This is the preprint from arxiv.org of a paper subsequently published in the Monthly Notices of the Royal Astronomical Society and available from http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2966.2006.10311.x. The definitive version is available at www.blackwell-synergy.com.We report the spectroscopic confirmation of four further white dwarf members of Praesepe. This brings the total number of confirmed white dwarf members to eleven making this the second largest collection of these objects in an open cluster identified to date. This number is consistent with the high mass end of the initial mass function of Praesepe being Salpeter in form. Furthermore, it suggests that the bulk of Praesepe white dwarfs did not gain a substantial recoil kick velocity from possible asymmetries in their loss of mass during the asymptotic giant branch phase of evolution. By comparing our estimates of the effective temperatures\ud and the surface gravities of WD0833+194, WD0840+190, WD0840+205 and WD0843+184\ud to modern theoretical evolutionary tracks we have derived their masses to be in the range 0.72−0.76M⊙ and their cooling ages ~300Myrs. For an assumed cluster age of 625±50Myrs the infered progenitor masses are between 3.3−3.5M⊙. Examining these new data in the context of the initial mass-final mass relation we find that it can be adequately represented by a linear function (a0=0.289±0.051, a1=0.133±0.015) over the initial mass range 2.7M⊙ to 6M⊙. Assuming an extrapolation of this relation to larger initialmasses is valid and adopting a\ud maximum white dwarf mass of 1.3M⊙, our results support a minimum mass for core-collapse supernovae progenitors in the range ~6.8-8.6M⊙
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