An ultraluminous supersoft source with a 4 hour modulation in NGC 4631

Context.Supersoft X-ray sources (SSSs) are characterised by very low temperatures (<100 eV). Classical SSSs have bolometric luminosities in the range of 10 36-1038 erg$\,$s-1 and are modelled with steady nuclear burning of hydrogen on the surfaces of white dwarfs. However, several SSSs have been discovered with much higher luminosities. Their nature is still unclear. Aims.We report the discovery of a 4 h modulation for an ultraluminous SSS in the nearby edge-on spiral galaxy NGC 4631, observed with XMM-Newton in 2002 June. Temporal and spectral analysis of the source is performed. Methods.We use a Lomb-Scargle periodogram analysis for the period search and evaluate the confidence level using Monte-Carlo simulations. We measure the source temperature, flux and luminosity through spectral fitting. Results.A modulation of $4.2\pm0.4$ h (3$\sigma$ error) was found for the SSS with a confidence level >99%. Besides dips observed in the light curve, the flux decreased by a factor of 3 within ~10 h. The spectrum can be described with an absorbed blackbody model with $kT\sim67$ eV. The absorbed luminosity in the 0.2-2 keV energy band was $2.7\times10^{38}$ erg$\,$s-1 while the bolometric luminosity was a hundred time higher ( $3.2\times10^{40}$ erg$\,$s-1), making the source one of the most luminous of its class, assuming the best fit model is correct. Conclusions.This source is another very luminous SSS for which the standard white dwarf interpretation cannot be applied, unless a strong beaming factor is considered. A stellar-mass black hole accreting at a super Eddington rate is a more likely interpretation, where the excess of accreted matter is ejected through a strong optically-thick outflow. The 4 h modulation could either be an eclipse from the companion star or the consequence of a warped accretion disk.