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 eleven known white dwarf members (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 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 dwarf masses, 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 isochrone
fitting to the Gaia colour magnitude diagram.
