Expansion of hydrogen-poor knots in the born-again planetary nebulae A30 and A78

We analyze the expansion of hydrogen-poor knots and filaments in the born-again planetary nebulae A30 and A78 based on Hubble Space Telescope (HST) images obtained almost 20 yr apart. The proper motion of these features generally increases with distance to the central star, but the fractional expansion decreases, i.e., the expansion is not homologous. As a result, there is not a unique expansion age, which is estimated to be 610-950 yr for A30 and 600-1140 yr for A78. The knots and filaments have experienced complex dynamical processes: the current fast stellar wind is mass loaded by the material ablated from the inner knots; the ablated material is then swept up until it shocks the inner edges of the outer, hydrogen-rich nebula. The angular expansion of the outer filaments shows a clear dependence on position angle, indicating that the interaction of the stellar wind with the innermost knots channels the wind along preferred directions. The apparent angular expansion of the innermost knots seems to be dominated by the rocket effect of evaporating gas and by the propagation of the ionization front inside them. Radiation-hydrodynamical simulations show that a single ejection of material followed by a rapid onset of the stellar wind and ionizing flux can reproduce the variety of clumps and filaments at different distances from the central star found in A30 and A78.

New effective recombination coefficients for nebular N II lines

Here we report new ${it ab initio}$ calculations of the effective recombination coefficients for the ion{N}{ii} recombination spectrum. We have taken into account the density dependence of the coefficients arising from the relative populations of the fine-structure levels of the ground state of the recombining ion, an elaboration that has not been attempted before for this ion, and it opens up the possibility of electron density determination via recombination line analysis. Photoionization cross-sections, bound state energies, and the oscillator strengths of ion{N}{ii} with $n leq 11$ and $l leq 4$ have been obtained using the close-coupling R-matrix method in the intermediate coupling scheme. Photoionization data were computed that accurately map out the near-threshold resonances and were used to derive recombination coefficients, including radiative and dielectronic recombination. Also new is including the effects of dielectronic recombination via high-$n$ resonances lying between the $^2$P$^{rm o}$,$_{1/2}$ and $^2$P$^{rm o}$,$_{3/2}$ levels. The new calculations are valid for temperatures down to an unprecedentedly low level (approximately 100 K). The newly calculated effective recombination coefficients allow us to construct plasma diagnostics based on the measured strengths of the ion{N}{ii} optical recombination lines (ORLs). The derived effective recombination coefficients are fitted with analytic formulae as a function of electron temperature for different electron densities. The dependence of the emissivities of the strongest transitions of ion{N}{ii} on electron density and temperature is illustrated. Potential applications of the current data to electron density and temperature diagnostics for photoionized gaseous nebulae are discussed. We also present a method of determining electron temperature and density simultaneously.