Don’t torque like that

Measuring compact object magnetic fields with analytic torque models

¹ Dr. Karl Remeis-Sternwarte and Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Sternwartstr. 7, 96049 Bamberg, Germany
² Department of Physics, National and Kapodistrian University of Athens, University Campus Zografos, GR 15784, Athens, Greece
³ Institute of Accelerating Systems & Applications, University Campus Zografos, Athens, Greece
⁴ University of Maryland College Park, Department of Astronomy, College Park, MD 20742, USA
⁵ NASA Goddard Space Flight Center, Astrophysics Science Division, 8800 Greenbelt Road, Greenbelt, MD 20771, USA
⁶ Departamento de Física, Universidad de Santiago de Chile, Av. Victor Jara 3659, Santiago, Chile
⁷ Center for Interdisciplinary Research in Astrophysics and Space Exploration (CIRAS), USACH, Santiago, Chile
⁸ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, I-00076, Monte Porzio Catone (RM), Italy
⁹ Department of Astronomy and Astrophysics, University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0424, USA
¹⁰ European Space Agency (ESA), European Space Astronomy Centre (ESAC), Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain
¹¹ CRESST and Center for Space Sciences and Technology, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA

^⋆ Corresponding author: jakob.stierhof@fau.de

Received: 19 January 2025
Accepted: 10 April 2025

Abstract

Context. Changes in the rotational period observed in various magnetized accreting sources are generally attributed to the interaction between the infalling plasma and the large-scale magnetic field of the accretor. A number of models have been proposed to link these changes to the mass accretion rate, based on different assumptions on the relevant physical processes and system parameters. For X-ray binaries with neutron stars, with the help of precise measurements of the spin periods provided by current instrumentation, these models provide a way to infer such parameters as the strength of the dipolar field and a distance to the system. Often, the obtained magnetic field strength values contradict those from other methods used to obtain magnetic field estimates.

Aims. We want to compare the results of several of the proposed accretion models. To this end, an example application of these models to data was performed.

Methods. We reformulated the set of disk accretion torque models in a way that their parameterizations are directly comparable. The application of the reformulated models is discussed and demonstrated using Fermi/GBM and Swift/BAT monitoring data covering several X-ray outbursts of the accreting pulsar 4U 0115+63.

Results. We find that most of the models under consideration are able to describe the observations to a high degree of accuracy and with little indication that one model is preferred over the others. Even so, the derived parameters from these models show a large spread. Specifically, the magnetic field strength ranges over one order of magnitude for the different models. This indicates that the results are heavily influenced by systematic uncertainties.

Conclusions. The application of torque models provides a generic way to access system parameters of the accreting object. The values obtained via these models must be treated with caution, since the systematics of the models must be taken into account. Our example suggests that the current state of analytic torque models does not allow for quantitative measurements of the magnetic field of an accreting object. Systematic application to a sample of sources with known magnetic fields and distances will provide a selection criterion between models in the future.