The second data release from the European Pulsar Timing Array
Authors:   EPTA Collaboration and InPTA Collaboration:, Antoniadis J. , Arumugam P. , Arumugam S. , Babak S. , Bagchi M. , Bak Nielsen A.-S. , Bassa C. G. , Bathula A. , Berthereau A. , Bonetti M. , Bortolas E. , Brook P. R. , Burgay M. , Caballero R. N. , Chalumeau A. , Champion D. J. , Chanlaridis S. , Chen S. , Cognard I. , Dandapat S. , Deb D. , Desai S. , Desvignes G. , Dhanda-Batra N. , Dwivedi C. , Falxa M. , Ferdman R. D. , Franchini A. , Gair J. R. , Goncharov B. , Gopakumar A. , Graikou E. , Grießmeier J.-M. , Guillemot L. , Guo Y. J. , Gupta Y. , Hisano S. , Hu H. , Iraci F. , Izquierdo-Villalba D. , Jang J. , Jawor J. , Janssen G. H. , Jessner A. , Joshi B. C. , Kareem F. , Karuppusamy R. , Keane E. F. , Keith M. J. , Kharbanda D. , Kikunaga T. , Kolhe N. , Kramer M. , Krishnakumar M. A. , Lackeos K. , Lee K. J. , Liu K. , Liu Y. , Lyne A. G. , McKee J. W. , Maan Y. , Main R. A. , Mickaliger M. B. , Niţu I. C. , Nobleson K. , Paladi A. K. , Parthasarathy A. , Perera B. B. P. , Perrodin D. , Petiteau A. , Porayko N. K. , Possenti A. , Prabu T. , Quelquejay Leclere H. , Rana P. , Samajdar A. , Sanidas S. A. , Sesana A. , Shaifullah G. , Singha J. , Speri L. , Spiewak R. , Srivastava A. , Stappers B. W. , Surnis M. , Susarla S. C. , Susobhanan A. , Takahashi K. , Tarafdar P. , Theureau G. , Tiburzi C. , van der Wateren E. , Vecchio A. , Venkatraman Krishnan V. , Verbiest J. P. W. , Wang J. , Wang L. , Wu Z. 
Published: June 2023

We present the results of the search for an isotropic stochastic gravitational wave background (GWB) at nanohertz frequencies using the second data release of the European Pulsar Timing Array (EPTA) for 25 millisecond pulsars and a combination with the first data release of the Indian Pulsar Timing Array (InPTA). A robust GWB detection is conditioned upon resolving the Hellings-Downs angular pattern in the pairwise cross-correlation of the pulsar timing residuals. Additionally, the GWB is expected to yield the same (common) spectrum of temporal correlations across pulsars, which is used as a null hypothesis in the GWB search. Such a common-spectrum process has already been observed in pulsar timing data. We analysed (i) the full 24.7-year EPTA data set, (ii) its 10.3-year subset based on modern observing systems, (iii) the combination of the full data set with the first data release of the InPTA for ten commonly timed millisecond pulsars, and (iv) the combination of the 10.3-year subset with the InPTA data. These combinations allowed us to probe the contributions of instrumental noise and interstellar propagation effects. With the full data set, we find marginal evidence for a GWB, with a Bayes factor of four and a false alarm probability of 4%. With the 10.3-year subset, we report evidence for a GWB, with a Bayes factor of 60 and a false alarm probability of about 0.1% (≳3σsignificance). The addition of the InPTA data yields results that are broadly consistent with the EPTA-only data sets, with the benefit of better noise modelling. Analyses were performed with different data processing pipelines to test the consistency of the results from independent software packages. The latest EPTA data from new generation observing systems show non-negligible evidence for the GWB. At the same time, the inferred spectrum is rather uncertain and in mild tension with the common signal measured in the full data set. However, if the spectral index is fixed at 13/3, the two data sets give a similar amplitude of (2.5 ± 0.7) × 10−15at a reference frequency of 1 yr−1. Further investigation of these issues is required for reliable astrophysical interpretations of this signal. By continuing our detection efforts as part of the International Pulsar Timing Array (IPTA), we expect to be able to improve the measurement of spatial correlations and better characterise this signal in the coming years.