THE DISCOVERY OF THE FIRST He iλ10830 BROAD ABSORPTION LINE QUASAR

The infrared spectroscopic observations were made at the NASA Infrared Telescope Facility (IRTF) using the SpeX spectrograph (Rayner et al. 2003) in the short cross-dispersed mode with an effective bandpass of 0.8–2.4 μm as part of another project. The observations were made on 2008 March 28–30 and 2008 August 22–24. Conditions were non-photometric. As noted above, the scope of this paper is limited to the He i absorption, and so we will defer the detailed description of the observations and reduction to S. Barber et al. (2011, in preparation) which will include analysis of the entire data set. For this paper, we use the spectra from FBQS J1151+3822, PG 1543+489, PHL 1811, and FBQS J1702+3247; these were all observed with a 08 slit for effective exposures of 2, 1.7, 2.9, and 1 hr, respectively. Flat-field lamps and line lamps were observed along with each object. A nearby early A-type star was also observed along with each object. The spectra were reduced using the IDL software SpexTool (Cushing et al. 2004). The flux calibration and correction for telluric features was performed using the A star spectrum and employing distributed IDL software that use the methods described in Vacca et al. (2003). In the vicinity of the He i absorption feature (at approximate 1.4 μm in the observed frame), the FWHM resolution measured from the line-lamp spectra ranged from ∼350 to ∼400 km s⁻¹ at the short-wavelength end of the fourth spectral order to ∼300 km s⁻¹ at the long-wavelength end of the fifth spectral order. The spectrum is shown in Figure 1.

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The short-wavelength end of the absorption feature occurs at the long-wavelength end of the fifth spectral order. There is a prominent telluric absorption band between ∼1.35 and 1.45 μm. In addition, the effective area is dropping off at the end of the order. Unfortunately, our feature is partially compromised by these issues. Is it possible that the absorption feature is somehow an artifact of the data reduction? This is not likely, primarily because the long-wavelength end of the absorption feature is found on both the long-wavelength end of the fifth spectral order and on the short-wavelength end of the fourth spectral order, and both have the precisely the same shape. In addition, FBQS J1151+3822 is a relatively bright quasar for the IRTF, and the telluric correction method is very reliable (Vacca et al. 2003).

The spectra were corrected for Galactic reddening using E(B − V) = 0.023 (derived from the infrared cirrus; Schlegel et al. 1998) using the CCM reddening curve (Cardelli et al. 1989). The redshifts were derived from the IRTF spectra assuming that Hα, Paschen β, and Paschen α are observed at the rest wavelengths. For FBQS J1151+3822, PG 1543 + 489, PHL 1811, and FBQS J1702 + 3247, the redshifts were found to be 0.3354, 0.4104, 0.1928, and 0.1644, respectively. These are insignificantly different from the values listed in NED. The spectra were shifted into the rest frame using these redshift values. Finally, the spectra were modestly smoothed.⁴

As discussed in, e.g., Savage & Sembach (1991), the apparent optical depth of an absorption feature is given by τ(λ) = ln [I₀(λ)/I_obs(λ)], where I_obs(λ) is the observed spectral intensity and I₀(λ) is the unabsorbed spectral intensity. The IRTF spectrum of FBQS J1151+3822 yields I_obs(λ), of course. In order to obtain the apparent optical depth, we need to obtain the intrinsic continuum I₀. The lines in the near IR spectra of quasars are relatively unblended, compared with the optical and near UV bands; however, the continuum in this region of the spectrum transitions from the AGN power law at longer wavelengths to the dust-reprocessing feature at shorter wavelengths (Figure 1). In FBQS J1151+ 3822, it appears that this change in the continuum occurs very near the absorption feature.

To obtain I₀, we used the following procedure. First, we determined that of the 12 objects that we observed, PG 1543+489, PHL 1811, and FBQS J1702+3247 had spectra most similar to that of FBQS J1151+3822 outside of the absorption region. In addition, we downloaded the spectra presented by Landt et al. (2008) and found two additional objects that resemble FBQS J1151+3822: PDS 456 and HE 1228+013. The spectra were similar to that of FBQS J1151+3822 in terms of emission lines, but different in their continuum slopes. We used line-free regions in FBQS J1151+3822 and each of the comparison objects to determine power laws that the comparison-object spectra could be divided by so that their continua would match that of FBQS J1151+3822. We then performed this continuum transformation.

The procedure above works quite well for the continuum correction. However, several of the objects have significantly higher equivalent widths than FBQS J1151+3822. To scale the lines, we need to divide each spectrum by its continuum. We focus on a limited wavelength range between 0.79 and 1.4 μm and fit the line-free continuum bands of each object with a fourth-order polynomial. Each spectrum was then divided by this polynomial. Finally, the spectra were suitably scaled. The following scale factors were used: PG 1543+489: 0.73; PHL 1811: 1.1; FBQS J1702+3247: 0.75; PDS 456: 1.0; HE 1228+013: 0.61. The results are shown in Figure 2.

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The figure shows that all objects are rather similar over most of the range shown except for the long-wavelength side of the He i/Paγ feature. In particular, in the region of the absorption feature which is seen to stretch between 1.044 and 1.082 μm, most objects are quite similar except for PDS 456 which is seen to exhibit some strange feature near 1.07 μm (Landt et al. 2008). Since PHL 1811 has by far the best signal-to-noise ratio of all of the spectra presented, we use the scaled version shown in Figure 2 as the intrinsic spectral intensity I₀. Except for PDS 456, the other spectra match that of PHL 1811 within about 5%, and we take that value as the systematic uncertainty in our estimate of I₀.

The resolution of the IRTF spectra in the region of the feature is about 350 km s⁻¹. Binning the FBQS J1151+3822 spectrum by a factor of two yields slightly more than two bins per resolution element. The PHL 1811 spectrum was resampled on the same wavelengths as the FBQS J1151+3822 spectrum.

The IRTF spectra were extracted using the optimal extraction technique (Cushing et al. 2004). This method produces statistical errors that appear to be too small. Specifically, the standard deviation in the data in relatively flat and smooth regions of the continua is systematically several factors larger than the assigned errors. To account for this trend, we increase the size of the error bars by a factor of six for the PHL 1811 spectrum, and a factor of four for the FBQS J1151+3822 spectrum. Then, between 1.0 and 1.1 μm, in the region of the absorption feature, the signal-to-noise ratios range between about 16 and 130 for the FBQS J1151+3822 spectrum and are about 200 uniformly for the PHL 1811 spectrum.

Using these spectra, the ratio and apparent optical depth were computed as a function of velocity. The resulting ratio is shown in Figure 3. The maximum velocity v_max is ∼11,000 km s⁻¹, showing that FBQS J1151+3822 is truly a broad absorption line quasar.

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We analyzed two optical spectra of FBQS J1151+3822. The Sloan Digital Sky Survey (SDSS) observed the object 2005 March 11 for 4600.4 s. The spectrum was extracted from the archive, rewritten in the text format, and a moderate amount of smoothing was applied as mentioned in Section 2.1. The SDSS redshift was 0.3351 ± 0.002. We remeasured the redshift using the Balmer lines and estimated it to be 0.3341. The spectrum was corrected for redshift and reddening as above.

The object was also observed at the MDM observatory 2.4 m Hiltner telescope and the CCDS spectrograph on 2009 January 3 for 1 hr. We used a grating with 350 mm⁻¹ and a 1'' slit yielding observed-frame spectra between ∼4300 Å and ∼5800 Å. Conditions were non-photometric. The spectra were reduced in a standard way independently using MIDAS⁵ (M.D.) and IRAF⁶ (K.M.L., S.B.); the results were consistent. The signal-to-noise ratio of the FBQS J1151+3822 was estimated to be approximately 70. The FWHM resolution in the vicinity of the He iλ3889 line was found to be about 175 km s⁻¹ from the line lamps.

Extraction of the apparent optical depth of the He i*λ3889 feature from either the SDSS or MDM spectrum is challenging. First, as can be seen in Figure 4, the apparent optical depth of the 3889 Å feature is quite small. This is expected, since the ratio of f_ikλ between the 10830 and 3889 Å components is 23.3, which means that on the linear part of the curve of growth, the true optical depths of these lines should have a ratio of 23.3 (Savage & Sembach 1991). Second, the continuum is not a power law; rather, FBQS J1151+3822 is a strong Fe ii emitter and the continuum includes a forest of Fe ii lines. In fact, to the casual observer, the only clearly apparent absorption lines are the Ca ii H and K lines. Without knowing that there is a 10830 Å absorption trough in this object, the He i lines are easily confused with the Fe ii continuum. Thus, FBQS J1151+3822 had never before been recognized to be a BALQSO.

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We need a suitable estimation of the Fe ii continuum to extract the optical depths. The usual I Zw 1 template (Boroson & Green 1992) is inadequate because it does not cover the shorter wavelengths around He i*λ3889 that we need, so we developed a template from SDSS spectra. We selected a sample of 28 bright low-redshift quasars that have sufficiently narrow lines that the Fe ii complexes near Hβ are resolved. From these, we constructed an average line spectrum as follows. The spectra, dereddened and transformed to the rest frame, were resampled onto a common wavelength range between 2869 Å (the lower wavelength limit of the SDSS spectrum of FBQS J1151+3822) and 4750 Å (considered the upper limit to avoid Hβ, as that line can be quite variable between objects). The spectra were normalized by dividing by the average flux obtained from a 21-element bin located in the middle of the chosen wavelength range. The power-law slope of the continuum was estimated by fitting a power law to the flux in line-free bands, and all spectra were normalized using this estimated value to a slope of 1.96 (i.e., where F(λ) ∝ λ^−1.96). At each wavelength, the mean spectrum was computed, and finally, the power law estimated from the line-free bands was subtracted yielding an average line spectrum.

The SDSS and MDM spectra were then fitted using this Fe ii line model excluding the regions where absorption lines, both originating in He i and Ca ii, may be present. For the SDSS spectrum, the excluded regions were 3015–3188.7 Å and 3678–3958 Å. For the MDM spectrum, with its more limited wavelength coverage, only the second region was excluded. Four parameters were fit: the reddening of the input spectrum (i.e., the observed spectrum was dereddened by an input amount), the power-law index, the power-law normalization, and the line normalization. A figure of merit was computed at each grid point and the minimum of the grid identified the best fit. The figure of merit used was the absolute value of the difference between the unreddened input spectrum, and the power law plus line flux model, divided by the unreddened uncertainty in the case of the SDSS spectrum (the MDM spectrum, produced by IRAF, had no formal uncertainties).

The SDSS spectrum includes a notable feature between ∼3200 and 3300 Å probably originating in Fe ii multiplets M6 and M7 (e.g., Phillips 1978). The shape of the iron continuum varies from object to object in the UV (e.g., Leighly et al. 2007) and so it is possible that it also varies in the optical. We therefore create an alternative line spectrum from 7 of the 28 objects which shows the largest excess variance⁷ between 3170 and 3300 Å. A large value of excess variance chooses objects which both have prominent features and good signal-to-noise ratios. We then fit the MDM and SDSS spectra with this alternative Fe ii continuum.

It is clear that the uncertainty in the results produced by the procedure described above will be dominated by the systematic errors associated with the fact that the Fe ii spectrum is not identical among AGNs. An estimate of the systematic error can be obtained from the standard deviation of the mean spectrum from the sample used to create the Fe ii continuum. The standard deviation in the region of the absorption feature has an offset due to normalization offsets in the average spectra, plus fluctuations with scales of tens of angstroms with an amplitude of about 2%. The offset is unimportant since the fitting routine will remove uncertainty associated with that. However, the fluctuations in the standard deviation are important since they measure the differences in the spectrum among AGNs. Thus, we assign a systematic uncertainty of 1% to the model spectrum. The statistical uncertainty in the SDSS spectrum in the region of interest is about 2%. Thus, the ratio will have an uncertainty of about 2.2%, and the apparent optical depth should have an uncertainty of about the same value. Based on the number of counts in the MDM raw spectrum, we estimate a statistical uncertainty of about 1.5%. Propagating our estimated 1% uncertainty in the model spectrum yields an uncertainty in the ratio for the MDM spectrum of about 1.8%. The results of fitting the 28-SDSS-spectrum model to the SDSS spectrum of FBQS J1151+3889 are shown in Figure 4; the other combinations of spectra and Fe ii model were similar. The resulting ratio of data to model for the SDSS and MDM spectra is shown in Figure 3.

In principle, we should also observe He i*λ3188 absorption in the SDSS spectrum. But λf_ik is 79.4 times smaller for that component than that of He i*λ10830, so it is expected to be even weaker than He i*λ3889, where the λf_ik ratio is 23.3. Furthermore, the region of the spectrum around 3188 Å has exceptionally strong and complex Fe ii emission in it. In addition, the Fe ii emission in this region seems to vary from object to object more profoundly than it does around 3889 Å. So while there is some suggestion of absorption in this object (Figure 4), we cannot robustly extract an apparent optical depth profile and therefore ignore this line for the rest of the analysis.

We do not see any significant Balmer-line absorption in these spectra. However, it may be present at low equivalent widths. We fitted the SDSS spectrum in the vicinity of the Hα emission line with a power-law continuum, a Lorentzian profile for the Balmer line, two Fe ii templates (which will be described in K. M. Leighly et al. 2011, in preparation), and the optical depth profile obtained from the He i* λ10830 absorption line. The resulting component was transformed to a ratio as a function of velocity, which could be used to estimate the Balmer column density upper limit (Section 2.8).

The MDM spectral bandpass did not cover Hα. The IRTF bandpass does (Figure 1), but the spectrum had lower signal-to-noise ratio in the vicinity of this line compared with the SDSS spectrum. Therefore, we use the limit obtained from the SDSS spectrum henceforth.

Ca ii H and K absorption lines are visible in the optical spectra. There are two relatively narrow (∼300 km s⁻¹ FWHM) features that peak at ∼−1200 km s⁻¹ and ∼−2000 km s⁻¹. Both sets of features lie redward of the He i* absorption.

These two features have low apparent optical depth and are a challenge to analyze. We begin with the ratio of continuum to model derived in Section 2.4 for the MDM and SDSS spectra obtained using the two models for the Fe ii emission discussed in Section 2.4. The MDM and SDSS profiles appear consistent, so we average the ratios for each Fe ii model, leaving us with two spectra. We extract the apparent optical depths from both and display the results for the 28-spectrum Fe ii model in Figure 5.

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Ca ii is a lithium-like ion and like other resonance transitions in lithium-like atoms, the λf_ik for the 3934 Å component is about two times that of λf_ik for the 3969 Å (actually equal to 2.05). We found that the apparent optical depths shown in Figure 5 appear to have a ratio of 2:1, and indeed, if we double the apparent optical depth of the 3969 Å component (dashed line in Figure 5) we find a good correspondence with the apparent optical depth of the 3934 Å component (solid line). This implies that partial covering is not important for these lines and that they are not saturated. Indeed, if we use the apparent optical depth profiles to estimate the column density of Ca⁺ ions, we find that the measured column density from the two lines among the two spectra ranges between 9.4 × 10¹² cm⁻² and 1.07 × 10¹³ cm⁻². These estimates are consistent, given the uncertainties on the ratio spectra. We take the mean of these estimates (1.0 × 10¹³ cm⁻²) to be the column density of the Ca⁺ ions.

We believe that this absorption arises in different gas than the He i* absorption. First, the He i* absorption profile is much broader; had that broad profile been present in the Ca ii lines, the 3969 Å component would have severely altered the 3934 Å component, as these two lines are separated by only 2655 km s⁻¹. Likewise, the 3934 Å component would have altered the low-velocity region of the He i* line, and strong absorption would have been seen between the He i*λ3889 and the Ca iiλ3934 lines (separated by 6100 km s⁻¹). These features are not seen. In addition, the Cloudy simulations discussed in Section 3.1 for the relatively high-ionization He i* lines do not produce significant Ca⁺ column density. The highest log column density predicted is log N_Ca+ = 12.3, a factor of five too low; the highest column densities are found at the lowest ionization parameters. Generally speaking, the ionization parameter is higher and the column density is lower in our simulations than is generally required for Ca ii absorption (e.g., Hall et al. 2003). Our interest in this paper is in the He i* lines, and we do not discuss the Ca ii absorption further.

As discussed by Savage & Sembach (1991) and others, the optical depth is related to the ratio of the observed continuum I(λ) to the true continuum I₀(λ) by

$$\begin{eqnarray*} &&\tau (\lambda)=\ln [I(\lambda)/I_0(\lambda)]. \end{eqnarray*}$$

If the absorption line is not saturated and the absorber fully covers the source, the column density of the absorbing ion can be obtained from the optical depth (e.g., Savage & Sembach 1991)

$$\begin{eqnarray*} &&N=\frac{m_e c}{\pi e^2 f \lambda } \int \tau (v) dv, \end{eqnarray*}$$

where m_e is the mass of the electron, c is the speed of light, e is the charge on the electron, f and λ are the oscillator strength and wavelength for the transition, respectively, and v is the velocity relative to the rest frame with respect to λ.

Using the ratio profiles discussed in Sections 2.2, and 2.4, we find that the log of the column density of He i* is ∼14.3 from the He i*λ10830 line, and ∼14.75–14.95 from the various spectra for the He i*λ3889 line. These two estimates do not agree, although physically they have to be equal. This means that the assumption that the absorber fully covers the source is incorrect, and a partial covering analysis is appropriate (Section 2.8).

We discuss the Balmer absorption limit in the next section.

He i*λ10830 and He i*λ3889 are transitions from the same lower level. Therefore, the ratio of optical depths is fixed by atomic physics, provided that the lines are not saturated. We can use these ratios to solve for the parameters of a two-parameter inhomogeneous absorption model as a function of velocity. The simplest example is the partial covering model, where

$$\begin{eqnarray*} &&R_{10830}=(1-C_f)+C_f e^{-\tau _{10830}}\\ &&R_{3889}=(1-C_f)+C_f e^{-\tau _{3889}}, \end{eqnarray*}$$

where R is the ratio of the observed spectrum to continuum, C_f is the covering fraction, and τ₁₀₈₃₀ and τ₃₈₈₉ are the true optical depths. All of these parameters are functions of velocity (e.g., Sabra & Hamann 2005). We can solve these equations for C_f, τ₁₀₈₃₀, and τ₃₈₈₉, subject also to the constraint that τ₁₀₈₃₀ = 23.3τ₃₈₈₉.

Partial covering models have been widely applied to quasar spectra. One of the first applications was reported by Hamann et al. (1997), who analyzed metal resonance lines which have τ ratios very close to two. In that case, the two equations can be reduced to one analytically. For our τ ratio, an analytic expression cannot be derived. We found that the following method worked most reliably. First, we computed a grid of simulated R₁₀₈₃₀ and R₃₈₈₉ for a large range of input covering fractions and τ₃₈₈₉ (specifically, 5001 covering fraction points between 0 and 1, and 4001 logarithmically spaced τ₃₈₈₉ points between 0.01 and 100). Then for each velocity, we determine which pair of (C_f, τ₃₈₈₉) best matches the data, where our figure of merit is χ²; specifically, $\sqrt{\vphantom{A^A}\smash{\hbox{${(D_{3889}^2 + D_{10830}^2)}$}}}$ and the D values are the difference between the data points and the models divided by the uncertainty in the data points. At the point where the figure of merit is minimized, we evaluate an uncertainty on the model point where the confidence criterion is our best fitting χ² plus 1.0, corresponding to 1σ for one parameter of interest, in the direction along the parameter axis. Note that the best-fitting χ² values were all very small fractions of 1 since we have two equations and two unknowns, essentially, and since our grid was finely meshed. Finally, we exclude points that are unphysical, where R₃₈₈₉ > R₁₀₈₃₀ > R^23.3₃₈₈₉ is not obeyed (e.g., Hamann et al. 1997). Generally, this amounts to only a few points; i.e., of the 69 points in the velocity profile, 5–8 points are rejected (Table 1).

Figure 6 shows the results for the IRTF ratio for the He i*λ10830 line and the SDSS spectrum fit with the 28-SDSS-spectrum Fe ii model for the He iλ3889 line; the others were similar. The top panel shows the data and the model fit. The second panel shows the optical depth for the 3889 Å line; the value for the 10830 Å line would be 23.3 times larger. The third panel shows the covering fraction as a function of velocity. The fourth panel shows the incremental column density as a function of velocity (e.g., Savage & Sembach 1991) computed from the average τ, i.e., the value integrated over the spatial dimension (e.g., Arav et al. 2005). For the partial covering model, $\bar{\tau }=C_f \tau$. The uncertainties in the incremental column density are conservatively estimated from the products of the limits of the optical depth and covering fraction.

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The simple partial covering model, above, posits a physical scenario where 1 − C_f of continuum source is seen directly, while C_f of the source is uniformly covered by gas with a single value of τ. This scenario may be appropriate in some cases, for example, when a fraction of the continuum is scattered into our line of sight by electrons located in the vicinity of the symmetry axis; the presence of these electrons is indicated by the large polarization frequently seen in the absorption troughs (e.g., Ogle 1998). But it is also possible that the optical depth is not uniform over the source. These so-called inhomogeneous absorbers have been discussed by, e.g., De Kool et al. (2002), Sabra & Hamann (2005), and Arav et al. (2005). We choose to investigate the power-law inhomogeneous absorber model. We use a power-law function, i.e., τ(x) = τ_maxx^a, where τ_max and a are fit parameters. We use the analytical formula for the ratio of the data to model given in Sabra & Hamann (2005, their Equation (14)), and follow the approach outlined above. Our model grid consisted of 3501 values of a spaced logarithmically between 0.0316 and 100, and 4001 values of τ_max spaced logarithmically between 0.01 and 100. The resulting fit for the IRTF spectrum and the SDSS spectrum fit with the 28-spectrum Fe ii model is shown in Figure 7. In this case, the average optical depth is τ_max/(a + 1). The upper limit on the column density was conservatively estimated using the upper limit on τ_max divided by the lower limit on a; similarly, the lower limit was estimated using the lower limit of τ_max and the upper limit of a.

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For both models, the total He i* column density is obtained by integrating over the average τ(v) profile (e.g., Savage & Sembach 1991) and the uncertainties obtained by integrating over the upper and lower bounds. The results are given in Table 1. The values for the partial covering model and power-law model are essentially identical. In addition, the values are very similar among the four different He i*λ3889 ratio profiles. The average of the log of the eight column density estimates is 14.9. This is the value that we use for Cloudy simulations and the remainder of the paper.

The derived value of He i* column density is very similar to the lower limit derived from the 3889 Å component (Section 2.7; Table 1). This is not an accident. To obtain the lower limit, we assume

$$\begin{eqnarray*} &&R_s \approx \exp (-\tau _s) \end{eqnarray*}$$

for the weaker component, for example. As noted above, the partial covering model is

$$\begin{eqnarray*} &&R_s=(1-C_f)+C_f \exp (-\tau _s). \end{eqnarray*}$$

If the optical depth of the weaker component is sufficiently small, the exponent can be Taylor expanded as follows:

$$\begin{eqnarray*} &&R_s \approx (1-C_f)+C_f(1-\tau _s)=1-C_f \tau _s. \end{eqnarray*}$$

Inverting the Taylor expansion, we find that

$$\begin{eqnarray*} &&R_s \approx \exp (-C_f \tau _s)= \exp (-\bar{\tau _s}). \end{eqnarray*}$$

Thus, for sufficiently low optical depth, the apparent optical depth is approximately equal to the average optical depth.

We use this fact to derive the upper limit on the column density of the hydrogen n = 2. As discussed in Section 2.5, there is no apparent Balmer-line absorption in this object, and we treat the observed small optical depth as a lower limit. Needless to say, the optical depth is very small. Thus, we can assume that the apparent optical depth is approximately equal to the average optical depth. Next, we need the oscillator strength for the Balmer absorption line. The sum of the oscillator strengths for the 2s state is 0.44 and the sum for the 2p state is 1.42. If the n = 2 hydrogen is distributed among the 2s and 2p states according to their oscillator strengths, we obtain an estimate of the log of the hydrogen n = 2 column equal to 12.9. But there is no permitted transition to ground from the 2s state, so one might expect that it be more highly populated than the 2p state. If all the absorption lines were from 2s only, we would obtain an estimate of the log of the hydrogen n = 2 column equal to 13.5. In the Cloudy modeling, we can separate hydrogen n = 2 in the 2s state and in the 2p state, and we will adjust the hydrogen n = 2 column upper limit according to the fraction predicted in these two states. We discuss this in the next section.

Armed with our estimates of the He i* column density and hydrogen n = 2 column density upper limit, we can proceed to use these to constrain the properties of the absorbing gas. We use Cloudy 08.00, last described by Ferland et al. (1998). Initially, we used the so-called Cloudy AGN continuum with the same parameters as used by Korista et al. (1997)⁸; this is taken to be a typical AGN continuum. We examine a wide range of ionization parameters (−2.0 ⩽ log U ⩽ 1.2) and densities (3.0 ⩽ log n ⩽ 9.0). We use the full Fe ii model (i.e., 371 levels; Verner et al. 1999) for every run. He i* is populated essentially solely by recombination of He⁺, and therefore, we expect the metastable state of the He i ion to be coincident with He⁺. Therefore, initially, we set the column density equal to log N = 24.5 + log U; this integrates through the hydrogen ionization front and therefore certainly through the entire He⁺ region.

The column density of He i* can be obtained from the output in two ways. First, the total column density can be output using the punch some column densities command.⁹ Second, the fraction of helium in different states in every calculational zone can be output if the print every command is used. The fraction can be converted to a density using the helium abundance; it can then be integrated over depth. We process our Cloudy results by first obtaining the log of the total He i* column density and determining whether or not it is greater than or equal to 14.9. If it is not, that combination of ionization parameter and density is rejected. If it is, we interpolate to determine the thickness of the gas required to reach a log He i* column density of 14.9. Using the gas density and this thickness, we obtain the total hydrogen column density. We then run a second set of Cloudy models as a function of ionization parameter and density in which the total column density is set to the value estimate from the depth and density.

The density as a function of depth of hydrogen in various levels such as n = 2 s and p can be output using the punch hydrogen populations command. The output of the second set of runs is examined and the total column density of hydrogen in the 2s and 2p states is computed. The upper limit constraint is computed based on the fraction of the n = 2 hydrogen in the two states. If the amount exceeds the limit that combination of ionization parameter and density is rejected. It is interesting to note that we cannot combine this step with the previous one because the density of hydrogen in n = 2 differs whether it is in the middle or back side of the cloud, as a consequence of radiative transfer.

The results are shown in Figure 8. Solutions at low ionization parameter are rejected because they fail to produced sufficient He i*. Basically, for solutions with the lowest allowed ionization parameter, we are integrating through the entire He i* zone. For higher ionization parameter solutions, we integrate only part of the way through the He i* zone. Solutions at high density are rejected because they produce too much n = 2 hydrogen. The inferred log hydrogen column density is larger than 21.6 and may be as large as 23.8, or even larger, although it should be noted that Thompson scattering becomes important for the higher column densities. The ionization parameter is greater or equal to log U = −1.4.

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The total hydrogen column density inferred, as well as the extent of the allowed log U–log n parameter space, will also depend on the shape of the input SED, the metallicity of the gas, and whether or not the gas has a differential velocity field (i.e., turbulence). The effect of these factors is discussed in Appendices A–C, respectively.

How do these results compare with results from studies of BALQSOs? Dunn et al. (2010) compile a collection of results from analyses of eight quasars where partial covering has been taken into account. The range of column densities in their Table 9 is 19.9–22.2; however, our minimum value is larger than all but two. Dunn et al. (2010) find a range of log U between −3.1 and −0.7; our object has a larger ionization parameter than all but three. But these objects were not chosen as high-column candidates. Hamann (1998) report analysis of the P v quasar PG 1254+047. They find, for solar metallicity, that log U > − 0.6 and log N_H > 22. These values are larger than our minimums, but we note that if the ionization parameter were log U = −0.6, then the column density would be ∼22.3, larger than Hamann's (1998) estimated lower limit. Thus, it appears that FBQS J1151+3822 is a high-column BALQSO. In addition, as we will discuss later, these results suggest that He i* is useful to constrain high-column outflows.

Our solutions encompass a fairly large range of ionization-parameter–density parameter space. Is it possible to constrain the solution better? Certainly, we cannot with our current spectra, limited, as they are, to the rest optical and infrared bandpass. However, the rest UV offers numerous transitions that may produce absorption in FBQS J1151+3822.

Which ions could help us constrain log U–log n parameter space? Ideally, we need ions that have column densities large enough to make detectable absorption lines, but not so large that the lines become saturated. Savage & Sembach (1991) show that the optical depth as a function of velocity is τ(v) = 2.654 × 10⁻¹⁵f_ikλN(v). This equation has to be integrated over velocity; in our case, the column-weighted mean velocity is ∼5, 500 km s⁻¹, so we multiply τ(v) by that value to estimate the integrated column density. Many of the resonance lines of interest have total f_ik ∼ 0.3–1.0, and the lines are in the UV, so λ is of the order of, say, 1500 Å. Then, a ratio of observed to continuum of ∼0.5 corresponds to a column density of ∼2 × 10¹⁵ cm⁻². The natural log of the ratio is correlated with the column density. So a 10 time higher column density would yield a ratio of ∼0.001 and the line would be saturated. Thus, for the commonly observed resonance lines (e.g., C iv), an ionic column around 10¹⁶ cm⁻² would be likely to be saturated. Likewise, a column density 10 times lower would produce a ratio of 0.93, and as we saw with He i*λ3889, such a weak absorption line would be somewhat difficult to detect. So we are looking for ions with log column densities in the vicinity of 14.7–16. This analysis of course breaks down for transitions with lower oscillator strengths; such lines could be detected at higher column densities.

We use Cloudy models to estimate the ratio of spectrum to continuum by making use of the fact that $I/I_0\approx \exp (-\bar{\tau })$ and τ(v) = 2.654 × 10⁻¹⁵f_ikλN(v) (Savage & Sembach 1991) where N(v) is the ionic column density as a function of velocity in the units of cm⁻² per km s⁻¹. The total ionic column densities are obtained from the Cloudy models. To estimate N(v), we make the approximation that the total column density is equally distributed in velocity space over the 11, 000 km s⁻¹ absorption line. We examined most of the lines predicted to be bright in quasar absorption systems by Verner et al. (1994) for wavelengths longer than 900 Å. He i* is essentially a high-ionization line, and many low-ionization species¹⁰ have low column densities and are predicted to produce essentially no absorption lines. A few, including C ii, Al iii, and Si ii, are predicted to produce weak lines for the lower ionization parameter range, but none at the higher ionization parameters. Others, such as the resonance lines of C iii, C iv, N v, O vi, and Si iv, are expected to be saturated. But some lines fall mid-way between these two extremes, showing strong evolution in ratio as a function of ionization parameter, and in some cases, also dependence on density. The most important of these (plus C ii as an example of a line expected to be present only at lowest ionization parameters) are shown in Figure 9.

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3.2.1. Ionization Parameter and Density Discrimination

3.2.2. Blending and Simulated Spectra

The discussion in the previous section indicates that there should be several lines that are neither too weak nor saturated that can help us discriminate among densities and ionization parameters for the solutions shown in Figure 9. However, with v_min ∼ 500 km s⁻¹ and v_max ∼ 11, 000 km s⁻¹, blending will be a problem. To explore that issue, we use the results of the Cloudy simulations to simulate spectra. We make the assumption that the optical depth profile as a function of velocity can be uniformly approximated by the apparent optical depth profile from the He i*λ10830 line, so that we do not take into account partial covering explicitly. We also assume that the integrated optical depth for each line corresponds to the ionic column density predicted for the appropriate ion. One hundred four transitions were considered. The resulting ratio of spectrum to continuum is shown in Figure 10 for three combinations of ionization parameter and density from Figure 9.

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Comparison of the top and middle panels (both simulations using a relatively low ionization parameter) with the bottom panel shows that we should be able to distinguish between ionization parameters using UV spectra. This is important because the total hydrogen column density is degenerate with the ionization parameter (Figure 8). Several low-ionization lines (Mg ii, C ii) are sufficiently isolated that they can clearly be identified for the low ionization parameter models. P v is also sufficiently isolated to identify in high-ionization models.

Almost all of the density discriminators discussed above are predicted to be strongly blended. P ivλ951 is obliterated by a combination of C iii, N iii, and S vi. As we noted previously, S iv is predicted to be highly saturated. Si iii* near 1112 is not modeled by Cloudy but may not be present in these data due to the high critical density; recall that high densities are excluded for these data due to the lack of Balmer absorption (Section 3.1). However, information about C iiiλ1176 may be useful. It is predicted to be present for low ionization parameters, but not for high ionization parameters. It is partially blended with S iiiλ1195, which is very strong at low ionization parameters (Figure 20), but the higher velocity portion of the trough should be unblended.

As mentioned above, this simulated spectrum is constructed only considering the absorption component responsible for the He i*. There may be both lower and higher ionization absorption components. We know there is a lower-ionization component that is responsible for the Ca ii absorption; the simulations shown here, even for the lowest ionization parameters, do not predict any Ca ii absorption. But that feature is relatively narrow and has low velocity, so confusion caused by blending would be less of an issue.

3.2.3. Broadband Continuum

If the simulated UV spectrum approximates the real one, then we expect that FBQS J1151+3822 should be highly attenuated in the UV simply due to the absorption lines. For example, between 800 and 1600 Å, the simulated spectra predict that the observed flux should be about half of the intrinsic flux. With the covering fraction taken into account, the observed flux would be a somewhat higher fraction of the intrinsic flux.

Figure 11 shows the infrared–UV broadband continuum spectrum constructed from the SDSS, Two Micron All Sky Survey, and Galaxy Evolution Explorer (GALEX) photometry. It is compared with the SED constructed by Richards et al. (2006) scaled to roughly match the flux at the 1 μm dip. It is also compared with the SDSS spectrum of FBQS J1151+3822 (reddening corrected; see below). For a redshift of 0.3344, the GALEX FUV band spans ∼1000–1300 Å. In this band, the flux from the simulated spectra is predicted to be about 45% of the intrinsic flux; this is marked by the arrow in Figure 11. Partial covering would increase the flux; hence the upward-pointing arrow. The observed flux in the FUV GALEX filter (central rest wavelength of 1136 Å) is only about 5% of the observed spectrum. So, the observed flux is much fainter than can be explained by the simulated absorption alone.

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The optical continuum from the SDSS spectrum and also from the photometry (which may not be strongly affected by absorption lines except possibly in the U band) is slightly flat. This could be a consequence of reddening, but it is somewhat difficult to estimate how much reddening is present. We assume that the spectrum would have the same slope as the Richards et al. (2006) SED once the reddening has been removed. We deredden the SDSS spectrum using various values of E(B − V) and a Small Magellanic Cloud (SMC) reddening law (Pei 1992). We find that the maximum reddening that the spectrum can accommodate without becoming much bluer than the composite is E(B − V) = 0.1. Figure 9 shows the spectrum and photometry points dereddened by this amount. In this case, the dereddened observed flux in the FUV filter is about 0.23 dex below the Richards et al. (2006) curve, corresponding to ∼18% of the intrinsic flux. So, with reddening taken into account, the FUV flux is still lower than expected from the simulated spectrum. Partial covering would increase the discrepancy. It should be noted that these observations were not simultaneous, and evidence for variability is seen between the two GALEX observations separated by 11 months.

Interestingly, the dereddened SDSS spectrum matches the (Richards et al. 2006) photometry quite well. We use the scaled (Richards et al. 2006) photometry to obtain the intrinsic flux at 2500 Å, measuring that to be 8.95 × 10⁻¹⁵ erg cm⁻² s⁻¹ Å⁻¹. This corresponds to a luminosity density of 6.8 × 10³⁰ erg s⁻¹ Hz⁻¹ at 2500 Å.

Using the results presented in Section 3.1, we can compute physical parameters of the outflow as a function of ionization parameter and density. The combination of the ionization parameter and the density yields the radius of the outflow. These are shown as a function of ionization parameter and density in Figure 12.

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We can compute the mass outflow rate given by, e.g., Dunn et al. (2010),

$$\begin{eqnarray*} &&\dot{M}=8 \pi \mu m_p \Omega R N_{{\rm H}} v, \end{eqnarray*}$$

where μ = 1.4 is the mean molecular weight, m_p is the mass of the proton, Ω is the global covering fraction, and v is a characteristic velocity. For v, we use the column-weighted velocity from the modeling. This value depended slightly (range of ∼14%) on the form of the derivation of the He i*λ3889 optical depth, and whether we used a partial covering or power-law model. We used a central value of −5400 km s⁻¹. The mass outflow rate is also shown in Figure 12.

The kinetic luminosity is given by, e.g., Dunn et al. (2010)

$$\begin{eqnarray*} &&\dot{E}_k=\frac{\dot{M}v^2}{2}=4 \pi \mu m_p \Omega R N_{{\rm H}} v^3. \end{eqnarray*}$$

These are also shown in Figure 12.

We compute the bolometric luminosity by integrating over the Cloudy input flux density scaled to the dereddened flux density (Figure 11) and using a luminosity distance of 1748.7 Mpc. For some of the higher ionization, higher column-density models, a considerable electron column density is present which, by Thompson scattering, would attenuate the incident flux, making the observed flux smaller. The Cloudy simulations show that this attenuation can be up to ∼50%. However, the covering fraction of the electrons is unknown. If the electrons are only present in the gas responsible for the UV absorption, then using a typical value of the covering fraction of 0.3, we find a maximum attenuation of only 15%. On the other hand, the fraction of the source not absorbed by He i* may be transmitted through completely ionized gas, yielding no absorption lines but resulting in attenuation due to Thompson scattering. Given these geometrical complications, we ignore the effects of Thompson scattering. The bolometric luminosity then is 5.3 × 10⁴⁶ erg s⁻¹. The log of the ratio of the kinetic luminosity to the bolometric luminosity is shown in Figure 12.

Assuming an efficiency of 10% of converting matter into radiation, the inferred bolometric luminosity corresponds to a mass accretion rate of 9.3 solar masses per year. The outflow rate is larger than this in every part of the allowed parameter space, ranging from being almost equal at high densities and low ionization parameters, to being more than 1000 times larger at the lowest densities. The log of the ratio of the outflow rate to the accretion rate is also shown in Figure 14.

How do these results compare with others? Dunn et al. (2010) compile results from partial covering analyses of eight quasars. Their radii estimates range from 1 pc to 28 kpc. Our possible solutions encompass that range, with the smaller radii being inferred for higher density or higher ionization parameter regions of parameter space. Their mass fluxes range from 0.2 to 590 M_☉ yr⁻¹. Our minimum mass flux is about 10 M_☉ yr⁻¹. Their log kinetic luminosity ranges from 41.1 to 45.7, while our minimum log kinetic luminosity is ∼44, and so is higher than at least half of their sample, and can be very large in the low-density high-ionization region of parameter space. Thus, it appears that FBQS J1151+3822 is a relatively powerful BALQSO.

It is not known how BALQSO winds are accelerated, and several theories have been proposed. An attractive model supposes that the wind is accelerated by the scattering of the photons that create the absorption lines (radiative line driving). This mechanism is also believed to accelerate winds in other objects such as stars and cataelysmic variables. There is some observational evidence that this mechanism is at work in at least some BALQSOs. The "ghost of Lyα" is one piece of evidence (Arav et al. 1995; Arav 1996; Korista et al. 1993; North et al. 2006; Cottis et al. 2010). This is observed as a decrease in optical depth near −5900 km s⁻¹. It occurs at this velocity offset because that is where Lyα broad-line region photons are resonantly scattered by N v ions. These extra photons, above the continuum, create additional acceleration causing a decrease in optical depth in velocity space. This feature has not, by any means, been found in all objects, but it has been confirmed in more than a few.

Another piece of evidence is the observed correlation of the maximum velocity of the outflow, v_max, with the UV luminosity (Laor & Brandt 2002; Ganguly et al. 2007). More precisely, an upper envelope has been found so that low-luminosity objects have only low values of v_max, while high-luminosity objects have a range of high to low values. Models of radiative acceleration predict that v_max ∝ L^α, where the power-law index α lies in the range 0.25–0.5 (see Laor & Brandt (2002); Ganguly et al. (2007) for details of these arguments). This correlation argues that radiative acceleration of some kind is generally active in BALQSOs because the correlation is seen in different large samples of objects. Note, though, that the driving force need not necessarily be line driving; acceleration via dust-scattering opacity would also apply (Laor & Brandt 2002). Note also that this behavior has been seen to be violated in at least one object (WPVS 007; Leighly et al. 2009).

Other mechanisms besides radiative line driving have been suggested for the acceleration of the outflowing gas. Radiative acceleration by dust-scattering opacity has been hypothesized (e.g., Scoville & Norman 1995). This mechanism is promising since dust grains have large opacity. However, the outflow needs to originate beyond the dust sublimation radius, though. For our object, with estimated bolometric luminosity of 5.3 × 10⁴⁶ erg s⁻¹ (Section 4.1), the sublimation radius is estimated to be about 1.2 pc (Scoville & Norman 1995). As shown in Figure 12, that radius is spanned by our Cloudy modeling solutions. In addition, we have found evidence for reddening in this object (Section 3.2.3).

Another model appeals to a magnetocentrifugal wind (e.g., Everett 2005 and references therein). In this model, gas is attached to large-scale magnetic field lines, and then the rotation of the accretion disk flings the matter away from the disk, like beads on a wire. Therefore, in a pure magnetocentrifugal wind, the dynamics of the outflow are divorced from the radiation field. Many people consider a hybrid model, assuming both magnetocentrifugal acceleration and radiative line driving. Finally, thermally driven winds have been proposed (Krolik & Kriss 2001), where the wind is essentially evaporated off the inner edge of the torus. This model has been applied principally to warm absorbers rather than BALQSOs.

As an interesting combination of the above, Gallagher & Everett (2007) propose that different models may be appropriate for different regions of the outflow. The X-ray absorbing region may be dominated by magnetocentrifugal acceleration, the UV-absorbing region may be dominated by radiative line driving, and the IR absorbing region may be dominated by dust acceleration.

In this section, we apply several of the radiative-driving models to our results for FBQS J1151+3822.

Hamann (1998) presents a derivation of an equation that can be used to determine, in an approximate way, if radiative-line driving is sufficient to accelerate gas of a given column density to a particular terminal velocity. Basically, the equation of motion is solved making the assumption that a fraction of the total luminosity f_l is scattered or absorbed by the outflowing gas as follows:

$$\begin{eqnarray*} &&m_{{\rm H}} N_{{\rm H}} v \frac{dv}{dr} = \frac{f_l L}{4\pi R^2 c} - \frac{m_{{\rm H}} N_{{\rm H}} G M_{{\rm BH}}}{R^2}, \end{eqnarray*}$$

where N_H is the column density of the outflowing gas. To put it another way, the momentum of that fraction of the total radiation is converted to momentum of the wind, mediated naturally by the gravitational attraction of the black hole.

To use this equation, we need to estimate the black hole mass; we do that using standard methods from the SDSS spectrum. We measure a rest-frame flux at 5100 Å of 2.6 × 10⁻¹⁵ erg s⁻¹ cm⁻² Å⁻¹ from the dereddened SDSS spectrum shown in Figure 11. We compute the broad-line-region radius using the regressions found by Bentz et al. (2006) using the flux and a luminosity distance of 1773.7 Mpc appropriate for their (inferred) cosmological parameters of H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_M = 0.27, and Ω_Λ = 0.73. That is found to be log(R_BLR) = 2.47 in units of light-days. Finally, we compute the dispersion of the Hβ line profile obtained after subtracting the other fitted components, and referring to Collin et al. (2006), we use a scale factor of 1.5 to obtain a black hole mass of 8.2 × 10⁸ M_☉. For the bolometric luminosity of 5.3 × 10⁴⁶ erg s⁻¹, we find that the object is radiating at about half the Eddington luminosity.

The fraction of the bolometric luminosity that can be used to accelerate the wind, f_l, can be estimated as the fraction of the incident continuum that is absorbed. This is easily obtained from the Cloudy output by integrating over the transmitted continuum and dividing the result by the integral over the incident continuum. A difficulty is that for high column densities, the transmitted continuum is attenuated significantly by Thompson scattering. Thompson scattering will not transfer much momentum, so we correct the incident continuum by multiplying it by the Thompson fraction discussed in Section 4.1. We plot this fraction in Figure 13. The fraction available is relatively large, equal to or greater than 1/2 over the entire parameter space. It has a broad minimum near log U = −0.5. At lower ionization parameters, more low-ionization species contribute to the optical depth; at high ionization parameters, Compton scattering becomes important.

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Next, we can compute the terminal velocity. The bolometric luminosity, obtained above, is estimated to be 5.3 × 10⁴⁶ erg s⁻¹. We need a value of the launch radius. Above we computed the radius of the wind from the density and the ionization parameter used in the Cloudy modeling. This is the radius at which the wind has reached its observed velocity and is absorbing the continuum, and so this value would be somewhat larger than the launch radius. Arav & Li (1994) point out that a general characteristic of radiation-driven winds is that most of the acceleration occurs on a length scale comparable to the starting radius. Therefore, for a rough estimate, we use a launch radius that is half the radius of the absorbing wind derived from the Cloudy simulations. The column density is that shown in Figure 8. The resulting predicted terminal velocity is shown in Figure 13. A positive velocity (outflow) is attained over most of the parameter space, with higher values attained at higher densities and lower ionization parameters. Higher densities correspond to a smaller launch radius, where the flux is more intense; lower ionization parameters correspond to smaller column densities which are easier to accelerate. Although most of parameter space is characterized by an outflow, the maximum velocity (∼6400 km s⁻¹) is almost a factor of two below the terminal velocity observed in this object. Still, that we can attain high positive velocities in this object is perhaps not surprising as it is radiating at a large fraction of the Eddington limit.

Could this outflow be a disk wind? It does not seem likely that it is. The disk wind model predicts acceleration to 15,000 km s⁻¹ at about 10¹⁷ cm from the central engine in a 10⁸ M_☉ black hole (Proga et al. 2000). Our photoionization modeling results show that the minimum radius predicted in our parameter space is about 1 pc for the models with the highest density, out to hundreds of parsecs for lower density models. The distances then range from ten to thousands of times larger than the disk wind radius.

The above estimate does not take into account the fact that the opacity due to a single line is enhanced by the velocity gradient in an optically thin outflowing gas. Thus, the momentum transfer for a given column density is greater in an outflowing gas than in a static gas, and higher velocities can be attained. To take this into account, we use the CAK formalism (Castor et al. 1975), originally applied to stellar winds but adapted for use in quasars by, e.g., Arav & Li (1994) and Arav et al. (1994).

We compute the force multiplier due to line scattering as a function of the equivalent electron optical depth t in the standard way according to Equation (2.7) in Arav & Li (1994) using the ionic column densities obtained from our Cloudy simulations and line opacities obtained from Verner et al. (1994). We ignore bound-free transitions, which will of course also contribute to the acceleration, but probably to a lesser degree than the lines (e.g., Arav et al. 1994, Figure 2). Figure 14 shows the log of the force multiplier for an example value of t = 10⁻⁶. For this particular value of t (and noting that the force multiplier has a strong ∼1/t dependence), we find that the force multiplier is higher for larger ionization parameter. This is because, as discussed in Section 3.1, the column densities need to be larger at higher ionization parameters to produce the observed He i* column density.

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Next, we assume a terminal velocity of v_term = 11, 000 km s⁻¹ and a launch radius that is one-half of the radius derived above for the absorbing gas and solve the equation of motion for the force multiplier and equivalent optical depth t_needed required to reach that terminal velocity. The equation of motion that we solve is

$$\begin{eqnarray*} &&v\frac{dv}{dr}=\frac{\sigma _T}{1.2 m_{{\rm H}}c} \frac{L}{4\pi r^2} M_L(U,t) - \frac{GM_{{\rm BH}}}{r^2}, \end{eqnarray*}$$

where we have assumed that n_e = 1.2n_H, i.e., the electron density is approximately 1.2 times the hydrogen density, L is the bolometric luminosity, and M_L(U, t) is the force multiplier. The results are shown in Figure 14. They show almost the same dependence as the radius of the absorbing gas, shown in Figure 12. This makes sense because the flux decreases rapidly with radius, so the optical depth enhancement due to the velocity gradient has to be higher at larger radii to attain the same terminal velocity. This enhancement is equivalent to a larger value of force multiplier. Likewise, we can solve for the equivalent electron optical depth t needed to attain the observed terminal velocity. That is also shown in Figure 14. The equivalent electron optical depth t is smaller for larger values of the radius.

The equivalent electron optical depth scale is defined as

$$\begin{eqnarray*} &&t=\sigma _T \epsilon n_e v_{{\rm th}} \left(\frac{dv}{dr}\right)^{-1}, \end{eqnarray*}$$

where is the filling factor in the wind and v_th is the thermal velocity of the gas. We assume a temperature of 10⁴ K, appropriate for a photoionized gas, and we again assume that the electron density is 1.2n_H. We make the zeroth-order assumption that dv/dr is approximately equal to the terminal velocity divided by the radius where the absorption occurs. Then, we can solve for the filling factor . That is also shown in Figure 14.

The filling factor can be used to estimate the dimensions of the outflow. For a continuous flow, the length scale l would be N_H/n_H. For a flow consisting of small clouds with filling factor , the length scale is increased by 1/, i.e., N_H/n_H. For the outflow to be physical, the length scale of the outflow must be less than the radius where the absorption occurs; otherwise, there would not be sufficient length to accelerate the outflow to the observed terminal velocity. Working through the approximations given above, we find

$$\begin{eqnarray*} &&\frac{l}{R_{{\rm abs}}}=\frac{1.2 \sigma _T N_{{\rm H}} v_{{\rm th}}}{t_{{\rm needed}} v_{{\rm term}}}. \end{eqnarray*}$$

This equation shows that larger column densities require larger region sizes to accelerate all the gas to the terminal velocity. The terminal velocity appears on the bottom of the equation as it was originally part of, dv/dr, the differential expansion rate. The region size has to be larger for smaller differential expansion rates in order to attain the same terminal velocity.

The log of the ratio of the region size to the radius where the absorption occurs is shown in Figure 14. This shows that at densities lower than ∼10⁷ cm⁻³, the flow is unphysical since the region size is larger than the absorption radius. This happens because low density flows occur at larger radii, and at a large radius the flux is low, so a large equivalent electron optical depth scale is needed to counteract the low flux and accelerate the flow to the observed terminal velocity. The equivalent electron optical depth scale is linearly dependent on .

This argument, based on the flow dynamics, provides strong constraints on the physical parameters of the outflow, excluding most of the previously allowed parameter space. Examining Figures 8 and 12 and considering areas of parameter space where the region size is smaller or equal to the radius size (l/R_abs ⩽ 1), we find that the log of the total hydrogen column density is constrained to be between 21.7 and 22.9, the radius is between 2 and 12 pc, the mass flux is between 11 and 54 solar masses per year, the kinetic luminosity is between 1 and 5 × 10⁴⁴ erg s⁻¹, and the kinetic luminosity is between 0.2% and 0.9% of the bolometric luminosity. If we now compare with previous results from Dunn et al. (2010), we find that FBQS J1151+3822 has an absorbing region relatively close to the central engine, a higher than average column density, a relatively high kinetic luminosity, but a relatively low mass outflow rate.

It is also interesting to note that the allowed region lies in the area where we expect C iii*λ1176 to be a useful density diagnostic. We would also expect P v to be weak in the UV spectrum as the ionization parameter is now constrained to be between −1.4 and 0.2 (Figure 10; middle panel).

This analysis assumes that radiative line driving is the acceleration mechanism operating in this BALQSO; however, that is the favored acceleration mechanism for the UV absorbing gas. At any rate, it implies that radiative line driving is feasible for higher densities in our parameter space. Lower densities would require an additional acceleration mechanism, perhaps hydromagnetic. In addition, we have assumed that the flow is radial. It may be simply crossing our line of sight; in that case, the terminal velocity would be larger than the observed 11, 000 km s⁻¹.

Following Hamann et al. (2010), we can compute the size of the absorbers. Reviewing their argument, since partial covering is significant, the upper limit on the size of the individual absorbing structure is the size of the emitting region. This is an upper limit since the absorbers can be smaller, and there can be many of them.

We compute the size of the emission region using classical relations from accretion disk theory, namely, for a sum-of-blackbodies accretion disk,

$$\begin{eqnarray*} &&T_{{\rm disk}}=\bigg (\frac{3G M\dot{M}}{8 \pi \sigma R^3}\bigg)^{1/4}. \end{eqnarray*}$$

We use the black hole mass and accretion rate derived in Section 4.2, namely, M = 8.2 × 10⁸ M_☉ and $\dot{M}=9.3\;M_\odot \rm \;yr^{-1}$. This equation yields a temperature that decreases with radius as R^−3/4. It has been argued that this radial dependence is too steep (e.g., Gaskell 2008, who suggests that the index should be 0.57) yet may be acceptable for the estimations made here. Using this equation, we find that the 3888 Å and 10830 Å emissions are emitted at 0.011 and 0.045 pc, respectively. Thus, the 10830 Å emission region is a factor of 3.9 times larger than the 3888 Å emission region; for a flatter temperature dependence of −0.58 that difference increases to a factor of 5.8. These sizes are comparable to those inferred by Hamann et al. (2010), despite the fact they are examining far UV lines. The reason for this coincidence is that the black hole mass in their object is much larger.

These numbers become more interesting when compared with the much smaller emission region size expected for 1121 Å, where P v absorption should be seen in the continuum. For FBQS J1151+3822 that is 0.0022 pc, a factor of 21 times smaller than the 10830 Å emission region size (and a factor of 50 times smaller for the flatter radial temperature dependence). So, if partial covering in P v were observed in FBQS J1151+3822, it would imply that a swarm of at least 20–50 very small clouds cover the 10830 Å emitting region.

These numbers become even more extreme when considering the low black hole mass BALQSO WPVS 007 (Leighly et al. 2009). That object has a black hole mass of 4.1 × 10⁶ M_☉ and an accretion rate between 0.0086 and 0.0114 solar masses per year. Yet, it also shows evidence for partial covering in P v. Following the analysis above, we obtain a continuum emission region for 1121 Å of (3.6–4.8) × 10⁻⁵ pc.

A comparison of the covering fractions of He i* and P v in the same object could be interesting due to the large differences in size of the emitting region (a factor of 20–50, depending on the radial dependence of the temperature). Note that the covering fractions of these lines can be directly compared because the gas presents the same optical depth in these lines (Figure 15); as discussed by Hamann et al. (2001), lines that have higher optical depths may have naturally higher covering fractions. It is possible that the swarm of small clouds may completely cover the 1121 Å emitting region, but not cover the entire 10830 Å emitting region. If this were the case, the covering fraction would be different.

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4.4.1. Comparison with Other Lines

High column density outflows are of great interest in BALQSOs. For radiative acceleration models, the force multiplier is predicted generally to decline with column density (e.g., Arav & Li 1994). So high-column flows place the most stringent constraints on radiative acceleration models. In addition, the kinetic luminosity depends linearly on the column density, so, depending on the velocity and radius, these outflows may have the largest kinetic luminosities, thus placing the most stringent constraints in general on outflow-acceleration models.

The study of BALQSOs underwent a paradigm shift about 15 years ago. Previously, it was thought that the absorber completely covered the continuum, and column densities could be measured directly from the troughs. But the observation of strong P v in some objects was puzzling, given that the solar abundance of phosphorus is about 765 times lower than that of carbon. This conundrum was resolved with the realization that the column densities were much larger than previously thought, but the troughs are not black because the absorber only partially covers the continuum source (Hamann 1998).

The low abundance of phosphorus means that P v lines will be present only when the column densities are high. Thus, P v is a good probe of high-column outflows. But there is a practical problem with using P v to detect high-column outflows in general: the resonance lines are in the far UV (at 1118 and 1128 Å) and shortward of Lyα. So low-redshift objects must be observed from space, while in high-redshift objects, when P v is shifted in to the optical bandpass (for redshifts larger than ∼2), P v can be obscured by Lyα forest absorption.

We propose that He i* is an equally effective probe of high column densities in BALQSOs. We discuss the situation analytically first, and then investigate using simulations.

As shown in Savage & Sembach (1991), the optical depth is a function of λf_ikN_ion, where λ and f_ik are the wavelength and the oscillator strength of the transition, respectively, and N_ion is the column density of the relevant ion. For P v, λf_ik is 752 (for both of the resonance transitions for this doublet). For He i*λ3889, the product is 251, while for He i*λ10830, the product is 5842.

For an analytic estimation, the relevant metric is the λf_ik times the fraction of the ion or metastable state relative to hydrogen. The lower the value, the higher the column density can be before the line is saturated.

What is the ratio of P⁺⁴ to hydrogen, approximately? For solar abundances, there is one phosphorus atom for every 312,536 hydrogen atoms. From Hamann (1997) we see the fraction of phosphorus ionized three times is no larger than about 0.5–0.6. Assuming 0.5, we then estimate the abundance of P⁺⁴ to be 1.6 × 10⁻⁷. Then, the λf_ikN_ion value for P v is 1.2 × 10⁻⁴.

What is the ratio of He i* to hydrogen, approximately? For solar abundances, the helium abundance is 0.1. The metastable level is populated by recombination of He⁺. As discussed by Clegg (1987) and Clegg & Harrington (1989), it is depopulated principally by collisions. Clegg (1987) give an empirical formula for the ratio of helium in the metastable state relative to the number of He⁺

$$\begin{eqnarray*} &&\frac{N(2^3S)}{N({\rm He}^+)}=\frac{5.79\times 10^{-6} t_e^{1.18}}{1+3110 t_e^{-0.51} N_e^{-1}}, \end{eqnarray*}$$

where t_e is the electron temperature in units of 10⁴ K and N_e is the electron density in  cm⁻³. This function shows that the number of helium in the metastable state is an approximately constant fraction of the number of once-ionized helium.

In an ionized gas slab, only a fraction of helium will be He⁺. As long as the slab is not too thick (i.e., optically thin to the hydrogen continuum), the helium will be split between once and twice ionized atoms. Given that quasar photon continua fall steeply, we can assume that the majority of the helium will be He⁺. Thus, the abundance of metastable helium is approximately 5.8 × 10⁻⁷. Then, λf_ikN_ion is 1.5 × 10⁻⁴ for He i*λ3889 and 3.4 × 10⁻³ for He i*λ10830. Recalling that the λf_ikN_ion value for P v is 1.2 × 10⁻⁴, we see that He i*λ3889 component is equally sensitive as P v, while He i*λ10830 is a bit less sensitive. In contrast, a similar estimation for C ivλ1549 (for an assumed fraction of C⁺³ of 0.65) is 7.0 × 10⁻². So, for example, C iv will become saturated at column densities a factor of 20 lower than He i*λ10830, and a factor of ∼470 lower than He i*λ3889.

The analytical analysis is limited because the fraction of these ions in a slab depends on the ionization parameter and column density, as well as the abundances. So, we use the simulations discussed in Section 3.1 to investigate the sensitivity of these absorption lines to high columns further. As discussed in Section 3.1, we assume the Cloudy AGN Kirk continuum, solar abundances, and log(n) = 5. Since all the transitions discussed here are resonance transitions,¹¹ we expect negligible dependence on density. We extract ionic column densities as a function of ionization parameter and log N_H − log U from the Cloudy model results. Contours of log τ(v) = log(2.654 × 10⁻¹⁵λf_ikN_ion) − log(10, 000) are show in Figure 15. We divide by 10,000 km s⁻¹ to approximate the optical depth of a square line profile with a width of 10,000 km s⁻¹, consistent with the approximate width of the line observed in FBQS J1151+3822. A smaller velocity width would yield a larger optical depth for any combination of parameters.

These contour plots show that resonance-line absorption from abundant ions, such as O vi and C iv, are saturated at relatively low column densities. But lines such as P v and He i*λ3889, and to a slightly lesser extent, He i*λ10830, remain optically thin over a wide range of parameter space.

These figures also show that the metal lines experience greater ionization parameter dependence than the He i* lines. That is, for example, Si iv optical depth is greater for any value of log N_H − log U at log U ∼ −2.2 than for other values of ionization parameter. This is of course due to the fact that at log U ∼ −2.2, a greater fraction of silicon is Si⁺³ than other ionization states, while at lower and higher values of log U, there are relatively fewer Si⁺³ ions. Metastable He i is more monotonic; for a fixed radiation-bounded slab depth, the number of metastable helium ions increases as the depth of the helium ionization front increases.

4.4.2. Sensitivity Examined Using Simulated Spectra

As discussed above, He i* is a valuable probe of high column density in quasars. Moreover, using both the He i*λ3889 and He i*λ10830 lines, we can solve for the true column density and covering fraction. In this section, we discuss the range of columns that can be probed using He i*, and we discuss the prospects of identifying low-redshift BALQSOs using He i*.

Each quasar absorption line is sensitive to a certain range of column density. If the column is too low, the absorption line will not be distinguishable from the continuum. If the column is too high, the absorption line will be saturated. Obviously, the sensitivity will depend on the properties of the transition, through the oscillator strength, and it will depend on the abundance of the ion. But it will also depend on the properties of the outflow; in particular, it will depend on the range of velocity over which the line is spread, Δv. A low column density is detectable in a narrow line, where Δv is small, while absorption spread over a large range of velocity would be indistinguishable from the continuum. The sensitivity depends on the data properties, i.e., signal-to-noise ratio, obviously, with this factor being more important for weak lines. In addition, in some cases, there is systematic uncertainty, such as the uncertainty in defining the continuum.

We explore the sensitivity of the He i* lines using simulations. We use the optical depth profile as a function of velocity obtained from the infrared spectrum. Furthermore, we use this for both lines, that is, we ignore velocity dependence of the optical depth and covering fraction. We smooth the profile slightly using the function mentioned in Section 2.1. We investigate the region around the 3889 Å and 10830 Å lines in velocity space. We add Gaussian noise to the initial ratio of observed to continuum (equal to 1) so that the resulting signal-to-noise ratio is 150. Clearly, there will be sensitivity dependence on the signal-to-noise ratio, but since we are more interested in the characteristics of the lines, we do not explore that dependence here. We investigate log He i* column densities between 14.0 and 17.0. As discussed above, this corresponds to approximate log hydrogen column densities of 20.25–23.25. We emphasize again that the results depend on the absorption profile assumed here to have Δv ≈ 11, 000 km s⁻¹. We also investigate a range of covering fractions between 0.1 and 0.9. For each input column density of He i*, we scale the optical depth profile appropriately to produce the desired column density. Then, for each input covering fraction, and using Equations (3) and (4) from Sabra & Hamann (2005), we simulate the observed ratio of absorbed to continuum spectra for both the 3889 Å region and the 10830 Å region. Finally, we fit the two resulting simulated ratios with the partial covering model using the technique discussed in Section 2.8. For each combination of parameters, we run 10 simulations and plot the mean.

As discussed qualitatively above, metastable helium is a valuable probe of high column densities because helium in this state is relatively rare in the gas. In that way, metastable helium absorption is similar to P⁺⁴ absorption. But the He i*λ10830 and He i*λ3889 lines have another unique property: the high λf_ik ratio of 23.3. In contrast, the P vλλ1118, 1128 lines, like other lithium-like ions, have a λf_ik ratio of 2. What effect does the λf_ik ratio have on the sensitivity? To explore this question, we do another set of simulations in which λf_ik for the 3889 Å line is a factor of two lower than λf_ik for the 10830 Å line, instead of the normal case where the ratio is 23.3.

The results are shown in Figures 16–19. We plot the measured properties as a function of the input parameters. We first plot the number of points retained in Figure 16. The optical depth profile had 69 points, and as noted in Section 2.8, the software removes unphysical points where R₃₈₈₉ > R₁₀₈₃₀ > R^23.3₃₈₈₉ is not obeyed. We see that the number of points retained is lower for the lowest and highest column densities. This makes sense for the lowest column densities, since in that case, the optical depth of both lines is low, and it is more likely that a fluctuation due to noise will cause a point to become unphysical. At highest column densities, the lines become saturated, and the ratio of the observed to continuum looks the same for both lines. Again, in this case, it is likely that a fluctuation due to noise will cause a point to become unphysical. The number of points retained drops less rapidly for λf_ik = 23.3 as the low value of the oscillator strength of the 3889 Å line means that it is not saturated until the column density becomes very high.

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Next, we plot the measured covering fraction and column density from the partial covering model in Figure 17. The measured covering fraction and column density is consistent with the input for intermediate log  He i* column densities for both sets of simulations. For lower column densities, the measured covering fraction is consistently low, while the column density is consistently high. At lower column densities, the weaker line becomes indistinguishable from the continuum, and unphysical points are dropped. Points are deemed physical if there is a downward fluctuation in the 10830 Å component, and an upward fluctuation in 3889 Å. This situation looks the same as a higher column and a lower covering fraction. For the highest column densities, the measured column is consistent with the input for the λf_ik ratio = 23.3 case, while it is consistently underestimated for the λf_ik ratio = 2 case. This is because at high column densities, both lines become saturated when λf_ik ratio = 2.

How would we fare if we had only one of the two He i* lines? Figure 18 shows the apparent column densities measured from the 10830 Å line and the 3889 Å lines separately. We find that the column density is uniformly less than the observed, as expected. The discrepancy is less for high covering fractions; the presence of significant partial covering, i.e., small values of the covering fraction, makes the optical depth look too low. There is also a saturation of column at high column densities for a given covering fraction. This is due to saturation of the lines. The 3889 Å line (with λf_ik ratio = 23.3) performs the best at high column densities because the low oscillator strength of this line prevents it from becoming saturated. The apparent column density is lower than the input for small values of the covering fraction, for the same reason as above: low values of the covering fraction make the apparent optical depth low.

Finally, in Figure 19 we plot the difference between the log of the measured average column density and the log of the input average column density. Recall that the average column density for the partial covering model is the product of the covering fraction and the column density. This is the relevant parameter for the photoionization and dynamical modeling. For smaller column densities, the accuracy is better for larger covering fractions; for smaller covering fractions, the observed column is overestimated but by less than an order of magnitude. More importantly, this plot shows that the average column is accurately reproduced for input log He i* column densities larger than ∼15 when the λf_ik ratio = 23.3. For a λf_ik ratio = 2, both lines become saturated at high column densities, and the input column density is estimated to be too low by an order of magnitude.

In summary, these simulations show that while there is some bias in measuring parameters at low column density (which is not surprising since as the lines become indistinguishable from the continuum), the large λf_ik ratio = 23.3 for He iλ10830 and He iλ3889 makes it superior for measuring high column densities. Basically, the large ratio gives these lines an increased dynamic range for measuring high column densities. An important point, though, is that the values in these simulations apply for the optical depth profile derived for He iλf_ik for FBQS J1151+3822; the columns measurable will vary depending on the distribution of column over velocity, dN/dv.

In this paper, we report the discovery of the first He i*λ10830 broad absorption line quasar. Are there any more of them? In principle, there should be. He i* is a high-ionization ion that appears in the He⁺ region of the outflow, coincident with C⁺³ and Si⁺³. If the column densities are generally large, then any high-ionization outflow should have He i*λ10830.

Actually, we have already found some. An observing run in 2010 April using SPEX on the IRTF has netted four additional objects. In addition, observations using Lucifer on the LBT have yielded two more (K. M. Leighly et al. 2011, in preparation). But not all BALQSOs have He i*λ10830; we observed several well-known low-redshift BALQSOs using SpeX on the IRTF and found that they do not have significant He i*λ10830 absorption. These are bright objects for the IRTF so the limits on He i*λ10830 will provide interesting upper limits on the column density in these objects (K. M. Leighly et al. 2011, in preparation).

How can we find more candidates? The SDSS spectra provide a useful starting place. If we can identify He i*λ3889 in SDSS spectra, then, because of the large λf_ik ratio, He i*λ10830 will certainly be seen. How can we identify objects with He i*λ3889? As discussed in Section 2.4, it can be difficult as it is generally a weak line that can be confused with strong Fe ii emission. One way is to look at objects that have both Mg ii and He i*λ3889 in the bandpass. An informal examination of a low-redshift subsample of BALQSOs cataloged by (Gibson et al. 2009) shows that ∼1/3 have something at 3889 Å that may correspond to the Mg ii absorption.

Identifying He i* BALQSOs using both Mg ii and the 3889 Å component limits us to Lo-BALs. How can we identify high-ionization BALQSOs? One way is to look for objects that do have He i*λ3889 but do not have Mg ii. Another possibility is to look at the broadband photometry. The FBQS J1151+3822 photometry shown in Figure 11 is rather distinctive, as the decline in the UV is too steep to be explained by reddening. Depending on the redshift, the usefulness of this technique will depend on the availability of GALEX photometry.

Observing He i*λ10830 limits us to low-redshift objects. If we observe He i*λ3889 in the optical band, we will observe the 10,830 component in the 0.8–2.4 μ short-wavelength band; then, we are limited to objects with redshifts less than 1.2. But these nearby objects may be quite interesting. Only a handful of low-redshift BALQSOs are known (e.g., Sulentic et al. 2006). Many of these were discovered serendipitously; for example, they were observed because they are PG quasars, or because they have weak [O iii] in their optical spectra (Turnshek et al. 1997). These low-redshift objects have lower luminosities than the SDSS and LBQS BALQSOs (e.g., Figure 7 in Ganguly et al. 2007), and so they define the low-v_max end of the correlation between v_max and luminosity. That region of the plot is rather sparsely populated, but it may be important in our understanding of outflows in AGNs as it bridges the very low velocity outflows seen in Seyfert galaxies (e.g., Crenshaw et al. 2003) and the high-velocity BALQSOs beyond z > 1.5. FBQS J1151+3822 is a luminous object; for Ganguly et al.'s (2007) cosmology, the dereddened 3000 Å log λL_λ is 45.9 (without the reddening correction, log λL_λ = 45.7; Figure 11). From Ganguly et al. (2007), we see that lower luminosity objects of interest should have log λL_λ < ∼45.1, or greater than 2 mag fainter than FBQS J1151+3822. But FBQS J1151+3822 is a relatively bright object for SDSS, with an observed g magnitude of 15.8. The DR7 SDSS Quasar Catalog (Schneider et al. 2010) has 37,430 quasars with redshift smaller than 1.2, and the distribution of g-magnitude peaks at 19, while there are only 35 quasars brighter than FBQS J1151+3822. Thus, it seems quite reasonable that an interesting low-redshift low-luminosity sample could be defined and studied.