The Abundances of Light Neutron-Capture Elements in Planetary Nebulae III. The Impact of New Atomic Data on Nebular Selenium and Krypton Abundance Determinations

The detection of neutron(n)-capture elements in several planetary nebulae (PNe) has provided a new means of investigating s-process nucleosynthesis in low-mass stars. However, a lack of atomic data has inhibited accurate trans-iron element abundance determinations in astrophysical nebulae. Recently, photoionization and recombination data were determined for Se and Kr, the two most widely detected n-capture elements in nebular spectra. We have incorporated these new data into the photoionization code Cloudy. To test the atomic data, numerical models were computed for 15 PNe that exhibit emission lines from multiple Kr ions. We found systematic discrepancies between the predicted and observed emission lines that are most likely caused by inaccurate photoionization and recombination data. These discrepancies were removed by adjusting the Kr$^+$--Kr$^{3+}$ photoionization cross sections within their cited uncertainties and the dielectronic recombination rate coefficients by slightly larger amounts. From grids of models spanning the physical conditions encountered in PNe, we derive new, broadly applicable ionization correction factor (ICF) formulae for calculating Se and Kr elemental abundances. The ICFs were applied to our previous survey of near-infrared [Kr III] and [Se IV] emission lines in 120 PNe. The revised Se and Kr abundances are 0.1-0.3 dex lower than former estimates, with average values of [Se/(O, Ar)]=0.12$\pm$0.27 and [Kr/(O, Ar)]=0.82$\pm$0.29, but correlations previously found between their abundances and other nebular and stellar properties are unaffected. We also find a tendency for high-velocity PNe that can be associated with the Galactic thick disk to exhibit larger s-process enrichments than low-velocity PNe belonging to the thin disk population.Comment: 73 pages, 6 figures, 18 tables, accepted for publication in ApJ

The Abundances of Light Neutron-Capture Elements in Planetary Nebulae. II. S-Process Enrichments and Interpretation

We present the results of a large-scale survey of neutron(n)-capture elements in Galactic planetary nebulae (PNe), undertaken to study enrichments from s-process nucleosynthesis in their progenitor stars. From new K-band observations of over 100 PNe supplemented by data from the literature, we have detected the emission lines [Kr III] 2.199 mu m and/or [Se IV] 2.287 mu m in 81 of 120 objects. We determine Se and Kr elemental abundances, employing ionization correction formulae derived in the first paper of this series. We find a significant range in Se and Kr abundances, from near solar (no enrichment) to enhanced by > 1.0 dex relative to solar, which we interpret as self-enrichment due to in situ s-process nucleosynthesis. Kr tends to be more strongly enriched than Se; in 18 objects exhibiting both Se and Kr emission, we find that [Kr/Se] = 0.5 +/- 0.2. Our survey has increased the number of PNe with n-capture element abundance determinations by a factor of 10, enabling us for the first time to search for correlations with other nebular properties. As expected, we find a positive correlation between s-process enrichments and the C/O ratio. Type I and bipolar PNe, which arise from intermediate-mass progenitors (> 3-4 M-circle dot), exhibit little to no s-process enrichments. Finally, PNe with H-deficient Wolf-Rayet central stars do not exhibit systematically larger s-process enrichments than objects with H-rich nuclei. Overall, 44% of the PNe in our sample display significant s-process enrichments (> 0.3 dex). Using an empirical PN luminosity function to correct for incompleteness, we estimate that the true fraction of s-process enriched Galactic PNe is at least 20%.NSF AST 97-31156, AST 04-06809Astronom

Nucleosynthesis Predictions for Intermediate-Mass AGB Stars: Comparison to Observations of Type I Planetary Nebulae

Type I planetary nebulae (PNe) have high He/H and N/O ratios and are thought to be descendants of stars with initial masses of ~3-8Msun. These characteristics indicate that the progenitor stars experienced proton-capture nucleosynthesis at the base of the convective envelope, in addition to the slow neutron capture process operating in the He-shell (the s-process). We compare the predicted abundances of elements up to Sr from models of intermediate-mass asymptotic giant branch (AGB) stars to measured abundances in Type I PNe. In particular, we compare predictions and observations for the light trans-iron elements Se and Kr, in order to constrain convective mixing and the s-process in these stars. A partial mixing zone is included in selected models to explore the effect of a 13C pocket on the s-process yields. The solar-metallicity models produce enrichments of [(Se, Kr)/Fe] < 0.6, consistent with Galactic Type I PNe where the observed enhancements are typically < 0.3 dex, while lower metallicity models predict larger enrichments of C, N, Se, and Kr. O destruction occurs in the most massive models but it is not efficient enough to account for the > 0.3 dex O depletions observed in some Type I PNe. It is not possible to reach firm conclusions regarding the neutron source operating in massive AGB stars from Se and Kr abundances in Type I PNe; abundances for more s-process elements may help to distinguish between the two neutron sources. We predict that only the most massive models would evolve into Type I PNe, indicating that extra-mixing processes are active in lower-mass stars (3-4Msun), if these stars are to evolve into Type I PNe.Comment: 39 pages, accepted for publication in Ap

Kang-Redner Anomaly in Cluster-Cluster Aggregation

The large time, small mass, asymptotic behavior of the average mass distribution \pb is studied in a $d$-dimensional system of diffusing aggregating particles for $1\leq d \leq 2$. By means of both a renormalization group computation as well as a direct re-summation of leading terms in the small reaction-rate expansion of the average mass distribution, it is shown that \pb \sim \frac{1}{t^d} (\frac{m^{1/d}}{\sqrt{t}})^{e_{KR}} for $m \ll t^{d/2}$, where $e_{KR}=\epsilon +O(\epsilon ^2)$ and $\epsilon =2-d$. In two dimensions, it is shown that \pb \sim \frac{\ln(m) \ln(t)}{t^2} for $m \ll t/ \ln(t)$. Numerical simulations in two dimensions supporting the analytical results are also presented.Comment: 11 pages, 6 figures, Revtex