The Indian Pulsar Timing Array Data Release 2: III. Search for a Stochastic Gravitational Wave Background

We present the first independent search for an isotropic stochastic gravitational wave background in the second data release of the Indian Pulsar Timing Array, comprising of 27 millisecond pulsars monitored simultaneously in two frequency bands with the upgraded Giant Metrewave Radio Telescope over a maximum 7.2 year baseline. Building on a comprehensive single pulsar noise analysis, we search for a common uncorrelated red noise process within a Bayesian inference framework and with the noise-marginalized optimal statistics, and we test the robustness of the result through per-pulsar dropout analyses and solar-wind exclusion cuts. Leaving the spectral index free, we recover a broad amplitude posterior, $\log_{10} A_{\rm CURN} = -13.71^{+1.06}_{-3.28}$, with an unconstrained spectral index $\gamma_{\rm CURN} = 2.98^{+3.62}_{-2.70}$ and a Savage-Dickey Bayes factor of $2.5$ for a common red process over the no signal model. The optimal-statistic signal to noise ratios for the monopole, dipole, and Hellings-Downs correlations are all consistent with zero. Fixing the spectral index to $\gamma = 13/3$, the value predicted by an idealized toy model in which the background is sourced by a population of supermassive black hole binaries in circular orbits evolving purely under leading-order gravitational radiation reaction, we place a $95\%$ upper limit on the common-process amplitude of $A_{\rm GWB} < 3.4\times10^{-14}$, stable across solar elongation cuts of $10^\circ$, $20^\circ$, and $30^\circ$. This limit lies approximately an order of magnitude above the amplitudes reported by other, longer-running pulsar timing array experiments. We also demonstrate through simulated datasets with the addition of simple chromatic and achromatic noise components that it will take at least a 10 year baseline to start recovering the common red noise signal.