Long-term evolution of cyclotron resonant scattering features in the accreting pulsar Vela X-1: A pulse-to-pulse approach

TL;DR

This work addresses how the cyclotron resonant scattering features in Vela X-1 evolve over two decades and how they depend on luminosity. By combining Swift/BAT's long-term monitoring with NuSTAR's pulse-to-pulse spectroscopy, the authors disentangle intrinsic magnetic-field evolution from luminosity-driven effects. They find that the long-term decay of the harmonic line energy $E_{ m cyc,H}$ has ended and document a transient rise around 2020–2023, with $E_{ m cyc,H}$ remaining near $^${54}$ keV$ post-break; the fundamental energy $E_{ m cyc,F}$ stays at $\\sim$25 keV with little to no time or luminosity evolution. The results imply localized polar-cap magnetic-field reconfiguration and complex accretion geometry, and demonstrate that the pulse-to-pulse method effectively expands the dynamic luminosity range for CRSF studies.

Abstract

We investigated the long-term evolution of the cyclotron line energy, as well as the relationship between cyclotron line energy and luminosity in the high-mass X-ray binary Vela X-1, based on archival Swift/BAT monitoring from 2005 to 2024 and pulse-to-pulse analysis of nine NuSTAR observations from 2012 to 2024. Our results provide the first confirmation that the long-term decay of the harmonic line energy ($E_{\rm cyc,H}$) in Vela X-1 has ended. We further report the first detection of a transient increase in $E_{\rm cyc,H}$ between 2020 and 2023, which suggests a sudden and significant change in the magnetic field configuration or accretion geometry. In addition, $E_{\rm cyc,H}$ shows slightly lower values at low luminosities and tends to flatten at higher luminosities, in the range of $(0.13\text{--}1.21) \times10^{37} $erg $\rm{s}^{-1}$. The fundamental line energy ($E_{\rm cyc,F}$) exhibits no significant variation with time or luminosity, remaining stable at approximately 25 keV.

Figures (6)

• Figure 1: Long-term evolution of the centroid energy of the harmonic cyclotron line in Vela X-1 as observed with Swift/BAT. The gray shaded regions indicate epochs of apparent $E_{\rm cyc,H}$ humps and the red points represent the time-averaged results from NuSTAR observations in Section \ref{['nu_average']}.
• Figure 2: (a) Spectrum and best-fit model for ObsID 91002349002 in energy range 3--70 keV using the model const$\times$tbabs$\times$pcfabs(gauss+gauss+gabs$\times$gabs$\times$fdcut). The FPMA data is in red and the FPMB data in blue. The best-fit model is shown in black. (b) Residuals for the best-fit model. (c) Residuals after fitting without the feature around 10 keV. (d) Residuals after fitting without the CRSFs.
• Figure 3: Flux-resolved spectral parameters derived from nine NuSTAR observations in the 3--70 keV energy range, shown as a function of intrinsic source luminosity. From top to bottom: Energy of the fundamental line, energy of the harmonic line, width of the harmonic line, strength of the harmonic line, photon index, cutoff energy, and folding energy.
• Figure 4: Distributions of counts per individual pulse (i.e. of pulse amplitudes). The red dashed lines indicate the boundaries of the amplitude bins used for extracting pulse-to-pulse spectra. In each distribution, the total number of counts is evenly distributed among the bins.
• Figure 5: Flux-resolved spectral parameters derived from the pulse-to-pulse analysis in the 3--70 keV energy range. Different colors represent different observation years, and distinct marker styles indicate observation IDs; time-averaged results for the short-exposure observations (30002007002, 90602328002, 90602328004, and 90602328006) are also shown. The dashed line in the second panel is the theoretical prediction for $E_* = 28.097 \pm 0.052$ keV (see equation \ref{['eqt:E_theo']}).