Active-sterile neutrino oscillations at INO-ICAL over a wide mass-squared range

We perform a detailed analysis for the prospects of detecting active-sterile oscillations involving a light sterile neutrino, over a large $\Delta m^2_{41}$ range of $10^{-5}$ eV$^2$ to $10^2$ eV$^2$, using 10 years of atmospheric neutrino data expected from the proposed 50 kt magnetized ICAL detector at the INO. This detector can observe the atmospheric $\nu_{\mu}$ and $\bar\nu_{\mu}$ separately over a wide range of energies and baselines, making it sensitive to the magnitude and sign of $\Delta m^2_{41}$ over a large range. If there is no light sterile neutrino, ICAL can place competitive upper limit on $|U_{\mu 4}|^2 \lesssim 0.02$ at 90\% C.L. for $\Delta m^2_{41}$ in the range $(0.5 - 5) \times 10^{-3}$ eV$^2$. For the same $|\Delta m^2_{41}|$ range, ICAL would be able to determine its sign, exploiting the Earth's matter effect in $\mu^{-}$ and $\mu^{+}$ events separately if there is indeed a light sterile neutrino in Nature. This would help identify the neutrino mass ordering in the four-neutrino mixing scenario.