The second data release from the European Pulsar Timing Array

II. Customised pulsar noise models for spatially correlated gravitational waves

¹ Institute of Astrophysics, FORTH, N. Plastira 100, 70013, Heraklion, Greece
² Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
³ Department of Physics, Indian Institute of Technology Roorkee, Roorkee-247667, India
⁴ Department of Electrical Engineering, IIT Hyderabad, Kandi, Telangana 502284, India
⁵ Université Paris-Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁶ The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India
⁷ Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
⁸ Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
⁹ ASTRON, Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4, 7991 PD, Dwingeloo, The Netherlands
¹⁰ Department of Physical Sciences, Indian Institute of Science Education and Research, Mohali, Punjab 140306, India
¹¹ Laboratoire de Physique et Chimie de l’Environnement et de l’Espace, Université d’Orléans / CNRS, 45071 Orléans Cedex 02, France
¹² Observatoire Radioastronomique de Nançay, Observatoire de Paris, Université PSL, Université d’Orléans, CNRS, 18330 Nançay, France
¹³ Dipartimento di Fisica “G. Occhialini”, Università degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
¹⁴ INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
¹⁵ INAF – Osservatorio Astronomico di Brera, via Brera 20, 20121 Milano, Italy
¹⁶ Institute for Gravitational Wave Astronomy and School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
¹⁷ INAF – Osservatorio Astronomico di Cagliari, via della Scienza 5, 09047 Selargius (CA), Italy
¹⁸ Hellenic Open University, School of Science and Technology, 26335 Patras, Greece
¹⁹ Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, PR China
²⁰ Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Navy Nagar, Colaba, Mumbai 400005, India
²¹ Department of Physics, IIT Hyderabad, Kandi, Telangana 502284, India
²² Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
²³ Department of Earth and Space Sciences, Indian Institute of Space Science and Technology, Valiamala, Thiruvananthapuram, Kerala 695547, India
²⁴ School of Physics, Faculty of Science, University of East Anglia, Norwich NR4 7TJ, UK
²⁵ Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muühlenberg 1, 14476 Potsdam, Germany
²⁶ Gran Sasso Science Institute (GSSI), 67100 L’Aquila, Italy
²⁷ INFN, Laboratori Nazionali del Gran Sasso, 67100 Assergi, Italy
²⁸ National Centre for Radio Astrophysics, Pune University Campus, Pune 411007, India
²⁹ Kumamoto University, Graduate School of Science and Technology, Kumamoto, 860-8555, Japan
³⁰ Università di Cagliari, Dipartimento di Fisica, S.P. Monserrato-Sestu Km 0,700, 09042 Monserrato (CA), Italy
³¹ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
³² Department of Physical Sciences,Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, India
³³ Center of Excellence in Space Sciences India, Indian Institute of Science Education and Research Kolkata, 741246, India
³⁴ School of Physics, Trinity College Dublin, College Green, Dublin 2, D02 PN40, Ireland
³⁵ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
³⁶ Department of Physics, St. Xavier’s College (Autonomous), Mumbai 400001, India
³⁷ National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, PR China
³⁸ E.A. Milne Centre for Astrophysics, University of Hull, Cottingham Road, Kingston-upon-Hull HU6 7RX, UK
³⁹ Centre of Excellence for Data Science, Artificial Intelligence and Modelling (DAIM), University of Hull, Cottingham Road, Kingston-upon-Hull HU6 7RX, UK
⁴⁰ Department of Physics, BITS Pilani Hyderabad Campus, Hyderabad 500078, Telangana, India
⁴¹ Joint Astronomy Programme, Indian Institute of Science, Bengaluru, Karnataka 560012, India
⁴² Arecibo Observatory, HC3 Box 53995, Arecibo, PR 00612, USA
⁴³ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
⁴⁴ Raman Research Institute India, Bengaluru, Karnataka, 560080, India
⁴⁵ Institut für Physik und Astronomie, Universität Potsdam, Haus 28, Karl-Liebknecht-Str. 24/25, 14476, Potsdam, Germany
⁴⁶ Department of Physics, IISER Bhopal, Bhopal Bypass Road, Bhauri, Bhopal 462066, Madhya Pradesh, India
⁴⁷ Ollscoil na Gaillimhe – University of Galway, University Road, Galway H91 TK33, Ireland
⁴⁸ Center for Gravitation, Cosmology, and Astrophysics, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
⁴⁹ Division of Natural Science, Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
⁵⁰ International Research Organization for Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
⁵¹ Laboratoire Univers et Théories LUTh, Observatoire de Paris, Université PSL, CNRS, Université de Paris, 92190 Meudon, France
⁵² Florida Space Institute, University of Central Florida, 12354 Research Parkway, Partnership 1 Building, Suite 214, Orlando, FL 32826-0650, USA
⁵³ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), 44780 Bochum, Germany
⁵⁴ Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai 519087, PR China

Received: 8 May 2023
Accepted: 28 June 2023

Abstract

Aims. The nanohertz gravitational wave background (GWB) is expected to be an aggregate signal of an ensemble of gravitational waves emitted predominantly by a large population of coalescing supermassive black hole binaries in the centres of merging galaxies. Pulsar timing arrays (PTAs), which are ensembles of extremely stable pulsars at approximately kiloparsec distances precisely monitored for decades, are the most precise experiments capable of detecting this background. However, the subtle imprints that the GWB induces on pulsar timing data are obscured by many sources of noise that occur on various timescales. These must be carefully modelled and mitigated to increase the sensitivity to the background signal.

Methods. In this paper, we present a novel technique to estimate the optimal number of frequency coefficients for modelling achromatic and chromatic noise, while selecting the preferred set of noise models to use for each pulsar. We also incorporated a new model to fit for scattering variations in the Bayesian pulsar timing package temponest. These customised noise models enable a more robust characterisation of single-pulsar noise. We developed a software package based on tempo2 to create realistic simulations of European Pulsar Timing Array (EPTA) datasets that allowed us to test the efficacy of our noise modelling algorithms.

Results. Using these techniques, we present an in-depth analysis of the noise properties of 25 millisecond pulsars (MSPs) that form the second data release (DR2) of the EPTA and investigate the effect of incorporating low-frequency data from the Indian Pulsar Timing Array collaboration for a common sample of ten MSPs. We used two packages, enterprise and temponest, to estimate our noise models and compare them with those reported using EPTA DR1. We find that, while in some pulsars we can successfully disentangle chromatic from achromatic noise owing to the wider frequency coverage in DR2, in others the noise models evolve in a much more complicated way. We also find evidence of long-term scattering variations in PSR J1600-3053. Through our simulations, we identify intrinsic biases in our current noise analysis techniques and discuss their effect on GWB searches. The analysis and results discussed in this article directly help to improve the sensitivity to the GWB signal and they are already being used as part of global PTA efforts.