We have studied the long-term (~ years) temporal variability of the prototype supersoft X-ray source (SSS) CAL 83 in the LMC, using data from the MACHO and OGLE projects. The CAL 83 light curve exhibits dramatic brightness changes of ~1 mag on timescales of ~450 days, and spends typically ~200 days in the optical low state. Combined with archival XMM-Newton X-ray observations these represent the most extensive X-ray/optical study to date of this system, and reveal in much greater detail that the X-ray light curve is anti-correlated with the optical behaviour. This is remarkably similar to the behaviour of the transient SSS, RX J0513.9-6951, where the SSS outbursts recur on a timescale of ~168 days, and also anti-correlate with the optical flux. We performed simple blackbody fits to both high and low state X-ray spectra, and find that the blackbody temperature and luminosity decrease when the optical counterpart brightens. We interpret these long-term variations in terms of the limit-cycle model of Hachisu & Kato (2003a), which provides further support for these systems containing massive (~1.3 Msun) white dwarfs. In addition, we have refined their orbital periods in the MACHO and OGLE-III light curves to values of 1.047529(1) days and 0.762956(5) days for CAL 83 and RX J0513.9-6951, respectively.
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