The nature of the supersoft X-ray source RX~J0513--69

We present spectroscopy and photometry of the LMC supersoft binary system RX~J0513.9-6951. We derive a refined spectroscopic period of P$=0.761\pm0.004$~d, which is consistent with the value obtained from long term photometric monitoring (P$=0.76278\pm0.00005$~d). We see bipolar outflow components of He{\sc ii} and H$\beta$, with velocities of $\sim 3800$\,km\,s$^{-1}$, strongly suggesting that the compact object is a white dwarf. Using all the available optical and X-ray data, we construct a theoretical model to explain the principal features of the unusual variability of this source. In particular, we note that X-ray outbursts have only been seen at times of optical minima. From this, we conclude that the most likely cause of the X-ray outbursts is a photospheric contraction during a nuclear shell burning phase, rather than a thermonuclear flash or shocked emission. The system probably comprises a relatively massive white dwarf accreting at a high rate ($\sim 10^{-6} M_{\odot}~{\rm yr}^{-1}$) from an evolved donor star, and is observed close to pole-on.