Hot bubbles of planetary nebulae with hydrogen-deficient winds. II. Analytical approximations with application to BD + 30°3639

Context. The first high-resolution X-ray spectroscopy of a planetary nebula, BD +30° 3639, opened the possibility to study plasma conditions and chemical compositions of X-ray emitting "hot" bubbles of planetary nebulae in much greater detail than before.
Aims: We investigate (i) how diagnostic line ratios are influenced by the bubble's thermal structure and chemical profile, (ii) whether the chemical composition inside the bubble of BD +30° 3639 is consistent with the hydrogen-poor composition of the stellar photosphere and wind, and (iii) whether hydrogen-rich nebular matter has already been added to the bubble of BD +30° 3639 by evaporation.
Methods: We applied an analytical, one-dimensional (1D) model for wind-blown bubbles with temperature and density profiles based on self-similar solutions including thermal conduction. We also constructed heat-conduction bubbles with a chemical stratification. The X-ray emission was computed using the well-documented CHIANTI code. These bubble models are used to re-analyse the high-resolution X-ray spectrum from the hot bubble of BD +30° 3639.
Results: We found that our 1D heat-conducting bubble models reproduce the observed line ratios much better than plasmas with single electron temperatures. In particular, all the temperature- and abundance-sensitive line ratios are consistent with BD +30° 3639 X-ray observations for (i) an intervening column density of neutral hydrogen, N_H = 0.20_-0.10^+0.05 × 10²²cm^-2, (ii) a characteristic bubble X-ray temperature of T_X = 1.8 ± 0.1 MK together with (iii) a very high neon mass fraction of about 0.05, virtually as high as that of oxygen. For lower values of N_H, we cannot exclude the possibility that the hot bubble of BD +30° 3639 contains a small amount of "evaporated" (or mixed) hydrogen-rich nebular matter. Given the possible range of N_H, the fraction of evaporated hydrogen-rich matter cannot exceed 3% of the bubble mass.
Conclusions: The diffuse X-ray emission from BD +30° 3639 can be well explained by models of wind-blown bubbles with thermal conduction and a chemical composition equal to that of the hydrogen-poor and carbon-, oxygen-, and neon-rich stellar surface.