Hot bubbles of planetary nebulae with hydrogen-deficient winds II. Analytical approximations with application to BD+30 degrees 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, NH = 0.20-0.10+0.05 × 1022cm-2, (ii) a characteristic bubble X-ray temperature of TX = 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 NH, 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 NH, 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