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 IGWN and begin operations in the early 2030s. We study the impact of A1 on the accuracy of determining the direction of incoming transient signals from coalescing BNS sources with moderately high SNRs. 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 PSDs. One mirrors the conditions during the O4 run 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 ($\Delta \Omega_{90\%}$) 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! Even in the worst-case scenario, where signals are sub-threshold in A1, we demonstrate its critical role in reducing the localization uncertainties of the BNS source. Our results are obtained from a large Bayesian PE 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 GWTC-like events injected in real data and demonstrate A1's role in resolving the degeneracy between the luminosity distance and inclination angle parameters.