Combining the second data release of the European Pulsar Timing Array with low-frequency pulsar data

¹ Dipartimento di Fisica, Università di Cagliari, Cittadella Universitaria, I-09042 Monserrato (CA), Italy
² INAF – Osservatorio Astronomico di Cagliari, via della Scienza 5, 09047 Selargius (CA), Italy
³ ASTRON, Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands
⁴ Florida Space Institute, University of Central Florida, 12354 Research Parkway, Orlando, FL 32826, USA
⁵ Physics, School of Natural Sciences, Ollscoil na Gaillimhe – University of Galway, University Road, Galway H91 TK33, Ireland
⁶ National Centre for Radio Astrophysics, Pune University Campus, Pune 411007, India
⁷ Dipartimento di Fisica “G. Occhialini”, Università degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
⁸ INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
⁹ Institute of Astrophysics, Foundation for Research & Technology – Hellas (FORTH), GR-70013 Heraklion, Greece
¹⁰ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, DE-53121 Bonn, Germany
¹¹ The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India
¹² School of Physics, Trinity College Dublin, College Green, Dublin 2 D02 PN40, Ireland
¹³ Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
¹⁴ Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str 1, D-85741 Garching, Germany
¹⁵ Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China
¹⁶ LIRA, Observatoire de Paris, CNRS, PSL, Sorbonne U., U. Paris Cité, Meudon, France
¹⁷ ORN, Observatoire de Paris, CNRS, PSL, U. Orléans, Nançay, France
¹⁸ Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, P.R. China
¹⁹ Key Laboratory of Radio Astronomy and Technology, Chinese Academy of Sciences, Beijing 100101, P.R. China
²⁰ LPC2E, OSUC, Univ Orleans, CNRS, CNES, Observatoire de Paris, F-45071 Orleans, France
²¹ Université Paris Cité and Université Paris Saclay, CEA, CNRS, AIM, 91190 Gif-sur-Yvette, France
²² Thüringer Landessternwarte, Sternwarte 5, 07778 Tautenburg, Germany
²³ Department of Physics, IIT Hyderabad, Kandi Telangana 502284, India
²⁴ Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010 6500 GL Nijmegen, The Netherlands
²⁵ Indian Institute of Technology, Roorkee 247667, India
²⁶ Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
²⁷ Institute of Radio Astronomy of the National Academy of Sciences of Ukraine, Mystetstv St. 4, Kharkiv 61002, Ukraine
²⁸ High Energy Physics, Cosmology & Astrophysics Theory (HEPCAT) Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town 7700, South Africa
²⁹ Department of Astronomy, University of Cape Town, Cape Town 7700, South Africa
³⁰ Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Colaba, Mumbai 400005, India
³¹ Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
³² Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
³³ Department of Physics, GLA University, Mathura 281406, India
³⁴ International Research Organization for Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
³⁵ Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
³⁶ Ruhr-Universität Bochum, Fakultät für Physik und Astronomie, Astronomisches Institut (AIRUB), 44801 Bochum, Germany

^⋆ Corresponding authors: francesco.iraci@inaf.it; chalumeau@astron.nl

Received: 14 May 2025
Accepted: 26 August 2025

Abstract

Context. Low radio frequency data are highly valuable for enhancing the sensitivity of pulsar timing arrays (PTAs) to propagation effects, such as dispersion measure (DM) variations. These low-frequency observations are particularly sensitive to DM fluctuations and can therefore significantly improve noise characterization in PTA datasets, which is essential for detecting the stochastic gravitational wave background (GWB).

Aims. For this work we incorporated for the first time low-frequency observations from LOFAR (100 − 200 MHz) and NenuFAR (30 − 90 MHz) into a PTA context by combining them with the most recent data release from the European and Indian PTAs (in particular, with the subsample labeled DR2new+, which includes only data from the new backends). This new combined dataset, labeled DR2low, consists of 12 pulsars observed over a time span of ∼11 years, with radio frequencies spanning the range 30 − 2500 MHz. The expanded frequency coverage of DR2low enables us to update and refine the noise models of DR2new+, and this is crucial in order to increase the PTA sensitivity when searching for the stochastic gravitational wave background, which is the primary goal of PTA observations. This work is a milestone in the integration of low-frequency data into the upcoming third data release of the International PTA, which is posed to achieve the 5σ detection of the GWB.

Methods. We used the pulsar timing software packages LIBSTEMPO and ENTERPRISE to perform a noise analysis of DR2low. At first, we applied a standard noise model including red noise (RN) and time-variable dispersion measure (DMv) as power laws, with Fourier components up to 30 and 100 frequencies, respectively. Next, we performed a fully Bayesian model selection to identify the favored noise model for each pulsar and compute the Bayes factors across all combinations of RN, DMv, and a noise term with a chromatic index of 4 (CN₄). Finally, we carried out a detailed analysis on the choice of the chromatic index for CN₄ and the contribution of the solar wind.

Results. The comparison between DR2low and DR2new+ using the standard noise model highlights the benefits of including low-frequency data. In particular, the additional frequency coverage improves the constraints on the DM variations and helps disentangle the DM and RN noise components in most pulsars. Through a Bayesian model selection, we found that the RN is required in the final model for 10 out of 12 pulsars, compared to only 5 in the DR2new+ dataset. The improved sensitivity to plasma effects provided by DR2low also favors the identification of significant CN₄ in eight pulsars, while none showed such evidence in DR2new+. The chromatic index of this process is consistent with four of the five pulsars, while two (PSRs J0030+0451 and J1022+1001) show significant deviations from such a value. We attribute this discrepancy to unmodeled contributions from the solar wind, especially because of the high DM sensitivity of LOFAR and NenuFAR and the high observing cadence provided by these datasets near solar conjunction. A dedicated analysis confirms that the current solar wind model fails to fully capture the observed delay, and residual power is absorbed into the DM component of the model.