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Planetary nebulae in Galactic open star clusters are rare objects; only threeare known to date. They are of particular interest because their distance canbe determined with high accuracy, allowing one to characterize the physicalproperties of the planetary nebula and its ionizing central star with highconfidence. Here we present the first quantitative spectroscopic analysis of acentral star in an open cluster, namely the faint nucleus of IPHASXJ055226.2$+$323724 in M37. This cluster contains 14 confirmed white dwarfmembers, which were previously used to study the initial-to-final-mass relationof white dwarfs, and six additional white dwarf candidates. We performed anatmosphere modeling of spectra taken with the 10m Gran Telescopio Canarias. Thecentral star is a hot hydrogen-deficient white dwarf with an effectivetemperature of 90,000 K and spectral type PG1159 (helium- and carbon-rich). Weknow it is about to transform into a helium-rich DO white dwarf because therelatively low atmospheric carbon abundance indicates ongoing gravitationalsettling of heavy elements. The star belongs to a group of hot white dwarfsthat exhibit ultrahigh-excitation spectral lines possibly emerging fromshock-heated material in a magnetosphere. We find a relatively high stellarmass of $M= 0.85^{+0.13}_{-0.14}$ M$_\odot$. This young white dwarf isimportant for the semi-empirical initial-final mass relation because anyuncertainty related to white-dwarf cooling theory is insignificant with respectto the pre-white-dwarf timescale. Its post-asymptotic-giant-branch age of$170,000-480,000$ yr suggests that the extended planetary nebula isextraordinarily old. We also performed a spectroscopic analysis of the sixother white dwarf candidates of M37, confirming one as a cluster member.

The unusual planetary nebula nucleus in the Galactic open cluster M37 and six further hot white dwarf candidates