A deep X-ray and UV look into the reflaring stage of the accreting millisecond pulsar SAX J1808.4−3658

¹ INAF – Osservatorio Astronomico di Roma Via Frascati 33 I-00078 Monte Porzio Catone (RM), Italy
² Dipartimento di Fisica, Sapienza Università di Roma Piazzale Aldo Moro 5 I-00185 Rome, Italy
³ ASI – Agenzia Spaziale Italiana Via del Politecnico snc I-00133 Rome, Italy
⁴ INAF – Osservatorio Astronomico di Brera Via Bianchi 46 I-23807 Merate (LC), Italy
⁵ Dipartimento di Fisica e Chimica – Emilio Segrè, Università di Palermo Via Archirafi 36 90123 Palermo, Italy
⁶ Dipartimento di Fisica, Università degli Studi di Cagliari SP Monserrato-Sestu km 0.7 I-09042 Monserrato, Italy
⁷ Institute of Space Sciences (ICE, CSIC), Campus UAB Carrer de Can Magrans s/n E-08193 Barcelona, Spain
⁸ Institut d’Estudis Espacials de Catalunya (IEEC) E-08860 Castelldefels (Barcelona), Spain
⁹ INAF/IASF Palermo Via Ugo La Malfa 153 90146 Palermo, Italy
¹⁰ INAF – Osservatorio Astronomico di Cagliari Via della Scienza 5 09047 Selargius (CA), Italy
¹¹ INAF Istituto di Astrofisica e Planetologia Spaziali Via del Fosso del Cavaliere 100 00133 Roma, Italy
¹² Department of Physics and Astronomy FI-20014 University of Turku, Finland
¹³ Department of Physics P.O. Box 64 FI-00014 University of Helsinki, Finland

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Received: 24 June 2025
Accepted: 17 January 2026

Abstract

We present a detailed X-ray and UV high-time-resolution monitoring of the final reflaring phase of the 2022 outburst of the accreting millisecond pulsar SAX J1808.4−3658, based on simultaneous XMM-Newton and Hubble Space Telescope (HST) observations. The uninterrupted coverage provided by XMM-Newton enabled a detailed characterization of the spectral and temporal evolution of the source X-ray emission, as the flux varied by approximately one order of magnitude. We detected coherent X-ray pulsations during the whole X-ray observation, down to a 0.5–10 keV luminosity of L_{X(low), 0.5−10} ≃ 6.21_{0.20−0.15d²3.5 erg s⁻¹}; this is among the lowest ever observed in this source during the outburst state. At the lowest flux levels, we observed significant variations in pulse amplitude and phase. These variations were anticorrelated with the X-ray source flux. We found a sharp phase jump of ∼0.4 cycles, accompanied by a doubling of the pulse amplitude and a softening of the X-ray emission. We interpreted changes in the X-ray pulse profiles as drifts of emission regions on the neutron-star surface, driven by an increase in the inner-disk radius when the mass-accretion rate decreased. The dependence of the pulse phase on the X-ray flux was consistent with a magnetospheric radius scaling as R_m ∝ Ṁ^Λ, with Λ = −0.17(9), which is in broad agreement with theoretical predictions. Simultaneous HST observations confirmed the presence of significant UV pulsations at an X-ray luminosity approximately a factor of two lower than during the 2019 outburst, extending the range of mass accretion rates at which UV pulsations have been detected. The measured pulsed UV luminosity, L_pulsed^UV = 1.1(3) × 10³² erg s⁻¹, was consistent with that observed during the 2019 outburst. Yet, such a UV luminosity exceeds the predictions of standard emission models, as further confirmed by the shape of the pulsed spectral energy distribution.