Pulse profile variations in the accreting X-ray pulsar Vela X-1

TL;DR

The paper investigates how the energy-resolved X-ray pulse profile of the accreting pulsar Vela X-1 varies across timescales from individual pulses to years. Using three long XMM-Newton observations (covering different orbital phases) in the 1–10 keV band, it constructs consistent energy-resolved pulse profiles and analyzes both mean profiles and single-pulse cycles, including synthetic light curves scaled from the mean profile. The main findings are that the mean pulse profile is remarkably stable across epochs, with most epoch-to-epoch variability driven by absorption, particularly at soft energies, and that short-timescale pulse-to-pulse variations are largely nonperiodic with a tendency to resemble the mean profile at higher flux. The study provides empirical benchmarks for the emission geometry and absorption effects in Vela X-1 and offers a framework to test emission models against energy-resolved pulse-profile variability observed in accreting X-ray pulsars.

Abstract

Vela X-1 is a well-studied accreting X-ray pulsar, with a distinctive pulse profile that has been found to be very similar in different observations spread out over decades. On the other hand, significant variations down to the timescale of individual pulses have been observed. The physical mechanisms leading to the energy-resolved pulse profile and its variations are not fully understood. Long, uninterrupted observations of Vela X-1 with XMM-Newton in 2000, 2006 and 2019 at different orbital phases allow us to study variations of the pulse properties in the soft X-ray range on all timescales in detail. We aim to characterize and quantify the variations of pulse profiles and individual pulse cycles on all timescales probed, and to identify possible factors driving the observed variations on these timescales. We generated consistent energy-resolved pulse profiles for each observation, as well as profiles built from subsets of individual pulse cycles selected by time, flux, or similarity to the mean profiles. We identified five pulsed phases based on the profile morphology and hardness, and examined the relative contributions over time. To quantify short-timescale variability, we compared individual pulse cycles with synthetic light curves derived from scaled versions of the average profiles. The pulse profile of Vela X-1, when averaged over many pulse cycles, remains remarkably stable, as expected. The most prominent variations between epochs are attributable to changes in absorption. Residual systematic differences are primarily flux-dependent, with profiles showing less variability at higher flux levels. On shorter timescales, most individual pulse cycles resemble the average profile, even though significant, sporadic deviations are also present.

Figures (12)

• Figure 1: Top view of the Vela X-1 system during the three XMM-Newton observations analyzed in this article. The red circles represent the periastron (filled) and the apastron (empty). The observer is located facing the system at $x = 0$ and at minus infinity along the y-axis. The gray zone represents the eclipse range.
• Figure 2: Energy-resolved light curves (top panels) and HRs (Eq. \ref{['eq:hardness ratio']}) between the 8--10 and 3--6 keV bands (bottom panels), with a time resolution of the respective pulse period, for the three observations. The width of each column is proportional to the duration of the corresponding observation. The light curves are plotted on a logarithmic scale for clarity. The colors represent different energy bands following the legend in the plot. Gray areas mark intervals of bright flares excluded for time-resolved analysis (see Sect. \ref{['sec:pulse periods and pulse cycles']} and Table \ref{['tab:pulse periods, offsets and pulse ranges']}).
• Figure 3: HR evolution during the three XMM-Newton observations of Vela X-1 compared to the orbit-averaged MAXI/GSC trend (2009–2024), adapted from Abalo+2024. MAXI HRs, based on Crab-like spectra, appear systematically harder and are rescaled for comparison with XMM-Newton, which uses count-based HRs.
• Figure 4: Mean pulse profiles of the three observations in the four energy bands used throughout this article and the corresponding HRs between the 8--10 and the 3--6 keV bands. In the rightmost column, we compare the profiles across observations, normalizing the individual profiles by their respective mean count rates. The error bars are smaller than the line width in nearly all of the panels. Dashed lines indicate the five defined phase regions, $A1$ to $B3$, as explained in the text.
• Figure 5: Top panels: 8--10 keV light curves with a time resolution of an individual phase-bin ($\sim$ 8.86 s). We mark in color the time ranges used to build the time-resolved profiles shown in the lower panels.