treasure trove of signals from compact binary coalescences. None of these events have shown a confident signature of eccentricity. With upgrades to the existing network and potential next generation gravitational wave detectors, we will be able to see much further into the universe increasing the likelihood of detecting eccentric systems. We improve upon the phenomenological approach of providing eccentricity constraints using an effective chirp mass model in the time frequency domain. We introduce an improved pixel collection method along with a likelihood based sampling approach inspired by Bayesian parameter estimation. Our approach constructs a likelihood from the product of energies collected across different eccentric harmonics in the time frequency representation. This formulation enables coarse but meaningful constraints on orbital eccentricity. Additionally, we incorporate information from the energy ratios between eccentric harmonics, further refining the eccentricity estimates. We test our approach on 500 non spinning equal mass eccentric systems and demonstrate that we can constrain the eccentricity within 0.2 around the true value. Moreover, our approach can deliver these constraints in 5 minutes on a machine with 50 cores. These results demonstrate that our phenomenological approach provides fast and reasonably accurate eccentricity estimates, making it a promising tool for rapid gravitational wave data analysis.

Figures (10)

• Figure 1: A histogram of SNRs for signals simulated with the GWTC-3 population parameters over an observation time of 1.5 years, assuming a merger rate density of $44\mathrm{Gpc^{-3}yr^{-1}}$
• Figure 2: Schematic explaining the bright pixel extraction methodology. In subfigure (b), we have plotted the Q-transform of a gw data, which is obtained by injecting a signal for an eccentric-bbh system ($\mathcal{M}=15 M_{\odot}$, $e_{10}=0.2$) into Advanced LIGO noise with SNR=100. The subfigure (a) on the top plots the corresponding energy distribution of the pixels. The green patch in this figure denotes the bright pixels with an energy lower cutoff (denoted by the vertical black dashed line). The subfigure (c) plots the bright pixels separately to show the fundamental and first eccentric harmonic track.
• Figure 3: Comparison of the performance of the new pixel extraction and stochastic sampling recovery methodology. Subfigure (d) plots the pixels extracted from bright pixels obtained in Fig. \ref{['fig:tfmap']} using the energy-informed method for the fundamental mode. It also plots the fundamental track for the injected ($15 M_{\odot}$, $0.2$) system (denoted by black solid line) using ECMM. The three subfigures on top plot the recovery contours for the injected system using (a) Fixed-Width pixel extraction with grid-based recovery, (b) Energy Informed pixel extraction with grid-based recovery, and (c) Energy Informed pixel extraction with stochastic sampling-based recovery. The blue star denotes the injected ($15 M_{\odot}$, $0.2$) system.
• Figure 4: 90th percentile contours for a few injections as recovered with the product likelihood and a restricted chirp mass prior along with the injected parameters. The points within the contours mark the injected values
• Figure 5: This figure plots 500 systems injected in A+ noise at an SNR of 100 and shows the eccentricity constraint as recovered by the product likelihoods for a known chirp mass. We discard systems where the injected value lies outside the 90th percentile contour.