QPOs in a highly magnetized ultra-compact X-ray binary 4U 1626-67

TL;DR

This study analyzes $ν_{QPO} \approx 47$ mHz QPOs in 4U 1626$-$67, a highly magnetized ultra-compact X-ray binary, during spin-down using a novel Hilbert-Huang Transform–based pipeline for QPO-phase-resolved timing and spectroscopy. By applying Variational Mode Decomposition, the authors isolate the QPO component (IMF1), reconstruct QPO waveforms, and map energy-dependent rms, uncovering that QPO amplitude increases with energy and that spin-pulse shapes remain stable across QPO phases. Phase-resolved spectroscopy with the NPEX model reveals that CRSF parameters remain constant while flux-related parameters track the QPO waveform and the photon index anti-correlates with flux, suggesting the QPO is driven by accretion-rate variability rather than geometric obscuration. The results favor a beat-frequency mechanism involving a magnetospheric boundary in a weak-propeller or trapped-disk regime near the corotation radius, offering new constraints on accretion physics in strongly magnetized neutron stars and informing models of QPO generation across X-ray binaries.

Abstract

We report the detection of mHz quasi-periodic oscillations (QPOs) in four NuSTAR observations of 4U 1626-67 during its recent spin-down episode. By using a novel method based on the Hilbert-Huang Transform (HHT), we present the first QPO-phase-resolved timing and spectral analysis of accreting X-ray pulsars in low mass X-ray binaries. Broadband QPO waveforms have been reconstructed and exhibit approximately sinusoidal shapes, with fractional amplitudes that vary with energy. In addition, we find that spin pulse profiles exhibit stable shapes between different QPO phases with different instantaneous fluxes, while the fractional root-mean-square (rms) is distinct for different observations. In this source, both QPO-phase-resolved and averaged spectra can be modeled with a negative and positive powerlaws exponential (NPEX) model, and their spectral evolutions show a similar trend, suggesting that the QPO modulation is caused by accretion rate variability instead of a geometric obscuration. These results provide new constraints on accretion physics in strongly magnetized neutron stars and the underlying mechanisms of QPOs.

Figures (11)

• Figure 1: A representative segment of the lightcurve for the obsID 90901318002 with a binsize 7.7 s.
• Figure 2: Left: power density spectra (PDS) of four NuSTAR observations of 4U 1626$-$67. Right: a representative PDS (black line) constructed for the observational ID 90901318002, together with PDSs of individual IMFs after the decomposition. The IMF1 (yellow line) corresponds to the QPO signal we considered. Here we assumed $K$=5 and a=1000 (see text).
• Figure 3: The QPO waveform reconstructed by folding the 4-79 keV lightcurve according to the instantaneous phase obtaining from the HHT using the data from ObsID 90901318002. Here we divide the QPO cycles into 32 phase bins and present two QPO cycles for clarity.
• Figure 4: The evolution of the fractional rms of QPO waveforms with energy in four observations of 4U 1626$-$67.
• Figure 5: Left: normalized pulse profiles of 4U 1626$-$67 at six equally spaced QPO phases (labeled 1–6) from ObsID 9090131808. Right: fractional rms of pulse profiles measured at different QPO phases across observations, as a function of the observed flux.