Praesepe white dwarfs in Gaia DR2.

We have exploited Gaia Data Release 2 to study white dwarfmembers of the Praesepe star cluster. We recovered eleven known white dwarfmembers (all DA spectral type) plus a new cluster WD never identified before. Two of the eleven known DA objects did not satisfy all quality indicators available in the data release. The remaining nine objects of known spectral type have then been employed to determine their masses (average error of 3-5%) and cooling times (average uncertainty of 5-7\%), by fitting cooling tracks to their colour-magnitude diagram. Assuming the recent Gaia Data Release 2 reddening and main sequence turn off age estimates derived from isochronefitting, we have derived progenitor masses and established the cluster initial-final mass relation. We found consistency with the initial-final mass relation we established for eight Hyades white dwarfs, also employing Gaia data. We have investigated also the effect on the derived initial masses of using self-consistently different sets of stellar models and isochronesfor determining cluster age and white dwarfprogenitor lifetimes. According to our established Hyades+Praesepe initial-final mass relation, recent sets of stellar evolutioncalculation that model the full asymptotic giant branchphase do on average underpredict the final white dwarfmasses, in the initial mass range covered by the Praesepe and Hyades observed cooling sequence. These results depend crucially on the assumed reddening for the cluster. To this purpose, we have also discussed the case of considering the traditional zero reddening for Praesepe, instead of E(B-V)=0.027 derived from isochronefitting to the Gaia colour magnitude diagram.