A ${\chi }^2$ statistic for the identification of strongly lensed gravitational waves from compact binary coalescences

Abstract

Gravitational waves (GWs) emanated by stellar mass compact binary coalescences (CBCs), and lensed by galaxy- or cluster-scale lenses, will produce two or more copies of the GW signal. These will have identical phase evolution but differing amplitudes. Such lensing signatures are expected to be detected by the end of the LIGO-Virgo-Kagra's (LVK's) fifth observing run (O5). In this work, we propose a novel ${\chi }_{\mathrm{lens}}^2$ statistic to segregate pairs of detected GW events as either lensed or unlensed, using templates typically used in GW searches. The statistic is an application of the generalized ${\chi }^2$ discriminator described in \citet{dhurandhar2017}, tailored to probe the similarity (or lack thereof) between the phase evolutions of two CBC signals. We assess the performance of ${\chi }_{\mathrm{lens}}^2$ on a realistic astrophysical dataset of lensed and unlensed CBCs detectable in O4, assuming a single LIGO-like detector at design sensitivity. We find that we can correctly identify lensed events with efficiencies comparable to existing Bayesian and machine learning methods. Evaluating ${\chi }_{\mathrm{lens}}^2$ is orders of magnitude faster than Bayesian methods. Moreover, the statistics of ${\chi }_{\mathrm{lens}}^2$, in stationary Gaussian noise, are fully understood, in contrast to machine learning methods. ${\chi }_{\mathrm{lens}}^2$ can, therefore, be used to rapidly and accurately weed out the vast majority of unlensed candidate pairs and identify lensed pairs.

16 pages, 8 figures

References in corpus (32)

• The NumPy array: a structure for efficient numerical computation
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
• Observation of gravitational waves from two neutron star-black hole coalescences
• Properties and astrophysical implications of the 150 Msun binary black hole merger GW190521
• The LIGO Open Science Center
• 4-OGC: Catalog of gravitational waves from compact-binary mergers
• Search for gravitational lensing signatures in LIGO-Virgo binary black hole events
• New binary black hole mergers in the LIGO--Virgo O3a data
• Probing the non-linear structure of general relativity with black hole binaries
• A template bank to search for gravitational waves from inspiralling compact binaries I: physical models
• What if LIGO's gravitational wave detections are strongly lensed by massive galaxy clusters?
• Advanced LIGO detector performance in the fourth observing run
• Observational signatures of microlensing in gravitational waves at LIGO/Virgo frequencies
• Gravitational waves from inspiralling compact binaries: hexagonal template placement and its efficiency in detecting physical signals
• Constraints on compact dark matter from gravitational wave microlensing
• Constraining cosmological parameters in FLRW metric with lensed GW+EM signals
• On the identification of individual gravitational wave image types of a lensed system using higher-order modes
• On building a cluster watch-list for identifying strongly lensed supernovae, gravitational waves and kilonovae
• Improved statistic to identify strongly lensed gravitational wave events
• Cosmography using strongly lensed gravitational waves from binary black holes
• Detection and parameter estimation challenges of Type-II lensed binary black hole signals
• Exploring the Impact of Microlensing on Gravitational Wave Signals: Biases, Population Characteristics, and Prospects for Detection
• Detectability of microlensed gravitational waves
• The Return of GOLUM: Improving Distributed Joint Parameter Estimation for Strongly-Lensed Gravitational Waves
• Identifying strongly lensed gravitational waves through their phase consistency
• A unified approach to ${\chi }^2$ discriminators for searches of gravitational waves from compact binary coalescences
• Microlensing bias on the detection of strong lensing gravitational wave
• GLANCE -- Gravitational Lensing Authenticator using Non-Modelled Cross-Correlation Exploration of Gravitational Wave Signals
• Prospects for the observation of continuous gravitational waves from spinning neutron stars lensed by the galactic supermassive black hole