X-ray and radio observations of the AMXP MAXI J1957+032 covering the 2022–2025 outbursts

¹ School of Science, Qingdao University of Technology Qingdao 266525, PR China
² SRON – Space Research Organisation Netherlands Niels Bohrweg 4 2333 CA Leiden, The Netherlands
³ Department of Astronomy, School of Physics, Peking University Beijing 100871, PR China
⁴ Kavli Institute for Astronomy and Astrophysics, Peking University Beijing 100871, PR China
⁵ Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences 19B Yuquan Road Beijing 100049, China
⁶ Department of Physics and Institute of Theoretical Physics, Nanjing Normal University Nanjing 210023, PR China
⁷ Key Laboratory of Stars and Interstellar Medium, Xiangtan University Xiangtan 411105 Hunan, PR China
⁸ University of Chinese Academy of Sciences Beijing 100049, China
⁹ Space Research Institute, Russian Academy of Sciences Profsoyuznaya 84/32 117997 Moscow, Russia

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Received: 14 October 2025
Accepted: 29 December 2025

Abstract

We presented a comprehensive multi-epoch timing and multiwavelength analysis of the accreting millisecond X-ray pulsar MAXI J1957+032, covering two major outbursts in 2022 and 2025. By reanalyzing the 2022 outburst data from the Neutron Star Interior Composition Explorer (NICER), we found the spin frequency and orbital parameters from the observations in 0.3–5 keV. For the 2025 outburst, we reported the detection of pulsations with the Einstein Probe (EP). Based on the ∼3-year baseline between these two outbursts, we measured a significant long-term spin-down rate of ν˙ = (−5.73 ± 0.28) × 10⁻¹⁴ Hz s⁻¹. Assuming that the quiescent spin-down is driven by magnetic dipole radiation, we inferred a spin-down luminosity of L ≈ 1.1 × 10³⁶ erg s⁻¹ and a surface dipolar magnetic field of B ≈ (7.3 − 10.4)×10⁸ G. Furthermore, we conducted a deep radio pulsation search with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) during the X-ray quiescent state in 2024, resulting in a non-detection with a 7σ flux density upper limit of 12.3 μJy. This corresponds to a radio efficiency upper limit of ξ < 2.8 × 10⁻¹⁰, which is significantly lower than that of typical millisecond pulsars with a similar spin-down power. This profound radio pulsation faintness can be explained by two primary scenarios: either a geometric effect, wherein the pulsar’s radio beam is directed away from our line of sight, or a physical suppression of the emission mechanism, potentially caused by a persistent low-level accretion flow during the X-ray quiescent state.