1. Recombination line spectroscopy - theory and applications Robert Bastin and Peter Storey UCL Mike Barlow (UCL) and Xiaowei Liu (Peking University) with particular thanks to XWL for use of some figures.

2. Collisionally-excited lines (CELs) and optical recombination lines (ORLs) in the spectrum of a planetary nebula Nebula formed from stellar ejecta Ionization is maintained by UV radiation from central star Classical temperature and density diagnostics give electron temperatures near 10000K and electron densities 100-100000/cm 3 Balmer jump temperatures tend to be lower than those derived from CELs

3. OIII forbidden and infra-red lines provide a measure of a) electron temperature due to different excitation energies (eg 4363 and 5007Å) b) O 2+ abundance by comparison with hydrogen recombination lines Other ions provide density diagnostics

4. The OII Grotrian diagram prominent optical recombination lines shown in green – no significant collisional excitation. until recently all calculations of the line intensities were carried out in LS-coupling. 4f-3d transitions might be expected to be well enough represented by hydrogenic approximations to use these lines to determine abundances of O 2+ relative to H +. Expect good reliability since hydrogen metal recombination lines have very similar dependence on temperature.

5. The O/H abundance ratio derived from ORL observations of OII is systematically larger than that derived from CEL observations of O 2+ for a range of photoionized nebulae. The most extreme example (so far) is Hf2-2 where the ORL abundance is 70x the CEL abundance. Similar results are obtained for C/H and N/H. O/H from CELs spans one order of magnitude – O/H from ORLs two. Oxygen abundances relative to hydrogen from ORLs and CELs

6. By contrast, Mg/H from MgII shows no such enhancement And relative abundances of C, N, O are approximately the same from CELs And ORLs (Resembles an inverse FIP effect?)

7. Images and spectra of Hf2-2 the Balmer jump is unusually large and the recombination lines (eg CII at 4267Å) are exceptionally strong the Balmer jump indicates a temperature of 900K while the CELs give 8820K

8. A possible explanation for the ORL/CEL abundance discrepancy is that the ORLs arise from a different physical region within the nebula. The ORL emitting region would have enhanced CNO abundances compared to the background material and would therefore be at a much lower temperature due to increased cooling from forbidden and infra-red fine-structure transitions. The colder metal-rich material would not be visible at all in CELs. Hydrogen recombination line emission would come from both regions The nebula A30 might be a model, with cold (500K) knots of material emitting very strong ORLs and very little CELs and containing only 1% hydrogen by number. Unfortunately such knots are not visible in any of the other nebulae with high ORL abundance discrepancies.

9. Recombination line diagnostics - measuring temperature If the cold, metal-rich knot model is correct it becomes important to try to determine the conditions in which the recombination lines are emitted. ie to find diagnostics of the temperature and density that use only ORLs and not CELs. The ratios of the intensities of ORLs from states of different orbital angular momentum shows some temperature dependence eg CII 4f-3d (4267Å)/4s-3p(3920Å). CII 4f-3d (4267Å)/4s-3p(3920Å) against electron temperature Emissivity of higher l states is enhanced at low temperature and also at higher temperatures due to high-temperature dielectronic recombination.

10. The recombination spectrum of OII holds out the prospect of measuring electron density as well as temperature since the relative populations of the 3 P J levels of O 2+ are sensitive to density in about the right density range for nebulae (assuming the CEL densities are appropriate). ORL temperatures may be very low, possibly below 500K. Since the OII recombination lines are observed between low-lying states a complete model of the atom is needed. The maximum bound state principal quantum number is n=62 in the 3 P 1 series The OII recombination spectrum

11. Relative populations of the 3 P J states of O 2+ as a function of electron density. Are these changes of population reflected in the intensities of the recombination lines between low-lying states, providing a way to measure density?

12. Below the collision limit, populations are assumed to be determined by radiative processes only. The appropriate coupling scheme varies from near pure LS-coupling for low l to near j-j coupling for l>3 and high n for any l. In the low-n, low-l region we perform an R-matrix calculation of all radiative data (bound-bound and bound-free). Note that some two-body magnetic terms are not implemented in the R-matrix code. States are described by J, parity and energy. For the remainder j-j coupling is assumed and various approximate methods used.

13. So for low n and l bound-bound O + (EJπ) --> O + (E'J' π') + hν and bound-free and free-bound O 2+ (Jπ) + e O + (EJ'π') + hv while for the remainder angular core momentum, J c, is conserved O + ( 3 P Jc nlj;EJπ) -> O + ( 3 P Jc n'l'j';E'J' π’) + hv and O 2+ ( 3 P Jc ) + e O + ( 3 P Jc nlj;EJπ) +hv

14. Above the collision limit, l-changing and energy changing collisions must also be included. O + ( 3 P Jc nlj;EJπ) + e --> O + ( 3 P Jc n'l'j';E'J'π') + e' These states are assumed hydrogenic in terms of energy, radiative and collisional properties Collisions with protons and heavier ions may also be important and are included.

15. Above the O + ionization limit dielectronic capture and autoionization can also occur O + ( 3 P Jc’ ) + e O + ( 3 P Jc ) nlj (EJπ) followed by radiative decay O + ( 3 P Jc nlj;EJπ) -> O + ( 3 P Jc n'l'j';E'J' π’) + hv via the outer electron. The rates for both these processes are relatively small at high n, so n and l changing collisions also compete and distribute the population to states with small dielectronic capture rates.. More complex than the usual di- -electronic mechanism where there is a rapid core decay that dominates. Autoionization probabilities are computed in intermediate coupling with Nigel Badnell’s AUTOSTRUCTURE for n.le.1000 and l.le.40. For l.le.3, radiation damping is neglected n>63

16. Results for the OII transition array 3p ( 4 D) --> 3s ( 4 P o ) The intensity of each component relative to the total is shown as a function of electron density and at 10 4 K. The strongest component at the higher densities is 3p ( 4 D 7/2 ) --> 3s ( 4 P o 5/2 ) whose upper state can only be formed from the 3 P 2 state of O 2+. The intensity variation mirrors the variation of population of the 3 P 2 state Also shown are observed values for two HII regions Densities from CELs are 5500/cm 3 for M42 and 310/cm 3 for 30Dor.

17. The same figure with observed values from two planetary nebulae. CEL densities are 390/cm 3 for S311 and 4000/cm 3 for NGC5882.

18. The variaton of the intensity of the strongest component of multiplet V1 with electron density the HII regions have densities down to 100/cm 3 and temperatures close to 10 4 K theoretical results in red with fine-structure dielectronic processes included show improved agreement with observation.

19. Line ratios from different multiplets as a function of density and temperature At “high” temperatures, both density and temperature can be determined from line ratios At low temperatures, all density information is lost The figure seems to confirm that for some nebulae the OII lines are being emitted at temperatures below 1000K

20. At low temperatures, the average free electron energy is comparable to the fine-structure energy separation. Rydberg states with a 3 P 1 or 3 P 2 core are populated by dielectronic capture from the 3 P 0 + e continuum, even at low density when the populations of the O 2+ 3 P 1 and 3 P 2 are negligible. Relative intensities are almost independent of density

21. Conclusions Atomic: Despite the complexity of the atomic model and the approximate treatments used, the observed spectral features can be reproduced. Fine-structure dielectronic processes are important in modelling ionic recombination spectra, particularly at low temperatures (comparable to the fine-structure energy separations) The absence of some two-body terms from the current R-matrix codes does not lead to serious errors in this case Astrophysical: Various workers have suggested that the line ratios that we have interpreted as arising from very low temperature material are actually caused by variations in the density of the material. These results show that low temperatures are obtained irrespective of the density. The physical cause of these observed phenomena is still uncertain. The continuation of this work forms part of the application to extend the funding of the UK members of the Iron Project, along with continued work on ions of importance in solar physics