Spectroscopic survey of faint planetary-nebula nuclei III. A [WC] central star and two new PG1159 nuclei

We present spectroscopy of three hydrogen-deficient central stars of faint planetary nebulae, with effective temperatures ($T_{\mathrm{e}\mathrm{f}\mathrm{f}}$) in excess of 100,000 K. The nucleus of RaMul 2 is a Population II Wolf-Rayet star of spectral type [WC], and the central stars of Abell 25 and StDr 138 are two new members of the PG1159 class. Our spectral analyses reveal that their atmospheres have a similar chemical composition. They are dominated by helium and carbon, which was probably caused by a late helium-shell flash. Coincidentally, the three stars have similar masses of about $M=0.53M_{\odot }$ and, hence, form a post-AGB evolutionary sequence of an initially early-K type main-sequence star with $M=0.8M_{\odot }$. The central stars cover the period during which the luminosity fades from about $3000$ to $250L_{\odot }$ and the radius shrinks from about $0.15$ to $0.03R_{\odot }$. The concurrent increase of the surface gravity during this interval from $\log g$ = 5.8 to 7.2 causes the shutdown of the stellar wind from an initial mass-loss rate of $\log (\dot{M}\mathrm{/}{M}_{\odot }$${\mathrm{y}\mathrm{r}}^{-1})=-6.4$, as measured for the [WC] star. Along the contraction phase, we observe an increase of $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$ from 112,000 K, marked by the [WC] star, to the maximum value of 140,000 K and a subsequent cooling to 130,000 K, marked by the two PG1159 stars.