Quasi-periodic whispers from a transient ULX in M 101: signatures of a fast-spinning neutron star?

We have studied the unusual time variability of an ultraluminous X-ray source in M 101, 4XMM J140314.2 + 541806 (henceforth, J1403), using Chandra and XMM-Newton data. Over the last two decades, J1403 has shown short-duration outbursts with an X-ray luminosity similar to 1-3 x 10(39) erg s(-1), and longer intervals at luminosities similar to 0.5-1 x 10(38) erg s(-1). The bimodal behaviour and fast outburst evolution (sometimes only a few days) are more consistent with an accretor/propeller scenario for a neutron star than with the canonical outburst cycles of stellar-mass black holes. If this scenario is correct, the luminosities in the accretor and propeller states suggest a fast spin (P approximate to 5 ms) and a low surface magnetic field (B similar to 10(10) G), despite our identification of J1403 as a high-mass X-ray binary. The most striking property of J1403 is the presence of strong similar to 600-s quasi-periodic oscillations (QPOs), mostly around frequencies of approximate to 1.3-1.8 mHz, found at several epochs during the ultraluminous regime. We illustrate the properties of such QPOs, in particular their frequency and amplitude changes between and within observations, with a variety of techniques (Fast Fourier Transforms, Lomb-Scargle periodograms, weighted wavelet Z-transform analysis). The QPO frequency range <10 mHz is an almost unexplored regime in X-ray binaries and ultraluminous X-ray sources. We compare our findings with the (few) examples of very low frequency variability found in other accreting sources, and discuss possible explanations (Lense-Thirring precession of the inner flow or outflow; radiation pressure limit-cycle instability; marginally stable He burning on the neutron star surface).