White dwarfs are often found in binary systems with orbital periods ranging from tens of minutes to hours in which they can accrete gas from their companion stars. In about 15% of these binaries, the magnetic field of the white dwarf is strong enough ($geq 10^6$ Gauss) to channel the accreted matter along field lines onto the magnetic poles. The remaining systems are referred to as non-magnetic, since to date there has been no evidence that they have a dynamically significant magnetic field. Here we report an analysis of archival optical observations of the non-magnetic accreting white dwarf in the binary system MV Lyrae (hereafter MV Lyr), whose lightcurve displayed quasi-periodic bursts of $approx 30$ minutes duration every $approx 2$ hours. The observations indicate the presence of an unstable magnetically-regulated accretion mode, revealing the existence of magnetically gated accretion, where disk material builds up around the magnetospheric boundary (at the co-rotation radius) and then accretes onto the white dwarf, producing bursts powered by the release of gravitational potential energy. We infer a surface magnetic field strength for the white dwarf in MV Lyr between $2 times 10^4 leq B leq 10^5$ Gauss, too low to be detectable by other current methods. Our discovery provides a new way of studying the strength and evolution of magnetic fields in accreting white dwarfs and extends the connections between accretion onto white dwarfs, young stellar objects and neutron stars, for which similar magnetically gated accretion cysles have been identified.
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