Issue 
A&A
Volume 550, February 2013



Article Number  C2  
Number of page(s)  2  
Section  Atomic, molecular, and nuclear data  
DOI  https://doi.org/10.1051/00046361/201116511e  
Published online  31 January 2013 
New effective recombination coefficients for nebular N ii lines^{⋆} (Corrigendum)
^{1}
Department of AstronomySchool of Physics, Peking University,
100871
Beijing,
PR China
email: fangx@pku.edu.cn
^{2}
Department of Physics and Astronomy, University College
London, Gower
Street, London
WC1E 6BT,
UK
^{3}
Kavli Institute for Astronomy and Astrophysics, Peking University,
100871
Beijing, PR
China
Key words: atomic data / line: formation / HII regions / ISM: atoms / planetary nebulae: general / errata, addenda
Corrected Tables 3–15 are all available at the CDS via anonymous ftp to cdsarc.ustrasbg.fr(130.79.128.5) or via http://cdsweb.ustrasbg.fr/vizbin/qcat?J/A+A/530/A18. Effective recombination coefficients at an extended temperature and density range are available from the authors.
1. Effective recombination coefficients
Errors in the computed effective recombination coefficients for nebular N ii lines in an earlier publication (Fang et al. ) have been discovered and are here corrected. Those errors were not due to the basic atomic physics (i.e. creation of the N^{2+} target and the target wave functions, and calculations of boundstate energies, oscillator strengths and photoionization crosssections for the N ii states) but due to mislabeling of five N ii boundstate energy levels. The 2p3p ^{3}${\mathit{P}}_{\mathrm{1}}^{\mathrm{e}}$ level was originally labeled as 2p3p ^{3}${\mathit{S}}_{\mathrm{1}}^{\mathrm{e}}$, the 2p3p ^{3}${\mathit{S}}_{\mathrm{1}}^{\mathrm{e}}$ level was labeled as 2p3p ^{1}${\mathit{P}}_{\mathrm{1}}^{\mathrm{e}}$, and the 2p3p ^{1}${\mathit{P}}_{\mathrm{1}}^{\mathrm{e}}$ level was labeled as 2p3p ^{3}${\mathit{P}}_{\mathrm{1}}^{\mathrm{e}}$; labels of the 2p3d ^{3}D$\begin{array}{}\mathrm{o}\\ \mathrm{2}\end{array}$ and 2p3d ^{1}D$\begin{array}{}\mathrm{o}\\ \mathrm{2}\end{array}$ levels were swapped. As a consequence, the effective recombination coefficients for the N ii lines that are directly related to the above five states were incorrect. We have corrected the labeling of the N ii energy levels and recalculated the effective recombination coefficients for the N ii lines at the same electron temperature and density ranges as in Fang et al. (2011). The newly calculated effective recombination coefficients are given in Tables 3–6.
2. Effective recombination coefficient fits
Analytical fits to the effective recombination coefficients as a function of electron temperature were carried out for the 55 strongest transitions of N ii in the optical (Tables 7–14 in Fang et al. ), using a nonlinear leastsquares algorithm. Two temperature regimes were defined, the lowtemperature regime (T_{e} < 10 000 K) and the hightemperature regime (10 000 ≤ T_{e} ≤ 20 000 K), and different fit equations were used for the two regimes (Eqs. (3) and (4) in Fang et al. ). However, the fit equation for the hightemperature regime (Eq. (4)) was not ideal. In the current corrigendum, we present new analytical fits for the 55 lines of N ii, using the single equation, valid for 125 K ≤ T_{e} ≤ 20 000 K, $\mathit{\alpha}\mathrm{=}\mathit{a}\mathrm{+}\mathit{b}\hspace{0.17em}\mathit{t}\mathrm{+}\mathit{c}\hspace{0.17em}{\mathit{t}}^{\mathrm{2}}\mathrm{+}\mathrm{(}\mathit{d}\mathrm{+}\mathit{e}\hspace{0.17em}\mathit{t}\mathrm{+}\mathit{f}\hspace{0.17em}{\mathit{t}}^{\mathrm{2}}\mathrm{)}{\mathrm{log}}_{\mathrm{10}}\mathit{t}\mathrm{+}\mathit{g}\hspace{0.17em}\mathrm{(}{\mathrm{log}}_{\mathrm{10}}\mathit{t}{\mathrm{)}}^{\mathrm{2}}\mathrm{+}\mathit{h}\mathit{/}\mathit{t,}$(1)where α = log _{10}α_{eff} + 15 and t = T_{e} [K]/10^{4}, and α_{eff} is the effective recombination coefficient of an N ii line as defined by Eq. (2) in Fang et al. (2011). a, b, c, d, e, f, g and h are fit parameters as given in Tables 7–10 (for Case B recombination) and Tables 11–14 (for Case A recombination). The fit equation Eq. (1) has taken into account the behaviour of the contribution from radiative recombination (RR), which has an approximately powerlaw dependence on electron temperature (${\mathit{\alpha}}_{\mathrm{RR}}\mathrm{\propto}{\mathit{T}}_{\mathrm{e}}^{\mathrm{}\mathit{a}}$, a ~ 1), and a possible contribution from dielectronic recombination (DR), which has an exponential dependence on temperature (${\mathit{\alpha}}_{\mathrm{DR}}\mathrm{\propto}{\mathit{T}}_{\mathrm{e}}^{\mathrm{}\mathrm{3}\mathit{/}\mathrm{2}}\mathrm{exp}\mathrm{(}\mathrm{}{\mathit{E}}_{\mathrm{ex}}\mathit{/}\mathit{k}{\mathit{T}}_{\mathrm{e}}\mathrm{)}$, where E_{ex} is the excitation energy of an autoionization state, to which an electron is captured.
At all densities and temperatures considered, the maximum fitting errors (the last column in Tables 7–14) of the effective recombination coefficients for the 55 transitions of N ii are no more than 0.86 per cent, except for the lines of the M5 (3p ^{3}P – 3s ^{3}P^{o}) multiplet at the density of 10^{5} cm^{3} and for T_{e} ≤ 250 K in case A, where the maximum fitting error is 1.45 per cent (Table 14). The average fitting errors (the penultimate column in Tables 7–14) are all less than 0.21 per cent, and less than 0.1 per cent for most of the transitions, except for the M5 lines at the density of 10^{5} cm^{3} in case A, where the average fitting errors are 0.26–0.33 per cent (Table 14). Figure 1 visually demonstrates the accuracy of the new analytical fits to the M3 λ5679.56 (2p3p ^{3}D_{3} – 2p3s ^{3}${\mathit{P}}_{\mathrm{2}}^{\mathrm{o}}$) line, which is the strongest line of N ii detected in the spectra of emission line nebulae.
Fig. 1 Analytical fits to the Case A (the red circles) and Case B (the black circles) effective recombination coefficients for the N ii M3 λ5679.56 (2p3p ^{3}D_{3} – 2p3s ^{3}${\mathit{P}}_{\mathrm{2}}^{\mathrm{o}}$) line, at an electron density of 10^{4} cm^{3}. Upper panel: the red dotted and the black solid curves are the analytical fits (Eq. (1)) to the Case A and Case B effective recombination coefficients, respectively. Lower panel: fitting errors (in percentage) of the Case A (the red dots) and Case B (the black dots) data. 
3. Total recombination coefficients
Table 15 is a comparison of our revised direct recombination coefficients to states of N^{+} with those of Kisielius & Storey (2002) and Nahar (1995).
Acknowledgments
X.F., P.J.S. and X.W.L. would like to thank Dr. D. Péquignot who found some anomalies in the published effective recombination coefficients and the unsatisfactory continuity of data fits at 10^{4} K. We also thank Dr. V. Escalante who first noticed that the differences between fits of Eqs. (3) and (4) in Fang et al. (2011) are larger than the stated accuracy of 0.5 per cent at 10^{4} K and, for some transitions, this difference exceeds 5 per cent. We also would like to thank Dr. C. Morisset for fruitful discussions and comments in several occasions. This work had been supported by a joint research grant
cosponsored by the National Science Foundation of China and the Royal Society of UK.
References
 Fang, X., Storey, P. J., & Liu, X.W. 2011, A&A, 530, A18 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Kisielius, R., & Storey, P. J. 2002, A&A, 387, 1135 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
 Nahar, S. N. 1995, ApJS, 101, 423 [NASA ADS] [CrossRef] [Google Scholar]
© ESO, 2013
All Figures
Fig. 1 Analytical fits to the Case A (the red circles) and Case B (the black circles) effective recombination coefficients for the N ii M3 λ5679.56 (2p3p ^{3}D_{3} – 2p3s ^{3}${\mathit{P}}_{\mathrm{2}}^{\mathrm{o}}$) line, at an electron density of 10^{4} cm^{3}. Upper panel: the red dotted and the black solid curves are the analytical fits (Eq. (1)) to the Case A and Case B effective recombination coefficients, respectively. Lower panel: fitting errors (in percentage) of the Case A (the red dots) and Case B (the black dots) data. 

In the text 
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