First Evidence of Enhanced Recombination in Astrophysical Environments and the Implications for Plasma Diagnostics

We established criteria to identify transitions whose upper levels are likely populated by RER and thus may produce detectable emission lines. The doubly excited upper levels must (i) be propinquitous to the ionization threshold, (ii) mix with Rydberg states, and (iii) be from an ion widely observed in astrophysical nebulae. We investigated the first two rows of the periodic table for transitions that fit these criteria, and C ii, C iii, O ii, and O iii were the most promising, with accurate energy levels available for the resonances. Table 1 shows the candidates for the search.

Energies from the NIST database were used for the wavelength predictions. We focused on the C ii lines λ7112.94, 7119.73 and 7115.53 due to the availability of high-resolution optical spectra of PNe, and C iii λ1553.38 using high-resolution UV spectra of symbiotic binaries. The UV RER lines are generally predicted to be stronger than optical lines due to higher dielectronic auto-transfer rates and branching ratios.

High-resolution spectroscopy is critical for identifying RER lines, both to resolve these lines from nearby features of other species and to provide greater line-to-continuum contrast for weak features. We searched for optical C ii RER lines (Table 1) in published high-resolution spectra of seven PNe observed with 4–8 m telescopes: IC 418 (Sharpee et al. 2003); IC 2501, IC 4191, NGC 2440, NGC 7027 (Sharpee et al. 2006); NGC 6369 (García-Rojas et al. 2012); and NGC 3918 (García-Rojas 2015). We also studied an unpublished spectrum of Hb 12, obtained with the 2D coudé spectrograph on the 2.7 m Harlan J. Smith Telescope at McDonald Observatory (Sherrard et al. 2017). We show six of these objects that exhibit C ii RER lines (Figure 2(a)), whose intensities relative to Hβ are given in Table 2.

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Table 2.  Intensities (on the Scale I(H_β = 100)) of the C ii RER Line λ7115.53 and Cascade Lines λ3876 and 5259 that Compete with RER to Populate these Levels

PN	10${}^{-3}I$(7115)/I(Hβ)	10−3I(3876)/I(Hβ)	10−3I(5259)/I(Hβ)	RER	I(7112)/
				Contribution	I(7115)b
				to I(7115)a
Hb 12	4.48 ± 0.90	⋯	⋯	1.00	1.76 ± 0.50
IC 2501	9.80 ± 2.94	14.00 ± 1.50	5.00 ± 1.00	0.22	0.76 ± 0.32
IC 418	4.30 ± 0.43	6.90 ± 1.38	6.33 ± 1.26	−0.34	1.21 ± 0.17
IC 4191	3.10 ± 0.62	96.00 ± 10.10	⋯	−10.00	0.90 ± 0.25
NGC 2440	23.00 ± 4.60	⋯	3.60 ± 0.72	0.92	1.13 ± 0.32
NGC 3918	6.80 ± 1.36	⋯	⋯	1.00	1.04 ± 0.29
NGC 6369	11.00 ± 4.40	⋯	⋯	1.00	0.636 ± 0.36
NGC 7027	14.70 ± 1.47	⋯	7.90 ± 1.58	0.72	1.22 ± 0.17

Notes.

^aSee the text for discussion of negative numbers. ^bThe last column shows the observed ratio of the strongest C ii RER multiplet lines.

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To verify the identities of C ii λλ7112.94, 7119.73 and 7115.53, we utilize the Atomic Line List v2.05b21⁹ to search for other possible identifications with rest wavelengths within 1 Å. We considered forbidden transitions of atomic ions with excitation energies below 10 eV, and permitted transitions of elements in the first three rows of the periodic table. For potential alternative identifications, we searched for multiplet members, lines from the same upper level, and forbidden transitions of iron-peak elements, the strongest optical lines expected given the physical conditions of the nebulae. Using this method, we ruled out alternative identifications for these C ii lines, in agreement with the identifications of Storey & Sochi (2013). Based on our vetting criteria and the detection of multiplet members, we are confident that C ii λλ7112.94, 7119.73 and 7115.53 have been detected in each of the eight PNe that we investigated.

It is also important to confirm that the C ii RER lines are not produced by another mechanism. Fluorescence is quantum-mechanically forbidden to populate these resonances from the ground (or metastable) states. Alternatively, cascade from higher (i.e., above threshold, populated by DR) doubly excited states in the same Rydberg series (e.g., 1s²2s2pnl) can provide a populating mechanism. We searched the spectra for cascade lines that can populate the upper level of C ii λ7115.53 based on their branching ratios, namely C ii 3876 and 5259 Å (Table 2). In five objects (NGC 6369, NGC 7027, NGC 2440, NGC 3918, and Hb 12), the cascade lines were either not detected, or are too weak to explain the observed intensities of the RER lines. This indicates that the C ii multiplet λλ7112.94, 7115.53, and 7119.73 is populated almost entirely by RER. In two PNe (IC 418 and IC 2501), the cascade contribution was close to the observed intensity in the two lines, indicating that RER has a negligible contribution. In IC 4191, the cascade line intensities are much larger than predicted compared to that of λ7115.53, suggesting that C ii λλ3876 and 5259 are either blended with unknown features or misidentified. When the summed cascade portion of the C ii λ7115.53 intensity is larger than that observed, we give a negative factor in Table 2.

For a quantitative comparison of observed and predicted line intensities, it is necessary to consider both observational and theoretical uncertainties. The emission lines produced by RER are weak, and the error bars on their observed intensities are 20%–25% in the objects investigated. Moreover, flux calibration of cross-dispersed echelle spectra can lead to additional systematic uncertainties. From the atomic physics perspective, the dielectronic auto-transfer rates are uncertain by ∼30%, depending on the coupling model adopted to compute them. The largest uncertainty in our predicted RER line intensities and modified recombination rate coefficients is likely in the computed Rydberg populations. These were calculated from collisional-radiative models that require accurate knowledge of the plasma conditions (e.g., temperature and density) of the emitting region(s), and comprehensive inclusion of RER. Our model predictions assumed uniform electron temperature and density, thus neglecting local variations of these parameters (Liu et al. 2000).

In Table 2 we show the observed intensity ratios of C ii 7112.94 and 7115.53 Å, which range between 0.76 and 1.78 (with an average of 1.15). These values agree with the predicted ratio of 0.63 to within the observational and modeling uncertainties estimated to be 40%.

Because RER transitions in the UV are predicted to be stronger than their optical counterparts, we investigated archival UV spectra of PNe and symbiotic binaries. Of the PNe whose optical spectra we investigated, sufficiently high-resolution IUE spectra exist for Hb 12, IC 418, NGC 3918, and NGC 7027. The individual data sets do not exhibit RER lines, but the low signal-to-noise ratio of the spectra do not provide strong constraints.

Symbiotic stars are binary systems in which a white dwarf accretes gas from a red giant. We analyzed the UV spectrum of the AG Pegasi symbiotic, whose luminosity decreased by a factor of four between 1984 and 1994 (Eriksson et al. 2006), as the broad C iv resonance lines from the white dwarf wind declined. The C iii λ1553.8 RER line was not visible in the earlier spectrum, but became apparent after the C iv emission faded (Figure 2(b)). The HST/GHRS observations used by Eriksson et al. (2006) clearly revealed the 1553 Å line, but it was not identified by those authors. We verified the identity of this feature in a manner similar to that for the optical C ii lines, comparing against the line lists in Eriksson et al. (2006), and visual inspection of the IUE SWP47715 spectrum (program PA047, PI: Vogel). Due to the preponderance of fluorescently excited Fe and Co transitions in the UV spectrum of AG Peg, we expanded our search to include permitted lines from elements up to Zn, but found no plausible alternate identifications.

In summary, we identify C ii multiplet λλ7112.94, 7115.53, and 7119.73 lines in eight PNe, and show that RER is the dominant populating mechanism for the upper levels of these transitions in five objects. The RER line C iii 1553.38 Å is seen in the AG Pegasi symbiotic binary. These observations and our analysis represent the first empirical evidence of the RER mechanism.

The inclusion of RER in the analysis of astrophysical plasmas is expected to change the ionization equilibrium, due to an increased rate of recombination, and hence elemental abundances.

To demonstrate these effects, we modified the DR rate coefficients in Cloudy (Ferland et al. 2017) to include contributions from RER. Figure 3 illustrates the modified recombination rate coefficients for C²⁺, comparing those used in Cloudy (Colgan et al. 2003) to our calculations and to measured rates (Fogle et al. 2005); the recommended rates are a hybrid of measured and calculated values. Below ∼10,000 K recombination rates are dominated by below-threshold resonances, and RER produces rates that are substantially higher than other recombination processes. The enhancement to the recombination rates due to RER can be seen from the difference between the measured rates (red) and the recommended rates (purple), a factor of 2.2 at T = 8100 K, and 7.5 at T = 3500 K.

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In our models, RER only modifies the populations of the upper levels of transitions in Table 1 (and hence their emissivities), but RER should be included in a comprehensive collisional-radiative modeling to predict its effects on the populations of all excited states (and hence their emission spectra). C²⁺ abundances are often deduced from optical lines like C ii λ4267, for which the effect of RER is yet to be determined. To illustrate how RER can affect line ratios (and hence abundance determinations), we calculated the line ratio of C ii λ4267 to C ii λ7115 with and without RER as a function of temperature. We found that the ratio is reduced by two orders of magnitude at T = 5000 K, and by an order of magnitude at T = 10,000 K due to the enhancement of C ii λ7115 line emissivity. The effect on other C ii lines requires full inclusion of RER in emissivity calculations, and incorporating density and temperature inhomogeneities (Liu et al. 2000) in radiative transfer models.

We evaluated models for the "Paris Meeting" PN, H ii region, and AGN narrow line region simulations in the Cloudy test suite¹⁰ both with and without the modified recombination rate coefficients for C²⁺ and C³⁺. In the PN model, we introduced density fluctuations spanning 10³–10⁴ cm⁻³. There is a notable shift in the fractional abundance curves of C²⁺ and C³⁺ as a function of radius in each model when enhanced recombination is included (middle and bottom panels of Figure 3). The volume-averaged abundances differ as well, with the C⁺ ionic fraction increased by a factor of 1.15–1.45 when RER is taken into account, while C²⁺ decreases by factors of 1.07–1.16 and C³⁺ by 1.15–1.50, depending on the model.

These results demonstrate that including RER in models alters the ionization balance and hence can affect elemental abundance determinations, particularly when ionization correction factors are invoked. The modifications to ionic fractions and elemental abundances could be more pronounced when RER is included for species beyond the two C ions we considered.

Dielectronic auto-transfer represents a transition between resonant Rydberg states and doubly excited states, and thus will disturb select Rydberg populations. Collisions with neighboring Rydberg ions can return Rydberg populations to their LTE values, but our models show that dielectronic auto-transfer timescales (∼ns) are much faster than Rydberg collisional timescales (∼100s).

Rydberg emission lines from H, He, and C have been detected and used to diagnose the physical conditions of nebulae (Gordon & Sorochenko 2009). In the presence of a strong source of radio continuum emission, the lines are described by non-LTE conditions and can be affected by stimulated emission (Shaver et al. 1977). Lines emission is observed in low density (∼10⁴ cm⁻³), low-temperature (≤10,000 K) gas, if there is a mechanism to drive the Rydberg states out of their LTE conditions (Shaver 1980; Anantharamaiah et al. 1993). Dielectronic auto-transfer is a mechanism that can cause population inversions in Rydberg states which leads to stimulated emission in their radio recombination lines (Goldberg 1966). Our model for C⁺ and C²⁺ indicates that the Rydberg states affected by RER will produce radio emission in the range 0.112 mm–4.41 mm and 2.92 mm–5.14 mm, respectively, but further observations are needed to verify this effect.