Unveiling hidden millihertz quasi-periodic oscillations in 1A 0535+262

¹ Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, China
² School of Physics and Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK
³ Kapteyn Astronomical Institute, University of Groningen, PO BOX 800, NL-9700 AV, Groningen, the Netherlands

^★ Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 25 January 2026
Accepted: 16 April 2026

Abstract

Context. Be/X-ray binary pulsars exhibit transient outbursts and complex timing behaviour, including millihertz quasi-periodic oscillations (QPOs), whose physical origin and energy dependence remain poorly understood. The bright outbursts of 1A 0535+262 in November 2020 provide an ideal laboratory to investigate these properties.

Aims. We aim to characterise the temporal evolution and energy-dependent properties of the millihertz QPO during its 2020 giant outburst, with a focus on trying to detect this feature at lower energies.

Methods. We used the multi-Lorentzian fitting framework that was recently introduced to jointly model the power spectra and the real and imaginary parts of the cross-spectrum. Our analysis incorporates simultaneous broadband X-ray observations from the Neutron Star Interior Composition Explorer (NICER) and Insight-HXMT, spanning the 0.2–120 keV energy range.

Results. We report the first detection of weak, but significant, millihertz QPOs at low X-ray energies (< 27 keV), extending their detection to a new energy regime. The centroid frequency evolves from 41 to 93 mHz, with the peak root-mean-square amplitude detected in the 50–65 keV range. Throughout the outburst, the QPOs generally exhibit a hard lag between 0.12π rad and 0.9π rad. However, at the outburst peak, the higher-energy bands (> 35 keV) display a soft lag of up to ∼ − 0.93π rad. We propose that interactions between soft seed photons and an extended outflow located outside the magnetosphere can account for the observed hard lags, although the physical origin of the transient soft lags remains uncertain. Furthermore, we detect a double-peaked millihertz QPO only at high energies (E > 35 keV) near peak luminosity. The two peaks maintain an approximately constant separation of 2ν_spin and exhibit anti-correlated phase evolution. The combination of this constant frequency separation and opposite phase trends is difficult to reconcile within existing theoretical models.

Conclusions. Our results indicate that the millihertz QPOs in the Be/X-ray binary 1A 0535+262 are closely linked to the coupled evolution of a soft-photon source and a Comptonising outflow or corona. The joint cross-spectral framework provides a complementary probe of millihertz QPOs beyond traditional power-spectral analyses.