A NEW BLACK HOLE MASS ESTIMATE FOR OBSCURED ACTIVE GALACTIC NUCLEI

First, we compare the velocity width of the neutral FeKα line core with that of the broad Balmer emission lines and that corresponding to the dust reverberation radius to examine the location of its emitting region.

In Figure 1, we plotted the FWHM of the neutral FeKα line core against those of the broad Hβ emission line and the polarized broad Balmer emission lines for the type 1 and type 2 target AGNs, respectively. We also plotted the line that represents the FWHM at the dust reverberation radius observed in the K band, which is estimated by scaling the FWHM of the broad Hβ emission line according to the virial relation based on the systematic difference of the reverberation radii of the broad Hβ emission line and the near-infrared dust emission (Koshida et al. 2014).

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As shown in Figure 1, we find that the FWHM of the neutral FeKα line core falls between that of the broad Balmer emission lines and the corresponding value at the dust reverberation radius for all  type 2 AGNs, and for most  type 1 AGNs except for the only outlier, NGC 7469. This suggests that a significant fraction of photons of the neutral FeKα line core originates between the outer BLR and the inner dust torus in most cases.

As a next step, we scaled the radius–luminosity scaling relation of the broad Hβ emission line according to the systematic difference between the FWHMs of the neutral FeKα line core and the broad Hβ emission line for the type 1 AGNs assuming the virial relation. It is estimated by linear regression analysis where the slope is fixed to unity, and the best-fit linear regression is ${\rm logFWH}{{{\rm M}}_{{\rm FeK}\alpha }}={\rm logFWH}{{{\rm M}}_{{\rm H}\beta }}-\;0.186\ (\pm 0.088)$ with an additional scatter of 0.11 dex in both directions for the reduced ${{\chi }^{2}}$ to achieve unity. Then, the emitting-region radius of the neutral FeKα line core is estimated as

$$\begin{eqnarray}&&{\rm log} {{r}_{{\rm FeK}\alpha }}={\rm log} {{r}_{{\rm H}\beta }}-0.37\ (\pm 0.18)\end{eqnarray} \tag{ 1 }$$

according to the virial relation. Koshida et al. (2014) estimated the luminosity scaling relation of the reverberation radii to the luminosity of the [O iv] emission line in the form of ${\rm log} r=\alpha +0.5{\rm log} {{L}_{[{\rm OIV}]}}/{{10}^{41}}\ {\rm erg}\ {{{\rm s}}^{-1}}$, as $\alpha =-1.94(\pm 0.07)$ and $\alpha =-1.28\ (\pm 0.07)$ for the reverberation radius of the broad Hβ emission line and the dust reverberation radius observed in the K-band, respectively. By scaling the former relation according to Equation (1), the luminosity scaling relation of the emitting region radius of the neutral FeKα line core is estimated as

$$\begin{eqnarray}\begin{array}{rcl} {\rm log} {{r}_{{\rm FeK}\alpha }} & = & -1.57\ (\pm 0.19) \\ {} & {} & +0.5{\rm log} {{L}_{[{\rm OIV}]}}/{{10}^{41}}\ {\rm erg}\ {{{\rm s}}^{-1}}. \\ \end{array}\end{eqnarray} \tag{ 2 }$$

The radius–luminosity scaling relation for the neutral FeKα line core of Equation (2) is located between the reverberation radii of the broad Hβ emission line and the dust torus emission in the K band as indicated by Figure 1, and we use it for the estimation of the black hole mass in the next section.

Next, we estimate the black hole mass of both type 1 and type 2 target AGNs using the neutral FeKα line core. The emitting-region radius ${{r}_{{\rm FeK}\alpha }}$ is estimated from ${{L}_{[{\rm OIV}]}}$ and the radius–luminosity scaling relation of Equation (2) because the hard X-ray flux seems to be attenuated in some heavily obscured AGNs in the targets. The ${{L}_{[{\rm OIV}]}}$ value is taken from Liu & Wang (2010), based on the original data of Melèndez et al. (2008) and Diamond-Stanic et al. (2009) for most of the targets; however, it is recalculated from the [O iv] emission-line flux of Diamond-Stanic et al. (2009), assuming the redshift-independent distance from the NASA/IPAC Extragalactic Database for very nearby objects. In addition, the ${{L}_{[{\rm OIV}]}}$ of NGC 2110 is calculated from the data of Weaver et al. (2010). We then estimate the black hole mass assuming the virial relation as

$$\begin{eqnarray}&&{{M}_{{\rm BH},{\rm FeK}\alpha }}=f\frac{{{r}_{{\rm FeK}\alpha }}\sigma _{{\rm FeK}\alpha }^{2}}{G}\end{eqnarray} \tag{ 3 }$$

where f is the virial factor and ${{\sigma }_{{\rm FeK}\alpha }}$ is the velocity dispersion of the neutral FeKα line core. We adopt f = 5.5 following the references of the broad emission-line reverberation for the type 1 target AGNs (Onken et al. 2004; Peterson et al. 2004; Bentz et al. 2006, 2007; Denney et al. 2010; Grier et al. 2012). The velocity dispersion is calculated as ${{\sigma }_{{\rm FeK}\alpha }}={\rm FWH}{{{\rm M}}_{\;{\rm FeK}\alpha }}/2.35$ because a Gaussian emission-line profile is used for the spectral fitting of the neutral FeKα line core in Shu et al. (2010, 2011). The ${{L}_{[{\rm OIV}]}}$ and the ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ for the type 1 and type 2 target AGNs are listed in Tables 1 and 2, respectively.

The FWHM of the neutral FeKα line core spreads between that of the broad Hβ line and that corresponding to the dust reverberation radii in most cases. This scatter causes a systematic uncertainty in the ${{r}_{{\rm FeK}\alpha }}$ derived from the radius–luminosity scaling relation, and also yields ±0.3 dex or a factor ∼2 uncertainty in these black hole mass estimates, ${{M}_{{\rm BH},{\rm FeK}\alpha }}$, including the measurement errors of the line widths in the data. As in the case of NGC 7469, in which the FWHM of the neutral FeKα line is significantly larger than that of the broad Hβ line, ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ could sometimes be overestimated.

Finally, the black hole mass ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ estimated from the neutral FeKα line core is compared with other estimates of the black hole mass for the same target to examine the consistency between them. For the type 1 AGNs, we compared ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ with the broad emission-line reverberation mass, ${{M}_{{\rm BH},{\rm rev}}}$, and for the type 2 AGNs, we compare it with the mass ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ based on the H₂O maser and the single-epoch mass estimate ${{M}_{{\rm BH},{\rm pol}}}$ based on the polarized broad Balmer lines. The ${{M}_{{\rm BH},{\rm pol}}}$ is calculated in the same way as the ${{M}_{{\rm BH},{\rm FeK}\alpha }}$, except that the radius–luminosity scaling relation of the broad Hβ emission line presented by Koshida et al. (2014) is used. The ${{M}_{{\rm BH},{\rm rev}}}$, ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$, ${{M}_{{\rm BH},{\rm pol}}}$, and their references are listed in Tables 1 and 2.

In Figure 2 ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ is plotted against other black hole mass indicators such as ${{M}_{{\rm BH},{\rm rev}}}$, ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$, and ${{M}_{{\rm BH},{\rm pol}}}$ for the type 1 and type 2 target AGNs. We then calculated Pearson's correlation coeffient, and also performed linear regression analysis to ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ and the other black hole mass indicators. The resultant values are listed in Table 3, and the best-fit linear regression lines are also presented in Figure 2.

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Table 3.  Correlation Coefficients and Linear Regressions to ${{M}_{{\rm BH},{\rm FeK}\alpha }}$

MBH,ref	n a	R b	log MBH,0c	a c	b c
			(M⊙)
MBH,revd	6	0.701	7.5	−0.19 ± 0.17	1.52 ± 0.92
				−0.15 ± 0.11	1.0 (fixed)
MBH,pol	6	0.831	7.5	−0.13 ± 0.13	1.05 ± 0.25
				−0.12 ± 0.11	1.0 (fixed)
${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$	4	0.960	6.5	0.70 ± 0.12	1.57 ± 0.33
				0.73 ± 0.14	1.0 (fixed)

^aThe number of the data. ^bPearson's correlation coefficient. ^cThe fitted model is ${\rm log} ({{M}_{{\rm BH},{\rm FeK}\alpha }}/{{M}_{{\rm BH},0}})=a+b\times {\rm log} ({{M}_{{\rm BH},{\rm ref}}}/{{M}_{{\rm BH},0}})$, where a and b are the parameters to be fitted. ^dNGC 7469 was excluded from the calculations of the correlation coefficient and the linear regression.

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For the type 1 AGNs, ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ and ${{M}_{{\rm BH},{\rm rev}}}$ are consistent within $\pm 2\sigma$ except for NGC 7469. The best-fit linear regression where the slope is fixed to unity is estimated as

$$\begin{eqnarray}\begin{array}{rcl} {\rm log} ({{M}_{{\rm BH},{\rm FeK}\alpha }}/{{10}^{7.5}}\;{{M}_{\odot }}) & = & -0.15\ (\pm 0.11) \\ {} & {} & +{\rm log} ({{M}_{{\rm BH},{\rm rev}}}/{{10}^{7.5}}\;{{M}_{\odot }}), \\ \end{array}\end{eqnarray} \tag{ 4 }$$

which indicates that the systematic difference between them is within a factor of several tens percent. However, the correlation between ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ and ${{M}_{{\rm BH},{\rm rev}}}$ is not clear, as in a preceding study (Jiang et al. 2011). Excluding the clear outlier NGC 7469, Pearson's correlation coefficient is calculated as R = 0.701, which indicates that the confidence level of the correlation is less than 90%. Their best-fit linear regression is estimated as

$$\begin{eqnarray}\begin{array}{rcl} {\rm log} ({{M}_{{\rm BH},{\rm FeK}\alpha }}/{{10}^{7.5}}\;{{M}_{\odot }}) & = & -0.19\ (\pm 0.17) \\ {} & {} & +1.52\ (\pm 0.92) \\ {} & {} & \times {\rm log} ({{M}_{{\rm BH},{\rm rev}}}/{{10}^{7.5}}\;{{M}_{\odot }}) \\ \end{array}\end{eqnarray} \tag{ 5 }$$

with an additional scatter in both directions for the reduced ${{\chi }^{2}}$ to achieve unity. The large uncertainty in the slope of the best-fit linear regression also indicates no or weak correlation between them.

For the type 2 AGNs, ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ are also consistent with ${{M}_{{\rm BH},{\rm pol}}}$ within ± 2σ. The best-fit linear regression for ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ and ${{M}_{{\rm BH},{\rm pol}}}$ is estimated as

$$\begin{eqnarray}\begin{array}{rcl} {\rm log} ({{M}_{{\rm BH},{\rm FeK}\alpha }}/{{10}^{7.5}}\;{{M}_{\odot }}) & = & -0.13\ (\pm 0.13) \\ {} & {} & +1.05\ (\pm 0.25) \\ {} & {} & \times {\rm log} ({{M}_{{\rm BH},{\rm pol}}}/{{10}^{7.5}}\;{{M}_{\odot }}), \\ \end{array}\end{eqnarray} \tag{ 6 }$$

which indicates that the systematic difference between ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ and ${{M}_{{\rm BH},{\rm pol}}}$ is also within a factor of several tens percent. In addition, ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ and ${{M}_{{\rm BH},{\rm pol}}}$ are well correlated and show an approximately proportional relationship, since the slope of the best-fit linear regression is positive at more than $3\sigma$ uncertainty and close to unity. Pearson's correlation coefficients are calculated as R = 0.831, which indicates that the confidence level of the correlation is more than 95%.

In contrast to the good agreement with ${{M}_{{\rm BH},{\rm pol}}}$, ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ seems to be systematically larger than ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ although they show a clear correlation with Pearson's correlation coefficient of R = 0.960, indicating a confidence level of more than 95%. The best-fit linear regression is estimated as

$$\begin{eqnarray}\begin{array}{rcl} {\rm log} ({{M}_{{\rm BH},{\rm FeK}\alpha }}/{{10}^{6.5}}\;{{M}_{\odot }}) & = & 0.70(\pm 0.12) \\ {} & {} & +1.57\ (\pm 0.33) \\ {} & {} & \times {\rm log} ({{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}/{{10}^{6.5}}\;{{M}_{\odot }}), \\ \end{array}\end{eqnarray} \tag{ 7 }$$

which indicates that ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ is systematically larger than ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ by about a factor of ∼5. We note that ${{M}_{{\rm BH},{\rm pol}}}$ is also larger than ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ by a similar factor for the three targets, NGC 1068, NGC 4388, and Circinus, for which both ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ and ${{M}_{{\rm BH},{\rm pol}}}$ are estimated.

To summarize the results, ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ is consistent with ${{M}_{{\rm BH},{\rm rev}}}$ for most of the type 1 AGNs and with ${{M}_{{\rm BH},{\rm pol}}}$ for all of the type 2 AGNs. ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ correlates well with ${{M}_{{\rm BH},{\rm pol}}}$ and ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ for the type 2 AGNs, although ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ is systematically smaller than the others. These results suggest that the black hole mass estimate using the neutral FeKα line is a potential indicator of the black hole mass, especially for obscured AGNs.

The systematic difference of ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ implies an ambiguous issue. Since ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ is considered to be the most precise estimate for the black hole mass, then, through the relations of ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ with ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ and ${{M}_{{\rm BH},{\rm pol}}}$, another reliable estimate ${{M}_{{\rm BH},{\rm rev}}}$ is suspected to considerably overestimate the black hole mass, which is difficult to be accounted for by the uncertainties in the virial factor f (5.5 in this paper and in Onken et al. 2004; 5.2 in Woo et al. 2010; 2.8 in Graham et al. 2011; 4.31 in Grier et al. 2013). In this section, the systematic differences between those black hole mass estimates and the possible origins of these differences are discussed.

In fact, the systematic difference between ${{M}_{{\rm BH},{\rm pol}}}$ and ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ has been indicated by preceding studies. Greene et al. (2010a) measured the stellar velocity dispersion ${{\sigma }_{*}}$ in the centers of galaxies hosting type 2 AGNs whose ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ was obtained, and found that ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ tended to be smaller than the black hole mass that was estimated from ${{\sigma }_{*}}$ and the ${{M}_{{\rm BH}}}$–${{\sigma }_{*}}$ relation of local elliptical galaxies. On the other hand, Zhang et al. (2008) estimated the radius of the BLR from the [O iii] luminosity via the luminosity scaling relation of the BLR to estimate ${{M}_{{\rm BH},{\rm pol}}}$ of 12 type 2 AGNs and found that ${{M}_{{\rm BH},{\rm pol}}}$ tended to be larger than the black hole mass that was estimated from ${{\sigma }_{*}}$ via the ${{M}_{{\rm BH}}}$–${{\sigma }_{*}}$ relation. According to these results, ${{M}_{{\rm BH},{\rm pol}}}$ would be systematically larger than ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$, as is the case in this study.

Recently, Ho & Kim (2014) presented that the virial factor f of reverberation-mapped AGNs is systematically different between two bulge types of the host galaxies: $f=6.3\pm 1.5$ for classical bulges and ellipticals, and $f=3.2\pm 0.7$ for psuedobulges. In fact, the black hole mass of the AGNs with psuedobulges tends to be smaller than that with classical bulges and ellipticals as shown in their Figure 2. Greene et al. (2010a) also argued that the mass of the black hole hosted by later-type and lower-mass galaxies tended to be less massive with larger scatter than that estimated from the ${{M}_{{\rm BH}}}$–${{\sigma }_{*}}$ relation for the elliptical galaxies. Since our type 2 AGN targets with H₂O maser observation tend to have a less massive black hole than the others if ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ is correct, then it is possible that the systematic difference of the target selection partly contributes to the systematic difference between ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ and the other black hole mass indicators.

Contrary to these studies, Kuo et al. (2011) estimated the radius of the BLR from the absorption-corrected luminosity in the 2–10 keV X-ray band ${{L}_{2-10{\rm keV}}}$ via the luminosity scaling relation of the BLR to estimate ${{M}_{{\rm BH},{\rm pol}}}$ of four type 2 AGNs whose ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ was obtained by them, and showed that ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ and ${{M}_{{\rm BH},{\rm pol}}}$ were consistent with each other. In fact, the three targets, NGC 1068, NGC 4388, and Circinus, for which a large systematic difference between ${{M}_{{\rm BH},{\rm pol}}}$ and ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ is presented in this paper are included in the targets of Kuo et al. (2011). The reason for the discrepancy between these studies is uncertain. Difficulty in estimating the luminosity of the central engine ${{L}_{2-10\,{\rm keV}}}$ for most of the targets with very large X-ray absorbing column density could be suspected, although the luminosity was estimated with particular care.

Assuming both ${{M}_{{\rm BH},{\rm rev}}}$ and ${{M}_{{\rm BH},{{{\rm H}}_{2}}{\rm O}}}$ are reliable estimates for the black hole mass, ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ and ${{M}_{{\rm BH},{\rm pol}}}$ are considered to overestimate the black hole mass in type 2 AGNs. The systematically larger ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ for the type 2 AGNs implies that the width of the neutral FeKα line core is systematically larger for large inclination angle for type 2 AGNs. If the emitting region of the neutral FeKα line core shows equatorial motion, then the virial factor f in Equation (3) decreases as the inclination angle increases. For example, f = 2 at the edge-on view, which is smaller than f = 5.5 for type 1 AGNs, is derived assuming an equatorial circular motion. However, it is not so small as to account for the difference of about a factor of ∼5. Outflow motions toward the equatorial plane might broaden the width of the neutral FeKα line core for type 2 AGNs.

On the other hand, the systematically larger ${{M}_{{\rm BH},{\rm pol}}}$ for the type 2 AGNs cannot be attributed to the inclination of AGNs from the point of view of the unified model of AGNs; when the broad emission line is scattered to the observer at the polar region well above the height of the dust torus, the viewing angle of the BLR from the scattering region would be similar to that from the observer for type 1 AGNs. Non-virial motions such as outflows in the scattering region are possible contributors, as Young et al. (2007) proposed to explain the broad Hα emission line in the polarized spectrum of the quasar PG 1700+518. However, a common or closely related mechanism to broaden the widths of both the neutral FeKα line core and the polarized broad Balmer emission lines systematically for type 2 AGNs is required to explain the approximate agreement between ${{M}_{{\rm BH},{\rm FeK}\alpha }}$ and ${{M}_{{\rm BH},{\rm pol}}}$.

As described in Section 3, the FWHM of the neutral FeKα line core falls between the FWHM of the broad Balmer emission lines and the corresponding values at the dust reverberation radius in most cases, which indicates that the emitting region of its major fraction is located between the outer BLR and the inner dust torus. It has been suggested by previous studies for some of the target AGNs. For NGC 4151, Takahashi et al. (2002) compared the variation of the continuum and excess flux around the neutral FeKα line and presented that the emitting region of the excess flux has an extent of 10¹⁷ cm, or 40 lt-days, which is consistent with or slightly smaller than the dust reverberation radius (Koshida et al. 2014). For NGC 5548, Liu et al. (2010) reported that the emitting region of the neutral FeKα line was located between the two reverberation radii of the broad Hβ emission line and the near-infrared dust emission based on its flux variation and line width.

The BLR and the dust torus are considered not to be decoupled from each other but to constitute a continuous structure, and the transition zone of the BLR and the dust torus would be located between the two reverberation radii (Nenkova et al. 2008; Koshida et al. 2009, 2014). In addition, recent reverberation observations of the optical Fe ii emission lines showed that its reverberation radius was comparable to or at most twice that of the broad Hβ emission line (Barth et al. 2013; Chelouche et al. 2014), which shows the presence of low ionization iron atoms there.

If the FeKα emitting region constitutes a tightly stratified structure with the BLR and the dust torus, a good correlation between the FWHMs of the neutral FeKα line and the broad Balmer emission lines is expected. However, as shown in Figure 1, there appears no clear correlation between them as has been reported by previous studies (Nandra 2006; Shu et al. 2010, 2011). A simple explanation for it would be that the neutral FeKα line is produced in different origins such as the outer accretion disk, the BLR, and the innermost dust torus, and the mixing ratio is different from target to target (e.g., Yaqoob & Padmanabhan 2004; Nandra 2006; Bianchi et al. 2008; Liu et al. 2010; Ponti et al. 2013). On the other hand, Shu et al. (2011) suggested that the neutral FeKα line may originate from a universal region at the same radius with respect to the gravitational radius of the central black hole, because its FWHM is almost constant and independent of the black hole mass. In any case, those uncertainties will result in the possible error of the black hole mass estimated from the neutral FeKα line.

In this study, We used the best spectral resolution data currently available, but the spectral resolution and sensitivity are still limited. As a result, the number of targets is small and relatively large uncertainties remain in the FWHM data, which would make it difficult to examine the location of the neutral FeKα line emitting region in more detail. In the near future, substantial progress is expected by the ASTRO-H X-ray satellite (Takahashi et al. 2010), which is capable of unprecedented energy-resolution spectroscopy with superior sensitivity at the FeKα band. It will enable us to study in more detail the origin of the neutral FeKα line core by examining the line profile of the neutral FeKα line and its time variation, then it will be able to measure the black hole mass with improved accuracy for a large number of obscured AGNs. The hard X-ray luminosity with precise absorption correction is obviously valuable for the isotropic luminosity indicator because the scaling relations of the reverberation radii to the hard X-ray luminosity are tighter than those to the [O iv] luminosity (Koshida et al. 2014).