[Paper Review] LIGO-Virgo events localization as a test of gravitational wave polarization state

Liudmila Fesik, Baryshev, Yu. V.+2 more|arXiv (Cornell University)|Feb 11, 2017

Pulsars and Gravitational Waves Research4 references3 citations

TL;DR

This paper proposes a novel method to determine the polarization state of gravitational waves using sky localization from LIGO-Virgo detector networks, leveraging time delays and strain ratios between detectors. It finds that apparent circles of allowed source positions for GW150914, GW151226, and LVT151012 are parallel to the Local Super-Cluster plane, suggesting these events may be associated with this large-scale structure, while GW170104's apparent circle is perpendicular but still consistent with the LSC plane via its optical counterpart ATLAS17aeu.

ABSTRACT

The detection of the gravitational wave events GW150914, GW151226, LVT 151012 and GW170104 by the Advanced LIGO antennas has opened a new possibility for the study of fundamental physics of gravitational interaction. We suggest a new method for determining the polarization state of a gravitational wave, which is independent of the nature of a GW source. For this, we calculate the allowed sky positions of GW sources along apparent circles. This is done for each polarization state by considering the sensitivity pattern of each antenna and relative amplitudes of detected signals. The positions of circles are calculated with respect to the line joining both LIGO antennas using the observed arrival time delay of the signal between them. The apparent circles (AC) on the sky for allowed positions of the GW sources for the GW150914, GW151226 and LVT151012 events are parallel to the plane of the disc-like large scale structure known as the Local Super-Cluster (LSC) of galaxies which extends up to radius $\sim 100$ Mpc and having thickness $\sim 30$ Mpc. For the GW170104 event, the AC is perpendicular to the LSC plane but the predicted position of the source may also belong to the LSC plane, which is consistent with detection of possible optical counterpart ATLAS17aeu. The next aLIGO-aVirgo observing runs are proposed to test the possibility of clustering the GW sources along the LSC plane.

Motivation & Objective

• To develop a polarization-independent method for determining gravitational wave polarization states using interferometric detector networks.
• To test whether observed gravitational wave events are consistent with tensor or scalar polarization modes.
• To investigate whether the spatial distribution of detected GW sources correlates with large-scale structures like the Local Super-Cluster.
• To provide a framework for distinguishing between tensor and scalar polarization states using strain ratios and time delays between detectors.
• To guide future observing runs in testing the clustering of GW sources along the supergalactic plane.

Proposed method

• The method calculates apparent circles (ACs) on the sky for allowed GW source positions based on detector sensitivity patterns and relative signal amplitudes for each assumed polarization state.
• It uses the time delay between signals at two detectors (LIGO-Livingston and LIGO-Hanford) to constrain the source direction relative to the baseline between them.
• For each polarization state—plus, cross, scalar longitudinal, and scalar transverse—theoretical strain ratios are computed and compared with observed strain ratios from the detectors.
• The G-factor formalism is applied to model detector response, and the ratio of G-factors at detector pairs is used to predict strain ratios for different polarization modes.
• Theoretical ACs are computed in supergalactic coordinates and compared with actual event localizations to infer polarization.
• Artificial sources are simulated both inside and outside the supergalactic plane to test the method’s ability to distinguish polarization states.

Experimental results

Research questions

• RQ1 Can the polarization state of a gravitational wave be determined independently of the source’s astrophysical nature using only detector response and time delay information?
• RQ2 Do the observed sky localizations of LIGO-Virgo events align with the plane of the Local Super-Cluster, suggesting a physical association?
• RQ3 Can a network of two-armed interferometers distinguish between tensor and scalar polarization modes based on strain ratio and beam pattern analysis?
• RQ4 Is the apparent circle of allowed source positions for a GW event sensitive to the polarization state, and can this be used to test alternative gravity theories?
• RQ5 Does the presence of an optical counterpart (e.g., ATLAS17aeu) for GW170104 support the hypothesis that the event lies within the Local Super-Cluster plane?

Key findings

• For GW150914, GW151226, and LVT151012, the apparent circles of allowed source positions are parallel to the supergalactic plane of the Local Super-Cluster, indicating possible association with this large-scale structure.
• For GW170104, the apparent circle is perpendicular to the supergalactic plane, but the predicted source position still lies within ±30° of the plane, consistent with the optical counterpart ATLAS17aeu being located in the Local Super-Cluster.
• The method successfully distinguishes between tensor and scalar polarization modes using two-armed interferometers, but cannot differentiate between scalar longitudinal and transverse modes without one-arm detectors.
• Simulations with artificial sources confirm that the method can distinguish polarization states based on strain ratio and AC geometry, especially when sources are located inside or outside the supergalactic plane.
• The observed clustering of GW events along the supergalactic plane is unlikely to be a random coincidence, especially given the high distances (~400–1000 Mpc) of the events.
• The results support the hypothesis that future aLIGO-aVirgo observing runs should test for clustering of GW sources along the supergalactic plane to further validate polarization-dependent localization.