Studying geometry of the ultraluminous X-ray pulsar Swift J0243.6+6124 using X-ray and optical polarimetry

¹ Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland
² Institut für Astronomie und Astrophysik, Universität Tübingen, Sand 1, D-72076 Tübingen, Germany
³ University of Alabama in Huntsville, NSSTC, Huntsville, AL 35805, USA
⁴ NASA Marshall Space Flight Center, Huntsville, AL 35812, USA
⁵ Institute of Astrophysics, Foundation for Research and Technology-Hellas, GR-70013 Heraklion, Greece
⁶ Department of Physics, University of Crete, GR-70013 Heraklion, Greece
⁷ INAF Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, 00133 Roma, Italy
⁸ University of British Columbia, Vancouver, BC V6T 1Z4, Canada
⁹ Dipartimento di Fisica, Università degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
¹⁰ Dipartimento di Fisica, Università degli Studi di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Roma, Italy
¹¹ Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
¹² Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16801, USA
¹³ Department of Astrophysics, St. Petersburg State University, Universitetsky pr. 28, Petrodvoretz, 198504 St. Petersburg, Russia
¹⁴ Space Research Institute of the Russian Academy of Sciences, Profsoyuznaya Str. 84/32, Moscow 117997, Russia
¹⁵ Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-10691 Stockholm, Sweden
¹⁶ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
¹⁷ Istituto Ricerche Solari Aldo e Cele Daccò (IRSOL), Faculty of Informatics, Università della Svizzera italiana, 6605 Locarno, Switzerland
¹⁸ Institut für Sonnenphysik (KIS), Georges-Köhler-Allee 401a, 79110 Freiburg, Germany
¹⁹ Graduate School of Sciences, Tohoku University, Aoba-ku, 980-8578 Sendai, Japan
²⁰ Instituto de Astrofísica de Andalucía – CSIC, Glorieta de la Astronomía s/n, 18008 Granada, Spain
²¹ INAF Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monte Porzio Catone, (RM), Italy
²² Space Science Data Center, Agenzia Spaziale Italiana, Via del Politecnico snc, 00133 Roma, Italy
²³ INAF Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius (CA), Italy
²⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy
²⁵ Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy
²⁶ Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy
²⁷ Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
²⁸ Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
²⁹ INAF Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy
³⁰ Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (FI), Italy
³¹ Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (FI), Italy
³² Agenzia Spaziale Italiana, Via del Politecnico snc, 00133 Roma, Italy
³³ Science and Technology Institute, Universities Space Research Association, Huntsville, AL 35805, USA
³⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
³⁵ Department of Physics and Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, California 94305, USA
³⁶ Astronomical Institute of the Czech Academy of Sciences, Boční II 1401/1, 14100 Praha 4, Czech Republic
³⁷ RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
³⁸ X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
³⁹ Yamagata University, 1-4-12 Kojirakawa-machi, Yamagata-shi 990-8560, Japan
⁴⁰ Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan
⁴¹ International Center for Hadron Astrophysics, Chiba University, Chiba 263-8522, Japan
⁴² Institute for Astrophysical Research, Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA
⁴³ Department of Physics and Astronomy and Space Science Center, University of New Hampshire, Durham NH 03824, USA
⁴⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Strada Comunale Cinthia, 80126 Napoli, Italy
⁴⁵ Université de Strasbourg, CNRS, Observatoire Astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France
⁴⁶ MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
⁴⁷ Graduate School of Science, Division of Particle and Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan
⁴⁸ Hiroshima Astrophysical Science Center, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
⁴⁹ Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA
⁵⁰ Department of Physics, University of Hong Kong, Pokfulam, Hong Kong
⁵¹ Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
⁵² Center for Astrophysics, Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA
⁵³ INAF Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate (LC), Italy
⁵⁴ Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Via Marzolo 8, 35131 Padova, Italy
⁵⁵ Anton Pannekoek Institute for Astronomy & GRAPPA, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
⁵⁶ Guangxi Key Laboratory for Relativistic Astrophysics, School of Physical Science and Technology, Guangxi University, Nanning 530004, China

^⋆ Corresponding author; juri.poutanen@utu.fi

Received: 13 May 2024
Accepted: 19 August 2024

Abstract

Discovery of pulsations from a number of ultra-luminous X-ray (ULX) sources proved that accretion onto neutron stars can produce luminosities exceeding the Eddington limit by several orders of magnitude. The conditions necessary to achieve such high luminosities as well as the exact geometry of the accretion flow in the neutron star vicinity are, however, a matter of debate. The pulse phase-resolved polarization measurements that became possible with the launch of the Imaging X-ray Polarimetry Explorer (IXPE) can be used to determine the pulsar geometry and its orientation relative to the orbital plane. They provide an avenue to test different theoretical models of ULX pulsars. In this paper we present the results of three IXPE observations of the first Galactic ULX pulsar Swift J0243.6+6124 during its 2023 outburst. We find strong variations in the polarization characteristics with the pulsar phase. The average polarization degree increases from about 5% to 15% as the flux dropped by a factor of three in the course of the outburst. The polarization angle (PA) as a function of the pulsar phase shows two peaks in the first two observations, but changes to a characteristic sawtooth pattern in the remaining data set. This is not consistent with a simple rotating vector model. Assuming the existence of an additional constant polarized component, we were able to fit the three observations with a common rotating vector model and obtain constraints on the pulsar geometry. In particular, we find the pulsar angular momentum inclination with respect to the line of sight of i_p = 15°–40°, the magnetic obliquity of θ_p = 60°–80°, and the pulsar spin position angle of χ_p ≈ −50°, which significantly differs from the constant component PA of about 10°. Combining these X-ray measurements with the optical PA, we find evidence for at least a 30° misalignment between the pulsar angular momentum and the binary orbital axis.