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

Context. 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. Aims. 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. Methods. 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. Results. 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.