Discovery of a recurrent spectral evolutionary cycle in the ultra-luminous X-ray sources Holmberg II X–1 and NGC 5204 X–1

Context. Most ultra-luminous X-ray sources (ULXs) are now thought to be powered by stellar-mass compact objects accreting at super-Eddington rates. While the discovery of evolutionary cycles have marked a breakthrough in our understanding of the accretion flow changes in the sub-Eddington regime in Galactic black hole binaries, their evidence in the super-Eddington regime has so far remained elusive. However, recent circumstantial evidence hinted at the presence of a recurrent evolutionary cycle in two archetypal ULXs: Holmberg II X–1 and NGC 5204 X–1. Aims. We aim to build on our previous work and exploit the long-term high-cadence monitoring of Swift-XRT in order to provide robust evidence of the evolutionary cycle in these two sources and investigate the main physical parameters inducing their spectral transitions. Methods. We studied the long-term evolution of both sources using hardness-intensity diagrams (HID) and by means of Lomb–Scargle periodograms and Gaussian process modelling to look for periodic variability. We also applied a physically motivated model to the combined Chandra, XMM-Newton, NuSTAR, and Swift-XRT data of each of the source spectral states. Results. We robustly show that both sources follow a clear and recurrent evolutionary pattern in the HID that can be characterised by the hard ultra-luminous (HUL) and soft ultra-luminous (SUL) spectral regimes, and a third state with characteristics similar to the super-soft ultra-luminous (SSUL) state. The transitions between the soft states seem consistent with aperiodic variability, as revealed by a timing analysis of the light curve of Holmberg II X–1; albeit, further investigation is warranted. The light curve of NGC 5204 X–1 shows a stable periodicity on a longer baseline of ∼200 days, possibly associated with the duration of the evolutionary cycle. Conclusions. The similarities between both sources provide strong evidence of both systems hosting the same type of accretor and/or accretion flow geometry. We support a scenario in which the spectral changes from HUL to SUL are due to a periodic increase of the mass-transfer rate and subsequent narrowing of the opening angle of the super-critical funnel. The narrower funnel, combined with stochastic variability imprinted by the wind, might explain the rapid and aperiodic variability responsible for the SUL–SSUL spectral changes. The nature of the longer periodicity of NGC 5204 X–1 remains unclear, and robust determination of the orbital period of these sources could shed light on the nature of the periodic modulation found. Based on the similarities between the two sources, a long periodicity should be detectable in Holmberg II X–1 with future monitoring