Ultradense Gas Tracked by Unshifted Broad Absorption Lines in a Quasar

If we can detect the Al iii absorption lines in a quasar hosting H i Lyman absorptions, it indicates that the optical depth at the deepest point of the Al iii trough is within the range of 0.05–3 (in this case, the corresponding normalized residual flux, e^−τ , is 0.95–0.05 in the absorption trough), so that the line is neither too weak nor severely saturated (Zhou et al. 2019). Assuming a Gaussian velocity profile (FWHM = 1000 km s⁻¹), the measurable column density of Al iii is therefore 1.94 × 10¹³ cm⁻² < N_{Al III} < 1.16 × 10¹⁵ cm⁻², which enables measurement of column density over about two orders of magnitude. We then carried out systematic photoionization simulations using Cloudy to study the diagnostic power by combining the information of N_{H I} and N_{Al III} . We assume a slab-shaped, homogeneous gas with solar abundance and spectral energy distribution (SED) consisting of a blackbody big bump with a temperature of 1.5 × 10⁵ K (see details in Section 4.1), hereafter denoted as 4B SED. The simulations were run over $-4\,\leqslant \mathrm{log}\,U\leqslant 4$ and $0\leqslant \mathrm{log}\,{n}_{{\rm{H}}}\,({\mathrm{cm}}^{-3})\leqslant 15$. For each (U, n_H), N_H and N_{Al iii} were recorded when the predicted N_{H i} reached a given value (e.g., observed one). The N_{Al iii} contour distributions for different N_{H i} , varied from 10^15.4 to 10^16.9 cm⁻², are plotted as black dotted lines in Figure 1. Also included in this figure are the N_H distribution contours. As has been illustrated, if the Al iii absorption line is detected, it indicates that the column density of Al iii is within the range of 1.94 × 10¹³ cm⁻² < N_{Al III} < 1.16 × 10¹⁵ cm⁻². We denote this range as cyan regions in Figure 1. It can be seen that in the case when N_{H I} is relatively low at $15.4\leqslant \mathrm{log}\,{N}_{{\rm{H}}{\rm\small{I}}}\,({\mathrm{cm}}^{-2})\leqslant 16.5$, if the Al iii absorption line can still be detected, the absorbing gas should be of high density (n_H > 10¹⁰ cm⁻³). Such a high n_H is similar to that of the gas in the BLR, where the density is probably close to 10¹¹ cm⁻³.

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The reason why the density (n_H) can be diagnosed by combining the information of N_{H I} and N_{Al III} is that H⁰ and Al²⁺ have dramatically different ionization potentials, thus their ionization structures have very different dependences on the parameters, including the absorbing gas density. To illustrate this better, we show how the parameters of the absorbing gas vary in two models. One is with low density (n_H = 10⁴ cm⁻³) and the other is with high density (n_H = 10¹² cm⁻³). Both models have the same U at $\mathrm{log}U=-1$. In Figure 2, we plot the ionic column densities of Al²⁺ and H⁰ as functions of N_H. The dashed and solid curves represent the models of low (n_H = 10⁴ cm⁻³) and high (n_H = 10¹² cm⁻³) densities, respectively. It can be seen that the ${N}_{{{\rm{H}}}^{0}}$ are significantly different between the low- and high-density models, starting as early as N_H ≈ 10²¹ cm⁻². The difference becomes even more prominent when the gas transfers from the ionized (H ii) zone to the neutral (H i) zone. In the low-density case, this transfer occurs at N_H ≈ 10²² cm⁻², while in the high-density case, the transfer occurs at N_H ≈ 10^23.3 cm⁻². Intriguingly, the difference is remarkable even in the ionized zone, at a given N_H, ${N}_{{{\rm{H}}}^{0}}$ in the case of n_H = 10¹² cm⁻³ is lower than that in case of n_H = 10⁴ cm⁻³. Therefore, the total hydrogen column density measured at, e.g., ${N}_{{{\rm{H}}}^{0}}={10}^{16.6}\,{\mathrm{cm}}^{-2}$ is N_H = 10^21.1 cm⁻² when n_H = 10⁴ cm⁻³, but N_H = 10^21.7 cm⁻² when n_H = 10¹² cm⁻³. Since ${N}_{{\mathrm{Al}}^{2+}}$ as function of N_H varies little from low density to high density at around N_H ≈ 10²¹ ∼ 10²³ cm⁻², the same ${N}_{{{\rm{H}}}^{0}}$ value would introduce very different ${N}_{{\mathrm{Al}}^{2+}}$ values. Thus, the combination of Al iii and H i might be a robust diagnostic for the gas density. We note that the above analysis is for models with a fixed value of $\mathrm{log}U=-1$ and is for illustration purpose only. The real solution will require the full modeling that surveys the values of parameters, including U, which is shown in Figure 1.

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We experimented with other SEDs as inputs to our models, including MF87 (Mathews & Ferland 1987) and HE0238 (Arav et al. 2013). We also tried different metallicities for different SEDs, using both solar (1.0 Z_⊙) and super-solar metallicities (3.0 and 10.0 Z_⊙). Different SEDs with the same metallicity give very similar results. For models with the HE0238 and MF87 SEDs and the solar metallicity, it is found that if the N_{H i} is in the range of log N_{H I} (cm⁻²) ∼ [15.4, 16.7] and [15.4, 17.0], and if the Al iii absorption line is detected, the inferred gas density would be n_H > 10¹⁰ cm⁻³. We get similar results for other models with different metallicities. That is, if the log N_{H I} (cm⁻²) values range at [15.1, 16.3], [15.0, 16.3], and [15.2, 16.6] for 3.0 Z_⊙ metallicity and [14.7, 15.8], [14.7, 15.8], and [14.9, 16.1] for 10.0 Z_⊙ metallicity, with the 4B SED, HE0238 SED, and MF87 SED, respectively, the inferred gas density would also be n_H > 10¹⁰ cm⁻³ if the Al iii absorption line is detected. In what follows in this paper, we use the 4B SED model.

Thus, it would be interesting to launch a systematic search for BAL quasars that show detectable Al iii absorption lines, while the H i absorption is not too strong. We carried out such a search from the 12th data release of the Sloan Digital Sky Survey (SDSS DR12; Dawson et al. 2013), with two criteria: (1) redshift 3.0 < z < 4.47 and (2) spectral signal to noise ratio (S/N > 20). Al iii absorption lines were visually detected in 19 sources, among which SDSS J122017.06+454941.1 (hereafter SDSS J1220+4549) had the highest spectral quality, and we report it in this paper. This paper is organized as follows. The data we used is described in Section 2. We analyze the absorption lines and estimate the corresponding ionic column densities in Section 3. We compare the observational results with photoionization models in Section 4 and discuss the results in Section 5. Our main findings are summarized in Section 6. Throughout this paper, we use a cosmology with Ω_m = 0.3, Ω_Λ = 0.7, and H₀ = 70 km s⁻¹ Mpc⁻¹.

We identified the HiBAL troughs of C iv λ λ1548.20, 1550.77, Si iv λ λ1393.76, 1402.77 and N V λ λ1238.82, 1242.80, and the LoBAL troughs of Al iii λ λ1854.72, 1862.79, C ii λ1334.53, and Si iii λ1206.50, as well as the Lyman series absorption troughs in the spectra of J1220+4549. In this section we will analyze the absorption lines in the spectrum of our source, deriving the column densities of the observed species. In the next section, these column densities will be used to derive the physical conditions in the absorbing gas.

The pair-matching method is used to estimate the unabsorbed level of background flux, which is required for getting the normalized spectra of the abundant absorption lines and estimating the optical depth of each absorption line. A description of the philosophy and procedures can be found in Zhang et al. (2010) and Liu et al. (2015). Each individual BOSS spectrum from a library of non-BAL quasars was used to fit the spectral features of J1220+4549 surrounding BALs, with the absorption troughs being carefully masked out. A reduced χ² threshold (i.e., ${\chi }_{\mathrm{reduced}}^{2}\lt 1.5$) was often used to select the templates (Liu et al. 2015; Shi et al. 2016a). In addition, Tian et al. (2019) introduced a method to determine the most appropriate number of templates (N_temp) to be used. First, the candidate templates are sorted by the reduced χ² in increasing order. We then constructed a composite template using the best N_temp templates. Thus, the standard deviation (σ_nor) of the target spectrum divided by the composite template in absorption-free regions and the root mean square error (RMSE) of the composite template spectrum are estimated. We determine N_temp to be the value when σ_nor = σ_nor(N_temp) is minimum. The median RMSE is less than ∼15% of the median error of the object spectrum. The details can be seen in Section 3.2 in Tian et al. (2019). The composite template is obtained by combining the selected individual candidate templates, each weighted according to their spectral S/N (the solid red lines in Figures 4(a1)–(a7)). The RMSE is much smaller than the error of the observed spectrum and is ignored in the rest of the analysis. After dividing the object spectrum by the composite template, the normalized spectra are obtained, as shown in the right panels of Figure 4.

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In the left-hand panels of Figures 4(a1)−(a9) and the corresponding right-hand panels of Figures 4(b1)−(b9), we plot the spectral details of SDSS J1220+4549 around C iv λ1548.20, C iv λ1550.77, Si iv λ1393.76, Si iv λ1402.77, Al iii λ1854.72, Al III λ 1862.79, C II* λ1335.70, C II λ 1334.53, and Si III λ1206.50, respectively. The C iv absorption trough, which is likely saturated, has a box-shaped bottom at a flux level of 1%–4% of the unabsorbed flux, indicating a nearly full coverage on the background source. The velocity range of the C iv trough is ∼2000 km s⁻¹, which agrees with the BAL definition (Weymann et al. 1991). The weight-averaged velocity of the absorption troughs, calculated from the Al iii absorption trough, is −210 km s⁻¹.

3.3.1. Al iii

The Al iii λ λ1854, 1862 absorption lines are well separated, as shown in Figure 4, benefited from the larger separation (1300 km s⁻¹) of these two lines. Theoretically, the optical depth (τ) is defined as (Savage & Sembach 1991)

$$\begin{eqnarray}&&{I}_{r}(v)=(1-{C}_{f}(v))+{C}_{f}(v){e}^{-\tau (v)},\end{eqnarray} \tag{ 1 }$$

where I_r is the normalized flux, and C_f is the covering factor. Using the covering factor (C_f ∼ 1) suggested by the C iv absorption trough, the optical depth of Al iii λ λ1854, 1862 can be calculated directly from the residual flux, I_r , in the normalized spectra according to $\tau =-\mathrm{ln}({I}_{r})$, which are shown in Figure 5. The ratio of the optical depths of the two Al iii lines agree with the theoretical ratio of λ f_ik (2: 1) within 1σ error. This reiterates that the Al iii absorbing gas fully obscures the continuum source and the covering factor is close to 1.

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Using the obtained optical depths, the column density of Al iii is calculated according to Equation (2)

$$\begin{eqnarray}&&{N}_{\mathrm{ion}}=\displaystyle \frac{3.7679\times {10}^{14}}{f{\lambda }_{0}}\int \tau (v){dv}({\mathrm{cm}}^{-2}).\end{eqnarray} \tag{ 2 }$$

The mean column density measured from the two lines is (3.1 ± 0.5) × 10¹³ cm⁻².

It would be satisfactory to calculate the covering factor and the optical depth as a function of velocity. The data quality of the SDSS spectra (both of the moderate resolution and S/Ns), however, is not high enough for this calculation. We instead try to assess the effect of the covering fraction on the measurement of the Al iii absorption lines, through the following exercise: we assume a uniform covering fraction, i.e., a covering factor C_f across the absorption trough that is independent of velocity. We think this is a reasonable assumption. In a recent study by Chen et al. (2021), a uniform coverage is assumed in the absorption-line analysis using the Keck/High Resolution Echelle Spectrometer and Very Large Telescope/UV-Visual Echelle Spectrograph spectra with R ≳ 30,000, much higher than that of SDSS data with R ∼ 2000 used in this work. We let C_f vary from 0.2–1. The lower limit of C_f is chosen as the absorption depth of the Al iii λ1854.72 trough. We calculated the reduced ${\chi }_{\nu }^{2}$ between the spectrum of Al iii λ1854.72 and Al iii λ1862.79 for different C_f , and plot ${\chi }_{\nu }^{2}$ as a function of C_f in the bottom panel in Figure 6. The column densities of Al iii derived from Al iii λ1854.72 and Al iii λ1862.79 with different C_f are plotted in the top panel of this figure. The ${\chi }_{\nu }^{2}$ reaches the minimum value of ∼0.8 when C_f = 1, and it increases monotonically as the C_f decreases. This suggests that the Al iii absorption gas very likely has a full coverage of the background source, consistent with the adopted assumption. We also try to estimate 1σ, 2σ, and 3σ confidence intervals of C_f ( shown as gray, cyan, and green plus signs). For example, N_{Al iii} is ∼6 × 10¹³ cm⁻² when the C_f is at the 1σ level (C_f ∼ 0.67), which is nearly two times that when assuming C_f = 1. Al iii absorption gas does not necessarily have the same covering fraction as that of C iv. If it indeed had a partial coverage, the Al iii column density we measured should be taken as a lower limit. The true N_{Al iii} might be larger than the value given here, and we would expect an even higher n_H, as predicted in Figure 1.

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3.3.2. C ii

3.3.3. Si iv Lower Limits

3.3.4. Neutral Hydrogen

To estimate the neutral hydrogen column density for the absorber in J1220+4549, the absorption-free spectrum in the Lyman series wavelength region should be determined first. In the Lyα region, the pair-matching method (see Section 3.2 for details) was used to construct the absorption-free template. For the wavelength regions shorter than the Lyα region, we modify the composite spectrum of Zheng et al. (1997) to roughly match the absorption-free level in the Lyβ region and blueward of it. The composite spectrum is multiplied by a one-order polynomial to take into account of the possible reddening and flux calibration problems. Then we reconstruct the absorption-free spectrum by stitching the two parts together, shown as the orange line in Figure 7(a). The corresponding normalized spectrum are plotted in Figure 7(b) and the absorption line details of Lyα, Lyβ, Lyγ, Lyδ, and Ly are presented in Figures 7(c)–(g).

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Assuming the velocity structures of the Lyman series absorption troughs are the same as that of Si iv, we estimate the neutral hydrogen column density by shifting the Si iv λ1402.77 absorption profile to the Lyman series wavelength region and use the profile as a template to match these absorption lines. The relative optical depth values τ_i of Lyman series absorption lines are determined by the known oscillator strengths. ⁷ It is found that the center and blue side of Lyδ, as well as the center and red side of the Ly absorption lines, can be well reproduced when the neutral hydrogen column density reaches ∼4.0 × 10¹⁶ cm⁻². The best fit corresponds to a chi-square denoted as ${\chi }_{0}^{2}$. We then calculated the upper and lower limits of N_{H i} when the chi squares are ${\chi }_{0}^{2}\pm 1$, and the results are listed in Table 2. As shown in Figure 7(b) (the details are presented in Figures 7(f) and (g) for Lyδ and Ly), the simulations mismatch the red side of Lyδ and the blue side of the Ly absorption troughs, which might be due to contamination from intervening Lyman series absorption lines (e.g., Lynds 1971; Weymann et al. 1981). There are also remarkable residual fluxes for the Lyα and Lyβ absorption troughs, and the origin of them will be discussed in Section 5.3.The estimated ion column densities are summarized in Table 2.

Table 2. Estimated Column Densities of the Absorber in SDSS J1220+4549

Ion	Nion (cm−2)
Si iv	>1.3 × 1015
Si iii	>2.3 × 1014
C ii	(5.0 ± 2.6) × 1013
Al iii	(3.1 ± 0.5) × 1013
H i	${4.0}_{-1.0}^{+0.9}\times {10}^{16}$

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The Lyman series absorption troughs might be contaminated by the Lyα forest. The number density of the Lyα forest is ${dN}/{dz}=3.5{\left(1+z\right)}^{2.7}$ in the redshift range of [2.1, 3.5] (Kim et al. 1997). We use Lyδ absorption as an example, which is at ∼950 Å in the quasar's rest-frame spectrum (∼4061 Å in observed frame), with a width of about 1000 km s⁻¹, corresponding to a δ z = 0.014. Thus, we are likely to have one Lyα forest absorption line around the Lyδ absorption trough. Since typical forest absorbers have $\mathrm{log}\,{N}_{{\rm{H}}{\rm\small{I}}}$ of [14–17.2] cm⁻² and a broadening width b of 20–40 km s⁻¹ (Kim et al. 1997). We then generate the Lyα absorption line using $\mathrm{log}\,{N}_{{\rm{H}}{\rm\small{I}}}=17.2\,{\mathrm{cm}}^{-2}$ and b = 40 km s⁻¹ with the typical resolution of SDSS spectrum. Since the b value of the Lyα forest system is very low, the modeled absorptions are quite weak as compared with the observed Lyδ absorptions. The contribution to observed N_{H i} should be less then ∼22%, which can be neglected. The contribution is only ∼6% in the case of the Lyα forest with $\mathrm{log}\,{N}_{{\rm{H}}{\rm\small{I}}}=14\,{\mathrm{cm}}^{-2}$ and the same b value. In addition, the contamination from potential Lyα forest absorptions will lead to an overestimation of H i column density, which will in turn also favor a larger n_H as predicted by photoionization simulations (see Figure 1).

3.3.5. Si iii Lower Limit

With the existing data at hand, we can also estimate the BH mass and the accretion rate of this quasar. We used the method reported by Vestergaard & Peterson (2006, their Equation (7)), which is based on the FWHM (C iv) and λ L_λ (1350 Å), to estimate the mass of the central BH. The λ L_λ luminosity is corrected for the broadband extinction using the LMC extinction curve. The FWHM(C iv) is 5217 km s⁻¹, estimated from the rebuilt C iv emission line by the pair-matching method (see Section 3.2). Thus, the central BH mass is estimated to be 6.7 × 10⁹ M_⊙. Then, we calculated the bolometric luminosity using the conversion by Runnoe et al. (2012, their Equations (9) and (13)), which is based on λ L_λ (1450 Å), giving L_bol ≈ 4.27 × 10⁴⁷ erg s⁻¹. The corresponding Eddington luminosity is 1.01 × 10⁴⁸ erg s⁻¹, and the Eddington ratio is L_bol/L_Edd ∼ 0.42. The accretion rate of the central BH, based on the bolometric luminosity, is

$$\begin{eqnarray}&&\dot{{M}_{\mathrm{acc}}}=\displaystyle \frac{{L}_{\mathrm{bol}}}{\eta {c}^{2}}=75.2\,{M}_{\odot }\,{\mathrm{yr}}^{-1},\end{eqnarray} \tag{ 3 }$$

where we assumed an accretion efficiency η of 0.1, and c is the speed of light.

Armed with the column density measurements of the H i, C ii, and Al iii and the lower-limit results of Si iv and Si iii, we can proceed to use them to constrain the properties of the absorber. The most key parameters characterizing the physical conditions of the absorber are N_H, n_H, and U. The other parameters, such as the distance to the central BH (r_abs), mass-flow rate (${\dot{M}}_{\mathrm{out}}$) and kinetic luminosity (${\dot{E}}_{k}$), can be obtained accordingly (e.g., Borguet et al. 2012a).

We use the Cloudy (c17; Ferland et al. 1998, 2017) model to estimate the three parameters. We assume a slab-shaped geometry, a uniform density, a homogeneous chemical composition (solar values), and no dust from the medium (Shi et al. 2016a, 2016b). The incident SED applied is a combination of the big bump component and a power-law X-ray component spanning 13.6 eV−100 keV (formalized as ${\nu }^{{\alpha }_{\mathrm{UV}}}{\exp }^{(-h\nu /{{kT}}_{\mathrm{BB}})}{\exp }^{(-{{kT}}_{\mathrm{IR}}/h\nu )}$ and $\alpha {\nu }^{{\alpha }_{X}}$ in Cloudy, respectively), as observed in a typical AGN. These parameters are chosen to ensure the big bump peaked at 1 Ryd, the optical to UV slope, α_UV, to be −0.5 (Elvis et al. 1994), and the X-ray to UV slope to be 1.4 (Zamorani et al. 1981), and lastly, the slope of the X-ray component, α_X , is −1 (Elvis et al. 1994).

However, exploring the best model that can simultaneously reproduce the observed column densities of several ions, in the 3D parameter space (N_H, n_H, and U), is challenging. Thus, we use the observed H i column density to reduce the number of free parameters by 1. We will keep the n_H and U free, and for each set of n_H and U values, N_H can be determined from the observed H i column density.

Adopting the solar abundance, we run the simulations over $-4\leqslant \mathrm{log}\,U\leqslant 4$, $0\leqslant \mathrm{log}\,{n}_{{\rm{H}}}\,({\mathrm{cm}}^{-3})\leqslant 15$. For a given n_H and U, we find the N_H value where the predicted H i column density matches the observed one. In the end, the relations between N_H and (U and n_H) can be built,

$$\begin{eqnarray}&&{N}_{{\rm{H}}}=f\left(U,{n}_{{\rm{H}}}\right).\end{eqnarray} \tag{ 4 }$$

We plot the N_H contours as a function of $\mathrm{log}\,U$ and $\mathrm{log}\,{n}_{{\rm{H}}}$ in Figure 8.

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For a set value of (U and n_H), N_H can be determined via the H i column density (Figure 8). With these three values, we can use the model to estimate the absorption strengths of various metal ions, which can be compared with the observed absorption lines. In Figure 9, we show what would be the parameter spaces in (U and n_H) that different observed ionic column densities allow or do not allow. First, the areas marked by gray are excluded by the lower limits of the Si iv and Si iii column densities. The parameter spaces suggested by the measured column densities of C ii and Al iii are shown as the red and blue regions, respectively. The best model is the intersection of these two areas, marked as the open square. It gives the best-estimated log N_H, log U, and log n_H to be 21.0 ± 0.3 cm⁻², −1.25 ± 0.40, and 11.03 ± 0.35 cm⁻³. ⁸ It is clear that the best model agrees with the lower limits given by the N_{Si iv} and N_{Si iii} . The Si iv column density, suggested by the best model is ∼3.0 × 10¹⁵ cm⁻², only slightly larger than the observed lower-limit value listed in Table 2. We note that the estimated density of absorbing gas from the best model is very high. This is well within the regime of densities of the BLR gas. We discuss this further in Section 5.

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The errors of the three parameters propagated from the error of N_{H i} are considered as follows. Two figures similar to Figure 9 are drawn, using the upper and lower limits of N_{H i} as listed in Table 2, to derive the corresponding gas densities, which are treated as the lower and upper limits of n_H. Thus, the n_H error is about ±0.5 dex. Meanwhile, the errors of U and N_H contributed from the error of N_{H i} are very small.

We also try to find out how the best model depends on the metallicity of the simulated gas. We consider four other metallicities, 2.0, 3.0, 5.0, and 10.0 Z_⊙, respectively. We found that in the case of 2.0 Z_⊙, as shown in the 2.0 Z_⊙ panel in Figure 10, the best model is very similar to that of 1.0 Z_⊙. In the case of 3.0 Z_⊙, high density was also obtained, $\mathrm{log}\,{n}_{{\rm{H}}}\sim 10\,{\mathrm{cm}}^{-3}$, with similar U and N_H to that of 1.0 and 2.0 Z_⊙. In the case of 5.0 and 10.0 Z_⊙, it is clear that there are no set of parameters which could predict the measured Al iii and C ii column densities simultaneously, as shown in the 5.0 and 10.0 Z_⊙ panels in Figure 10. Therefore, we suppose that the metallicity might be lower than 5 Z_⊙. A similar upper limit of metallicity was also found by Lu et al. (2008), who reported that the gas metallicity is likely no higher than 4 Z_⊙.

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For quasars of similar redshift as our object, the properties of the absorbing gas can be probed via the P v λλ1117.98, 1128.01 absorption lines, located in the far-UV wavelength region (e.g., Hamann 1998), as these two lines are usually not blended. However, they are heavily contaminated by the Lyα forests, which makes accurate measurements difficult.

The P v λλ1118.98, 1128.01 absorption doublets are also covered by SDSS/BOSS observations, but they are embedded in the Lyα forest, and we have to make certain assumptions regarding their profiles to measure their absorption strengths. The P v column density predicted by our best model is ∼6.1 × 10¹³ cm⁻². We simulated the absorption troughs of these two lines using the best model, assuming their absorption profiles are the same as that of Si iv λ1402.77, as the blue and red lines show in the top panel in Figure 11. We also simulated the S iv λ1062.66 and S iv* λ1073.02 ⁹ absorption troughs using the same methods as used for P v, as shown in the bottom panel in Figure 11. The depths of simulated absorption troughs, especially for P v λ1118.98 and S iv λ1062.66, are shallower than the corresponding observations. This is reasonable, considering that there are non-negligible contaminations from the absorption troughs of the Lyman series. In addition, we noticed that J1200+4549 showed no Si ii λ1260 and Si ii* λ1264 absorptions. The predicted column densities with our best model of Si ii and Si ii* are 1.55 × 10¹² and 3.04 × 10¹² cm⁻², which is hard to observe with the present S/N. These observations are all in agreement with the solution we obtained as shown in Figure 9.

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As shown in previous sections, we demonstrated that by combining the H i column density and the Al iii column density, it can be powerful to identify the high-density absorbing gas, in a way that if the Al iii absorption line can be detected in the condition of $15.4\lesssim \mathrm{log}\,{N}_{{\rm{H}}{\rm\small{I}}}\,({\mathrm{cm}}^{-2})\lesssim 16.5$, the absorber should be in high dense (n_H > 10¹⁰ cm⁻³) regions. For our quasar, the observed H i column density is around $\mathrm{log}\,{N}_{{\rm{H}}{\rm\small{I}}}\,({\mathrm{cm}}^{-2})\sim 16.6$, and the best-fit log n_H is 11.03 ± 0.50 cm⁻³.

Previously, the estimation of the densities of the absorbing gas usually relied on detecting the excited states of singly or multiply ionized absorption lines, such as Si ii* λ1264.73, C ii* λ1335.70, N iii* λ991.57, S iii* λ1015.63, S iv* λ1072.97, Fe ii, etc. The ratios of these excited states absorbing lines to their ground-state counterparts are sensitive to the densities. The detection of these excited-state ion lines, however, often requires spectra of high resolution. They are also not always available for quasars at various redshifts. In addition, absorbing gas probed via these lines are often of much lower density (e.g., Borguet et al. 2012a; Chamberlain & Arav 2015; Ji et al. 2015; Xu et al. 2018, 2019), for the reasons we lay out below. In this aspect, the method mentioned in this paper is complementary to these previously used methods in measuring gas densities.

It is helpful to compare our results with these previous studies to understand why they often obtain low-density solutions for the absorbing gas of their objects, while we get the high-density solution for J1220+4549. Our result suggests that if the N_{H i} of the absorber is measured to be relatively low at $15.4\lesssim \mathrm{log}\,{N}_{{\rm{H}}{\rm\small{I}}}\,({\mathrm{cm}}^{-2})\lesssim 16.5$, and if the Al iii absorption line doublet can be detected, the absorbing gas can be diagnosed as high density. As can be seen, there are two conditions for the diagnosis to work: a measured relatively low N_{H i} and a detection of the Al iii absorption line. First, the Al iii wavelength region was not covered in the spectrum in Borguet et al. (2012a), where they reported the n_H of two trough systems (T2) and (T3) (log n_H < 10² cm⁻³). Although the observed log N_{H i} ([15.97, 16.19] for T2, 15.63 for T3) are in our suggested range, the simulated log N_{Al iii} using our model with the reported parameters are too small (12.63 and 11.96 cm⁻² for T2 and T3) to be detected, thus the small n_H (Borguet et al. 2012a) does not contradict with our work (see Figure 1). Second, Al iii absorption troughs were detected in six sources in previous works with observed n_H ≲ 10⁴ cm⁻⁴ (Borguet et al. 2012b; Chamberlain & Arav 2015; Xu et al. 2018, 2019); however, the reported N_{H i} are are all lower limits and the predicted value using our model with the reported parameters are all larger than 10¹⁷ cm⁻³, which are greater than our suggested range. Third, the reported n_H in J1135+1615 are lower limit (logn_H > 5.4 cm⁻³) (Xu et al. 2019). The log N_{H i} we predicted is log N_{H I} < 17.30 cm⁻². We found that the predicted N_{H i} is smaller with larger n_H. The predicted log N_{H i} is 16.7 cm⁻² when log n_H is 11.0 cm⁻³, which is very similar to our source. In conclusion, these previously reported results do not contradict our conclusions.

With the density of the absorbing gas measured, we can estimate the distance (r_abs) of the absorber away from the central source. We use the definition of the ionization parameter U,

$$\begin{eqnarray}&&U=\displaystyle \frac{{Q}_{{\rm{H}}}}{4\pi {r}^{2}{n}_{{\rm{H}}}c},\end{eqnarray} \tag{ 5 }$$

where Q_H is the total rate of hydrogen-ionizing photons emitted by the central source (e.g., Dunn et al. 2010). Q_H equals $L(\lt 912)/\overline{{E}_{\mathrm{ph}}(\lt 912)}$, where L(<912) is the ionizing luminosity of the continuum source, and $\overline{{E}_{\mathrm{ph}}(\lt 912)}$ is the average energy for all ionizing photons. Thus, Q_H can be obtained when the luminosity and the SED shape of the central engine are known. Applying the observed continuum flux in the SDSS rest-UV spectrum and the AGN SED used in the simulation, we determine the distance of the absorber as being ${r}_{\mathrm{abs}}={0.3}_{-0.13}^{+0.23}$ pc for our best model. This distance is very close to the central BH. We discuss the origin of this absorber in the next subsection.

5.2.1. From Dusty Torus

5.2.2. From the BLR

As mentioned before, the density of the absorbing gas and its distance to the central BH are both estimated to be close to the BLR. Could the absorbing gas actually come from the BLR? We first use the results from the RM (for reviews, see Peterson 1993) to estimate the size scale of the BLR of our source and make comparisons. Two of the main results of RM campaigns are that high-ionization ions reside at smaller distances from the accretion disk than low-ionization ions (Clavel et al. 1991) and that for the emission line from different AGNs, the R_BLR is roughly positively correlated with the square root of AGN luminosity (Kaspi et al. 2005).

Bentz et al. (2009) analyzed a sample of AGNs with a wide luminosity range and gave a relationship between the H_β BLR size and the quasar UV luminosity of

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}({R}_{\mathrm{BLR}}) & = & -21.0\pm 1.8\\ & & +\ (0.511\pm 0.041)\,\mathrm{log}(\lambda {L}_{\lambda }(5100\,\mathring{\rm A} )).\end{array}\end{eqnarray} \tag{ 6 }$$

Assuming that J1220+4549 has a similar spectral shape as typical quasars from the SDSS quasar sample (Vanden Berk et al. 2001), then λ L_λ (1350 Å) is about twice λ L_λ (5100 Å). λ L_λ (1350 Å) of 1.86 × 10⁴⁷ erg s⁻¹ gives λ L_λ (5100 Å) = 9.3 × 10⁴⁶ erg s⁻¹ and R_BLR = 1002 lt-days = 0.84 pc.

We also use the C iv radius–luminosity relation given by Lira et al. (2018, their Equation (1)), which is updated from Kaspi et al. (2007) but incorporates 11 high-redshift, high-luminosity quasars. They gave an empirical relation between the C iv BLR size and the quasar UV luminosity

$$\begin{eqnarray}&&\displaystyle \frac{{R}_{{\rm{C}}{\rm\small{IV}}}}{10\,\mathrm{lt} \mbox{-} \mathrm{days}}=(0.22\pm 0.10){\left[\displaystyle \frac{\lambda {L}_{\lambda }(1345\mathring{\rm A} )}{{10}^{43}\mathrm{erg}{{\rm{s}}}^{-1}}\right]}^{(0.46\pm 0.08)}.\end{eqnarray} \tag{ 7 }$$

For J1220+4549, the estimated R_BLR is ≈ 202 lt‐days = 0.17 pc.

Since C iv is of higher excitation than Hβ, it is expected that the C iv BLR locates closer to the central BH than that of Hβ (e.g., Clavel et al. 1991). The estimated location of the absorber of our quasar (see Section 5.1 for details) lies in between C iv and Hβ R_BLR, and agree well with the idea that the absorbing gas of J1220+4549 might be from the BLR. Adopting the above parameters derived from the absorption lines, we export the expected line intensity ratio of C iv/Hβ, and found this ratio is 15 times larger than the averaged value of SDSS quasars (Vanden Berk et al. 2001). This indicates that the absorber might be closer to the C iv high-ionization emission line region, which consists with the above distance estimates.

This absorbing BLR gas might have an origin from further within. It is suggested that some of the outflowing wind originated from the accretion disk may not gain enough acceleration (e.g., Risaliti & Elvis 2010) and can get accumulated at the BLR regions (e.g., Różańska et al. 2014) to form the absorbing gas in the BLR. The properties of our quasar also agree with this picture. It is well known that the escape velocity of the outflowing medium is ${v}_{\mathrm{esc}}=\sqrt{2{{GM}}_{\mathrm{BH}}/r}$, where G, M_BH, and r are the gravitational constant, BH mass, and distance to the central BH, respectively. For J1220+4549, the v_esc at a distance of r = 0.3 pc, where the absorber is estimated to be located at, is ∼13,849 km s⁻¹. This is much larger than the radial velocity (v_abs ∼ 200 km s⁻¹) measured from the blueshifted absorption lines. Thus, it is very likely that the absorber in our source cannot escape from the gravitational field of the central BH. In fact, with such a small v_abs, only when the absorber is located at a galactic scale, as far as 1.45 kpc (v_esc = v_abs, as shown in Figure 9), can the absorber have the chance to escape from the gravitational field of the central BH. Or when the central BH mass is less than 6.0 × 10⁶ M_⊙, an absorber can escape at 0.3 pc with ∼200 km s⁻¹. This is three orders of magnitude smaller than that of J1220+4549 (see Section 3.4). This suggests that the absorber might be the failed disk wind, which can be observed if they happen to locate on the line of sight, as predicted by simulations (Risaliti & Elvis 2010; Quera-Bofarull et al. 2020). The simulations of Różańska et al. (2014) show that the disk wind from the outermost accretion disk atmosphere can build up a dense absorber (n_H = 10¹⁰–10¹² cm⁻³), with a location of 0.1 pc, which is similar to that of our source.

Significant residual flux upon the Lyα (Figure 7(c)) and Lyβ (Figure 7(d)) absorption troughs were detected, and weak residual flux was also seen on the Lyγ (Figure 7(e)) absorption trough. The absorbing gas is radiated from the center ionizing source. At the same time, it should produce emission lines through photoionization processes. The residues in the absorbing lines can be naturally interpreted as the emission from absorbing gas. Adopting the above parameters derived from the absorption lines, we use the Cloudy code to export the expected emission line intensities and compare them with the absorbing lines residues measured in this object. We found that the model expected Lyα intensity is about twice C iv, while the observed Lyα residue is much larger than the C iv residue. A possible explanation is that a large fraction of the Lyα residue is contributed by the scattered photons of the neutral hydrogen, rather than by the emitted photons by the absorbing gas.