[Abridged] Classical novae (CNe) represent the major class of supersoft X-ray sources (SSSs) in the central region of our neighbouring galaxy M 31. We performed a dedicated monitoring of the M 31 central region with XMM-Newton and Chandra between Nov 2007 and Feb 2008 and between Nov 2008 and Feb 2009 respectively, in order to find SSS counterparts of CNe, determine the duration of their SSS phase and derive physical outburst parameters. We systematically searched our data for X-ray counterparts of CNe and determined their X-ray light curves and spectral properties. We detected in total 17 X-ray counterparts of CNe in M 31, only four of which were known previously. These latter sources are still active 12.5, 11.0, 7.4 and 4.8 years after the optical outburst. From the 17 X-ray counterparts 13 were classified as SSSs. Four novae displayed short SSS phases (< 100 d). Based on these results and previous studies we compiled a catalogue of all novae with SSS counterparts in M 31 known so far. We used this catalogue to derive correlations between the following X-ray and optical nova parameters: turn-on time, turn-off time, effective temperature (X-ray), t2 decay time and expansion velocity of the ejected envelope (optical). Furthermore, we found a first hint for the existence of a difference between SSS parameters of novae associated with the stellar populations of the M 31 bulge and disk. Additionally, we conducted a Monte Carlo Markov Chain simulation on the intrinsic fraction of novae with SSS phase. This simulation showed that the relatively high fraction of novae without detected SSS emission might be explained by the inevitably incomplete coverage with X-ray observations in combination with a large fraction of novae with short SSS states, as expected from the WD mass distribution. In order to verify our results with an increased sample further monitoring observations are needed.
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