N III Bowen Lines and Fluorescence Mechanism in the Symbiotic Star AG Peg

To compare FWHMs and line intensities of N III Bowen lines, we have examined N III ordinary lines. The intensities of ordinary N III lines are generally very weak, and some lines were not measurable in a specific epoch. The detected lines are λλ 3,745.95 (3p ⁴S_3/2→3s ${}^4{\text{P}}_{1/2}^{\text{o}}$ ), 4,195.74 (3p ²D_3/2→3s 2Po _1/2), 4,379.11 (5g ²G→4f ²F), 4,510.88 (3p ⁴D_3/2→3s ${}^2{\text{P}}_{1/2}^{\text{o}}$ ), 4,518.14 (3p ⁴D_1/2→3s ${}^4{\text{P}}_{1/2}^{\text{o}}$ ), 4,523.56 (3p ⁴D_3/2→3s ${}^4{\text{P}}_{1/2}^{\text{o}}$ ), 4,534.58 (3p ⁴D5/2→3s ${}^4{\text{P}}_{5/2}^{\text{o}}$ ), and 4,544.84 (5s ²S_1/2→4p ${}^2{\text{P}}_{3/2}^{\text{o}}$ ). The transition of 4,379.11 was obtained from Feklistova & Kholtygin (1997), and the others were obtained from National Institute of Standards and Technology (NIST, http://physics.nist.gov/ PhysRefData/ASD/lines_form.html). The wavelength range of N III Bowen lines is 4,000-4,700 Å, and as shown in the 1998 spectrum in Fig. 2, we have found a total of five Bowen lines marked by arrows, including λ 4,10³.39 located in the right edge of Hδ λ 4,101.74. Similar to the 1998 data, five N III lines appeared in 2001 and 2002. Eriksson et al. (2005) reported that in AG Peg, they could not observe six O III Bowen lines, but they observed five N III Bowen lines, consistent with our findings.

Fig. 2. The spectrum of the five N III lines in 1998. Wavelength unit in horizontal axis: Angstrom (Å). Flux unit in vertical axis: 10-12 erg·cm^-2s-1Å-1.

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We have measured FWHMs of N III Bowen lines for 1998, 2001, and 2002, by Gaussian fitting through StarLink DIPSO, made by ESO (European Southern Observatory). However, in some cases, N III ordinary lines were too weak to analyze the components using DIPSO. Thus, we have measured FWHMs using IRAF splot. The FWHMs measured through DIPSO or IRAF splot include the increment of FWHMs induced by other external factors. Since electron temperatures at three epochs are different from each other, thermal FWHM increments (V_th) were obtained considering electron temperatures. Moreover, FWHM increments due to fine structure (V_f-s), instrumental factors induced by the spectrometer and telescope (V_inst), and the turbulence (V_turb) were obtained. Detailed calculation procedures are described in Lee & Hyung (2007). Also, the final FWHMs (or pure kinematical line broadening width) calculated by 2V_exp = (V_FWHM² - V_th² - V_inst - V_f-s² - V_turb²)_1/2 are shown in Table 4. As can be seen in Fig. 2, the measured FWHM of λ 4,10³.39 by using DIPSO is not clear because it is located in the right edge of the strong Hδ λ 4,101.74 line, overlapping together. In the latest study, Eriksson et al. (2005) reported that they found five N III lines in AG Peg but did not indicate the FWHM. Hence, the FWHMs measured in RR Tel of the symbiotic star (Selvelli et al. 2007) are shown in Table 4 for comparison.

The average FWHM of N III ordinary lines was 41.0 km·s^-1, 34.2 km·s^-1, and 38.2 km·s^-1 for the data of 1998, 2001, and 2002, respectively. There were no common N III ordinary lines for the three epochs, and the lines were weak, showing a large discrepancy that included large uncertainties. Comparing the FWHMs with those of Bowen lines is difficult. However, contrary to our expectation, the FWHMs of N III Bowen lines are not greater than those of ordinary lines and was smaller by about 5 km·s^-1 in 1998 and 2002. For the same epochs, the average FWHM of O III Bowen lines was 35.8 km·s^-1, 24.1 km·s^-1, and 33.0 km·s^-1 for 1998, 2001, and 2002, respectively. We can see that the average FWHMs are similar to the average FWHMs of N III Bowen lines in 1998 and 2002. However, in 2001, the average FWHM of N III Bowen lines was greater by about 15 km·s^-1. The large difference is likely to be caused by either the variation in the gas inflow rate from the giant star to the accretion disk around the WD or the WD stellar wind activity along its polar axis. The FWHM average for the three epochs was 35.8 km·s^-1, which was greater by about 5 km·s^-1 than the average FWHM of the O III Bowen lines for the same period.

We have measured the intensities of N III Ordinary Lines and Bowen Lines for the three epochs, using IRAF splot. The intensities were corrected by the extinction coefficient, C = 0.04 (Kim & Hyung 2008), to obtain the corrected intensities. For a similar reason similar to what is discussed about FWHMs in the previous section, while it is difficult to compare the measured intensities of ordinary lines and Bowen lines, the intensities of Bowen lines are generally greater by 5-8 times than those of ordinary lines (not presented in Table 5).

The results of previous studies on other objects are shown in Table 5 together with relative intensities predicted by Eriksson et al. (2005). The line intensities in Table 5 are relative intensities calculated with the line intensity of λ 4,640.64 set equal to 1.000. The intensity of λ 4,10³.39 is not so accurate since it is located at the right edge of the strong Hδ λ 4,101.74 line, overlapping together. Eriksson et al. (2005) calculated the predicted intensity (I_pred), a statistical intensity, through a six-stage semi-empirical formula, assuming that all N III lines were generated by the Bowen mechanism. On the whole, the observed values were greater than I_pred.

The suggested theories for the excitation mechanism of N III lines are LF, radiation recombination, and CF. While Eriksson et al. (2005) predicted I₄₆₃₄/I₄₆₄₀ to be 0.174 in AG Peg, this value is significantly smaller than the measured intensity ratio, I₄₆₃₄/I₄₆₄₀ = 0.433. They made an assertion that since the measured intensity ratio exhibits a large difference from the AG Peg theory, radiation recombination contributed to the excitation of N III lines, in addition to LF. The Bowen process requires resonance lines of high optical thickness (τ₀) (Selvelli et al. 2007). However, the semi-empirical formula, which Eriksson et al. (2005) used for the prediction of theoretical intensity, did not account for the average scattering number, , a function of τ₀, and assumed that all transitions were optically thin. For this reason, it is believed that a low value of intensity was predicted. In this study, the values of I₄₆₃₄/I₄₆₄₀ in AG Peg obtained from observations are 0.537, 0.562, and 0.557 for 1998, 2001, and 2002, respectively, as all values are relatively equal. Also, results from other investigations on I₄₆₃₄/I₄₆₄₀ produced values similar to 0.5.

Ferland (1992) performed calculations of a photo-ionization model through CF and reported that the intensity of N III 4,634.14 agreed well with the measured one. Thus, he made an argument that the three N III lines around λ 4,640 were the results of CF. Meanwhile, if CF contributed to N III λλ 374.198, 374.434, and 374.442 and produced three N III lines around λ 4,640, emission lines should be generated between 1,380- 4,890 Å for other N III extreme UVs (resonance lines of similar transition probability as λ 374 lines) (Selvelli et al. 2007). Hence, we have examined λλ 4,201.26, 4,855.16, 4,874.46, and 4,882.03, corresponding to the visible light range in our observation wavelength band for all three epochs, but we could not get any results. In other words, if N III 4,640.64 of the strongest intensity was influenced by the flux from a hightemperature central star, λλ 4,201.26, 4,855.19, 4,874.46, and 4,882.03 should appear in the visible light range, which did not agree with our spectroscopic observation data. This suggests that CF is not the contributor of excitation mechanism of N III lines. The description for the LF is given in Section 3.5.

In this section, we have predicted the intensities of O III and N III resonance lines around λ 374 and examined the amount of contribution by LF. First, when the Gaussian function is the normal distribution, we have calculated a using the correlation: area = $ac\sqrt{2\pi }$ , where a indicates the maximum intensity, c indicates the area under the curve, and the correlation of FWHM = $2\sqrt{2\ln 2c}$ 2.35482c holds true. In order to calculate c, we have utilized the average value of O III FWHM, 31 km·s^-1, and the average value of N III FWHM, 35.8 km·s^-1, for the three epochs of observation. As A_ij, which represents the transition probability between the two levels, is related to the line intensity, the A_ij value shown in Table 6 is put into the area to calculate the maximum intensity, a. We have set the intensity of N III λ 374.434, whose A_ij is the maximum, at 100 and calculated the relative intensities of O III λ 374 and N III λ 374. Next, using the Gaussian function,

we have plotted relative intensities, as shown in Fig. 3. In Eq. (3), b indicates the central wavelength and a and c have the same meaning described above. The value 0 km·s^-1 on the horizontal axis of Fig. 3 corresponds to λ 374.000. Since O III λ 373.803 shows a velocity difference of over 160 km·s^-1 with λ 374.004, it was excluded.

Fig. 3. Relative intensity curves of resonance lines O III and N III. It will be drawn using A_ij and FWHM that we have observed. Because A_ij of N III λ 374 is much larger than O III λ 374, the three lines of N III λ 374 are much larger than the five lines of O III λ 374. 0 km·s^-1 on the horizontal axis means λ 374.000. See the text.

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However, in Fig. 3, the intensities of five O III λ 374 lines are much smaller than the intensities of three N III λ 374 lines. That is, while the velocity difference between O III λ 374.162 and N III λ 374.198 is about 29 km·s^-1 and overlap is possible, the intensity of O III λ 374.162 is only 10.9 % of the N III λ 374.198 intensity. Also, as the velocity of O III λ 374.432 differs from those of N III λ 374.434, N III λ 374.442 by 2 km·s^-1, 8 km·s^-1, respectively, excitation is possible on account of almost perfect line matching. While the intensity of O III λ 374.432 is almost the same as that of N III λ 374.442, and it could contribute to the excitation to the level of 2s²3d 2D _3/2, as the intensity of O III λ 374.432 is only 13.1 % of the N III λ 374.434 intensity, the excitation to the level of 2s23d 2D is not possible. Thus, as the expected intensity through A_ij described previously cannot explain the reason why O III λλ 374.162, 374.432 excites N III λλ 374.198, of contribution by LF. First, when the Gaussian function is the normal dist_ribution, we have calculated a using the correlation: 374.434, 374.442 to the levels of 2s²3d ²D_3/2 and 2s²3d ²D_5/2, we have considered other possibilities.

According to the results of the comparison between our three-year observation data and the observation data of Selvelli et al. (2007), the intensities of the N III Bowen lines are greater than those of the O III Bowen lines. Considering only the 1998 data of this study reveals that the intensities of five N III Bowen lines are 2.2 times greater than those of the O III Bowen lines in 3,750-3,800 Å. The measured intensity data of the O III Bowen lines were obtained from Hyung et al. (2017). The Grotrian diagram, which represents the transition of O III Bowen lines, explains why the intensities of N III Bowen lines are stronger (Hyung et al. 2017). The A_ij of the first transition line indicates that the A_ijs of O III λ 3,444.06 and O III λ 3,132.79 are quite large, and the contribution to the line intensity by these two lines is about 88 %. In addition, including the contribution of O III λ 3,428.62 adds up to about 92 %, and these decay to 6 O III lines around λ 374, which makes the intensity of resonance lines very strong. The A_ijs of other emission lines (O III λλ 2,836.28, 2,818.66, and 2,807.90) of the first decay are about 8 %, and these lines contribute to the O III Bowen lines. Thus, the intensities of the O III Bowen lines are weak.

Note that the He II lines are also an important fluorescence source. The other UV He II 303 line eventually goes down to another optical channel, such as He II λ 4,685.68 (see Hyung et al. 2017). From the measured intensity of He II λ 4,685.68, we can estimate the intensity of He II Ly-α (λ 303.783) (Storey & Hummer 1995). In this study, due to the line matching between the estimated He II Ly-α and O III λ 303.800, the entire amount of the estimated intensity of He II Ly-α, which is about 1 %, is assumed to transfer to O III λ 303.800. Then, we can calculate the theoretical intensity of six O III resonance lines around λ 374 emitted from the first decay, second decay, and final third decay based on the transition and A_ij ratio, according to Grotrian diagram. As a result of the calculation of the theoretical intensities of O III resonance lines, the intensity of O III λ 374.073 was the strongest, the intensity of O III λ 374.162 was the weakest, and the intensity of λ 374.073 was 5.7 times stronger than that of λ 374.162.

We have calculated the expected intensities of three N III lines λλ 374.198, 374.434, and 374.442, contributing to the intensity of N III Bowen lines described below. Among the emitting lines from the first decay, O III λ 3,444.06 was observed from the 2002 observation data only and the fraction of transition probability A_ij was 22.5 %. The other UV lines of first decay were not observable since those were out of the observation wavelength range. Thus, in order to make the observation intensity of O III λ 3,444.06 100 %, the observed intensity was multiplied by 4.4 to produce the intensity of 4.74×10^-11 erg·cm^-2s-1. However, the sum of the intensity of five N III Bowen lines observed were 4.89×10^-12 erg·cm^-2s^-1. The ratio of the observed intensity of O III λ 3,444.06 multiplied by 4.4 to the sum of five N III Bowen line intensities were 1:0.10³. Thus, 10.3 % of total intensity of five O III λ 374 resonance lines, with the exception of O III λ 373.803, contributed to the three N III resonance lines, and it was assumed that the ratio was proportional to A_ij. For the 1998 data, the intensity of eight resonance lines of O III and N III were estimated. As a result, the intensity of O III λ 374.073 was the strongest, and the intensity of N III λ 374.442 was the weakest, with the ratio of two lines equal to 60.6. In Fig. 4, the eight intensity curves of O III resonance lines and N III resonance lines are shown using the average of the O III FWHM, 31 km·s^-1, and the average of the N III FWHM, 35.8 km·s^-1, and utilizing the Gaussian function. Fig. 4 represents the relative intensities with the strongest O III λ 374.073 set to 100. Only O III λ 374.162 contributed to N III λ 374.198, and the overlap between the two lines are 33 %. While the wavelength of N III λλ 374.434 and 374.442 matched O III λ 374.432 with almost 100 % agreement, there was a big difference in line intensities. In the case of 100 % wavelength match, the expected intensity of N III resonance lines was obtained considering the overlap fraction by line intensity ratio.

Fig. 4. Relative intensity curves of resonance lines O III and N III. It will be drawn using predicted intensity and FWHM that we have observed. Unlike Fig. 3, the O III resonance lines are much stronger than the N III resonance lines. 0 km·s^-1 on the horizontal axis means λ 374.000. See the text.

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As described above, in Fig. 4, O III λ 374.004 and λ 374.073 never contribute to N III λ 374.198, and only O III λ 374.162 makes a contribution. Hence, the excitation effect from 2s²2p EQ to 2s²3d ²2D_3/2, due to the line matching of O III λ 374.162 and N III λ 374.198, depends on the overlap between the two lines. For N III λ 374.434 and λ 374.442, O III λ 374.432 makes almost 100 % contribution. Thus, the excitation from the level of 2s²2p ${}^2{\text{P}}_{3/2}^{\text{o}}$ to the levels of 2s²3d ²2D_3/2 and 2s23d 2D5/2 can be explained with ease by the complete overlap between O III λ 374.432 and N III λ 374.434 or N III λ 374.442. On this basis, the assertion that LF is not effective (Eriksson et al. 2005) seems to be based upon the tiny line overlap between O III λ 374.162 and N III λ 374.198, which could not make up for the excitation energy to 2s23d ²2D_3/2. This does not look reasonable.

If it is true that the excitation mechanism of N III Bowen lines is LF due to line matching, FWHMs play an important role in the excitation in addition to the wavelength match of resonance lines of O III and N III around λ 374. When the FWHM of resonance lines becomes greater than the observed average FWHMs for O III and N III and, also, when the other O III resonance lines, excluding O III λ 374.162 and O III λ 374.432, have small overlaps on the edge, they can contribute to the line intensity, though perhaps insignificantly. We could not obtain the FWHM data for O III resonance lines. In most cases, the FWHM of resonance lines are broader than those of recombination lines or quasicombination lines, due to the increase in FWHM resulting from the Doppler effect (Selvelli et al. 2007). Oegerle et al. (1983) suggested that the opacity broadening of resonance lines is proportional to $\sqrt{\ln \left({\tau }_0\right)}$ and has a large impact on the contour of lines. If the optical thickness (τ₀) of the line center is in the range of 10³-10⁷, the FWHM will be 2.6-4.0 times greater than that for optically thin cases. Although our study was not carried out using the exact value of opacity and optical thickness at the line center, the present work was largely based on an optically thick assumption.

The efficiency of N III Bowen lines, R, indicates the conversion ratio of O III resonance line photons into Bowen line photons around N III λ 4,640. R can be calculated easily from the intensity ratio of the strongest O III Bowen lines (λ 3,132.79 or λ 3,444.06) to N III Bowen lines (λ 4,634.14, λλ 4,640.64, and λ 4,641.85). Kallman & McCray (1980) calculated R for 18 planetary nebulae, and they were in the wide range of 0.23-1.56. They also expressed the efficiency, R, of N III Bowen lines by the observed intensity ratio of O III λ 3,444.06 and N III λλ 4,634.14 and 4,640.64

In this study, we could only calculate R for the 2002 data in which O III λ 3,444.06 (I = 10⁷.8×10^-13 erg·cm^-2sec^-1) was measured, and R of AG Peg obtained from the Eq. (4) was 0.50. The R calculated using the photon number (N_ν) of O III λ 3,444.06 (N_ν = 1.869 cm^-2sec^-1), N III λ 4,634.14 (N_ν = 0.188 cm^-2s^-1), and N III λ 4,640.64 (N_ν = 0.337 cm^-2s-1), which were converted from line intensities, was 0.67, which was slightly higher. Meanwhile, Selvelli et al. (2007) calculated R of RR Tel to be 0.48. The efficiency of AG Peg being higher than RR Tel implies that the ionized shell of the former consists of much higher gas density, causing a large optical depth.

Based on the expected intensities for the resonance lines of N III λλ 374.198, 374.434, and 374.442 discussed in the previous section, we have calculated the expected intensity (I_pred) of N III Bowen lines, which experiences a lower transition with transition probability, A_ij, using the N III Grotrian diagram in Fig. 1. When calculating the expected intensity of 4,097.36 and 4,10³.39, extreme UVs whose A_ijs were large enough to impact the expected intensity were considered for those transitioning from the same level. In other words, for 4,097.36, the A_ij of extreme UVs, λλ 691.193 and 871.862, transitioning from the same level, were considered, and for 4,10³.39, the A_ij of extreme UVs, λλ 691.397 and 872.135, transitioning from the same level, were considered.

We did not calculate the theoretical expected intensities for the three observation epochs because the positions and the line intensities of GS and WD are different, depending on the phase of a symbiotic star, AG Peg. Only for 1998, when the phase was 0.24, were both GS and WD visible, and the expected intensities (I_pred and I_relpred) were obtained, as shown in Table 7. As mentioned above, Eriksson et al. (2005) obtained the ratio of expected intensities for AG Peg as I₄₆₃₄/ I₄₆₄₀ = 0.174 and argued that LF was not effective since the ratio was too small compared to the ratio of observed line intensities, 0.433. Selvelli et al. (2007) obtained the expected line intensity ratio I₄₆₃₄/I₄₆₄₀ = 0.09 under the assumption that the level 2s²3d²P_3/2 excitation was possible only by N III λ 374.442. As this value was less than the observed ratio of line intensity, 0.49, they made an assertion that O III λ 374.073 and λ 374.328 had an impact. However, in this study, since the observed line intensity ratio, I₄₆₃₄/I₄₆₄₀ = 0.537 for 1998 data was similar to the expected line intensity ratio, 0.617, it appeared that λλ 374.004, 374.073, and 374.328 had an impact in addition to O III λ 374.162 and λ 374.432, and it was confirmed that the excitation mechanism was LF.

To find out the energy balance in the N III transition, the photon number of N III emission lines, related to the Bowen fluorescence shown in the AG Peg spectrum, was calculated and summarized in Table 7, together with transition probability, A_ij, according to the wavelength.