Millihertz quasi-periodic oscillations in accreting X-ray pulsars

Abstract

Accreting neutron stars exhibit pulsed X-rays and complex temporal variability across multi-wavelengths and different timescales. This variability could be driven by various physical processes including instability or inhomogeneous motions within the accretion flow, thermonuclear bursts on the neutron star surface. In this review, we present a concise overview of the observational features for millihertz (mHz) quasi-periodic oscillations (QPOs) at a frequency range of $\sim 1- 1000$ mHz observed in light curves of X-ray pulsars for both low-mass X-ray binaries and high-mass X-ray binaries, based on recent X-ray missions, e.g., NICER, Insight-HXMT and NuSTAR. We further summarize current theoretical interpretations, discuss remaining challenges and propose potential directions for future studies to advance the understanding of the nature and physical origin of these QPOs.

Figures (18)

• Figure S1: The temporal evolution of the 2021 and 2022 outbursts of 4U 1730–22. The blue arrow marks the single Type-I burst in 2021, while the red arrows mark all Type-I bursts detected in 2022. The vertical axis indicates the X-ray count rate. Data points from NICER (black data points, 0.5–10 keV) and with MAXI (grey data points, 2–20 keV) are shown. The figure is taken from mancuso2023detection
• Figure S2: Long-term X-ray light curves of EXO 2030+375 (left) and 4U 0115+63 (right), taken from reig2011x. The vertical axis indicates the X-ray count rate. EXO 2030+375 shows one rare Type II outburst and frequent regular Type I outbursts, while 4U 0115+63 exhibited several Type I outbursts, and four Type II outbursts between 1996 and 2009.
• Figure S3: Schematic illustration of accretion onto a strongly magnetized neutron star (e.g., $B\sim 10^{12}$ G). The central black circle represents the neutron star, with magnetic field lines shown in black curves. Matter from the accretion disc (thick horizontal lines) is funneled along magnetic field lines, forming interior flows (shaded regions) toward the magnetic poles. The inner disc radius $r_0$, the Alfvén radius $r_A$, and the corotation radius $r_{co}$ are labeled. Arrows indicate the direction of plasma motion along the field lines.
• Figure S4: Simulated signal and its spectral analysis illustrating transient amplitude modulation due to an orbiting structure that absorbs and scatters X-rays from the pulsar beam. (Top) The time-domain signal $x(t) = f(t)\cos(2\pi\nu_{\rm s}t) + \cos(2\pi\nu_{\rm blob}t)$, where the spin frequency $\nu_{\rm s} = 0.08~{\rm Hz}$ and the modulation frequency $\nu_{\rm blob} = 0.03~{\rm Hz}$. The amplitude modulation function $f(t)$ is applied only during a limited interval from $t = 10$ to $110~{\rm s}$, representing the transient interaction. (Middle) The Fourier spectrum shows the main spin frequency peak and two sidebands at $\nu_{\rm s} \pm \nu_{\rm blob}$, characteristic of amplitude modulation. (Bottom) The wavelet power spectrum reveals that the modulation is temporally localized, consistent with the transient influence of a single orbiting structure.
• Figure S5: (Left) Average power spectra of 4U 1636-53 from four XMM-Newton observations (top to bottom) in the 0.2-5 keV adapted from lyu2015spectral. (Right) A clear mHz QPO around 8-10 mHz is visible in each observation, accompanied by a weaker second harmonic. Dynamic power spectrum of 4U 1636-53 from XMM-Newton observations taken from lyu2014discovery. The grey vertical line marks the occurrence of an X-ray burst.