Praesepe white dwarfs in Gaia DR2

We have exploited Gaia Data Release 2 to study white dwarf members of the Praesepe star cluster. We recovered 11 known white dwarf members (all DA spectral type) plus a new cluster WD never identified before. 2 of the 11 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 per cent) and cooling times (average uncertainty of 5-7 per cent), 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 isochrone fitting, 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 isochrones for determining cluster age and white dwarf progenitor lifetimes. According to our established Hyades + Praesepe initial-final mass relation, recent sets of stellar evolution calculation that model the full asymptotic giant branch phase do on average underpredict the final white dwarfmasses, in the initialmass 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 isochrone fitting to the Gaia colour-magnitude diagram.