2023A&A...678A..89W

Planetary nebulae in Galactic open star clusters are rare objects; only three are known to date. They are of particular interest because their distance can be determined with high accuracy, allowing one to characterize the physical properties of the planetary nebula and its ionizing central star with high confidence. Here we present the first quantitative spectroscopic analysis of a central star in an open cluster, namely the faint nucleus of IPHASX J055226.2+323724 in M37. This cluster contains 14 confirmed white dwarf members, which were previously used to study the initial-to-final-mass relation of white dwarfs, and six additional white dwarf candidates. We performed an atmosphere modeling of spectra taken with the 10m Gran Telescopio Canarias. The central star is a hot hydrogen-deficient white dwarf with an effective temperature of 90 000 K and spectral type PG1159 (helium- and carbon-rich). We know it is about to transform into a helium-rich DO white dwarf because the relatively low atmospheric carbon abundance indicates ongoing gravitational settling of heavy elements. The star belongs to a group of hot white dwarfs that exhibit ultrahigh-excitation spectral lines possibly emerging from shock-heated material in a magnetosphere. We find a relatively high stellar mass of M = 0.85_–0.14^+0.13M_⊙. This young white dwarf is important for the semi-empirical initial-final mass relation because any uncertainty related to white-dwarf cooling theory is insignificant with respect to the pre-white-dwarf timescale. Its post-asymptotic-giant-branch age of 170 000-480 000 yr suggests that the extended planetary nebula is extraordinarily old. We also performed a spectroscopic analysis of the six other white dwarf candidates of M37, confirming one as a cluster member.