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

¹ Center for Space Science and Technology, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
² X-ray Astrophysics Laboratory, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
³ Center for Research and Exploration in Space Science and Technology, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁴ School of Physics and Centre for Space Research, University College Dublin, Belfield, Dublin 4, Ireland
⁵ European Space Agency (ESA), European Space Astronomy Centre (ESAC), Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain
⁶ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), E-39005 Santander, Spain
⁷ European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁸ Huygens-Kamerlingh Onnes Laboratory, Leiden University, Postbus 9504, 2300 RA Leiden, The Netherlands
⁹ Departamento de Física, Universidad de Santiago de Chile, Av. Victor Jara, 3659 Santiago, Chile
¹⁰ Center for Interdisciplinary Research in Astrophysics and Space Exploration (CIRAS), USACH, Santiago, Chile
¹¹ American Physical Society, Hauppauge, New York, NY 11788, USA

^⋆ Corresponding authors: vmadurga@umbc.edu; vmadurgafavieres20@gmail.com

Received: 31 July 2025
Accepted: 26 October 2025

Abstract

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.