The Distance of Quasar Outflows from the Central Source: The First Consistent Values from Emission and Absorption Determinations

The quasar 3C 191 was observed with VLT/X-shooter on 2013 December 3, with a total exposure time of 3000 s (as part of program 092.B-0393, PI: Leipski). The data covers a spectral range of 2989–10200 Å, with resolution R ≈ 4100. The spectrum was processed by ESO through its standard pipelines (see A. Modigliani et al. 2010 for a detailed description of the X-shooter pipeline) to remove instrument and atmospheric signatures and perform flux and wavelength calibration. The processed spectrum was then made available on the ESO science archive.¹² Several noise spikes less than 3 pixels wide (originating from the impact of cosmic rays with the detector) were seen throughout the processed spectrum. We omitted these affected pixels using 3σ clipping and obtained the final spectrum (shown in Figure 1) for our analysis.

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Q. Zhao et al. (2025) determined the redshift of 3C 191 using the narrowest component of the [O iii] 5007 Å emission line extracted from the central 0$\mathop{.}\limits^{\unicode{x02033}}$25 around the quasar nucleus. They determined the systematic redshift of the quasar to be z = 1.9527 ± 0.0003 (see their Section 3.1 for a detailed description of the emission model). This was also found to be in agreement with the redshift determined from the [O ii] λλ3727, 3729 doublet (z = 1.9527 ± 0.0003) detected in emission in the VLT/X-shooter spectrum and therefore we adopt this redshift for our analysis.

In order to identify the troughs and determine their column densities, we need to obtain a normalized spectrum by dividing the data by the unabsorbed emission model. In the spectrum of 3C 191, we first select spectral regions free from significant emission or absorption (λ_obs ≃ 3165, 3370, 4000, 4300, and 5300 Å) to use as anchor points for our continuum fit. We find that a single power law is unable to describe the emission in the observed wavelength range analyzed in this paper and therefore we employ a broken power law of the form ${F}_{\lambda }={F}_{4000}{({\lambda }_{\mathrm{obs}}/4000)}^{\alpha }$, where α takes different values before (α₁) and after (α₂) λ_obs = 4000 Å. The best-fit parameters for the model obtained using nonlinear least squares are α₁ = 0.34 ± 0.09, α₂ = −1.08 ± 0.01, and F₄₀₀₀ = 1.104 (± 0.003) × 10⁻¹⁶ erg s⁻¹ cm⁻² Å⁻¹ with ${\chi }_{{\rm{red}}}^{2}$ (reduced chi-square) = 0.754.

The X-shooter spectrum also shows clear signatures of many prominent emission features and thus we obtain a best-fit model using nonlinear least squares for each of these features by considering absorption-free regions in their vicinity. The Lyα/N v complex is modeled with four independent Gaussian components. The C iv emission feature also requires separate broad emission line and narrow emission line components and is therefore modeled using two independent Gaussians. The Si iv emission feature, on the other hand, is well modeled with a single Gaussian component. Finally, we also detect weak emission in two regions: 3800 Å ≲ λ_obs ≲ 3900 Å and 4700 Å ≲ λ_obs ≲ 5000 Å. Based on the composite quasar Sloan Digital Sky Survey (SDSS) spectra of D. E. V. Berk et al. (2001), the first region is likely to be a blend of O i/Si ii, whereas the latter could contain contribution from He ii along with a blend of O iii]/Al ii/Fe ii. We are able to model these regions with one and three independent Gaussians, respectively. Table 1 reports the wavelength ranges (rounded off to the nearest integer) used as anchor for fitting each emission complex and the ${\chi }_{\mathrm{red}}^{2}$ for the respective fits. Combining the continuum model and the different emission components gives us the unabsorbed emission model, which is shown in Figure 1 by the red dashed curve.

Table 1. Wavelength Ranges Used for Fitting the Emission Lines in the VLT/X-shooter Spectrum and the Resulting ${\chi }_{\mathrm{red}}^{2}$

Complex	Lines	Wavelength Ranges	${\chi }_{\mathrm{red}}^{2}$
		(Å)
1	Lyα + N v	3480–3485, 3493–3498	1.261
		3533–3543, 3562–3565
		3595–3636, 3667–3700
		3740–3770
2	O i + Si ii	3795–3835, 3870–3905	0.656
3	Si iv	4075–4090, 4117–4123	0.691
		4140–4146, 4180–4200
4	C iv	4400–4480, 4530–4540	0.944
		4580–4630
5	He ii + O iii]	4672–4732, 4745–4880	0.999
	+ Al ii + Fe ii	4900–4910, 4931–4990

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Having determined the systematic redshift and modeled the unabsorbed emission, we identify the main absorption system for the low-ionization species (Si ii, C ii, Al ii, Al iii, and Si iii), spanning a velocity range −950 ≲ v ≲ −500 km s⁻¹, with the deepest absorption at v ∼ −720 km s⁻¹. The same system is detected in the high-ionization species (C iv, Si iv, S iv, and N v) as well. However, the high-ionization troughs are broader and show a shift in velocity space with the deepest absorption at v ∼ −800 km s⁻¹. A similar shift in velocities for higher ionization potential (IP) ions has been previously reported in absorption troughs from an outflow in PKS J0352-0711 by T. R. Miller et al. (2020). Based on the width of the C iv trough (Δv ∼ 1500 km s⁻¹), the outflow system is characterized as a mini broad absorption line (BAL; F. Hamann & B. Sabra 2004).

The ionic column densities N_ion of the various observed species can be obtained from the troughs by assuming an absorber model for the cloud. The simplest model, known as the apparent optical depth (AOD) model, assumes a homogeneous outflow that completely covers the source. In this case, the normalized intensity profile as a function of velocity I(v) is related to the optical depth τ(v) as I(v) = e^−τ(v). N_ion for a transition with rest wavelength λ (in angstroms) and oscillator strength f is then given as (B. D. Savage & K. R. Sembach 1991)

$$\begin{eqnarray}&&{N}_{\mathrm{ion}}=\displaystyle \frac{{m}_{e}c}{\pi {e}^{2}f\lambda }\int \tau (v)dv=\displaystyle \frac{3.8\times 1{0}^{14}}{f\lambda }\int \tau (v)dv[{\mathrm{cm}}^{-2}]\end{eqnarray} \tag{ 1 }$$

where m_e is the electron mass, c is the speed of light, and e is the elementary charge. The homogeneous AOD model does not account for partial line-of-sight covering of the outflow and line saturation and therefore can only lead to lower limits for N_ion in most cases. If troughs from two or more lines corresponding to the same lower energy level of an ion are observed, we can employ a partial covering (PC) model. In this two-parameter model, the absorber is assumed to be covering a (velocity-dependent) fraction C(v) of a constant-emission source. The normalized intensities for the two lines are then given as

$$\begin{eqnarray}&&\begin{array}{r}{I}_{1}(v)=1-C(v)+C(v)\cdot {e}^{-\tau (v)}\\ {I}_{2}(v)=1-C(v)+C(v)\cdot {e}^{-R\tau (v)}\end{array}\end{eqnarray} \tag{ 2 }$$

where R is the expected line strength ratio given by $R={({g}_{i}{f}_{ik}\lambda )}_{2}/{({g}_{i}{f}_{ik}\lambda )}_{1}$ (where g_i is the degeneracy of the lower level i, f_ik is the oscillator strength of the transition between levels i and k, and λ is the transition's wavelength). Having obtained I₁(v) and I₂(v) from the spectrum, C(v) and τ(v) can be obtained numerically by solving for Equation (2) simultaneously (see N. Arav et al. 1999, 2005, for a detailed description of the model).

We model the troughs in velocity space using a Gaussian profile for the optical depth and note that for most of the observed ionic species (H i, N v, C ii, C iv, Si iii, and Si iv), the troughs appear saturated and therefore only lower limits for N_ion can be obtained for them based on the AOD model. We detect troughs from two different ionized species of Al: Al iii λλ1855, 1863 and Al ii 1671 Å. We first model the Al iii 1863 Å trough with a Gaussian profile and then use this model as a template for the Al iii 1855 Å and Al ii 1671 Å troughs by fixing the centroid and width of the profile while allowing its depth to vary independently (see Appendix for an alternate multicomponent modeling and the difference between the two approaches). The best-fit models (shown in Figure 2) are determined by nonlinear least squares. We note that for Al ii, the deepest part of the model and the trough show a slight offset (∼30 km s⁻¹). However, as this shift is less than one resolution element in the velocity space (∼73 km s⁻¹), we continue to use this model for our analysis as it is physically motivated. As the two Al iii lines originate from the same lower energy level, we can use the PC method to obtain a measurement for the N_ion. We find that the N_ion determined using the PC method differs by less than 20% from the AOD determination, thus indicating that these troughs are not affected greatly by nonblack saturation. As the Al ii 1671 Å trough appears shallower than the Al iii 1855 Å trough, it would be affected even less by nonblack saturation (see Section 2.2 in N. Arav et al. 2018 for a detailed description of nonblack saturation). This allows us to use the N_ion determined from the AOD method as a measurement. Reliable measurements of column densities from two different ionization states of Al play an important role in our photoionization analysis, which we describe in detail in the next section.

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For Si ii, we detect multiple troughs originating from both the ground state and the 287 cm⁻¹ metastable excited state. Among the detected Si ii transitions, the 1304 Å line has the smallest oscillator strength. It also appears much shallower than the other deeper Si ii troughs (at 1260 and 1527 Å) and can thus be considered unsaturated. Using the same argument to compare the different Si ii* transitions at 1265, 1309, and 1533 Å shows the 1309 Å trough can also be considered as unsaturated. Therefore, the AOD column densities derived from the Si ii/ii* 1304/1309 Å transitions can be used as measurements. Our modeling of these troughs follows the same procedure as that for the Al troughs. We first model the Si ii* 1309 Å trough with a Gaussian profile and use this as the template for obtaining the best-fit model for the Si ii 1304 Å trough (shown in Figure 3).

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We summarize the determined column density measurements and limits for the detected troughs in Table 2, along with the predictions of our best-fit photoionization model (Section 2.2.3). The reported errors include the uncertainty in determining the best-fit model for the unabsorbed emission. We first obtain the 1σ errors for the different components of our best-fit emission model (shown in red in Figure 1). Using them we construct two additional continuum models in which each component is shifted by +σ and −σ, respectively. We use these new continuum levels to renormalize the VLT/X-shooter spectrum individually and obtain the column densities of the different ionic species for them. Their deviation from the column densities obtained for the best-fit emission model (reported in Table 2) allows us to estimate their uncertainties due to our modeling of the emission features. We add them in quadrature with the 1σ uncertainties obtained similarly for our modeling of the absorption troughs. For Al ii, Al iii, and Si ii, we also include the uncertainty due to our choice of models for their troughs as outlined in Table 4 (see Appendix for a comparison between the single-component and multicomponent approaches).

Table 2. Ionic Column Densities for the Outflow in 3C 191

Ion	log(Nion)a	log(N${}_{\mathrm{mod}}$)b
	(cm−2)	(cm−2)
H i	$\gt 14.9{3}_{-0.10}^{}$	17.28
C ii	$\gt 14.9{0}_{-0.09}^{}$	15.21
C ii*	$\gt 15.0{7}_{-0.08}^{}$	⋯
C iv	$\gt 15.5{3}_{-0.10}^{}$	16.30
N v	$\gt 15.3{1}_{-0.08}^{}$	14.63
Al ii	$13.2{9}_{-0.07}^{+0.06}$	13.29
Al iii	$13.9{6}_{-0.09}^{+0.07}$	13.96
Si ii	$14.4{8}_{-0.04}^{+0.04}$	14.25
Si ii*	$14.2{1}_{-0.07}^{+0.05}$	⋯
Si iii	$\gt 14.2{6}_{-0.08}^{}$	15.46
Si iv	$\gt 14.8{1}_{-0.07}^{}$	15.56
S iv	$14.8{9}_{-0.10}^{+0.08}$	15.29
S iv*	$\lt 13.8{9}_{}^{+0.09}$	⋯

Notes. ^aMeasured column densities for the outflow from the VLT/X-shooter spectrum. ^bIonic column densities predicted by the best-fit Cloudy model shown by the black dot in Figure 4. The model values for C ii, Si ii, and S iv include the contribution from their excited states.

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Ionized outflows are dominated by photoionization equilibrium (K. Davidson & H. Netzer 1979; J. H. Krolik 1999; D. E. Osterbrock & G. J. Ferland 2006, and references therein) and are thus characterized by their total hydrogen column density (N_H) and ionization parameter (U_H), which is related to the rate of ionizing photons emitted by the source (Q_H) by

$$\begin{eqnarray}&&{U}_{{\rm{H}}}=\frac{{Q}_{{\rm{H}}}}{4\pi {R}^{2}{n}_{{\rm{H}}}c}\end{eqnarray} \tag{ 3 }$$

where R is the distance between the central emission source and the observed outflow component, c is the speed of light, and n_H is the hydrogen number density. Q_H is determined by (a) the choice of spectral emission distribution (SED) that is incident on the outflow, (b) the observed flux of the object's continuum at a specified wavelength, (c) the redshift of the object, and (d) the choice of cosmology. Having determined the column densities of the observed ionic species, we can constrain the physical state of the gas, using the spectral synthesis code Cloudy (version C23.01; M. Chatzikos et al. 2023), which solves the equations of photoionization equilibrium in the outflow. The outflow is modeled as a plane-parallel slab with a constant n_H and solar abundance, and is irradiated on by the modeled SED from the quasar HE0238-1904 (N. Arav et al. 2013), which is the best empirically determined SED in the extreme UV, where most of the ionizing photons come from. Figure 4 shows the result of our photoionization modeling. Using the methodology described by D. Edmonds et al. (2011), N_H and U_H are varied in steps of 0.1 dex, keeping all other parameters (n_H, abundances, and the incident SED) constant, leading to a two-dimensional grid of models in the parameter space with predictions for all the N_ion in the slab. The different-colored contours represent the allowed values in the (N_H, U_H) phase space that correspond to the observed column density constraints for the ionic species. The strongest such constraint comes from the column density measurements of the two Al ions. The ratio of the column densities of Al ii and Al iii serves as an indicator of the ionization state of the outflow that is independent of the assumed abundances. Therefore based only on the Al ii and Al iii N_ion measurements, we obtain log N_H = $20.5{0}_{-0.16}^{+0.13}$ [cm⁻²] and log U_H = $-2.0{6}_{-0.14}^{+0.12}$. This solution is shown in Figure 4, surrounded by an error ellipse that contains the phase space values within one standard deviation of our best-fit solution. We use this solution for the rest of our analysis. As can be seen, this solution underpredicts the Si ii column density (traced by the blue curve). Furthermore, the constraint for Si ii is almost parallel to that for Al ii and therefore they cannot simultaneously be satisfied by any point in the (N_H, U_H) parameter space. The simplest way to resolve this conflict is to postulate an abundance ratio of Si to Al that differs from the one observed in the Sun. We find that an increase of ∼0.4 dex in the relative abundance Si/Al (with respect to the solar abundances) would ensure that the measured column density for Si ii matches our prediction from the model solution. Similarly, our model overpredicts the S iv column density (traced by the pink curve). However, the measurement can be brought in complete agreement with our model with a decrease of ∼0.35 dex in the relative abundance of S with respect to Al. The proposed changes for both Si/Al and S/Al abundance ratios are well within the ranges allowed by empirical abundance models in quasar outflows (N. Arav et al. 2013). Finally, Figure 4 shows that our model solution satisfies the lower limit constraints (represented by dashed curves) from all ionic species except N v. We note that N v has an IP of ∼98 eV and is thus associated with a region with higher ionization than the other observed ionic species in our analysis, which have IP ≲64 eV. Observations of quasar outflows in the extreme UV have shown that when reliable column densities for higher-ionization species (e.g., Ne viii and Mg x) can be obtained, a single ionization phase is unable to provide an acceptable physical model for the outflow, thus requiring two distinct ionization phases (N. Arav et al. 2013, 2020). The high-ionization species then correspond to a phase with higher N_H and U_H. From the VLT/X-shooter spectrum of 3C 191, we cannot obtain reliable measurements for the column densities of other high-ionization species, and therefore cannot constrain the high-ionization phase completely. However, N v can still be ascribed to this phase, and that would explain why its N_ion constraint is not satisfied by our solution, which represents the low-ionization phase.

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The ratios of the column densities of excited lines to those of the resonance lines are an indicator of the electron number density (n_e) of an outflow under the assumption of collisional excitation (e.g., N. Arav et al. 2018). The identified outflow system in 3C 191 contains multiple troughs corresponding to the ground and excited states of Si ii. As discussed in Section 2.2.2, the Si ii 1304 Å and Si ii* 1309 Å transitions yield the most reliable measure of the column densities of Si ii and Si ii*. We obtain theoretical population ratios between the ground and excited states as a function of n_e using the Chianti atomic database (version 9.0; K. Dere et al. 1997; K. P. Dere et al. 2019).

A comparison of these theoretical predictions with the observed ratio of column densities of Si ii* and Si ii is shown in Figure 5. This leads to log(n_e) = $2.{78}_{-0.10}^{+0.08}$ [cm⁻³]. We also detect C ii 1335 Å and C ii* 1336 Å transitions, which appear to be saturated, and thus their AOD column densities will correspond to lower limits. Their ratio provides a lower limit of log(n_e) $\geqslant 2.1{2}_{-0.22}^{}$ [cm⁻³]. Although we do not detect the Si iv* 1073 Å trough, we use the Gaussian template obtained from the Si iv 1063 Å trough to obtain an upper limit for the column density of Si iv* based on its nondetection in the spectrum. The ratio of the Si iv* and Si iv column densities can then be used to determine an upper limit of log(n_e) $\leqslant 3.3{8}_{}^{+0.10}$ [cm⁻³]. Figure 5 shows that the obtained upper and lower limits are in agreement with our n_e determined from the Si ii* and Si ii population ratio.

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Having determined U_H and n_e, we can use Equation (3) to obtain the distance between the outflow and the central source (R):

$$\begin{eqnarray}&&R=\sqrt{\frac{{Q}_{{\rm{H}}}}{4\pi {U}_{{\rm{H}}}{n}_{{\rm{H}}}c}}.\end{eqnarray} \tag{ 4 }$$

Q_H can be obtained by integrating over the SED for energies above the Rydberg limit:

$$\begin{eqnarray}&&{Q}_{{\rm{H}}}={\int }_{{\nu }_{\mathrm{Ryd}}}^{{\rm{\infty }}}\displaystyle \frac{{L}_{\nu }}{h\nu }d\nu .\end{eqnarray} \tag{ 5 }$$

The spectrum obtained from quasars with low-ionization absorption line outflows can be strongly affected by extinction due to dust in the host galaxy (P. B. Hall et al. 2002; J. P. Dunn et al. 2010; K. M. Leighly et al. 2024). To account for this reddening, we follow the methodology described by P. B. Hall et al. (2002), which includes dereddening the spectrum until the continuum slope matches that of the composite SDSS quasar of D. E. V. Berk et al. (2001). In doing so, we find that the slope of the composite SDSS quasar matches that of the HE0238 SED for frequencies smaller than that of the Lyα line. The HE0238 SED is thus representative of a typical dereddened quasar spectrum. Therefore, to obtain the dereddened SED incident on the cloud, we scale the HE0238 SED, by matching its flux to the observed flux from the VLT/X-shooter spectrum at an observed wavelength of λ_obs = 10000 Å (λ_rest = 3386.78 Å). We choose the longest available wavelength for scaling as AGN extinction curves show that the extinction generally increases with an increasing wavenumber, and is therefore smaller for longer wavelengths (B. Czerny et al. 2004; C. M. Gaskell et al. 2004). The resulting scaled SED is shown in blue in Figure 6. The ionizing photons come from wavelengths shorter than the Lyman limit, which is not covered by VLT/X-shooter. Therefore to get a handle on the ionizing continuum we use the available Chandra observations of the object covering the 0.2–2 keV range, obtained from the second release of the Chandra Source Catalog (I. N. Evans et al. 2010, 2020). The photometric flux measurements (converted to luminosity) are shown in the quasar rest frame in Figure 6 as red points. The X-ray measurements are in agreement with the prediction from the scaled HE0238 SED, further strengthening our case for its use to model the incident flux on the cloud. Therefore, based on our scaled SED, we obtain Q_H = $4.4{3}_{-0.07}^{+0.07}$ × 10⁵⁶ s⁻¹ and bolometric luminosity L_Bol = $8.0{0}_{-0.13}^{+0.13}$ × 10⁴⁶ erg s⁻¹.

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Typically, n_H is estimated from n_e under the assumption of highly ionized plasma, which leads to the approximation n_e ≈ 1.2n_H. However, it has been shown that for the low-ionization phases of the outflow, the formation of the hydrogen ionization front can lead to a sudden drop in n_e and therefore to an underestimation for n_H (M. Sharma et al. 2025). We thus run a Cloudy model for our outflow with log(n_H) = log(n_e) = 2.78 and the parameters obtained in Section 2.2.3 and find that for this cloud, the hydrogen ionization front is not entirely developed, and thus while n_e deviates slightly from the assumption of highly ionized plasma, the drop is not significant and averaging over the cloud based on the zonewise Si ii column density yields n_e ≈ 1.1n_H. Substituting the determined values of Q_H, U_H, and n_H into Equation (4), we find that the outflow is located $5.{1}_{-1.0}^{+0.9}$ kpc away from the central source.

To obtain an estimate of the systematic error in the distance determination due to different SEDs, we check the difference between the Q_H and U_H determined from the HE0238 SED and the SED used by F. W. Hamann et al. (2001) in their Keck/HIRES analysis. The latter leads to a 25% increase in Q_H and a 7% decrease in U_H. Therefore, using Equation (4), we can estimate the systematic error in our distance determination to be ∼16%.

The outflow can be modeled as a partially thin spherical shell covering a solid angle Ω, and moving with velocity v (B. C. Borguet et al. 2012b). The total mass of the gas within the outflow can then be obtained as

$$\begin{eqnarray}&&M\simeq 4\pi {\rm{\Omega }}{R}^{2}{N}_{{\rm{H}}}\mu {m}_{p}\end{eqnarray} \tag{ 6 }$$

where R is the spatial extent of the outflow, N_H is the total hydrogen column density, m_p is the proton mass, and μ = 1.4 is the atomic weight of the plasma per proton. Defining the dynamic timescale as the time it takes the gas from the nucleus traveling at an average velocity v to reach the location of the outflow, t_dyn = R/v, we can obtain the mass-loss rate $\dot{M}$ and the kinetic luminosity $\dot{{E}_{k}}$ of the outflow as follows:

$$\begin{eqnarray}&&\dot{M}=\displaystyle \frac{M}{{t}_{\mathrm{dyn}}}=4\pi {\rm{\Omega }}R{N}_{{\rm{H}}}\mu {m}_{p}v\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray*}&&\dot{{E}_{k}}=\frac{1}{2}\dot{M}{v}^{2}.\end{eqnarray*}$$

We assume Ω = 0.2 based on the ratio of quasars that show a C iv BAL (P. C. Hewett & C. B. Foltz 2003). Using the velocity at the deepest absorption (v = −$72{0}_{-12}^{+12}$ km s⁻¹) as the average velocity of the outflow leads to a mass-loss rate of $\dot{M}$ = $3{3}_{-12}^{+13}$ M_⊙ yr⁻¹ and kinetic luminosity $\dot{{E}_{k}}$ = $5.{5}_{-2.0}^{+2.1}$ × 10⁴² erg s⁻¹ for the outflow, which is $6.{8}_{-2.5}^{+2.7}$ × 10⁻³% of L_Bol. This is much smaller than the ≳0.5% required for efficient AGN feedback as determined by P. F. Hopkins & M. Elvis (2010).

We first model the Al iii 1863 Å trough with two independent Gaussian profiles for optical depth. We then use this model as a template for the Al iii 1855 Å and Al ii 1671 Å troughs by fixing the centroid and width of both Gaussians while allowing their depth to vary independently. In the case of Al ii 1671 Å, we allow for an additional component to model the absorption blend in the red wing. The results for the best-fit model templates (determined by nonlinear least squares) for these troughs are shown in Figure 10.

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The absorption trough for the Si ii* 1309 Å transition is well modeled by a single Gaussian component as shown in Figure 3. However the Si ii 1304 Å trough shows evidence for multiple components (four in particular, as can be noted by the two inflection points on the blue wing, and one more on the red wing). Therefore, we model the Si ii trough with four Gaussian components, of which one has a fixed centroid and width based on the Si ii* 1309 profile. The other three components are allowed to have centroids and widths that vary independently, and the depths of all the four components are allowed to vary as well. The results for the best-fit model templates (determined by nonlinear least squares) for these troughs are shown in Figure 11.

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