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LIGO-Aundha (A1), the Indian gravitational wave detector, is expected to jointhe IGWN and begin operations in the early 2030s. We study the impact of A1 onthe accuracy of determining the direction of incoming transient signals fromcoalescing BNS sources with moderately high SNRs. It is conceivable that A1'ssensitivity, effective bandwidth, and duty cycle will improve incrementallythrough multiple detector commissioning rounds to achieve the desired `LIGO-A+'design sensitivity. For this purpose, we examine A1 under two distinct noisePSDs. One mirrors the conditions during the O4 run of the LIGO Hanford andLivingston detectors, simulating an early commissioning stage, while the otherrepresents the A+ design sensitivity. We consider various duty cycles of A1 atthe sensitivities mentioned above for a comprehensive analysis. We show thateven at the O4 sensitivity with a modest $20\%$ duty cycle, A1's addition tothe IGWN leads to a $15\%$ reduction in median sky-localization errors ($\Delta\Omega_{90\%}$) to $5.6$~sq.~deg. At its design sensitivity and $80\%$ dutycycle, this error shrinks further to $2.4$~sq.~deg, with 84\% sources localizedwithin 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 inreducing the localization uncertainties of the BNS source. Our results areobtained from a large Bayesian PE study using simulated signals injected in aheterogeneous network of detectors using the recently developed meshfreeapproximation aided rapid Bayesian inference pipeline. We consider a seismiccut-off frequency of 10 Hz for all the detectors. We also present hypotheticalimprovements in sky localization for a few GWTC-like events injected in realdata and demonstrate A1's role in resolving the degeneracy between theluminosity distance and inclination angle parameters.

How I wonder where you are: pinpointing coalescing binary neutron star sources with the IGWN, including LIGO-Aundha