The angular resolution of GRAPES-3 EAS array after correction for the shower front curvature

The angular resolution of an extensive air shower (EAS) array plays a critical role in determining its sensitivity for the detection of point $\gamma$-ray sources in the multi-TeV energy range. The GRAPES-3 an EAS array located at Ooty in India (11.4$^{\circ}$N, 76.7$^{\circ}$E, 2200 m altitude) is designed to study $\gamma$-rays in the TeV-PeV energy range. It comprises of a dense array of 400 plastic scintillators deployed over an area of 25000 m$^2$ and a large area (560 m$^2$) muon telescope. A new statistical method allowed real time determination of the propagation delay of each detector in the GRAPES-3 array. The shape of shower front is known to be curved and here the details of a new method developed for accurate measurement of the shower front curvature is presented. These two developments have led to a sizable improvement in the angular resolution of GRAPES-3 array. It is shown that the curvature depends on the size and age of an EAS. By employing two different techniques, namely, the odd-even and the left-right methods, independent estimates of the angular resolution are obtained. The odd-even method estimates the best achievable resolution of the array. For obtaining the angular resolution, the left-right method is used after implementing the size and age dependent curvature corrections. A comparison of the angular resolution as a function of EAS energy by these two methods shows them be virtually indistinguishable. The angular resolution of GRAPES-3 array is 47$^{\prime}$ for energies E$>$5 TeV and improves to 17$^{\prime}$ at E$>$100 TeV and finally approaching 10$^{\prime}$ at E$>$500 TeV.