Implications from the optical to UV flux ratio of FeII emission in quasars

Figure 1 shows a simplified Fe II Grotrian diagram. As can be seen, Level 3$-$Level 2 transitions give rise to optical Fe II emission lines such as the Fe II($\lambda$4570) bump. Branching ratio of Level 3$-$Level 1 UV resonance transitions is significantly higher than that of Level 3$-$Level 2 optical transitions. Hence strong optical Fe II emission requires a large optical depth between Level 1 and Level 3 such as $\tau_{13}>10^{3}$ in order to transform UV Fe II lines to optical Fe II lines through a large number of scatterings (cf. Collin & Joly 2000). Thus Fe II($\lambda$4570)/Fe II(UV) flux ratio must strongly depend on $\tau_{13}$ and $\tau_{23}$, which are the optical depths for photons emitted through Level 3$-$Level 1 and Level 3$-$Level 2 transitions, respectively. If so, the Fe II($\lambda$4570)/Fe II(UV) can be an indicator of the column density.

Here we use a quite simple model to indicate the dependence of Fe II($\lambda$4570)/Fe II(UV) on the column density. First, we ignore the Level 4 in Figure 1 and consider the Fe II as three-level system. Second, we assume thermal equilibrium population between Level 1 and Level 2. Third, we assume an expression of the local escape probability given by Netzer & Wills (1983) as $\epsilon_{ij}=(1-\tau_{ij})/\tau_{ij}$. Although the model adopting these assumptions is obviously too oversimplified, it is useful to qualitatively understand how the line ratio depends on the physical parameters. The flux ratio is then written as

where $n_{3}$ is the population of level 3, and $A_{ij}$ is the spontaneous emission rate from the level $i$ to the level $j$. Following the fact that $\tau_{13}\gg 1$, the ratio can be roughly reduced to Fe II($\lambda$4570)/Fe II(UV) $\propto 1-e^{-\tau_{23}}$. Since $\tau_{23}$ is proportional to the column density, the ratio is an increasing function of the column density. We will discuss further on this matter in the following.

Here we will show more sophisticated model calculations of Fe II($\lambda$4570)/Fe II(UV). We performed photoionization model calculations with version C06.02 of the spectral simulation code Cloudy, last described by Ferland et al. (1998), combined with a 371 level Fe⁺ model (up to $\sim$11.6 eV, Verner et al. 1999). The incident continuum is defined as

The first term in the right-hand side of the equation (3) expresses an accretion disk component, which is usually called Big Bump. The $kT_{BB}$ and the $kT_{IR}$ indicate the higher and the lower cut off energies, respectively. The second term expresses a power-law X-ray component, which is set to zero below 1.36 eV, while to fall off as $\nu^{-3}$ above 100 keV. The coefficient $a$ is set to produce the optical to X-ray spectral index $\alpha_{ox}$ ¹¹1The optical to X-ray spectral index $\alpha_{ox}$ is defined as $f_{\nu}(2$ keV$)/f_{\nu}(2500$Å$)=403.3^{\alpha_{ox}}$. We set these parameters to $(\alpha_{UV},\ \alpha_{X},\ \alpha_{ox},\ T_{BB},\ kT_{IR})=(-0.2,\ -1.8,\ -1.4,\ 1.5\times 10^{5}\ \mathrm{K},\ 0.136\ \mathrm{eV})$, which are adopted in Tsuzuki et al. (2006). This incident continuum illuminates a single cloud with hydrogen density $n_{H}$, ionization parameter $U$($\equiv\Phi/n_{H}c$, where $\Phi$ is the ionizing photon flux, $c$ is the velocity of light), column density $N_{H}$ and solar abundance. We calculated the models in a range of $N_{H}=10^{21}-10^{25}\ \mathrm{cm}^{-2},\ n_{H}=10^{7}-10^{14}\ \mathrm{cm}^{3}$ and $U=10^{-5}-10^{0}$.

In locally optimally emitting clouds (LOCs; Baldwin et al. 1995), each line is emitted from clouds with a wide range of gas hydrogen density and distance from the central continuum source, and the observed spectra is reproduced by integrating these clouds with an appropriate covering fraction distribution. The observed emission line flux is, then, expressed as:

where $F(r,n_{H})$ is the emission line flux of a single cloud at a distance $r$ from the central continuum source and with $n_{H}$, $f(r)$ is a cloud covering fraction with distance $r$, and $g(n_{H})$ is a fraction of clouds with $n_{H}$. Matsuoka et al. (2007) showed that O I and Ca II emission lines in quasars, which are likely to emerge from the same gas as the Fe II emission lines, are well reproduced by a LOC model with $f(r)\propto r^{-1}$ and $g(n_{H})\propto n_{H}^{-1}$, hence we have adopted these covering distributions. Baldwin et al. (1995) suggested that since clouds at large distances from the continuum source will form graphite grains which heavily suppress the line emissivity, clouds with $\Phi<10^{18}\ \mathrm{s^{-1}cm^{-2}}$ must be excluded from integration. Thus we have calculated equation (4) for clouds which correspond $\Phi\geq 10^{18}\ \mathrm{s^{-1}cm^{-2}}$.

Figure 2 illustrates Fe II($\lambda$4570)/Fe II(UV) as a function of the column density for photoionized clouds. Fe II($\lambda$4570)/Fe II(UV) increases as the column density increases. It also shows that Fe II($\lambda$4570)/Fe II(UV) decreases as the microturbulent velocity increases, consistent with Verner et al. (2003), and that Fe II($\lambda$4570)/Fe II(UV) is maximum when no microturbulence is assumed to exist. This is explained as follows. Increasing microturbulent velocities broadens the line absorption profile, resulting in enhancement of the continuum photoexcitation. This effect is relatively large for high energy levels where the collisional excitation is inefficient for their high excitation potential. Thus large microturbulent velocities relatively enhances the continuum photoexcitation to the Level 4 in Figure 1, leading to emit more fluxes in the UV Fe II emission lines, thus decreasing Fe II($\lambda$4570)/Fe II(UV). For photoionized clouds, Fe II($\lambda$4570)/Fe II(UV) can be used as a column density indicator unless microturbulent velocities vary much from cloud to cloud.

It is noted that calculations adopting the other shapes of the incident continuum²²2Two types of SED given by Nagao, Murayama & Taniguchi (2001) are adopted. One is set to reproduce the ordinary SED of broad-line Seyfert 1 galaxies, and the other is set to reproduce that of narrow-line Seyfert 1 galaxies. show little changes for Fe II($\lambda$4570)/Fe II(UV), indicating little dependence on the spectral energy distribution (SED) of ionizing continuum.

As an alternative to photoionization models, we consider models in which a cloud is assumed to be in collisional equilibrium at a given electron temperature $T_{e}$, and call them collisionally ionized models. In these models, the specific heating mechanism is not accounted and arbitrary electron temperatures are given. It is noted that Fe II is collisionally excited in either mechanically heated clouds such as through shocks or photoionized clouds. In the latter case, the heating mechanism is specified to be the eating of the incident UV and X-ray photons.

Joly (1987) offers collisionally ionized model calculations. In her models, Fe II is approximated by a 14-level (up to $\sim$5.7 eV), and the emission region is assumed to be a homogeneous slab with constant hydrogen density $n_{H}$, column density $N_{H}$, electron temperature $T_{e}$, and not to receive any external radiation. The electron temperature ranges from 6,000 K to 15,000 K, the density from $10^{10}$ to $10^{12}\ \mathrm{cm}^{-3}$ and the column density from $10^{21}$ to $10^{25}\ \mathrm{cm}^{-2}$.

Figure 3 shows Fe II($\lambda$4570)/Fe II(UV) as a function of the column density, taken from Joly (1987). As expected from equation (2), it can be seen that Fe II($\lambda$4570)/Fe II(UV) increases with the column density while decreases with temperature. However, Figure 3 shows that Fe II($\lambda$4570)/Fe II(UV) does not so much depend on the temperature in $6,000<T_{e}<10,000$ K. It is noted that Collin et al. (1980) and Joly (1987) showed emission line ratios including Fe II in quasars are well accounted by cold clouds with $6,000<T_{e}<10,000$ K. Thus it is reasonable to assume that Fe II-emitting clouds have the temperatures in a range of $6,000<T_{e}<10,000$ K, and the Fe II($\lambda$4570)/Fe II(UV) depends little on the temperature while strongly varies with the column density. We fit the data of $6,000<T_{e}<10,000$ K models by a 4th-order polynomial, and find

where $y=\log$ Fe II($\lambda$4570)/Fe II(UV) and $x=\log N_{H}[\mathrm{cm^{-2}}]-23$. We will use this relation to estimate the column density of quasars.

We have analyzed quasar spectra selected from the fourth edition of the SDSS Quasar catalog (Schneider et al. 2007). SDSS uses a dedicated 2.5 m telescope at the Apache Point Observatory equipped with a CCD camera to image the sky in five optical bands, and two digital spectrographs, one covering a wavelength range of 3800Å to 6150Å and the other from 5800Å to 9200Å. The spectral resolution ranges from 1850 to 2200. The fourth edition of the SDSS Quasar catalog consists of the objects in the Fifth Data Release, and contains 77,429 quasars.

In order to measure the Fe II(UV) and Fe II($\lambda$4570) emission lines simultaneously, we have selected spectra which cover the wavelength range of 2200 to 5100 Å in the rest frame, corresponding to the redshift range from 0.727 to 0.804. 2,189 objects meet this requirement. Then we have checked the signal to noise ratio (S/N) per pixel for each spectrum which fulfills median S/N $>$ 10 per pixel at their continuum levels for accurate flux measurements. 946 objects meet this requirement. All the spectra were inspected by eyes and 62 spectra were rejected because of wavelength discontinuity, terrible contamination by host galaxy star light, etc. Our final sample thus consists of 884 spectra.

Prior to the measurements, the quasar spectra were dereddened for the Galactic extinction according to the dust map by Schlegel, Finkbeiner & Davis (1998) using the Milky Way extinction curve by Pei (1992).

Since SDSS quasars are flux-limited in the survey, low luminosity quasars are lost in the SDSS sample. Figure 4 shows luminosity versus redshift for our sample. Because of the narrow redshift coverage for our sample, the minimum luminosity is almost constant and roughly estimated to be $\lambda L_{5100}=10^{44.7}$ ergs/s.

In the UV to optical, the quasar continuum is composed of (i) the power-law continuum $F_{\lambda}^{PL}$, (ii) the Balmer continuum $F_{\lambda}^{BaC}$ and (iii) the Fe II pseudo-continuum $F_{\lambda}^{FeII}$. Thus we assumed a following formula as a model continuum $F_{\lambda}^{cont}$:

For the classical black hole mass estimate in which the radiation pressure effect is neglected, we use the following formula given by McLure & Jarvis (2002):

The classical Eddington luminosity is given as follows:

where $c$ is the velocity of light, $m_{p}$ is the proton mass, and $\sigma_{T}$ is the Thomson cross-section.

On the other hand, Marconi et al. (2008) suggested that the force of the radiation pressure should be corrected to derive the black hole mass. They give the radiation pressure corrected black hole mass $M_{BH,rad}$ and Eddington luminosity $L_{Edd,rad}$ as follows:

where $L_{bol}$ is the bolometric luminosity, $L_{ion}$ is the total luminosity of the ionizing continuum (i.e., $h\nu>$ 13.6 eV), and $a$ is the ionizing photon fraction. The second term in the right hand side of equation (12) represents the correction term of the radiation pressure. We here adopt a bolometric correction $L_{bol}=9\lambda L_{5100}$ given by Kaspi et al. (2000).

We performed a Monte-Carlo simulation similar to those done in Hu et al. (2008) for estimating the measurement errors. The detail of the procedure is as follows.

(i) Generating a composite spectrum. Following Vanden Berk et al. (2001), we generated a composite spectrum using all of our samples. This composite spectrum represents a typical quasar spectrum for our samples. (ii) Obtaining typical emission line profiles. We applied the measurement methods written in §3.2 to the composite spectrum, and obtained typical emission line profiles for Fe II(UV), Fe II($\lambda$4570) and Mg II. (iii) Making artificial spectra. We combined these line profiles with the power-low continuum and the Balmer continuum. Thus the simulated spectrum is written as follows.

Note that, for simplicity, we ignored the broadening of the pseudo-Fe II continuum. Values of input parameters, which are given in the parentheses in equation (15), are randomly sampled from probability distributions that are made to reflect the observations. Thus, we generated 1,000 simulated spectra. (iv) Generating a noise template. Using all the noise spectra produced by the SDSS pipeline for our samples, we generated a composite spectrum following Vanden Berk et al. (2001) and named it a noise template. This noise template is scaled so that the resulting median S/N to be 10 per pixel at the continuum level for each simulated spectrum, and is treated as its noise.

Now we have the 1,000 simulated spectra with their noise. The measurement methods written in §3.2 are applied to these simulated spectra. We calculate the value $\delta_{sim}=(P_{out}-P_{in})/P_{in}$ for each simulated spectrum where $P_{in}$ represents the input parameters (i.e., the values given in the parentheses in equation (15)) and $P_{out}$ represents the corresponding measured values for the simulated spectra. We regard $\sigma_{sim}$, a standard deviation of $\delta_{sim}$, as $1\sigma$ error of the measurement. Thus we evaluate the measurement errors to be 16.4% for EW of Fe II(UV), 22.9% for EW of Fe II($\lambda$4570) and 7.9% for FWHM(Mg II). The simulation implies the measurement error to be 2.9% for the luminosity, which is less than 10% estimated in the power-law fitting. Therefore we decided to evaluate the measurement error to be 10% for $\lambda L_{3000}$ and $\lambda L_{5100}$.

Figure 7 shows the observed Fe II($\lambda$4570)/Fe II(UV) distribution. As can be seen from the comparison between this and Figure 2, our photoionization models underpredict the Fe II($\lambda$4570)/Fe II(UV) by a factor of 10, failing to account for the observations. This result is consistent with the preceding study by Baldwin et al. (2004). Additional microturbulence to the photoionized clouds gets the situation even worse. Thus, Figure 7 seems to challenge classical photoionized pictures of Fe II-emitting clouds. On the other hand, in the case of the collisionally ionized models shown in Figure 3, the observed Fe II($\lambda$4570)/Fe II(UV) flux ratios are well reproduced with $10^{22}<N_{H}<10^{24}\ \mathrm{cm^{-2}}$ and with $6,000<T_{e}<10,000$ K.

These results give two remarks: (1) the Fe II-emitting clouds in quasars are heated to $6,000<T_{e}<10,000$ K; (2) the UV and the X-ray photons, which are the heating source in our photoionization models, fail to heat the gas to such temperatures (probably heat the gas too hot!). One possible interpretation is that the Fe II-emitting clouds are heated by an alternative mechanism such as through shocks. Here we note that there is a reverberation mapping study implying shock heating for Fe II emission. Kuehn et al. (2008) analyzed optical Fe II emission bands in the Ark 120, finding that they do not respond to the continuum variation. Thus the optical Fe II-emitting region may be heated by other mechanism than photoionization. These results favor the shock heating for the optical Fe II-emitting region, but there are also difficulties. First, the amount of shock-processed matter would probably be too large. Second, as Kuehn et al. (2008) showed, collisionally ionized models failed to match the shape of the optical Fe II-emission band. Third, the fact that there is no response to the continuum variation for optical Fe II emission bands can also be interpreted as that the emitting region is too large to vary optical Fe II emission in observable timescales. Unless shocks are a viable solution, the failure of the photoionization model simply indicates that it is not predicting the correct heating rate, or that the radiative transport calculations are not correct.

One possible cause disturbing classical photoionization models to reproduce the observations may be the assumption that the Fe II emission is isotropic. Ferland et al. (2009) recently suggested that UV Fe II lines are beamed toward a central source while optical Fe II lines are emitted isotropically. Then photoionization models can reproduce the observed UV to optical Fe II flux ratio if the Fe II-emitting clouds are distributed asymmetrically so that we mainly observe their shielded faces. However, this needs special geometrical distributions like Type II AGNs; a thick Fe II-emitting gas surrounding the central source with a substantial covering factor, and intervening between the central region and our eyes. At the present time, it is not clear whether or not photoionization models can reproduce the emission line strengths other than Fe II under such the situation. Much broader exploration of photoionization model calculations is certainly needed.

Now we can roughly estimate column densities from the observed Fe II($\lambda$4570)/Fe II(UV) by using equation (5). The estimated column density distribution is shown in Figure 8. An average and a standard deviation of the distribution are found to be $(\overline{\log N_{H}},\sigma_{\log N_{H}})=(22.8,0.5)$. Marconi et al. (2009) has suggested that radiation pressure does play an important role in BLR gas dynamics if column densities of BLR clouds have intrinsic dispersion such as $(\overline{\log N_{H}},\sigma_{\log N_{H}})=(23.0,0.5)$. Our results support that the assumption adopted in Marconi et al. (2009) is appropriate and that the radiation pressure plays an important role in BLR clouds.

Figure 9 shows the relation between Fe II($\lambda$4570)/Fe II(UV) and the Eddington ratio. A positive correlation is seen. Linear regression analysis, using an IDL procedure “FITEXY.pro” (cf. Press et al. 1992), gives the relation as:

The Spearman’s rank correlation coefficient³³3Spearman’s rank correlation coefficient is non-parametric measure of correlation, that is, which assesses how well an arbitrary monotonic function could describe the relationship between two variables without making any other assumptions for assessing the nonlinear correlation is $r_{S}=0.58$. This means the probability of the null hypothesis that there is no correlation is less than $10^{-13}$. Thus the correlation between Fe II($\lambda$4570)/Fe II(UV) and the Eddington ratio is real. This implies that the column density increases with the Eddington ratio, because Fe II($\lambda$4570)/Fe II(UV) increases with the column density.

As was recently suggested by Dong et al. (2009), under the condition where the BLR clouds are subject to the radiation pressure, low-column-density clouds would be blown away by relatively large radiation pressure at large $L_{bol}/L_{Edd,0}$, so that only high-column-density clouds would be able to be gravitationally bound. Figure 9 is a supportive evidence for their suggestion.

Figure 10 plots our samples on $N_{H}-L_{bol}/L_{Edd,0}$ plane. Each line represents $L_{bol}=L_{Edd,rad}$, so that the lower region of the line corresponds super-Eddington area. If we adopt ionizing photon fraction $a=0.6$ (i.e., thick solid line in Figure 10), which is an average value for AGNs calculated by Marconi et al. (2008), almost all of our samples become super-Eddington. This result can be interpreted in two ways: (i) the conversion from Fe II($\lambda$4570)/Fe II(UV) to column densities (i.e, equation (5)) is wrong, or (ii) the adopted value of $a$ is inappropriate.

In the case (i), since Fe II($\lambda$4570)/Fe II(UV) is a function of the column density and the temperature, the false in the conversion is attributed to the assumed temperature. If we assume hot clouds such as $T_{e}>10,000$ K, the corresponding column densities would become large, resulting in the solution for this super-Eddington problem. However, as already discussed, the previous studies favor cold clouds such as $6,000<T_{e}<10,000$ K for Fe II emission (cf. Collin et al. 1980, Joly 1987). Thus this interpretation seems to be inappropriate.

In the case (ii), as can be seen from Figure 10, if we adopt small values for $a$ such as 0.01, the majority of our samples becomes gravitationally bound. This means that the fraction of ionizing photons irradiating on Fe II-emitting clouds is much less than those on usual BLR clouds. Then it seems quite natural to conclude that the Fe II emission does not originate in the region where usual emission lines such as H$\beta$ originate, but originate in outer parts of BLR where the incident ionizing photon fraction becomes as low as $a=0.01$. It is worth noting that from the studies of O I and Ca II emission lines, Matsuoka et al. (2008) also suggests that Fe II emission originates in outer parts of BLR.

Boroson & Green (1992) applied a principal component analysis to low-redshift quasars and found that the principal component 1 (which is called “Eigenvector 1”) links the strength of optical Fe II emission and the weakness of [O III] emission. After a while, Boroson (2002) showed that Eigenvector 1 is driven predominantly by an Eddington ratio. However, the physical causes making up the Eigenvector 1 has been left unknown.

Here we propose a physical interpretation of Eigenvector 1 in terms of the column density. As discussed in the previous section, small-column-density clouds would be driven away from the line-emitting region by the radiation pressure at large Eddington ratio, and only large-column-density clouds can be gravitationally bound. Radiative transfer effects make the optical Fe II emission become large in such large-column-density clouds. On the other hand, ionizing photons emitted from the central object are intervened by these large-column-density clouds and thus have less probabilities of ionizing photons reaching to NLR clouds, resulting in weak [O III] emission. In fact, Figure 10(t) in Tsuzuki et al. (2006) shows a negative correlation between the [O III]/H$\beta$ and Fe II(O1)/Fe II(U1), which is almost the same as our Fe II($\lambda$4570)/Fe II(UV), for 14 quasars.