Sky localization and polarization mode reconstruction of gravitational waves from GW170104 and GW150914

The detections (Abbott et al. in Astrophys. J. Suppl. Ser. 267(2):29, 2023; Abbott et al. in SoftwareX 13:100658, 2021) and analysis of gravitational waves (GWs) have introduced us in a new era of our understanding of the cosmos, providing new insights into astrophysical systems involving massive objects as black holes and neutron stars. Normally the precise sky localization of a GW source needs data from three or more observatories (Abbott et al. in Phys. Rev. Lett. 116(22):221101, 2016c; Abbott et al. in Phys. Rev. Lett. 119(14):141101, 2017c). However, the results presented in this article demonstrate that it is in fact possible to obtain the position of a GW source in a small region of the celestial sphere using data from just two GW observatories, in this case LIGO Hanford and LIGO Livingston. Furthermore, we are also able to reconstruct the gravitational-wave polarization (Poisson and Will in Gravity: Newtonian, Post-Newtonian, Relativistic, Cambridge University Press, Cambridge, 2014) modes (PMs) for the GW170104 (Abbott et al. in GW170104: observation of a 50-solar-mass binary black hole coalescence at redshift 0.2. Phys. Rev. Lett. 118(22):221101, 2017b) and GW150914 (Abbott et al. in Phys. Rev. D 93(12):122003, 2016a) events, with data from only these two detectors. The procedure only uses the spin 2 properties of the GW, so that it does not rely on specific assumptions on the nature of the source. Our findings are possible through careful data filtering methods (Moreschi in J. Cosmol. Astropart. Phys. 1904:032, 2019), the use of refined signal processing algorithms (Moreschi in Astrophys. Space Sci. 369(1):12, 2024), and the application of dedicated denoising (Mallat in A Wavelet Tour of Signal Processing: The Sparse Way, Elsevier, Amsterdam, 2009) techniques. This progress in the GW studies represents the first instance of a direct measurement of PMs using such a limited observational data. We provide detailed validation through the reconstruction of PMs for different polarization angles, and calculations of residuals for the GW170104 event. We also test the procedure with synthetic data with ten different source locations and polarization angles.