Pinpointing coalescing binary neutron star sources with the IGWN, including LIGO-Aundha

LIGO-Aundha (A1), the Indian gravitational wave detector, is expected to join the International Gravitational-Wave Observatory Network (IGWN) and begin operations in the early 2030s. We study the impact of this additional detector on the accuracy of determining the direction of incoming transient signals from coalescing binary neutron star (BNS) sources with moderately high signal-to-noise ratios. It is conceivable that A1's sensitivity, effective bandwidth, and duty cycle will improve incrementally through multiple detector commissioning rounds to achieve the desired 'LIGO-A+' design sensitivity. For this purpose, we examine A1 under two distinct noise power spectral densities. One mirrors the conditions during the fourth science run (O4) of the LIGO Hanford and Livingston detectors, simulating an early commissioning stage, while the other represents the A+design sensitivity. We consider various duty cycles of A1 at the sensitivities mentioned above for a comprehensive analysis. We show that even at the O4 sensitivity with a modest 20% duty cycle, A1's addition to the IGWN leads to a 15% reduction in median sky-localization errors (Δω90%) to 5.6 sq. deg. At its design sensitivity and 80% duty cycle, this error shrinks further to 2.4 sq. deg, with 84% sources localized within a nominal error box of 10 sq. deg. This remarkable level of accuracy in pinpointing sources will have a positive impact on Gravitational Wave (GW) astronomy and cosmology. Even in the worst-case scenario, where signals are subthreshold in A1, we demonstrate its critical role in reducing the localization uncertainties of the BNS source. Our results are obtained from a large Bayesian parameter estimation study using simulated signals injected in a heterogeneous network of detectors using the recently developed meshfree approximation aided rapid Bayesian inference pipeline. We consider a seismic cut-off frequency of 10 Hz for all the detectors. We also present hypothetical improvements in sky localization for a few Gravitational-Wave Transient Catalog-like events injected in real data after including a hypothetical A1 detector to the subnetwork in which such events were originally detected. We also demonstrate that A1's inclusion could resolve the degeneracy between the luminosity distance and inclination angle parameters, even in scenarios where A1 does not directly contribute to improving the network signal-to-noise ratio for the event.