THE QUASAR OUTFLOW CONTRIBUTION TO AGN FEEDBACK: VLT MEASUREMENTS OF SDSS J0318-0600^*

We identify each of the individual kinematic absorption components in the spectrum using the Al ii λ1671 absorption line profile, which is a singlet transition with no nearby strong absorption features. In Figure 2, we show that there are approximately 11 separate kinematic components (labeled a–k), with component e being clearly a blend of multiple inseparable components. Using Al ii as a template for the absorbers we search other ionic species for each of the 11 components.

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Next, we identify the broad, strong i component in as many lines as possible and select unblended troughs from which we are able to measure ionic column densities. Figure 1 shows the UV 38 Fe ii multiplet, which exhibits several absorption features from component i. We note that the absorption feature at ∼4727 Å is the k component of the Fe ii λ1608 resonance line. While this identification scheme is sufficient to locate the majority of the lines that show an i component, we also use the Al ii as a template (see Section 3.3) to search for the other 10 components in the Fe ii UV 1, 2, & 3 multiplet absorption complexes.

The Fe ii multiplets UV 1, 2, & 3 are the best candidates to identify Fe ii lines from the other 10 components to measure, because they contain the Fe ii transitions with the strongest oscillator strengths. However, this task proves to be non-trivial in SDSS J0318 − 0600. Identifying measurable lines from a saturated and heavily blended region (see Figure 2) is difficult, especially when considering the large number of strong resonance and excited state lines. Therefore, we attempt to identify as many of the 11 components in the UV 1, 2, and 3 multiplets using the Al ii template to search for these 11 components where blending is not so prevalent. We provide the full list of detected ions, transition wavelengths, their oscillator strengths, and lower level energies in the online version of Table 2.

We find that for the lowest and highest velocity components (k and a), enough measurements or limit determinations are available and that we can effectively determine the electron density (n_H), the ionization parameter (U_H), and the total hydrogen column density (N_H, see Section 4). Unfortunately, blending prevents us from identifying enough measurable troughs for components b–h for proper analysis. We opt for the limiting case by taking the sum of these latter systems (see Section 3.2).

With a list of measurable absorption troughs, we extract ionic column densities. We begin the process by measuring lines from the strongest component, (i), where we employ three primary methods for determining the column densities. We describe three additional methods for column density determination that are less reliable in Section 3.3. We provide the measured values of ionic column densities as well as the method applied in Table 3.

Our first method of measuring column densities is to model a set of observed Fe ii resonance lines (e.g., Figure 3) using an inhomogeneous absorption model, where we approximate the gas distribution across our line of sight (LOS) to the background source with a power law (see de Kool et al. 2002c; Arav et al. 2008, especially Figure 4, for a full description). The optical depth at a given velocity within the outflow is described by

$$\begin{equation} \tau _v(x) = \tau _{\rm max}(v) x^a, \end{equation} \tag{ 1 }$$

where x is the spatial dimension in the plane of the sky (simplified to one dimension without loss of generality, see Arav et al. 2005), a is the power law distribution index, and τ_max(v) is the highest value of τ at a given velocity. We simultaneously solve for both τ_max and a for each velocity resolution element of the resonance Fe ii lines and apply this distribution (a) to the excited Fe ii lines. We then apply the same distribution dictated by the Fe ii lines to all ions because this is the simplest assumption that imposes the strongest constraints.

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We convert the modeled τ_v to column density via (Savage & Sembach 1991)

$$\begin{equation} N(v) = 3.8 \times 10^{14} \frac{1}{f\lambda } \tau _v ({\rm cm}^{-2}\,{\rm km}^{-1}\,{\rm s}), \end{equation} \tag{ 2 }$$

where λ is the wavelength of the line in Å, f is the oscillator strength, and τ_v is the optical depth in velocity space in km s⁻¹, which is integrated over the spatial dimension x. Using Equation (2), we compute the column density for each velocity element and integrate over the range in velocity, which we justify later in this section. In Table 3, we quote the power law estimation of the column densities (when available) as this is the most accurate and most plausibly physical explanation of non-black saturated absorption at large distances (Arav et al. 2008; de Kool et al. 2002c). In Table 3 and throughout this paper, we will refer to this as method 1.

Method 2 is to model the Fe ii resonance lines with a velocity-dependent LOS covering factor. The LOS covering factor in this case is a geometric step-function distribution (see Figure 4 in Arav et al. 2008). In other words, a fraction of the extended source is completely obscured by the outflow, while the rest of the source is uncovered. We assume that each radial velocity element has an independent LOS covering factor, which we again determine using the Fe ii resonance lines. We solve a fitting equation for τ_v (Arav et al. 2005),

$$\begin{equation} I(v) = 1 - C(v) + C(v) e^{-\tau (v)}, \end{equation} \tag{ 3 }$$

where I is the normalized intensity within the trough and C(v) is the velocity-dependent LOS covering factor. First, we solve Equation (3) for C(v) and τ(v) using at least two resonance lines from Fe ii. We then calculate the velocity-dependent column density using τ(v) in Equation (2) and multiply the column density at each velocity by C(v) to obtain the average column density across the LOS. Finally, we compute the total ionic column density by integrating across the velocity range of the trough. This method is comparable in accuracy to method 1 (Arav et al. 2008), and the column density results are approximately the same as found by method 1.

The last of the three methods, method 3, is simply the apparent optical depth method (AOD; Savage & Sembach 1991). This method assumes that all photons traveling to the observer pass through the same amount of gas at a given velocity, which gives the equation for normalized intensity: I(v) = e^−τ(v). We again convert to column density via Equation (2) and integrate to find the total ionic column density. This method does not account for partial LOS covering and saturation effects in line centers, which can underestimate column densities by up to an order of magnitude. However, we find that for SDSS J0318-066, in most cases a LOS covering factor of 1 (i.e., the AOD approximation) yields similar N_ion values as those derived by the power law or partial covering method, a point we will discuss later in this section.

For the upcoming photoionization modeling, we adopt the ionic column densities as determined by method 1 (power law method) with some exceptions to this due to line blending that are noted in Table 3. We now present our analysis for the individual components.

3.2.1. Measurements of Component i

We begin our column density determination by fitting the Fe ii resonance lines from the strongest component, (i). In Figure 3, we show the fits for three Fe ii resonance lines using the power law method. We select these particular line transitions because they provide us with a range of oscillator strengths and are free of blending or telluric contamination. Using these lines, we derive velocity-dependent column densities that we integrate for the total ionic column density.

Unfortunately, all strong Fe ii lines from the lower energy level 385 cm⁻¹ are heavily blended in the UV 1, 2, or 3 multiplets with lines from both the resonance and other excited lines (e.g., Fe ii* λ2396, shown in Figure 2), which renders column density measurements based on these transitions to have large systematic errors. However, we find relatively strong lines outside of the UV 1, 2, or 3 multiplets for the 385 cm⁻¹ energy state that are useful such as the Fe ii line λ1622 from the UV 38 multiplet. We also find two weaker lines from this energy state at λ1619 and λ2281 that are unblended. The oscillator strength values for these three lines are taken from Fuhr & Wiese (2006). Of the three lines, both the λ1618 and λ1622 are reported to have accurate oscillator strengths (rated as "A"⁸ by Fuhr & Wiese), while the weaker λ2281 has a reasonably reliable oscillator strength (rated "B"). However, we find that using the oscillator strengths reported by Fuhr & Wiese is problematic. While the two weaker lines are well fit with these oscillator strengths, the trough depths relative to λ1622 are unphysical. For example, scaling the λ1619 trough in apparent optical depth by the ratio of oscillator strengths (∼1.8) should be equal to the apparent optical depth in λ1622 (or larger in the case of partial covering); however, the scaled optical depth of λ1619 is significantly smaller than that of the λ1622 trough. This means that at least one of the oscillator strengths could be less reliable than previously believed. Because of this issue, we quote an ionic column density for the 385 cm⁻¹ energy level that is the mean of the fit to the λ1622 line alone and the fit to the two weaker lines with an uncertainty equal to the range in column density.

The other excited state lines from Fe ii (e.g., arising from 668, 863, and 977 cm⁻¹) are also subject to heavy blending in the multiplets, but unlike the resonance and 385 excited state lines there is not sufficient column density to provide deep troughs with high signal-to-noise ratio for the weaker lines. Thus, the column density measurements from these energy levels are significantly more uncertain. The exceptions to this are lines from the lower energy level states 1873 cm⁻¹ (⁴F) and 7955 cm⁻¹ (⁴D).

We find five separate absorption troughs of Fe ii arising from the level at 1873 cm⁻¹, which are shown in Figure 4. We successfully fit these using the oscillator strengths from Kurucz & Bell (1995) to determine the column density for this level. However, the compilation of recommended oscillator strengths of Fe ii from Fuhr & Wiese (2006) yields values lower than ∼0.3 dex for two of the transitions, λ1637.4 and λ1702.0. For these transitions the recommended values are rated "C," while no oscillator strengths are given for the other two observed transitions. In addition to the difference in the absolute values, there is also a difference in the relative values, and in fact our fits to the absorption troughs in the spectrum favor the relative values of Kurucz & Bell (1995). Thus, we opt to use the relative oscillator strengths from Kurucz & Bell (1995) to fit all four troughs, but the level column density derived this way is increased by 0.3 dex, as required by the absolute oscillator strengths of Fuhr & Wiese (2006).

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We find that the results from all three models (Power law, covering factor, and AOD) are similar for the Fe ii column density measurements of component i, which suggests that the LOS covering factor of the system is close to 1. Further evidence for a LOS covering factor ≈1 case is shown in Figure 5, where we show that we can use the Al ii template to fit the Al iii doublet. We scale two Al ii templates (one for Al iii λ1855 and one for Al iii λ1863) in τ space for each individual kinematic component for the blue and the red line of the doublet by the expected ratio of 2:1 and coadd the templates to generate a fit to the data. There exist only small deviations, and the overall fit to the doublet is good. The most obvious and important deviation is in the fit to the λ1863 i component, which is due to some saturation in the core of the Al ii template. This demonstrates that AOD is an adequate approximation and the LOS covering factor for all components is approximately 1.0. This same procedure gives similar results when applied to the Mg ii doublet as well.

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3.2.2. The Physical Connection Between Material Seen in Different Troughs

Ultimately, we want to establish the physical characteristics of the outflow based on the column density determinations described above. In order to do so, we use the integrated column densities as input to photoionization models, which in turn determine the total hydrogen column density and number density in the outflow. This procedure depends on two assumptions: (1) that the physical conditions do not change as a function of velocity across a given trough. This assumption allow for the use of integrated column densities instead of working with each velocity resolution element separately (see Arav et al. 2008); (2) that the troughs of different ions correspond to the same outflowing gas, which is a necessary condition for using these measurements in the same photoionization models. Both assumptions can be checked using the data at hand.

The first assumption can be tested by checking whether the ratio of measured column densities among different lower levels of the same ion vary as a function of velocity. In Figure 6, we plot the ratios of column densities between those arising from excited levels to those from the ground state level of Fe ii and Si ii. Within the uncertainties, the ratios across the troughs are velocity independent, showing that the electron number density is constant across the flow (see Section 4 for elaboration). This result gives validity to our first assumption and justifies the use of integrated column densities for component i. We also tested this for Ni ii/Ni ii* and combinations between Ni ii, Si ii, and Fe ii resonances and excited lines and find that the ratio is constant in all cases. This constant ratio is also seen in the results for the outflow system in QSO 2359 − 1241 as described by Korista et al. (2008).

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In order to validate the second assumption, we need to check the column density ratio across troughs from different ions and especially to compare low- and high-ionization troughs. To do so, we use the τ(v) profile of Si ii λ1527 and attempt to fit the profiles of other troughs while using a single-scale factor for each line. The results are shown in Figure 7. It is evident that the scaled τ(v) profile of Si ii λ1527 fits the troughs of Si iv, Al ii, Al iii troughs and Mg ii remarkably well, lending strong support for the assumption that we are measuring the same outflowing gas. For C iv, which is the highest ionization line observed, the fit for the center of the trough is less conclusive since the trough is highly saturated at its core. However, we point out that the fit to the low-velocity wing (−3950 to −3850 km s⁻¹) is very good, which would be a coincident unless the C iv trough can be fitted with the same τ(v) profile of Si ii λ1527. In summary, the data support the two main assumptions that we need in order to use all integrated column densities in our photoionization models.

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To demonstrate the tie between the high- and low-ionization troughs for the other outflow components, we show in Figure 8 that the combination of the Si ii composite template (described in Section 3.3 for component i) and the Al ii template (for all other components) can be used to recreate the doublet troughs of Mg ii, Al iii, Si iv, and C iv. Similar to Figure 5, we add two templates together in τ(v). We scale the entire blue template (all 11 components) by one factor and scale the respective red template by 2:1 in τ(v). This method gives the fewest possible constraints for the fit. We find that all 11 kinematic components are present in both low- and high-ionization troughs and that there are no unexplained kinematic components in the higher ionization state lines, which is indication that this is the same outflowing gas for both the high- and low-ionization troughs. We also note that these fits could be better if we scaled each individual component for the blue member and kept the 2:1 ratio to the red, as we did for the Al iii fit in Figure 5.

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3.2.3. Measurements of the Other Components

For situations where blending between components in doublets is prevalent (i.e., C iv, Si iv, C ii, and C ii*) or where the trough is heavily saturated (i.e., C iv), our primary method of column density extraction fails. Thus, we resort to other, less accurate, methods to estimate the column densities, which are important when constraining photoionization models. We develop three additional methods in order to estimate column densities in blended regions, which we explain here in order of decreasing accuracy.

In the first of our estimation methods (4), we opt to employ a template to map out approximate profiles for the troughs. We utilize two templates for this process. The first template is a fit to the Al ii λ1671 line for all 11 components. However, due to moderate saturation in the core of the Al ii i component, we create a composite template using the Si ii resonance lines for the i component.

To create this template, we use both the Si ii λ1808 and λ1527 lines. The λ1527 line is similar in shape to the Al ii λ1671 line, and while the core is moderately saturated, it provides us with a good fit to the wings of the trough. In contrast, the λ1808 line has a significantly weaker oscillator strength and therefore the core of this trough is not saturated; however, the wings are buried in the noise. We therefore create a composite template using the AOD column densities of the λ1527 for the wings (−3820 to –3990 km s⁻¹ and –4390 to –4580 km s⁻¹), and the AOD column densities of the λ1808 line for the core (−4390 and −3990 km s⁻¹). We then convert the resultant Si ii column density profile to τ(v) template for the λ1527 line.

To measure column densities, we scale this composite τ(v) template to match the red wings of the Mg ii, Si iv, and C iv doublets as well as C ii*, which are apparently free of blending. We assume that the column density ratio is constant across the troughs, which is supported by Figure 7, scale the composite template for the i component to match and then integrate the total column (assuming a C_los ≈ 1) from the template. We refer to this method as the "wing" fitting method (method 4). The error estimation is provided by using two τ scaling values, one underestimating and one overestimating the noise level in the trough's wing. We note that these measurements use only one line, the red doublet member, which is reflected in Tables 3 through 6. To further test the validity of this method, we used the composite template to fit the wing of the Si ii λ1527 line and we find that the template is able to reproduce the column density we find in our power law fitting of the λ1808 line to within 10%.

The next method we designate as the "tip" fitting method, or method 5, where we estimate the column densities in a similar way to method 4. For example, we estimate the column density of O i λ1302 for the i component in the region containing blended lines from Si ii λ1304 and Si ii* λ1309. We find that the composite template fit for the i component agrees well with the deep trough at ∼3809 Å in velocity space (shown in online Figure 1), which appears to be the tip of O i absorption. Thus, we use the composite Si ii template to approximate the minimum and maximum amount of column density that could come from O i. Due to the uncertainty in continuum placement and possible saturation, we consider this method less accurate than method 4, which is reflected in the larger error bars.

Our last column density estimation method (the noise method or method 6) defines upper limits on the column density of ions based on the statistical error of the data. Because the column density of He i is important for photoionization models (see Arav et al. 2001; Korista et al. 2008), we estimate an upper limit for the column density of the excited 2³s level of He i (He i* hereafter) in component i for He i* λ3189. To do this, we scale the Si ii template for the i component and compare it to the region where the line would be detected. We vary the scaling to the noise level, find the largest possible optical depth that could be buried without detection and integrate across the template to determine the column density. We also perform this analysis for Mg i λ2853, Fe i λ2484, and C i λ1560 and quote the measured limits in Table 3.

Component k presents its own problems. Unlike the i component, here we effectively measure column densities for Fe ii resonance and excited levels (E = 0 cm⁻¹ to E = 668 cm⁻¹), but we lack a Si ii resonance line to provide a ratio to the Si ii λ1309 excited line. Therefore, we apply method 5 with the Al ii template to find limits on the Si ii. Moreover, we use the "wing" fitting method (method 4) with the same Al ii template to estimate the column density for C ii and C ii* in component k.

In component a, the number of measurable lines is even fewer than for component k. The only clean, unblended density diagnostic is C ii to C ii*. As the critical density for this ratio is low (∼10² cm⁻³, Blum & Pradhan 1992; Froese Fischer 1983), it is important to find another density check. Thus, using the Al ii template, we estimate an upper limit to the column density ratio of Si ii* to Si ii to be 0.49 for component a.

We recognize that there exist systematic errors that could contribute further to the uncertainty in our measurements. For example, our placement of the continuum, defined in Section 2, could result in increased errors of the Si ii λ1808 and Si ii* λ1817 column densities by 5%. The amount of saturation in the core of Si iv is another systematic error that could be a potential source of error in column density, which at maximum, could lead to an error in an ionization parameter of 0.1 dex. Both of these are negligible compared to the uncertainties due to the chemical abundance choice.

Under excitation equilibrium conditions, the column densities of lowly excited metastable levels can be used as diagnostics of electron density, assuming that the atomic parameters and excitation processes responsible for excitation are sufficiently well understood. We have measured column densities for the 0 cm⁻¹ ground state and low-lying metastable excited levels within Si ii, Fe ii, and Ni ii.

The simplest and probably most reliable of the electron density diagnostics is that from the ratio of the column densities of the Si ii levels, as shown in Figure 9. Here, the ratio of the excited 3s²3p ²P^o_3/2 at 287 cm⁻¹ to the 3s²3p ²P^o_1/2 ground level is calculated from three different sets of effective collision strengths, Dufton & Kingston (1991), Tayal (2008), and M. Bautista et al. (2010, in preparation). We measure this column density ratio from the pair of absorption lines at 1808.0 Å (resonant) and 1816.9 Å (excited state). As described above, we have a good deal of confidence in their measured integrated optical depths, especially their ratio, and we will thus place the greatest weight on this electron density diagnostic. We caution, however, that as the weakest among such pairs of transitions commonly measured in Si ii, there are moderate uncertainties in their oscillator strengths, even in their relative values (about 0.1 dex). Two other such pairs of transitions that lie within our spectrum, centered on 1307 Å and 1531 Å, have smaller uncertainties in their oscillator strengths but are saturated in our spectrum and are not useful for direct measurements. These uncertainties dominate over the statistical measurement errors in the column density fits to the observed troughs at 1808.0 Å and 1816.9 Å. Figure 9 illustrates the electron density dependence of this level specific column density ratio, wherein the solid and dotted horizontal lines represent our measurement of this ratio and an estimated range of its uncertainty, the latter dominated by the uncertainties in the transition oscillator strengths. We derive an electron density of log(n_e) = 3.3 ± 0.2 (cm⁻³).

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The various observed transitions arising from low-lying metastable levels of the Fe ii ion allow for independent electron density diagnostics. However, constraining the electron density from the relative populations within these metastable levels proved more difficult. We present these in Figure 10 for column densities of the 385 cm⁻¹, 1873 cm⁻¹, and 7955 cm⁻¹ levels. These are the only levels for which we have sufficient confidence in their measured column densities (see Table 2) to justify their utility as electron density diagnostics. In blue are the predictions from cloudy (ver. 06.02; Ferland et al. 1998) for photoionization models presented in Korista et al. (2008) for the main outflow system in QSO J2359 − 1241 (solar abundances, fixed ionization parameter, and total column density for which no hydrogen ionization front formed, and n_e ≈ n_H within the Fe⁺ zone). Relevant mainly for the ratios involving the 7955 cm⁻¹ level, the electron density weighted average temperature within the Fe⁺ zone of these models was approximately 11,000 K. In red are the predictions of the collisional equilibrium model Fe ii atom of Verner et al. (1999) for a fixed electron temperature (10,000 K) at each electron density. This difference in adopted temperature has no significant effect on the populations of the 385 cm⁻¹ and 1873 cm⁻¹ levels, while the population of the 7955 cm⁻¹ level is roughly linearly dependent on electron temperature for the conditions of interest (e.g., ∼10% differences are found for the two temperatures quoted). The horizontal solid and dashed lines are the measured values and estimated uncertainties, respectively. The small differences in the predictions pertaining to the 385 cm⁻¹ level and the large differences pertaining to the 1873 cm⁻¹ level are primarily due to differences in the radiative transition rates (A-values) for forbidden transitions used in the two sets of computations. A detailed inspection of the atomic data files of the Verner et al. (1999) model atom in cloudy revealed that for a few dipole forbidden transitions the model adopts A-values whose sources are neither known to us nor cited in their publication. For all other relevant transitions, the Verner et al. model atom in cloudy adopts the A-values from Quinet et al. (1996).⁹ The largest effects of the A-values of unknown origin present in cloudy are with respect to the population of the 1873 cm⁻¹ level, where the differences are substantial as indicated in the middle panel of Figure 10 (blue and red curves).¹⁰

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The electron density predicted by the Si ii lines (log(n_e) = 3.3 ±  0.2 cm⁻³; see Figure 9) and that from the 385 cm⁻¹ level in Fe ii (log(n_e) ≈ 3.9 cm⁻³) differ somewhat in value. However, considering the moderate uncertainties in the relevant atomic data of the Si ii and Fe ii 385 cm⁻¹ transitions available to us as diagnostics of electron density, and the larger uncertainties in the measurements in the Fe ii 385 cm⁻¹ troughs, we do not consider these differences to be significant.

In contrast, the predicted electron density based on the relative population of the Fe ii a ⁴F_9/2 level at 1873 cm⁻¹, being an order of magnitude smaller, does present a possible conundrum. Among all of the column density measurements of transitions from excited states of Fe ii we believe this one to be the most secure. However, the atomic data (A-values and collision strengths) involved in the computations of level populations of the a ⁴F term carry greater uncertainties than those pertaining to the levels of the a ⁶D (ground) term. This is because the a ⁴F and a ⁶D terms belong to different electron configurations, i.e., 3d⁷ and 3d⁶4s respectively, and the energy difference between these terms is comparable in magnitude to the relativistic corrections to the Hamiltonian. Thus, the computation of accurate transition rates among levels of these terms requires fine tuning of large atomic configuration expansions (see M. Bautista et al. 2010, in preparation for a more detailed discussion).

We also consider the possibility of some selective excitation process that might lead to a significantly lower population in Fe ii a ⁴F_9/2 than would be inferred by collisions alone. Neither photoexcitation by the continuum radiation field nor Lyα fluorescence can explain the observed discrepancy. Another mechanism, known to occur in spectra of circumstellar envelopes of symbiotic stars and in the environs of gamma-ray bursts, is Bowen fluorescence of Fe ii by C iv emission at 1548 Å (e.g., Johansson 1983; Eriksson et al. 2008; Vreeswijk et al. 2007; Hartman & Johansson 2000; Michalitsianos et al. 1992). Pumping occurs as the 1548.19 Å resonance line of C iv closely coincides with the 1548.20 Å transition from the a ⁴F_9/2 metastable level to the y ⁴H^o_11/2 level of Fe ii. Subsequently, this high level cascades down to the ground stage of the ion, so the population of the a ⁴F_9/2 level is re-distributed among other low-lying metastable levels (see also Verner et al. 2000). Fully self-consistent modeling of this fluorescence process requires a detailed treatment of radiative transfer of C iv and Fe ii lines within the cloud, which is beyond the scope of this paper. Nevertheless, we can estimate the relative level populations of the observed levels in our spectra under the fluorescence scenario by artificially including its effect in the Bautista & Pradhan (1998) collisional equilibrium Fe ii model. We find that solving this discrepancy requires a photoexcitation rate in the 1548.20 Å transition that is at least 10 times greater than what is available through photoabsorption of radiation from the adopted dereddened SED (Section 4.2). We show the resulting effects on the level populations as the green curves in Figure 10 (i.e., the red curve becomes the green one). Although, this fluorescence mechanism is able to correct the population of the a ⁴F_9/2 level to agree with the observed column density at the same electron density given by Si ii, the pumping rate required seems too large even when considering the inclusion of C iv emission from the broad emission line region. Further investigation of this effect is left for future work. After considering all of these issues pertaining to the various uncertainties, we adopt the Si ii-determined electron density of log(n_e) = 3.3 ± 0.2 (cm⁻³).

Finally, we measure column densities from the ground 3d^{9 2}D_5/2 level and the 3d⁸4s⁴F_9/2 metastable level at 8394 cm⁻¹ for the Ni ii ion. We find that the population of the metastable level exceeds the predictions of pure collisional excitation conditions for any value of the electron density. This is to be expected because Ni ii is very efficiently excited by continuum radiation (Bautista et al. 1996; Lucy 1995). As a consequence, Ni ii cannot be used as density diagnostic here, but instead serves as a check for the flux of photons below the hydrogen ionization threshold from the central source. As such, Ni ii can be used as a direct distance indicator to the outflow (see Section 4.4).

The SED incident on the outflowing gas has important consequences for the ionization and thermal structures within the gas. In what follows, we provide motivation for our choice of two standard SEDs to use in the photoionization models. While AGNs are routinely observed in the optical/UV and X-rays (see Elvis et al. 1994), the critical EUV spectral region (∼1 Ry to 0.1 keV, rest frame) is largely inaccessible except near its low- and high-energy extremes. The present working model is that a thermal accretion disk spectrum dominates the energy contained within the continuum spectrum feature known as the "UV bump," sometimes called the "big blue bump" (Shields 1978; Malkan 1983). Such a feature is expected to peak (in units of νF_ν) at energies of a few Rydberg, depending on the mass of the SMBH and the mass accretion rate (Shakura & Syunyaev 1973). Mathews & Ferland (1987) had this in mind when they constructed a simplified piece-wise power-law representation of a typical QSO SED, basing the relative strength and roll-over energy of the UV–FUV bump on measurements of the strengths of the He ii broad emission lines (photon counting) and overall energy balance within the broad emission line gas (e.g., comparing the strength of Lyα 1216 to the strengths of strong cooling lines such as C iv λ1549), and joining the turn-down onto a power-law representation of the X-ray spectrum for typical X-ray bright quasars (samples of which at that time were dominated by radio loud QSOs). This spectrum, hereafter referred to as MF87, has since been the standard SED in modeling photoionized gas associated with AGNs. We adopt the MF87 SED as one of two standards for our photoionization models.

By the late 1990s, improved UV and X-ray observations of AGNs led several investigators to reconsider the importance of accretion disk emission to the FUV spectra of AGNs. In a sample of luminous QSOs with Hubble Space Telescope (HST) spectra, Zheng et al. (1997) found surprisingly soft continuum SEDs at wavelengths shortward of ∼1000 Å. Shortly thereafter, Laor et al. (1997) reported that the soft X-ray spectra of quasars appeared to be pointing (in νF_ν space) at the soft FUV slopes found by Zheng et al.   and proposed that a large fraction of the UV bump inferred by Mathews & Ferland (1987) and standard accretion disk models was missing (see also Elvis et al. 1994). This led to investigations of cooler accretion disk models with thermal spectra that are Comptonized by a ∼10⁸ K plasma, which result in power-law like instead of exponential like high energy tails in the spectrum (e.g., Blaes et al. 2001). Telfer et al. (2002) followed up on the work of Zheng et al. with a larger sample of objects with HST spectra, which improved the statistics at the shorter wavelengths. They found similarly but not quite as soft FUV slopes and concluded for radio-quiet quasars "that it is plausible to represent the entire typical ionizing continuum from ∼10 eV to ∼2 keV by a single power law" (α≈ −1.6). With this in mind Hamann et al. (2001, 2002) constructed a simple piece-wise power law radio-quiet quasar SED to model intrinsic AGN absorption systems and broad emission lines. We adopt a slightly modified version of their SED as our second standard: from 1 μm to 1 Ry, α=−0.6; from 1 Ry to 2 keV, α=−1.6; from 2 keV to 50 keV, α=−0.9 and a high-energy break beyond. This SED has an α_ox≈−1.43, very nearly equal to that of the MF87 SED (α_ox≈−1.40), while effectively excluding the presence of a UV bump peaking at FUV energies.¹¹ We refer to this as the "UV-soft SED," and we show it along with the MF87 SED in Figure 11.

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With regard to these observational studies of quasar SEDs, the reader should bear in mind that significant uncertainties remain in the corrections in the UV for Galactic extinction (primarily in the adopted value of R_V), in the corrections for atomic absorption within the intervening intergalactic medium (mainly the Lyα forest), as well as in the quasar host galaxy extinction. No attempt was made to correct for the last of these in any of the above works. Thus, from an observational point of view, the existence and magnitude of the 1000 Å break and the apparent roll-down toward the observed X-rays, as suggested in Laor et al. (1997), remain unclear. Scott et al. (2004a), in a sample of Far Ultraviolet Spectroscopic Explorer spectra of luminous Seyfert1 galaxies and low redshift quasars, reported no FUV spectral break down to ∼600 Å. However, some of the differences between this finding and that in the more luminous AGN sample of Telfer et al. (2002) may be intrinsic, due to differences in the accretion disk physics. We refer the reader to Shang et al. (2005) and Bonning et al. (2007) for recent detailed comparisons between observations and modern accretion disk model predictions, as well as critical evaluations of the current uncertainties. We consider it plausible that actual quasar FUV/EUV SEDs fall somewhere between our two adopted standards.

In the previous section, we constructed a plausible UV-soft SED for SDSS J0318 − 0600. However, it is known that the UV spectrum of SDSS J0318 − 0600 is strongly affected by extinction due to dust. Hall et al. (2002) found that if the Small Magellanic Cloud (SMC) reddening curve, typical for QSOs, were adopted, the extinction correction E(B − V) would be between ∼0.1 and ∼0.4 depending on whether the 2000–3000 Å or 1250–2000 Å rest-frame wavelength ranges were fit to the SDSS composite QSO spectrum. Because the location of the bulk of the reddening of the SED is unknown, we must consider a scenario in which the SED incident on the outflow has been reddened by dust grains.

Figure 12 shows a portion of the SED centered around the rest-frame energy range of our observations. Here we show the unattenuated UV-soft SED described in the previous section and the FIRST Bright Quasar Survey composite spectrum of Brotherton et al. (2001). The observed spectrum of SDSS J0318 − 0600, also shown in the figure, is clearly affected by extinction. Five reddened versions of the UV-soft SED are also shown here; two of them are a result of the standard extinction curve of the SMC (Hutchings 1982) with E(B − V) = 0.1 and 0.4, and additional curves generated from cloudy models of pure silicate grains with a distribution of the form

$$\begin{equation} dn_{\rm gr} = C n_{\scriptscriptstyle H} \left(\frac{a}{a_0} \right)^{-\alpha } da,\quad 20\,{\AA} < a < 0.25\,\mu {\rm m}. \end{equation} \tag{ 6 }$$

These models were simulated with cloudy as the transmitted spectrum of a cloud with a Galactic dust to gas ratio, log n_H(cm⁻³) = 4.0, log N_H(cm⁻²) = 21.8 and log U_H = +2.0. This high-ionization parameter was chosen in order to minimize atomic features in the resulting spectrum and to allow grain extinction to dominate the attenuation. A cloud of this number density and ionization parameter would be located ∼30 pc from the central source roughly with the expected realm of the putative clumpy, dusty torus. The dust temperature in this cloud has a maximum value of 400 K, which is below the sublimation temperature of silicate grains (∼1400 K for silicates). See Pier & Voit (1995); Nenkova et al. (2008) for a more extensive discussion of the properties of illuminated dusty tori associated with AGNs. No graphite grains are included in the models because they lead to the 2175 Å peak, which is absent in the spectrum. On the other hand, a large absorption peak from silicates at approximately 690 Å (∼1.3 Ry) does correlate with the observed spectrum. The depth of such a peak is dependent on the size distribution of grains (i.e., in the value of α). A problem arises in determining the values of α and total extinction that are proportional to C, because from the UV spectrum alone no unique solution for both values can be found simultaneously. Fortunately, SDSS J0318 − 0600 was also observed by the Two Micron All Sky Survey (2MASS). The photometric measurements in the J, H, and K bands (rest frame 4162, 5602, and 7277 Å respectively) are marked in Figure 12. It is important to note here that the flux in the J band may be affected by Hδ and other emission lines in the rest frame of the quasar. With this large wavelength range we are able to determine the magnitude of extinction, while the value of α is determined by fitting the slope of the SDSS spectrum. We find E(B − V) = 0.15 for an extinction curve with a ratio of selective to total extinction R_V = A_V/E(B − V) = 4.4 and α = 3.4.

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The extinction curve of SDSS J0318 − 0600 with R_V = 4.4 is quite different from that of the SMC with R_V ∼ 2 and the diffuse Galactic Interstellar Medium (ISM) with R_V = 3.1. The steepness of the present curve is more similar to that of dense molecular clouds and star-forming regions with R_V ≈ 5. These large values of R_V are characteristic of a distribution of grains that favor larger grains than in typical ISM. This would result if either large grains are allowed to accrete in a dense environment shielded from UV radiation or small grains are efficiently destroyed in a violent event, e.g., shocks. Such may be the environment of the dusty clouds composing the clumpy tori of AGNs.

Once the extinction that affects the observed spectrum has been determined, we are in a position to compute the bolometric luminosity of the QSO. To do that we adopt the UV-soft SED shown in Figure 12 of the previous section and integrate over the whole energy space. This gives L_Bol = 5.0 × 10⁴⁷ erg s⁻¹, assuming cosmological parameters of H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_m = 0.3, and Ω_Λ = 0.7.

With the above normalization and our adopted (UV-soft) SED we find a hydrogen ionizing photon rate of Q = 3.6 × 10⁵⁷ photons s⁻¹. However, it is unclear at this time where most of the extinction occurs with respect to the outflow. If the grain extinction of the SED occurs interior to the outflow, Q should be determined from our preferred dust reddened model (α = 3.4 and E(B − V) = 0.15). For this case, the effective Q = 2.1 × 10⁵⁶ photons s⁻¹. We will later use Q in conjunction with the derived values of gas number density and ionization parameter to estimate the distance of the outflow from the central source.

We start by assuming constant total hydrogen density "clouds" of solar abundances from Lodders (2003). The optimization of all our models is based on the column densities of Si ii and Si iv. This is because they have constrained column density measurements from the spectrum, expand the whole range of ionization stages observed, and they come from the same chemical element, thus their relative strengths are independent of the chemical composition of the cloud.

In trying to reproduce the measured ionic column densities we have constructed a number of photoionization models exploring the physical conditions and our assumptions. For a qualitative description of the ionization structure of the cloud see Korista et al. (2008). It is important in all models that the average electron density predicted by the model coincide with that diagnosed from the Si ii lines in Section 4.1 within 0.1 dex. For every model, we compute the electron density averaged over the Si ii trough, as

$$\begin{equation} \langle n_e\rangle _{\rm Si\,\mathsc{ii}} = \frac{\int _0^{N_H}N_{\rm Si\,\mathsc{ii}} n_e(N_H) dN_H}{\int _0^{N_H}N_{\rm Si\,\mathsc{ii}} dN_H}. \end{equation} \tag{ 7 }$$

This value is presented in Table 7 together with the adopted n_H.

A summary of the results of different models is presented in Table 7. Here the first three column densities indicate the species observed, their measured column densities, and respective uncertainties. The subsequent column densities present the differences between observations and the results of various models as described below. Here, we also present the optimal U_H and N_H determined for every model.

We first try to model the cloud using solar abundances and two possible SEDs: our UV-soft SED described above and the UV-soft SED reddened as in the previous section. While the measured silicon column densities can be matched in both cases, this only happens when going very deep into the ionization front where n_e and temperature have started to drop. Therefore, we see that in order to reproduce a log(〈n_e〉) = 3.3 in the Si ii region, the particle density of the cloud must be log(〈n_H〉) = 3.8. Another concern about these models is their predictions for O i column densities, which come to be about 2 orders of magnitude greater than allowed by observations. These results are shown as models A and B in Table 7 for the unreddened and reddened SEDs, respectively. Because O i is tightly driven by H i through charge exchange, the observed column density of O i is a direct indicator of the depth of the ionization front with respect to the total column density of the cloud. The same argument is true for the column density of Fe ii. The problems with this model are illustrated in Figure 13. Despite the fact that our measurement of O i is poor, the discrepancy between this and models with solar composition is significant. The current measured column density is 1.9 − 10¹⁵ cm⁻² with an uncertainty of a factor of 2–3. On the other hand, models with solar composition overestimate the column density by 1.9 dex, i.e., 1.5 − 10¹⁷ cm⁻². This would be the largest column density of all ions in the spectrum, about 5 times that of C iv. Despite the oscillator strength of O i being smaller than that of C iv, a column density as predicted would yield a very strong and completely saturated trough in the spectrum. This is clearly not the case. The fact that the present model goes too deep into the ionization front to reach the high observed ratio of Si ii to Si iv column densities indicates that the abundance of Si relative to O must be higher than solar.

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Similar to Si, the Fe/O and Ni/O abundance ratios must also be supersolar because the ionic fractions of Fe ii, Ni ii, and O i are tied to neutral hydrogen through charge exchange. Thus, the Fe ii/O i and Ni ii/O i ratios are nearly independent of the physical condition of the cloud and can only be varied by changing the abundances of these elements (Bautista & Pradhan 1998; Bautista et al. 1996). Furthermore, we find that for solar abundances of all other elements, the minimum enhancement of Si, Fe, and Ni in gas phase that satisfies the are [Si/H] = +0.8 and [Fe/H] = [Ni/H] = +0.3.

We note that this abundances pattern is similar to that expected in high-metallicity bulges of galaxies. Ballero et al. (2008) studied the evolution of chemical abundances of spiral bulges hosting Seyfert nuclei by modeling the efficiency of star formation. They predict the abundances of various elements for Z/Z_☉ = 4.23, 6.11, and 7.22. We present these abundances, which we use for photoionization modeling in Table 8. We present these elemental abundances for the first and last of the metallicities, and use them in the photoionization modeling to investigate the effects of a realistic span in gas metallicity. Ballero et al. (2008) do not predict abundances for Al, which is present in our spectra, thus we simply scale this linearly with Z to [Al/H] = +0.50 and 0.86 at Z/Z_☉ = 4.23 and 7.22, respectively. We use the [He/H] versus Z relation from those predicted in the chemical evolution models of Hamann & Ferland (1993). The remaining elements through Zn untabulated by Ballero et al. were assigned abundances as estimated by Z.

The results of these models are given as models C through F in Table 7. It can be seen that these abundances yield better agreement with respect to the measured column densities than when solar abundances are used. Moreover, the abundance enhancements for Z/Z_☉ = 4.23 still yield overestimated column densities for O i by one to two sigma, depending on the SED used. On the other hand, the models with abundances for Z/Z_☉ = 7.2 agree well in terms of the O i predictions if the reddened UV-soft SED is adopted, but underestimate the O i column density when the non-extinguished UV-soft SED is used.

Given our arguments for metallicities greater than solar in the outflow and the fact that the solar models are unable to match the n_H, the true metallicity in QSO J0318 − 0600 is likely to be several times solar. Regardless of this we are able to well constrain U_H and N_H. Models C and E constrain log(U_H) to −2.75 and −2.85 and log(N_H) to 20.16 and 19.86 (cm⁻²), respectively, for the unreddened SED. While, models D and F constrain log(U_H) to −3.02 and −3.13 and log(N_H) to 20.07 and 19.73 (cm⁻²), respectively, for the reddened SED.

One significant discrepancy between all models and observations is in the carbon column densities. As indicated in Table 7, the [Si/C] ratio is rather large in these two elemental abundance models, and a relatively larger carbon abundance would reduce the discrepancies. Ballero et al. point out that their prediction for C is likely uncertain as it depends sensitively on the mass of the bulge. However, it is important to point out that our measurements for carbon are problematic, as we only have a lower limit for the C ii column density and large portions of the C iv troughs are highly saturated.

A relatively small uncertainty in U_H and N_H arises from the adopted standard SED. For example, should we adopt the MF87 SED rather than the UV-soft SED constructed in Section 4.2, our results for U_H and N_H would be affected at a ∼0.1 level. However, this effect is very small compared to the uncertainties resulting from the dust extinction of the SED and the adopted chemical abundances.

Another discrepancy in the models stems from the predictions for Al. Most of our models underestimate the column densities of Al ii and Al iii. The predicted column density ratios of Al ii to Al iii differ from observations by approximately a factor of 4. Again, it could be that the true Al abundance is higher than assumed, which is not surprising as there are only very rough approximations on how this element scales with metallicity. But, beyond the absolute column densities there may also be differences in the predicted ionization structure of Al. The other problem is that the predicted column densities of Mg i always exceed the upper levels derived from our spectra. It is clear that the ionization structure of neutrals that form by recombination across the ionization front is not well described by our models. The cause for this problem is a combination of inaccuracies in the atomic parameters for these species and limitations of photoionization modeling codes to treat neutral ions with low-ionization potential (<10.2 eV). The exception to this is He i*, which is consistent with the models predictions. This problem is intrinsic to all modeling codes that treat radiative transfer through the escape probability approximation, as neutral species with low-ionization potential are greatly affected by Lyman α radiation. Thus, a very accurate treatment of radiative transfer is needed to confidently model these neutral species, which is beyond the scope of this paper.

Lucy (1995) demonstrated that Ni ii could be efficiently photo-excited by continuum radiation under nebular conditions. Bautista et al. (1996) constructed a detailed 142 level model of the Ni ii system for spectral analysis, which was updated with improved atomic data by Bautista (2004).

Figure 14 shows the level populations ratio between the excited level at 8394 cm⁻¹ and the ground level. The upper panel shows the ratio versus n_e under pure collisional excitation conditions. It is noted that the uncertainty in the measured ratio column densities is dominated by that in the oscillator strengths, particularly for troughs from the 8394 cm⁻¹. For these transitions, we adopted oscillator strengths from Kurucz & Bell (1995), which in the case of the resonant transitions were discrepant by up to a factor of 2 from experimental determinations of Fedchak & Lawler (1999). Thus, we adopt a nominal 30% uncertainty in the observed ratios. Further theoretical and experimental work on the oscillator strengths of Ni ii is warranted.

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From Figure 14 one sees that the observed ratio is consistent with the predictions of pure collisional excitation for a wide range in n_e that includes the conditions of the absorbed as diagnosed from Si ii. Hence, it should be possible to set an upper limit to the continuum flux that also contributes to the excitation of the 8394 cm⁻¹ level. In the lower panel of the figure, we plot the ratio against the flux of ionizing photons Φ for the same SED used in our photoionization models. It is important to note that only photons less energetic than 1 Ry participate in photoexcitation of the ion and these are unaffected by the main atomic opacities of the cloud. It is found that the N(Ni ii 8394)/N(Ni ii 0) ratio is strongly enhanced by continuum fluorescence and this drives the ratio well above the Boltzman equilibrium populations. Under these conditions, induced photoexcitation of highly excited odd parity levels is balanced by rapid spontaneous radiative decay. For much more intense radiation fields, induced photoexcitation exceeds spontaneous decay and the level population ratio reaches a plateau. It can be seen that the observed column density ratio sets upper limits of log₁₀(Φ/c) ≈ +1.5 or +0.4 depending on whether one uses a reddened or unreddened SED. Thus, from a total particle density of log(n_H) = 3.3 one derives a value for the ionization parameter log₁₀(U_H)⩽−1.8 or ⩽−2.9, for reddened and unreddened SEDs respectively. Both of these values are consistent with that derived through photoionization modeling. It is unfortunate that more stringent constrains could not be derived due to the large uncertainties in the oscillator strengths for the absorption lines in the spectrum.

In the previous section, we determined the ionization parameter, number density, and total column density of the main outflow component, (i). Here, we calculate the mass and energetic characteristics of the outflow. First, we determine the mass contained within the wind. For simplicity, we assume that the outflow is in the form of a partial thin spherical shell at a distance R from the central source moving radially at constant speed v. The total mass contained in such an outflow is

$$\begin{equation} M = 4 \pi \mu m_p \Omega R^2 N_H, \end{equation} \tag{ 8 }$$

where N_H is the total column density of hydrogen, m_p is the mass of a proton, μ = 1.4 is the mean molecular weight of the plasma per proton, and Ω is the fraction of the shell occupied by the outflow. Therefore, assuming dN_H/dt = 0, the mass flux follows as the temporal derivative:

$$\begin{equation} \dot{M} = 8 \pi \mu m_p \Omega R N_H v, \end{equation} \tag{ 9 }$$

the momentum flux is given by

$$\begin{equation} \dot{p} = \dot{M} v, \end{equation} \tag{ 10 }$$

and the kinetic luminosity is given by

$$\begin{equation} \dot{E}_k = \frac{\dot{M} v^2}{2} = 4 \pi \mu m_p \Omega R N_H v^3. \end{equation} \tag{ 11 }$$

For component i: v = −4200 km s⁻¹ and Table 6 gives the N_H for each of our photoionization models. To calculate the distance R we use Equation (4), where n_e is determined in Section 4.1, U_H is taken from Table 6 and Q_H is given in Section 4.4, log Q_H (photons s⁻¹) as 56.3 and 57.6 photons s⁻¹ for the attenuated and unattenuated SEDs, respectively. In Table 9, we list the derived values for R, $\dot{E}_k$, and $\dot{M}$ for each photoionization model.

Table 9. Calculated Values for Each Photoionization Model

Parameter	Unattenuated SED			Attenuated SED
Abundances	Solar	4.2a	7.2b	Solar	4.2a	7.2b
Model	A	C	E	B	D	F
log UH	−2.25	−2.63	−2.85	−2.47	−3.02	−3.13
log NH (cm−2)	20.96	20.20	19.86	20.92	20.07	19.73
R (kpc)	9.4	14.6	18.7	2.9	5.5	6.3
$\dot{E}_k$ (Ω0.2 1045 erg s−1)c	12	3.1	1.8	3.3	0.9	0.5
$\dot{E}_k$/LBol (Ω0.2)	0.02	0.006	0.004	0.007	0.002	0.001
$\dot{M}$ (Ω0.2 M☉ yr−1)	2080	560	330	590	160	80

Notes. ^aBallero et al. (2008) abundances for Z/Z_☉ = 4.2. ^bBallero et al. (2008) abundances for Z/Z_☉ = 7.2. ^cΩ_0.2 ≡ Ω/0.2.

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As shown above, we determined N_H and R for the photoionization models and therefore each model is associated with a reliable estimate of the kinetic luminosity per unit solid angle. In order to obtain estimates for the total kinetic luminosity, we need to address the remaining variable in Equation (1), Ω, the fraction of the full sphere occupied by the outflow. There is no direct way to obtain the Ω of a given outflow from its spectrum as we only see the material along the LOS. Statistically, C iv BALs are seen in 20% of all quasars (Hewett & Foltz 2003). This can be interpreted as (1) all quasars have BAL winds covering 20% of the solid angle, (2) 20% of all quasars have winds covering the full solid angle, or (3) all quasars have a phase of full solid angle wind lasting 20% of their duty cycle. A combination of these three options is also possible. It is important to note that with all else equal, options (1) and (3) yield the same integrated mass flux and kinetic luminosity over the lifetime of an individual quasar, and that all three options yield similar integrated quantities for a sample of quasars.

However, we cannot measure distances to the majority of C iv outflows, but only to those outflows that show troughs from excited and metastable levels. For most of our objects (including SDSS J0318 − 0600), the spectra cover such transitions only from singly ionized species (e.g., Fe ii, Si ii, C ii, and Ni ii). Outflows with troughs from these ions are rare (Trump et al. 2006). Our comprehensive search of the 50,000 brightest SDSS quasars yielded 100 such outflows. We found that only ∼ 1% of the objects that show a C iv outflow show troughs from these singly ionized species. We therefore have two limits to explore with regard to the Ω of the outflow. First, outflows that exhibit troughs from these four singly ionized species excited states may represent all regular C iv outflows viewed through special conditions that allow for the formation of singly ionized troughs. This scenario yields Ω ≃ 0.2 as is the case for the frequency of C iv BALQSOs among all quasars. The second limit is Ω ≃ 0.002, which is the minimal covering fraction needed to explain the 100 occurrences in 50,000 objects.

Several arguments suggest that the first scenario is closer to the actual physical situation. Since outflows with troughs from singly ionized species are rare, we may simply be observationally biased by this low-ionization selection effect as we lack excited and metastable level troughs from C iv or species with similar ionization. One physically motivated picture is that we are looking at a normal C iv outflow through a LOS passing through semi-opaque material at the edge of the putative AGN torus. Such a scenario explains why we see the singly ionized species (lowering of the ionization parameter); why most of the objects we measure have strong dust reddening (torus dust) and why these systems are so rare (a solid angle that has sufficient torus material to lower the ionization parameter significantly but not enough to make it a type II quasar).

Recent observations by K. Aoki et al. (2010, in preparation) give support to the above scenario. A quasar showing strong Fe ii absorption troughs and strong dust reddning in 2002 showed much less dust extinction and very little Fe ii absorption in 2008. Thus, the amount of dust along our LOS changed drastically between two epochs separated by ∼3.5 years in the rest frame of the source. The interpretation is that the dust source has vacated the LOS, therefore increasing the ionization parameter of the outflow and reducing the column density of Fe ii. A 3.5 year timescale favors changes in a near-by obscuring material (i.e., the putative torus) over material at a kpc scale and therefore supports both of our assertions: (1) that the dusty material seen in the spectra of these outflows is indeed much closer to the source than the outflows themselves; (2) that these excited-state singly ionized absorption outflows are naturally explained by a special LOS grazing the putative torus.

Further support for this scenario comes from the fact that all our objects show a C iv BAL, which is morphologically indistinguishable from C iv BALs in the ubiquitous high ionization BALQSOs. We therefore conclude that it is more likely that we are seeing normal Ω ≃ 0.2 outflows through a rare LOS.

A direct resolution of this issue necessitates imaging of the winds. This is a difficult task due to the high redshifts of the objects and the presence of a very bright quasar at the center of the image. Nonetheless, we hope to pursue this line of research in the future. Another approach is to observe at wavelengths shortward of Lyα where there are a few excited state troughs from higher ionization species. In particular S iv/S iv*λλ1062.66,1072.97. This ion is similar to C iv in ionization structure and indeed S iv troughs are much more prevalent than those of the singly ionized species. Measuring N_H and R for these objects will therefore eliminate the uncertainty connected with the rarity of outflows showing troughs from singly ionized species, and will yield robust measurements for $\dot{M}$ and $\dot{E}_k$. We are currently pursuing this project, which is challenging due to the heavy Lyα forest contamination.

Given the bolometric luminosity and assuming that the SMBH is accreting near the Eddington limit we find that the amount of mass being accreted is

$$\begin{equation} \dot{M}_{\rm acc} = \frac{L_{\rm Bol}}{\epsilon _r c2} = 88\, M_{\odot }\,{\rm yr}^{-1}, \end{equation} \tag{ 12 }$$

where we assumed an accretion efficiency (_r) of 0.1 (Salpeter 1964) and c is the speed of light. This large accretion rate (the outcome of a very luminous quasar) suggests that the mass flux values we derive (see Table 8) are not unreasonable. We expect such an outflow to have roughly an order of magnitude higher mass flux than the accretion rate onto the SMBH since the original outflow entrained material on its journey to several kpc distance. Simple momentum conservation requires that an outflow which started at ∼20,000–30,000 km s⁻¹ have 5–7 times more mass flux by the time it slowed to 4200 km s⁻¹. Therefore, an outflow such as this could have begun with $\dot{M}_{\rm outflow}\sim \dot{M}_{\rm acc}$.

Next, assuming Eddington accretion, we can derive the SMBH mass and infer a mass for the host galaxy bulge. The black hole mass derived from Eddington accretion is (Peterson 1997, p. 238)

$$\begin{equation} M_{\rm{BH}} = \frac{L_{\rm Bol} \sigma _T}{4 \pi G m_p c} = 4.0\times 10^{9} M_{\odot }, \end{equation} \tag{ 13 }$$

where σ_T is the Thompson scattering cross-section for an electron, G is the gravitational constant, M_BH is the mass of the SMBH, and m_p is the mass of the proton. Thus, the spheroidal bulge component of the host galaxy (assumed to be approximately the mass of the host galaxy) has a mass M_bulge = 3.3 × 10¹²M_☉ based on a SMBH to bulge ratio of 0.0012 (McLure & Dunlop 2002). This mass can be compared with the total mass ejected by the outflow over the ∼10⁸ year duty cycle of the quasar, which is a few times 10¹⁰ M_☉.