Fe VII Lines in the Spectrum of RR Telescopii

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STIS the in ratio 1574 0 . 3 log 23, > E 3 ( aucitn.paper˙ref no. manuscript ( B σ HST niaigerr nteaoi aafrthe for data atomic the in errors indicating , N − vii ..Young P.R. vii e V / .Teeobservations These ). cm ,twrsR e rmtecmlt e feiso ie.The lines. emission of set complete the from Tel RR towards ), vii 3 ihteobserved the with − d 2 3 ie iet only to rise gives 7 = rudconfigu- ground . 25 1 ..Berrington K.A. , ± VLT 0 . 5 and 05, UE r sdt dniybed.Svnbacigrto ar ratios branching Seven blends. identify to used are /UVES d vii 2 ofiuaino Fe of configuration , E 03.Temdlcnit fal9fiesrcuelvl in levels structure fine 9 all 3 ground of the consists model Fe used The were the 2003). (2000) of database al. CHIANTI model et the a Berrington construct of to data atomic The data Atomic 2. Fe the allow and tested. lines, UV and cie nDr ta.(97,fricuini CHIANTI. in de- inclusion as of for accuracy splines, (1997), an transitions point have al. fits 5 36 The et with Dere all fit in were for scribed levels 9 (Υ) the amongst strengths collision averaged r on ihtedt fKea orntn(1987) Norrington & Keenan of discrepancies data from the Large rates data with (1982). decay found collision Storey are radiative & and electron Nussbaumer (1987) from of Norrington & use Keenan made CHIANTI h –,17ad47dcyrtssol e032 0.0150, 0.372, be incorrect. should s are rates 0.182 decay (2000) and 4–7 al. and et 1–7 Berrington values 1–4, of the The of 3 Table three however in (2000), given al. et Berrington from ag 4 range ( B 1 T aastaedmntae,adtelte sshown is latter the and demonstrated, are data-set n − h rvosmdlo Fe of model previous The http://www.chianti.rl.ac.uk. abig A018 U.S.A. 02138, MA Cambridge n density, and , TSisrmn fthe of instrument STIS e V t h eetaoi aao ..Brigo et Berrington K.A. of data atomic recent the ith y hffil,S W,U.K. 1WB, S1 Sheffield, ty, 2 ce ybedn.The blending. by ected odhr,O1 Q,U.K. 0QX, OX11 fordshire, ) n .Lobel A. and , . 3 ≤ E ≤ i lrvoe:sas–Aoi Data Atomic – stars Ultraviolet: – pii 0 − ( . 7 h xicini o well-constrained not is extinction The 27. B 1 d vii log λ . 2 27ln.Alatsursminimization least-squares A line. 5277 − ofiuaino h o.TeMaxwellian- The ion. the of configuration r dnie nutailtadoptical and ultraviolet in identified are T V N 0 = ) e ≤ fteR e eua n the and nebula, Tel RR the of , ..Brigo ta.electron al. et Berrington K.A. e 6 3 . 1 . .Terdaiedcyrtsare rates decay radiative The 0. 109 Dr ta. 97 on tal., et Young 1997; al., et (Dere +0 − ≤ ubeSaeTelescope Space Hubble λ 0 . . 5277/ 1 052 059 . vrtetemperature the over % 4 vii vii eie ausare: values derived eie eefrom here derived λ 93branching 4943 tmcmdlt be to model atomic o o nlso in inclusion for ion vii oebr7 2018 7, November sdin used e . 2 P.R. Young et al.: Fe VII lines in the spectrum of RR Telescopii

3. Observations 103 102 RR Tel was observed on 2000 October 18 with the STIS instrument on HST. Complete spectra were obtained over 1 10 the wavelength range 1140–7051A˚ in 3 HST orbits. The UV spectra (1140–3120A)˚ were obtained at a spectral 1.3 resolution of around 30–45,000, while the visible spectra (3022-7051A)˚ were obtained at a resolution of 5–10,000. 1.0 STIS data are processed automatically with the most 0.7 recent version of the STIS calibration pipeline when ac- A-value ratio cessed through the MAST2 archive. 1D spectra are pro- 10-1 vided with fluxes and flux errors. Absolute fluxes are accurate to 5 % (CCD spectra) and 8 % (MAMA spectra); 10-2 absolute wavelengths are accurate to 3–15 km s−1 (CCD -3 − 10 spectra) and 1.5–5.0 km s 1 (MAMA spectra). -5 -4 -3 -2 -1 0 1 2 10 10 10 10 10 10 10 10 The Fe vii lines are exceptionally strong in RR Tel, Berrington et al. A-values / s-1 and 13 lines can be identified, which are listed in Table 2. The lines were fit with Gaussian profiles through χ2 Fig. 2. Comparison of A-values from Berrington et al. minimization using the MPFIT curve fitting tools of (2000) with those of Nussbaumer & Storey (1982). The 3 4 C.B. Markwadt as distributed through Solarsoft . For 11 Y-axis gives the ratio of the Nussbaumer & Storey (1982) of the 13 lines, fitting errors were smaller than the accu- value to the Berrington et al. (2000) for a particular tran- racy of the STIS absolute calibration, and so the line fluxes sition, while the X-axis value gives the Berrington et al. are accurate to 5 and 8 % for lines in the CCD and MAMA (2000) value. The Y-axis is scaled as the square root of spectra, respectively. The weak λ2183 line has a significant the logarithm (base 10) of the ratio, allowing a wide range −14 −2 −1 fitting error, and the flux is 2.4±0.4×10 erg cm s . of values to be displayed. The solid line indicates perfect The Fe vii λ2143 line is blended with N ii λ2143.452. The agreement (ratio=1), and the dashed lines are placed at nearby N ii λ2139.687 line shares a common upper level ±30 %. with the latter, and the branching ratio λ2139/λ2143 is 0.406. The λ2139 flux is 7.87 × 10−14 erg cm−2 s−1, and by correcting for the branching ratio and subtracting this from the blended feature’s flux, we derive an estimate of as illustrated in Fig. 1 for four transitions from the vii ± × −14 −2 −1 3 the Fe line flux as 19.4 3.3 10 erg cm s . ground F2 level. The differences are due to resonance The low resolution optical spectra from STIS do not structure not accounted for by Keenan & Norrington allow line blending to be studied. For this purpose we (1987) – see Berrington et al. (2000) for more details. have analysed high resolution optical spectra obtained The radiative decay rates (A-values) of with the UVES instrument on the Kueyen telescope of Nussbaumer & Storey (1982) are in very good agreement the VLT in 1999 October. These spectra are not simul- with those of Berrington et al. (2000), as shown in Fig. 2. taneous with the STIS spectra and we note that emission All but five of the 24 A-values agree to within 30 %. The line fluxes have been found to vary in time for RR Tel 1 1 3 1 worst agreement is for the D2– G4 and P2– G4 transi- (Thackeray, 1977; Crawford et al., 1999), with low ioniza- tions where the Berrington et al. (2000) values are factors tion lines becoming weaker and high ionization lines be- 3.4 and 2.6 greater than those of Nussbaumer & Storey coming stronger. The 12 month separation of the UVES (1982). Both transitions are weak, however, and the and STIS spectra would have led to relative changes in 3 decays to the F3,4 are more important in de-populating emission line fluxes of at most 10 %, and the blending of 1 the G4 level. Fe vii lines with Fe ii lines discussed below will be overes- Träbert et al. (2003) describe a laboratory mea- timated by at most this amount. 1 surement of the lifetime of the S0 level, giving The UVES spectra were reduced using the MIDAS 29.6 ± 1.8 ms. This compares very well with 28.7 ms package by one of us (A. Lobel). The Fe vii optical from the Berrington et al. (2000) calculation. The lines are intrinscially asymmetric (Fig. 3a), and two of Nussbaumer & Storey (1982) calculations gave 33.1 ms. the lines clearly demonstrate blending: λ5160 and λ5277 Software available in the CHIANTI database allows (Fig. 3b,c). For λ5160, we identify the blending line as level populations and line emissivities to be calculated 2 Multimission Archive at Space Telescope, over a wide range of temperature and density (Dere et al., http://archive.stsci.edu. 1997). In Table 1, percentage level populations for the nine 3 http://astrog.physics.wisc.edu/∼craigm/idl/idl.html. vii 4 levels of Fe are given at two temperatures and three Solarsoft is a set of integrated software libraries, databases, densities. 25,000 K is a typical temperature for photoion- and system utilities that provide a common programming and ized plasmas, while 250,000 K is the temperature of max- data analysis environment for Solar Physics. It is available at imum ionization of Fe vii in an electron ionized plasma. http://www.lmsal.com/solarsoft. P.R. Young et al.: Fe VII lines in the spectrum of RR Telescopii 3

1.2 0.8 3F −1D 3F −3P 1.0 2 2 2 1 0.6 0.8

Υ 0.6 Υ 0.4

0.4 0.2 0.2

0.0 0.0 104 105 106 104 105 106 Temperature / K Temperature / K 1.5 0.20 3 1 3 1 F2− G4 F2− S0 0.15 1.0

Υ Υ 0.10

0.5 0.05

0.0 0.00 104 105 106 104 105 106 Temperature / K Temperature / K Fig. 1. Comparison of Maxwellian-averaged collision strengths (Υ) from Berrington et al. (2000) (solid line) with those of Keenan & Norrington (1987) (dashed line) for four transitions of Fe vii. The values have been derived from the spline ﬁts in CHIANTI. The original data cover 8000 ≤ T ≤ 120, 000 K (Keenan & Norrington, 1987) and 4.3 ≤ log T ≤ 6.0 (Berrington et al., 2000) and so values outside these ranges have been extrapolated.

7 4 6 3 4 Fe ii 3d a F9/2 –3d ( H)4sa H13/2 which has a vacuum blended STIS feature. This is consistent with the high res- wavelength of 5160.214 A.˚ Although this is a forbidden olution UVES spectrum (Fig. 3c). transition (and thus has a small A-value), it is the only vii 4 Selvelli & Bonifacio (2001) list the Fe λ3587 and transition from the a H13/2 upper level, and thus gives λ6087 lines as blended with Fe vi and Ca v lines, respec- vii rise to a strong emission line. The Fe λ4894/λ5160 tively. The blending Fe vi line (corresponding to ground branching ratio suggests a Fe ii contribution of 22 %, and 4 2 configuration transition P1/2– F5/2) has vacuum wave- this is consistent with the appearance of the UVES profile length 3588.680 A,˚ i.e., 1.339 A˚ from the Fe vii line, and so (Fig. 3b). As there are no branching ratios for the Fe ii vii 4 would be easily resolvable from the Fe line in the high a H13/2 level then it is not possible to estimate the Fe ii vii resolution UVES spectra, yet it is not seen. Further we contribution to λ5160 independently of the Fe lines. note that the Fe vi transition shares a common upper level 4 with the 2145.756 A˚ transition (decays to F3/2), and the −3 The Fe vii λ5277 line is blended on the short wave- branching ratio λ3588/λ2145 is 2.5×10 using the radia- ii tive decay rates from CHIANTI. The λ2145 line is found length side with an Fe transition that we identify as − − − 6 3 4 6 5 4 in the STIS spectra with a flux 4 × 10 14 erg cm 2 s 1, 3d ( G)4sa G9/2 –3d ( D)4pz F7/2, with vacuum wave- −16 −2 −1 ˚ implying a λ3588 flux of 1 × 10 erg cm s and thus length 5277.480 A. Another line from this upper level has vii a wavelength 4557.178A˚ and is identified in the STIS it makes no significant contribution to the Fe λ3587 spectrum with a flux 5.5 ± 0.7 × 10−14 erg cm−2 s−1. line. 3 1 The branching ratio (using radiative decay rates from the The Ca v line is the P1– D2 ground configuration CHIANTI database) implies that the λ5277.480 line has transition with vacuum wavelength 6088.058 A˚ and is thus a flux 7.4 ± 0.9 × 10−14, thus contributing 8.7 % to the 0.593 A˚ shortward of the Fe vii line. The large width 4 P.R. Young et al.: Fe VII lines in the spectrum of RR Telescopii of the feature at this wavelength means the two lines in astrophysical spectra are affected by interstellar extinc- would be blended. Another Ca v line at 5309.580 A˚ shares tion – wavelength dependent absorption and scattering by 1 the D2 upper level and the theoretical ratio is 0.19 interstellar dust grains – usually quantified by the quan- (using radiative decay rates from the NIST database). tity E(B − V ). A value of 0 corresponds to no extinction, The λ5309 line is found in the STIS spectra with a while 0.10 is the value typically assumed for RR Tel (e.g., flux 7.94 × 10−13 erg cm−2 s−1, thus implying a λ6088 Penston et al., 1983). Table 3 thus gives the theoretical flux of 1.51 × 10−13 erg cm−2 s−1 – only a 1.7 % con- ratio values calculated for these two extinction values, us- tribution to the λ6087 feature in the STIS spectrum. ing the extinction curve parameterisation of Fitzpatrick Correcting for this leads to a flux for the Fe vii compo- (1999). −12 −2 −1 nent of 8.56 × 10 erg cm s . Only three of the seven ratios agree with the theoret- The high resolution of the STIS/MAMA spectra allow ical values within the 1σ error bars on the fluxes. Of the line widths to be measured, and the λ2016 line has a width discrepant ratios, λ4894/λ5160 is affected by the blend to −1 of 53 km s (0.357 A).˚ A correlation between line width the λ5160 line mentioned in the previous section which and ionization potential has been noted before in RR Tel accounts for the observed ratio exceeding the theoretical +6 (Penston et al., 1983). The ionization potential of Fe is value. The discrepancy for the λ5277/λ4943 ratio can not 99.1 eV, and the λ2016 line width compares well with the be resolved by blending in the λ4943 line as this would +4 +4 widths of lines of Ne (97.1 eV) and Mg (109.3 eV): then make the λ4699/λ4943 disagree with theory. Future −1 the Ne v λ1574 line has a width of 46 km s , and the calculations of radiative decay rates should aim to resolve −1 Mg v λ1324 line has a width of 50 km s , both measured the problems highlighted here. from the STIS spectra. Fig. 4 shows part of the optical spectrum, with the Fe vii and several other prominent lines identified. 4.2. Derivation of physical parameters For an optically thin plasma the line ratios amongst Table 2. Fe VII line list for RR Telescopii. the various emission lines are determined entirely by the plasma temperature and density, and interstellar extinc- a λmeas (A)˚ Flux λvac (A)˚ Transition tion. From the STIS fluxes we can thus determine each 1 1 of these parameters. Rather than consider only individual 2015.570 67.4 2016.015 D2 – S0 b 3 1 line ratios as is often done, we instead employ a mini- 2143.085 38.8 2143.706 P1 – S0 3 1 2182.902 2.4 2183.421 P2 – S0 mization procedure to all of the observed emission lines 3 1 3586.830 555.6 3587.341 F3 – G4 simultaneously. This provides a much more stringent test 3 1 3759.526 838.0 3759.992 F4 – G4 on the atomic data, but gives greater confidence in the 3 3 4699.118 31.5 4699.557 F2 – P2 derived parameters. 3 3 4893.933 58.5 4894.739 F2 – P1 3 3 The method applied is as follows: lines from the same 4942.957 127.4 4943.863 F3 – P2 3 3 upper level are summed, thus giving six independent mea- 4988.927 59.9 4989.954 F2 – P0 c 3 3 sured quantities corresponding to the six upper emitting 5159.088 105.7 5160.332 F3 – P1 d 3 3 levels (see Table 2). The λ2143, λ5277 and λ6087 line 5276.792 85.0 5277.853 F4 – P2 3 1 fluxes have been corrected for line blending following the 5721.406 533.7 5722.297 F2 – D2 e 3 1 6087.220 870.9 6088.651 F3 – D2 discussion in Sect. 3, but the λ5160 is not included in a − − − the analysis as the blending contribution can not be esti- units: 10 14 erg cm 2 s 1. b mated independently of the λ4894/λ5160 branching ratio. blended with N ii λ2143.452. c blended with Fe ii λ5160.214. The summed line fluxes for each level are then divided d 1 blended with Fe ii λ5277.480. through by the summed flux for the D2 level, leading to e blended with Ca v λ6088.058. five independent measurables. A least-squares minimization procedure was applied using the MPFIT package such that the temperature is allowed to vary over the range 3.9 ≤ log T/K ≤ 5.5, the −3 electron density over 5.0 ≤ log Ne/cm ≤ 9.0, and the 4. Comparison with observations extinction 0.0 ≤ E(B − V ) ≤ 1.0. At each iteration, the level balance equations for Fe vii are solved at the tem- 4.1. Branching ratios perature and density values using the CHIANTI software, For emission lines that share a common upper level in the and emissivities for each line calculated. These are then ion, the line ratio is insensitive to the plasma conditions in adjusted for the extinction value, and line ratios compared an optically thin plasma and is proportional to the ratio of with the observed values. radiative decay rates for the transitions. Such ratios thus The final results of the minimization procedure were −3 provide a means for checking the quality of radiative data log T/K=4.50 ± 0.23, log Ne/cm = 7.25 ± 0.05 and for an ion. Seven such ratios are found in the STIS spec- E(B − V )=0.11 ± 0.16. The χ2 value was 2.3. A compar- tra of RR Tel, and are given in Table 3. Branching ratios ison between the observed ratios and the fitted values is P.R. Young et al.: Fe VII lines in the spectrum of RR Telescopii 5

1.2 2.0 0.5

(a) λ4943 (b) λ5160 (c) λ5277 1.0 0.4 1.5 0.8 0.3

0.6 1.0

0.2

Flux / arbitrary units 0.4 Flux / arbitrary units Flux / arbitrary units 0.5 0.1 0.2

0.0 0.0 0.0 4941 4942 4943 4944 5156 5157 5158 5159 5160 5274 5275 5276 5277 Wavelength / Å Wavelength / Å Wavelength / Å

Fig. 3. Spectra from UVES showing three Fe vii lines. The λ4943 line is unblended, while both λ5160 and λ5276 are blended with cooler species.

Fig. 4. A section of the optical spectrum of RR Tel from HST /STIS, covering 3500–6200 A.˚ The ten Fe vii lines are identiﬁed by their upper emitting level given in Table 4. Agreement is good, with three ratios ly- This same minimization procedure was repeated using ing within the error bars on the data. The discrepancy for the previous CHIANTI dataset, but the solution did not 3 the P2 level is likely due to the branching ratio problem converge within the prescribed parameter bounds, demon- 3 for the P2 level noted in Sect. 4.1. strating that the Keenan & Norrington (1987) data does not accurately reproduce the observed ﬂuxes.

The E(B − V ) value is poorly constrained due to the fact that low values of the extinction cause relatively little Previous estimates of the RR Tel nebula temper- change in line ﬂuxes even over the wide wavelength cover- ature through emission line diagnostics give values of age of the Fe vii lines. Performing the minimization with 10–25,000 K (Penston et al., 1983; Hayes & Nussbaumer, E(B −V ) ﬁxed at 0.10 gives temperature and density val- 1986; Doschek & Feibelmann, 1993; Espey et al., 1996), −3 ues of log T/K=4.50 ± 0.02, log Ne/cm =7.25 ± 0.05. consistent with the Fe vii result within the error bars. 6 P.R. Young et al.: Fe VII lines in the spectrum of RR Telescopii

Table 4. Comparison of observed line ratios with those and the UVES profile for the λ5160 is consistent with the derived from the fitting procedure. The ratios are formed blending Fe ii line accounting for the blend. by summing lines from a common upper level, and com- The accurate flux calibration of STIS, coupled with 1 paring with the summed lines from the D2 level. the strong Fe vii lines found in RR Tel, make the STIS RR Tel spectrum discussed here an excellent benchmark Upper Ratio for checking the accuracy of atomic physics calculations vii level Observed Fitted for Fe . 3 The atomic data used here will be included in version 5 P0 0.043 ± 0.003 0.039 3 of the CHIANTI atomic database. P1 0.042 ± 0.003 0.042 3 P2 0.170 ± 0.008 0.183 1 Acknowledgements. A.L. acknowledges financial support pro- G4 1.003 ± 0.051 1.016 1 vided by STScI grants HST-GO-09369.01-A and HST-GO- S0 0.064 ± 0.005 0.063 10212.01-A, and by NASA FUSE grants GI-D107 and GI-E068.

References Densities previously derived for the RR Tel nebula vary widely with ionization species, as best illustrated Berrington, K. A., Nakazaki, S., & Norrington, P. H. 2000, by Table 6 of Hayes & Nussbaumer (1986), where values A&AS, 142, 313 −3 4.9 ≤ log Ne/cm ≤ 9.0 are given. All the species stud- Dere K. P., Landi E., Mason H. E., Monsignori Fossi B. ied there, however, are low ionization and so not com- C., & Young P. R. 1997, A&AS, 125, 149 parable to Fe vii. Espey et al. (1996) adopt a density of Doschek, G. A., & Feibelmann, W. A. 1993, ApJS, 87, 331 −3 log Ne/cm = 6.0 from an analysis of Ne v and Ne vi Espey, B., Keenan, F. P., McKenna, F. C., Feibelman, W. lines in spectra from the Hopkins Ultraviolet Telescope A., & Aggarwal, K. M. 1996, ApJ, 465, 965 (HUT ). The ionization potentials of these ions are 97.1 Fitzpatrick, E. L. 1999, PASP, 111, 63 and 126.2 eV, compared to 99.1 eV for Fe+6, and so the Galavís, M. E., Mendoza, C., & Zeippen, C. J. 1997, ions are comparable. We note that the HUT spectra are A&AS, 123, 159 only of moderate spectral resolution, and high resolution Hayes, M. A., & Nussbaumer, H. 1986, A&A, 161, 287 spectra from FUSE would be valuable in improving the Keenan, F.P., & Norrington, P.H. 1987, A&A, 181, 370 density estimate from the Ne vi lines. Jordan, S., Mürset, U., & Werner, K. 1994, A&A, 283, 475 Previous estimates for the extinction towards RR Tel Crawford, F. L., Mckenna, F. C., Keenan, F. P., et al. include the value of E(B − V )=0.10 derived from He ii 1999, A&AS, 139, 135 recombination lines in IUE spectra (Penston et al., 1983), Nussbaumer, H., & Storey, P. J. 1982, A&A, 113, 2 and 0.08±0.03 from the Ne v λ2974/λ1574 branching ratio Penston, M. V., Benvenuti, P., Cassatella, A., et al. 1983, (Espey et al., 1996). This latter pair of lines are found MNRAS, 202, 833 in the STIS spectrum, and we find an observed ratio of Selvelli, P. L., & Bonifacio, P. 2001, A&A, 364, L1 0.469±0.053. The theoretical ratio is 0.376 (Galavís et al., Thackeray, A. D. 1977, Mem. RAS, 83, 1 +0.052 Träbert, E., Calamai, A. G., Gwinner, G., et al. 2003, J. 1997), leading to an extinction of 0.109−0.059, using the extinction curve parameterisation of Fitzpatrick (1999). Phys. B, 36, 1129 This is consistent with the upper limit (0.27) found here Young, P. R., Del Zanna, G., Landi, E., et al. 2003, ApJS, from the Fe vii lines. 144, 135

5. Conclusions The 3d2 ground conﬁguration transitions of Fe vii provide excellent plasma diagnostic opportunities for nebular plasmas illuminated by hot stars. The most recent Fe vii electron excitation data from Berrington et al. (2000) are a great improvement over the previous dataset of Keenan & Norrington (1987) and the complete set of Fe vii lines in the HST /STIS spectra of RR Tel yield values for the electron temperature and density, and extinction. The temperature and extinction are consistent with values derived from other ions, while we believe the density estimate is the most accurate obtained so far for RR Tel at ionization levels of around 100 eV. Four of the seven Fe vii branching ratios do not agree with the observed values within the error bars. One of these ratios (λ4894/λ5160) is aﬀected by blending in the λ5160 line P.R. Young et al.: Fe VII lines in the spectrum of RR Telescopii 7

Table 1. Percentage level populations for Fe vii calculated at two values of the electron temperature and three values 6 8 10 −3 of the electron density (Ne = 10 , 10 , 10 cm ).

25,000 K 250,000 K Index Level 106 108 1010 106 108 1010 3 1 F2 43.05 20.29 19.45 62.04 14.85 12.06 3 2 F3 34.60 26.79 25.63 26.19 21.87 16.79 3 3 F4 19.69 31.12 30.60 9.16 24.62 21.39 1 4 D2 0.56 6.31 7.10 0.40 8.70 10.93 3 5 P0 0.37 1.17 1.23 0.46 2.05 2.14 3 6 P1 0.81 3.43 3.60 0.88 6.24 6.43 3 7 P2 0.64 5.30 5.71 0.52 9.40 10.62 1 8 G4 0.30 5.57 6.61 0.35 12.15 18.20 1 9 S0 9.82(−5) 0.02 0.08 5.45(−4) 0.10 1.44

Table 3. Fe vii branching ratios with observed values from the RR Tel spectrum. Two theoretical values are given: one for no interstellar extinction; the other for an extinction E(B − V )=0.10. ⊳ denotes that the ratio is discrepant with theory by > 1σ; ◭ a discrepancy of > 3σ.

Upper E(B − V ) level Ratio Observed 0.00 0.10 1 a S0 λ2143 /λ2016 0.288 ± 0.054 0.242 0.224 ⊳ λ2183/λ2016 0.036 ± 0.007 0.038 0.036 1 G4 λ3587/λ3759 0.663 ± 0.047 0.715 0.704 3 P2 λ4699/λ4943 0.247 ± 0.017 0.226 0.221 ⊳ λ5277b/λ4943 0.609 ± 0.045 0.988 1.017 ◭ 3 c P1 λ4894/λ5160 0.553 ± 0.039 0.695 0.678 ⊳ 1 d D2 λ5722/λ6088 0.623 ± 0.044 0.656 0.642 a flux corrected for blend with N ii λ2143.452. b flux corrected for blend with Fe ii λ5277.480. c blended with Fe ii λ5160.214 (not corrected). d flux corrected for blend with Ca v λ6088.058.