2.1 Standard Ionizing SEDs

The ionizing radiation from the nucleus is expected to originate from thermal emission by gas accreting onto a supermassive black hole. Although thermal in nature, the energy distribution is broader than a blackbody since the continuum emission is considered to take place from an extended disk that covers a wide temperature range. In their photoionization models, (^{Ferguson et al. 1997}, hereafter Fg97) and (^{Richardson et al. 2014}, hereafter Ri14) assumed a SED where the dominant ionizing continuum corresponds to a thermal distribution of the form

where T _cut is the UV temperature cut-off and αUV the low-energy slope of the ‘big bump’, which is typically assumed to be αUV =-0.3. This thermal component dominates the ionizing continuum up to the X-ray domain where a power-law of index -1.0 takes over. The values for T _cut adopted by Fg97 and Ri14 are 10^6.0 and 10^5.62 K , respectively. Both distributions are shown in Figure 1. In both cases we have assumed a standard X-ray-to-optical spectral index² αOX of -1.35.

Figure 1: Ionizing spectral energy distributions described in § 2, in νFν units: (1) the SED adopted by Fg97 for their LOC calculations with    Tcut =106.0 K (long dashed line), (2) the optimized SED with    Tcut =105.62 K of Ri14 (dot-short dash line), and (3) the double-bump reprocessed distribution of La12 (thick grey line), and (4) two modified versions La  ⋆1 (cyan) and La  ⋆2 (blue) of the La12 reprocessed distribution. The La ⋆1 (cyan) and La ⋆2 (blue) SEDs were obtained by summing up the truncated La12 SED, FLa12pk1 (ν) (red dashed line), to both cyan and blue dotted linesF*pk2 (ν) distributions. The light-green dashed line corresponds to an accretion disk model including optically thick Compton emission by a warm plasma. It was calculated using the OPTXAGN model in XSPEC (Done et al. 2012, see § 5.3). The above SEDs were renormalized to νFν of unity at 5 eV (2480 Å). In the X-ray domain, a power-law of index -1.0 was assumed with an αOX of -1.35. The magenta line represents the average of the soft X-ray excess measurements inferred by Pi05, assuming αOX =-1.35 with respect to the La12 distribution. The color figure can be viewed online. 

2.2 The Proposition of a Double-Peaked SED

To address the temperature problem, (^{Lawrence 2012}, hereafter La12), explored the possibility that a population of internally cold very thick (NH>1024cm ^-2) dense clouds (n≈1012cm ^-3) covers the accretion disk at a radius of ≈35 Rs from the black-hole, where R _s is the Schwarzschild radius. The cloud’s high velocity turbulent motions blur its line emission as well as reflect the disk emission, resulting in a double-peaked SED superposed to the reflected SED. The first peak at ≈1100Å represents the clouds reprocessed radiation while the second corresponds to the disk radiation reflected by the clouds. The resulting SED is represented by the thick light-gray continuous line in Figure 1. The main advantage of this distribution is its ability to account for the ‘universal’ knee observed at 12 eV in quasars. The assumed position of the second peak at 40 eV would however need to be shifted to much higher energies in order to significantly increase the photoheating efficiency and subsequently reproduce the observed R _OIII ratio. This possibility, which is explored in the current work, might imply adjustments of the ‘reprocessing model’ since the turbulent clouds, hypothesised by La12, would likely need to extend to much smaller radii than the assumed value of 35 R _s . Alternatively, the hotter inner component of the accretion disk might progressively become uncovered at smaller disk radii. We note that similar double-peaked SEDs would arise if the primary disk emission was further Compton up-scattered to higher energies owing to the presence of an optically thick warm plasma in addition to the hot thin corona responsible for the hard X-rays ^{Done et al.(2012)}. We will further discuss this possibility in § 5.

2.3 Components of Our Modified Double-Peak La ⋆1SED

After experimenting with different shapes and positions for the second peak, it was found that the presence of a deep valley at ≃35 eV can result in an increase of the plasma temperature (i.e. higher R _OIII ratio). To explore double-peak SEDs, we proceeded as follows. First, we extracted a digitized version of the published La12 SED. To eliminate the 40 eV peak we extrapolated the declining segment of the first peak. The resulting distribution is represented by the red dashed line labelled FLa12pk1 (ν) in Figure 1. For the second peak, F*pk2 (ν), we adopted the formula, ν αUV exp(-hν/k   Tcut ) (i.e. equation 1). All the double-bump SEDs which we explored were obtained by simply summing both distributions:

where R= FLa12pk1 (νpk1)/ F*pk2 (νpk1) is the renormalization factor which we define at hνpk1=12 eV , the energy where the first peak reaches its maximum in νFν. The position and width of the second peak depends on both parameters αUV and T _cut while its intensity is set by the parameter r21pk2. The main benefit of the second peak is to increase the local heating rate due to He⁺ photoionization (c.f. § 5.1).

After comparing the plasma temperatures reached when different combinations of the parameters T _cut , αFUV and r21pk2 are considered, we concluded that the optimal position for the second peak is ≈200 eV . Moving it to higher values was not an option, as it generated an excessive flux in the soft X-rays that is not observed in Type II AGN.

Our first version for the optimal SED, labelled La ⋆1, is shown in Figure 1 (cyan solid line). It assumes an index αFUV =+0.3 as in Ri14 and Fg97, which corresponds essentially to the index of the standard Shakura-Sunyaev accretion disk model ^{Shakura Sunyaev (1973)}, ^{Pringle(1981)}, ^{Cheng et al.(2019)} of αFUV =1/3. The value derived for the parameter T _cut is 1.6 10⁶ K and the optimal value for the scaling factor is r21pk2 =0.08. Increasing r21pk2 further would require a reduction in T _cut , otherwise the resulting SED would extend too far into the soft X-rays.

2.4 An Alternative Double-Peak SED: La ⋆2

The La ⋆1 SED drops off around 800 eV (Figure 1). It is important to ensure that the predicted flux beyond 500 eV does not exceed the soft X-rays measurements. While some AGN show extreme emission in the so-called X-ray soft excess up to 1-2 keV , others do not. One solution would be to adopt larger values for the parameter αFUV. To illustrate this, our second version of the double-bump SED, labelled La ⋆2, uses a much larger αFUV of +3. In this case the optimal value for the parameter T _cut has to be as low as 0.5 10⁶ K so that the second peak occurs at essentially the same energy as in the La ⋆1 SED. Because the peak profile is much narrower (dotted blue line), the scaling parameter r21pk2 turns out to be much smaller, at 0.001.

Note that if we had assumed the Planck equation, as in La12, for the second peak instead of equation 1, the favored position of the second peak near 200 eV would correspond to a blackbody temperature of    TBB ≃500 000 K , that is, five times higher³ than the    TBB ≃100 000 K temperature proposed by La12.

2.5 The Unaccounted Soft X-Ray Excess Below 2 keV

There are few competing processes that have been proposed to explain the physical mechanism responsible for the so called X-ray soft excess. The most popular ones include a dual-coronal system (e.g. Done et al. 2012) or relativistic blurred reflection (e.g. ^{Ross & Fabian 2005}). For illustrative purposes, we show in Figure 1 the “average soft excess” component observed with XMM-Newton (magenta line) by (^{Piconcelli et al. 2005}, hereafter Pi05). It corresponds to the best-fit average of 13 quasars with z<0.4 using the parameters from Table 5 of Pi05, as described in ^{Haro-Corzo et al.(2007)}. This component was re-scaled so as to reproduce an αOX of -1.35 with respect to the La12 SED. The dotted section below 600 eV is speculative, as it is not reliably constrained by X-ray measurements.

The soft excess varies strongly among different individual objects and its nature might be completely different than the emission in the extreme UV postulated here. On the other hand, the Comptonization of disk photons by a warm plasma can explain the presence of the soft excess ^{Done et al.(2012)} and at the same time produce double-peaked SEDs with the second peak near 200 eV (see § 2.2). The same might be true for blurred reflection/emission, as relativistic line emission has been used to (1) model the soft excess in a successful way (e.g. ^{Ross & Fabian 2005}), and (2) produce specific ionizing SEDs that result in two emission bumps in the extreme UV (La12, see § 2.2). While tantalizing, exploring these possibilities is beyond the scope of this paper. The important point is that the proposed SEDs in this paper are consistent with the soft excess observed in quasars.

3.1 Seyfert 2 Samples

In order to compare our calculations with observed ratios among Type II AGN, we adopt the three samples used by BVM, which are represented in Figure 2 by black open symbols. They correspond to the following dereddened⁴ measurements:

Figure 2 Dereddened NLR ratios of [O III] / Hβ vs. R _OIII . Data set: line ratios from three samples of Type II AGN, all represented by open black symbols and consisting of: (1) the average of seven Seyfert 2’s from Kos78 (large circle); (2) the average of four Seyfert 2’s from Be06b (small circle); (3) the high excitation Seyfert 2 subset a41 from Ri14 (diamond). ENLR measurements are all represented by dark-green filled symbols consisting of: (1) the average of two Seyfert 2’s and two NLRGs (small dot) from BWS; (2) the Seyfert 2 IC 5063 long slit spectrum of Be06b (pentagon); (3) the average of seven spatially resolved optical filaments of the radio-galaxy Centaurus A (green square) from Mo91; (4) the 8 kpc distant cloud from radiogalaxy Pks 2152-699 by Ta87 (large green dot). Type I AGN ratios are overlaid consisting of 30 quasars studied by BL05 (open grey squares). Models: Five sequences of photoionization models are overlaid along which U _o increases from 0.01 (grey dot) to 0.46 in steps of 0.33 dex, assuming a constant plasma density of    nH  o =102cm ^-3. A square identifies models with      U  o =0.1. The SEDs were borrowed from Ri14 (yellow), La12 (red) and Fg97 (magenta). The dotted magenta arrow shows the effect caused by adopting a reduced abundance of 1.4 Z. Calculations using the two double-peaked La ⋆1 and La ⋆2 SEDs are coded in cyan and blue colors, respectively, while those that assume Comptonization of the accretion disk photons are coded in light-green. The color figure can be viewed online.  

3.2 Spatially Resolved ENLR

We superpose in Figure 2 the ratios observed from the spatially resolved emission component of AGN, the so-called ENLR, which consists of off-nuclear line emission from plasma with densities typically <103cm ^-3 (e.g. ^{Tadhunter et al. 1994}; ^{Bennert et al. 2006a},^b). The selected measurements are represented by the filled dark-green symbols, which stand for the following four samples: (1) the average (small filled dot) of two Seyfert 2’s and two NLRGs from ^{Binette et al.(1996, hereafter BWS)}; (2) the long-slit observations of the Seyfert 2 IC 5063 by Be06b (pentagon); (3) the average of seven spatially resolved optical filaments from the radio-galaxy Centaurus A (filled square) from (^{Morganti et al. 1991}, hereafter Mo91); and (4) the 8 kpc distant cloud from radio galaxy Pks 2152-699 observed by (^{Tadhunter et al. 1987}, hereafter Ta87) (large dot). Pseudo-error bars denote the RMS dispersion of the BWS sample.

3.3 Quasar Sample

For illustrative purposes, we overlay in Figure 2 the measurements of the NLR ratios (open grey squares) from 30 quasars of redshifts z<0.5, which were studied by BL05. The R _OIII ratios are found to extend from 0.01 up to 0.2, providing clear evidence that collisional deexcitation takes place within the NLR of Type I objects.

3.4 Data set Comparison

The detailed study of BVM of the Seyfert 2 sample from Kos78 rely on the measured density sensitive [Ar IV] λλ4711,40Å doublet. The authors found no evidence that significant collisional deexcitation was affecting the observed R _OIII ratios, even after considering a power-law distribution of the densities in their plasma calculations of R _OIII and [Ar IV] ratios. Furthermore, both Seyfert 2’s and ENLR measurements occupy a similar position in Figure 2, which is likely a consequence of LDR, since detailed studies of ENLR spectra are consistent with plasma densities ≪104 cm-3. By contrast, quasar NLR measurements of BL05 span a wide range in R _OIII , with the lowest ratios lying close to the values seen in Seyfert 2’s and in the ENLR plasma. This dichotomy between Type I and II objects is likely the manifestation of the observer’s perspective on the NLR as a consequence of the unified AGN geometry, whereby the densest NLR components become progressively obscured in Type II objects due to the observer’s lateral perspective on the ionizing cone. A graphical description of such geometry is illustrated by Figure 2 of ^{Bennert et al.(2006c)}.

4.1 Dust-Free Plasma with Abundances Above Solar

In this paper, we will only consider the case of a dust-free plasma. Insofar as plasma metallicities, it is generally accepted that gas abundances of galactic nuclei are significantly above solar values. The metallicities we adopt below correspond to 2.5 Z, a value within the range expected for galactic nuclei of spiral galaxies, as suggested by the ^{Dopita et al.(2014)} landmark study of the Seyfert 2 NGC 5427 using the Wide Field Spectrograph (WiFeS: ^{Dopita et al. 2010}). The authors determined the ISM oxygen abundances from 38 H II regions spread between 2 and 13 kpc from the nucleus. Using their inferred metallicities, they subsequently modelled the line ratios of over 100 ‘composite’ ENLR- H II region emission line spaxels as well as the line ratios from the central NLR. Their highest oxygen abundance reaches 3 Z (i.e. 12  +  logO/H =9.16. Such a high value is shared by other observational and theoretical studies that confirm the high metallicities of Seyfert nuclei ^{Storchi-Bergmann & Pastoriza(1990)}, ^{Nagao et al.(2002) Ballero et al.(2008)}. Our selected abundance set is twice the solar reference set of ^{Asplund et al.(2006)}, i.e. with O/H=9.8×10-4, except for C/H and N/H which reach four times the solar values owing to secondary enrichment.

We can expect the enriched metallicities of galactic nuclei to be accompanied by an increase in He abundance. We followed a suggestion from David Nicholls (private communication, ANU) of extrapolating to higher abundances the metallicity scaling formulas that ^{Nicholls et al.(2017)} derived from local B stars abundance determinations. At the adopted O/H ratio, the proposed scaling formula described by equation A1 in Appendix 6 implies a value of He/H = 0.12, which is higher than the solar ratio of 0.103 adopted by Ri14. The effect on the equilibrium temperature, however, is relatively small as the calculated R _OIII ratios are found to increase by only 0.06 dex whether one assumes the Fg97, Ri14 or La12 SED.

4.2 Characterization of the Temperature Problem

The difficulty in reproducing the observed R _OIII ratio is illustrated by the three ionization parameter sequences shown in Figure 2 that fall on the extreme left of the diagram. Two of the SEDs were borrowed from the standard NLR models of Ri14 (yellow) and Fg97 (magenta) while the third corresponds to the double-peaked SED from La12 (in red). Along each sequence, the ionization parameter⁵, U _o , increases in steps of 0.33 dex, from 0.01 (light gray dot) up to 0.46. These sequences do not reach the R _OIII domain occupied by our sample of Seyfert 2’s, with some models falling outside the plot boundaries.

4.3 Calculations with the La ⋆1and La ⋆2SEDs

The procedure followed to define the double-peaked La ⋆1 and La ⋆2 energy distributions (Figure 2) has been described in §2.3 and 2.4. Photoionization calculations using either SED are successful in reproducing the R _OIII ratios from the Seyfert 2 Kos78 sample (black circle), as shown by the solid cyan and dotted blue lines in Figure 2, which represent ionization parameter sequences with increasing in steps of 0.33 dex, from 0.01 (the light-gray dot) up to 0.46, assuming a constant plasma density of    nH  o =102cm ^-3. A square identifies models with      U  o =0.1. Our models suggest that either of the double-bump SEDs has the potential of resolving the temperature discrepancy encountered with conventional ionizing distributions.

We would qualify the two La ⋆1 and La ⋆2 SEDs as representing two extreme cases with respect to the parameter αFUV. Ionizing continua that assumed intermediate values, in the range 0.3< αFUV   <3, would be equally successful in reproducing the observed R _OIII ratios provided the parameters T _cut and r21pk2 were properly adjusted to maintain the second peak centered at 200 eV and at an intermediate height between La  ⋆1 and La ⋆2.

In order to compare our models with Type I AGN (open grey squares), we calculated density sequences along which the density increases in steps of 0.5 dex, from nH  o =100 to 10⁷ cm ^-3. These calculations are shown in Figure 3. For each sequence, we selected the U _o value that made the models cover the upper envelope of the quasar [O III] / Hβ ratios, which are      U  o =0.46 and 0.10 for the La ⋆1 and La ⋆2 SEDs, respectively. The vertical dispersion in the observed [O III] / Hβ ratios is noteworthy. The simplest interpretation might be the need of considering a distribution of cloud densities, as favored by the dual-density models of BL05. Alternatively, in the case of the Ri14 LOC models, the observed dispersion suggests that the density power-law index β might take different values.

Figure 3: Dereddened [O III] / Hβ (λ 5007Å/ λ 4861Å ) and He II / Hβ (λ 4686Å/ λ 4861Å) line ratios. The observational data sets of § 3 are represented by the same symbols as in Figure 2. Overlaid are two sequences of models along which n Ho increases from 10² to 10⁷ cm ^-3 in steps of 0.5 dex. The ionization parameter is      U  o =0.46 for the La ⋆1 sequence (cyan) and      U  o =0.10 for the La ⋆2 sequence (blue). The color figure can be viewed online.  

4.4 The He II / HβDiagnostic Ratio

When comparing different ionizing distributions, an important ratio to consider is He II / Hβ λ 4686Å/λ 4861Å since, as pointed out by Ri14, the latter is sensitive to the hardness of the ionizing continuum. Figure 4 illustrates the behavior of the dereddened [O III] / Hβ vs. He II / Hβ ratios assuming either the La ⋆1 or the La ⋆2 ionizing continua. They reproduce reasonably well the He II / Hβ ratio observed among the Seyfert 2’s of Kos78 and Be06b. Also overlaid is the γ sequence from the LOC calculations (yellow dashed line) of Ri14, assuming a density weighting parameter β of -1.4, the value favored by the authors when modeling their four AGN subsets⁶.

Figure 4 Dereddened [O III] / Hβ (λ 5007Å/ λ 4861Å ) and He II / β (λ 4686Å/λ 4861Å) line ratios. The observational data sets of § 3 are represented by the same symbols as in Figure 2. Both density sequences from previous Figure 3, using the La ⋆1 (cyan) and La ⋆2 (blue) SEDs, are overlaid. The light-green dotted line represents a density sequence assuming the accretion disk SED derived using the OPTXAGN routine. In each sequence, a cross identifies the lowest density model with    nH  o =100cm ^-3. The yellow dashed line represents the dust free LOC model sequence from Ri14 with β=-1.4, along which the radial weighing parameter γ varies from +0.75 to -2.0 in steps of-0.25. The color figure can be viewed online.  

If we compare the Type II samples (black open symbols) with the spatially resolved ENLR (dark-green symbols), we notice a wider dispersion among the He II / Hβ ratios than for the R _OIII ratios of Figure 3, which is surprising given the fact that the He II / Hβ ratio depends little on density or temperature. This could be an indication that the emitting plasma in some cases is not fully ionization-bounded, as proposed by BWS.

5.1 Plasma Heating from He ⁺ Photoionization

The presence of high excitation lines among NLR spectra such as He II , C III] , C IV , [Ne III] indicates a hard ionizing continuum. As a consequence of the SED hardness, the heating rate as well as the resulting equilibrium temperatures are higher than in H II regions, due to the higher energies of the ejected photoelectrons and to the significant contribution of He⁺ photoionization to the total heating rate, at least within the front layers of the exposed nebulae. The fraction of ionizing photons with energies above 54.4 eV is 24 % and 26 % for the La ⋆2 and La ⋆1 SEDs, respectively, and 23 % for the Fg97 distribution⁷. These values are quite similar, but when a dip takes place below 50 eV , as in the La ⋆2 and La ⋆1 SEDs (see Figure 1), the peak of the distribution in νFν shifts to higher energies (≃200 eV). Consequently, the plasma heating rate⁸ rises above the rate obtained with the Fg97 SED, essentially as a result of the increase in the mean energy of the photoelectrons ejected from ionization of He⁺.

5.2 The Shape of the EUV Dip Near 40 eV

Being able to reproduce the observed R _OIII measurements of Seyfert 2’s by assuming the above double-peaked La ⋆1 and La ⋆2 SEDs does not prove it is the right solution to the temperature problem, but it is a possibility worth exploring further. One advantage of the proposed distributions is that, unlike the conventional thermal SEDs of Ri14 or Fg97, they incorporate the ‘universal’ knee observed near 12 eV in high redshift quasars, which ^{Zheng et al.(1997)} and ^{Telfer et al.(2002)} studied using the Hubble Space Telescope archival database. Using the Far Ultraviolet Spectroscopic Explorer database, ^{Scott et al.(2004)} find an average index αν of -0.56 in AGN of redshifts <0.33, which is significantly flatter than the average of ≃-1.76 found at redshifts z ≥ 2 ^{Telfer et al.(2002)}. How steeply the flux declines beyond 12 eV is rather uncertain and could also depend on the AGN luminosity ^{Scott et al.(2004)}.

5.3 Comptonized Accretion Disk Models

The pertinence of a second peak to describe the harder UV component is provided by the work of ^{Done et al.(2012)}, who built a self-consistent accretion model where the primary emission from the disc is partly Comptonized by an optically thick warm plasma, forming the EUV. This plasma that, according to ^{Done et al.(2012)}, might itself be part of the disk would exist in addition to the optically thin hot corona above the disc responsible for producing the hard X-rays.

Using the OPTXAGN routine in XSPEC⁹, we calculated an accretion disk model that allowed the second peak to occur at a similar position as that of the La ⋆2 SED. It is represented in Figure 1 by the light green dashed curve. Different sets of parameters in the OPTXAGN model can match the double peaked La ⋆1 and La ⋆2 SEDs, provided extreme accretion rates are assumed (L/L Edd≥1). Such accretion rates are not proper of the Type II objects discussed here, but rather of extreme Narrow Line Seyfert 1 nuclei. Even though the OPTXAGN model was not developed to generate the double peak SEDs postulated in this work, we should note that a wide set of SEDs with different double peaks or even more extreme FUV peaks can be produced using different, less stringent, parameters. Our aim in presenting this SED, apart from matching our La ⋆2 SED, was to exemplify how different physical processes at different accretion disk scales might result in an ionizing distribution capable of reproducing the observed R _OIII ratio. We plan to fully explore under which conditions (e.g. more conservative SEDs with moderate accretion rates), dual temperature Comptonization disk models can achieve this.

An additional drawback is that the OPTXAGN model does not reproduce the knee observed at 12 eV . Expanding the range of parameters in this model might circumvent this issue. Overall, we note the striking similarity of the OPTXAGN with that of La ⋆2, considering that they were built independently and with completely different scientific motivations. Photoionization calculations with this SED indicate that, as expected, it can reproduce the observed R _OIII ratio, as shown by the light-green dotted line in Figure 2. The He II / Hβ ratio, however, is somewhat under-predicted, as shown in Figure 2. This appears to be caused by the first peak of the OPTXAGN SED being significantly thicker than in the La ⋆2 SED.