A new pulsar timing model for scalar-tensor gravity with applications to PSR J2222-0137 and pulsar-black hole binaries

¹ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
e-mail: abatrakov@mpifr-bonn.mpg.de
² Jodrell Bank Centre for Astrophysics, The University of Manchester M13 9PL, UK
³ Observatoire Radioastronomique de Nançay, Observatoire de Paris, Université PSL, Université d’Orléans, CNRS, 18330 Nançay, France
⁴ Laboratoire de Physique et Chimie de l’Environnement et de l’Espace, Université d’Orléans/CNRS, 45071 Orléans Cedex 02, France
⁵ Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada
⁶ E.A. Milne Centre for Astrophysics, University of Hull, Cottingham Road, Kingston-upon-Hull HU6 7RX, UK
⁷ Centre of Excellence for Data Science, Artificial Intelligence and Modelling (DAIM), University of Hull, Cottingham Road, Kingston-upon-Hull HU6 7RX, UK

Received: 18 October 2022
Accepted: 8 February 2023

Abstract

Context. Scalar-tensor gravity (STG) theories are well-motivated alternatives to general relativity (GR). One class of STG theories, Damour–Esposito–Farèse (DEF) gravity, has a massless scalar field with two arbitrary coupling parameters. We are interested in this theory because, despite its simplicity, it predicts a wealth of different phenomena, such as dipolar gravitational wave emission and spontaneous scalarisation of neutron stars (NSs). These phenomena of DEF gravity can be tested by timing binary radio pulsars. In the methods used so far, intermediate phenomenological post-Keplerian (PK) parameters are measured by fitting the corresponding timing model to the timing data whose values are then compared to the predictions from the alternative theory being tested. However, this approach loses information between intermediate steps and does not account for possible correlations between PK parameters.

Aims. We aim to develop a new binary pulsar timing model ‘DDSTG’ (called after Damour, Deruelle and STG) to enable more precise tests of STG theories based on a minimal set of binary parameters. The expressions for PK parameters in DEF gravity are self-consistently incorporated into the model. PK parameters depend on two masses which are now directly fitted to the data without intermediate steps. The new technique takes into account all possible correlations between PK parameters naturally.

Methods. Grids of physical parameters of NSs were calculated in the framework of DEF gravity for a set of 11 equations of state. Automatic differentiation (AutoDiff) technique was employed, which aids in the calculation of gravitational form factors of NSs with a higher precision than in previous works. The pulsar timing program TEMPO was selected as a framework for the realisation of the DDSTG model. The implemented model is applicable to any type of pulsar companions. We also simulated realistic future radio-timing datasets for a number of large radio observatories for the binary pulsar PSR J2222-0137 and three generic pulsar-black hole (PSR-BH) systems.

Results. We applied the DDSTG model to the most recently published observational data for PSR J2222-0137. The obtained limits on DEF gravity parameters for this system confirm and improve previous results. New limits are also the most reliable because DEF gravity is directly fitted to the data. We argue that future observations of PSR J2222-0137 can significantly improve the limits and that PSR-BH systems have the potential to place the tightest limits in certain areas of the DEF gravity parameter space.