Amongst the hydrogen-deficient accreting binaries known as the AM~CVn stars are three systems with the shortest known orbital periods: HM Cnc (321 s), V407 Vul (569 s) and ES Cet (620 s). These compact binaries are predicted to be strong sources of persistent gravitational wave radiation. HM Cnc and V407 Vul are undergoing direct impact accretion in which matter transferred from their donor hits the accreting white dwarfs directly. ES Cet, is the longest period of the three and is amongst the most luminous AM CVn stars, but it is not known whether it accretes via a disk or direct impact. ES Cet displays strong HeII 4686 line emission, which is sometimes a sign of magnetically-controlled accretion. Peculiarly, although around one third of hydrogen accreting white dwarfs show evidence for magnetism, none have been found amongst helium accretors. We present the results of Magellan and VLT spectroscopic and spectropolarimetric observing campaigns dedicated to ES Cet with the aim of understanding its accretion structure. We find strong variability in our spectra on the 620 s period. The lines show evidence for double-peaked emission, characteristic for an accretion disc, with an additional component associated with the outermost disc, rather than a direct impact, that is broadly consistent with S-wave emission from the gas stream/disc impact region. This confirms beyond any doubt that 620,s is the orbital period of ES Cet. We find no significant circular polarisation (below 0.1 %). The trailed spectra show that ES Cets outer disc is eclipsed by the mass donor, revealing at the same time that the photometric minimum coincides with the hitherto unrecognised eclipse. ES Cet shows spectroscopic behaviour consistent with accretion via a disc, and is the shortest orbital period eclipsing AM CVn star known.
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