Photoionization-driven Absorption-line Variability in Balmer Absorption Line Quasar LBQS 1206+1052

We needed to recover the absorption-free spectra (f_AbsFree) to analyze the variability in more detail. A reliable method to obtain the absorption-free spectra is the pair-matching method (e.g., Leighly et al. 2011). This method is based on the similarity of continua and emission-line profiles between quasars with and without absorptions. It is always possible to find enough unabsorbed quasars whose spectra resemble the spectral features surrounding the absorption line of a given absorbed quasar. This method has a big benefit such that the systematic error of the model can be taken into account. Liu15 developed the pair-matching method to analyze Mg ii and He i λ3889 BALs. Using a Monte Carlo simulation, Liu15 demonstrated that the method could precisely measure BAL parameters such as depth and EW and robustly estimate the uncertainty of the parameters. We applied the pair-matching method to LBQS 1206+1052. For the Mg ii doublet and the He i* optical absorption lines, we basically followed Liu15. We further developed the method by applying it to Balmer and He i* λ10830 absorption lines. The details of the pair-matching method that we used will be described in Appendix A, and the main idea is summarized as follows. We divided four ranges in the spectra: 2500–3300 Å for the Mg ii doublet and He i λλ2946, 3189 lines; 3800–4000 Å for He i λ3889; 4825–4892 Å and 6510–6610 Å for Hβ and Hα, respectively; and 10550–11150 Å for He i λ10830. For each range, the following things were done.

• 1.  
  We generated a library of unabsorbed quasar spectra.
• 2.  
  We looped over the library to fit the spectra of LBQS 1206+1052 from all the observations simultaneously, and the Gaussian blurred the library spectra with different widths for different observations to account for their spectral resolutions. Windows affected by absorption were masked during the fitting.
• 3.  
  We selected the 10 best fits according to χ² as the final absorption-free templates.

The pair-matching results are shown in Figure 4. The median spectra of the absorption-free templates are plotted with red lines. We also illuminated the systematic error of this pair-matching method by plotting the ranges (green lines) within 1σ standard deviation of the 10 best fits for each data point. Hereafter, when referring to absorption-free spectrum, we mean the median spectrum of the absorption-free templates.

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In previous works using the pair-matching method, the BAL EW and its uncertainty by considering both the random error (σ_ran) and the systematical error (σ_sys) were calculated. For each accepted pair-matching model, an EW_i can be calculated. The mean of all EW_i is a good estimate of the true value of EW, and the standard deviation indicates the systematic error of this pair-matching method. Then the total measurement of BAL EW can be expressed as ${\sigma }_{\mathrm{total}}=\sqrt{{\sigma }_{\mathrm{sys}}^{2}+{\sigma }_{\mathrm{ran}}^{2}}$. In this work, we need to not only measure the BAL EW but also fit the BAL parameters, such as centroids, widths, and integrated optical depths. We propose a new method to estimate the uncertainty of BAL parameters in the fitting based on the Monte Carlo algorithm. As with the previous method, we also considered both origins of errors. To account for the random error, we generated fake spectra f_fake using observed flux and error as

$$\begin{eqnarray}&&{f}_{\mathrm{fake}}(\lambda )={f}_{\mathrm{obs}}(\lambda )+R(\lambda )\times {{error}}_{\mathrm{obs}}(\lambda ),\end{eqnarray} \tag{ 1 }$$

where R(λ) is a series of random numbers in standard normal distribution. To account for the systematic error, we randomly selected one template from the accepted fits for each pair-matching region. The fitting procedure was then done using the fake spectrum and the absorption-free templates by minimizing χ², which is expressed as

$$\begin{eqnarray}&&{\chi }^{2}={({f}_{\mathrm{obs}}(\lambda )-{f}_{\mathrm{model}}(\lambda ))}^{2}\times \mathrm{Weight}(\lambda ).\end{eqnarray} \tag{ 2 }$$

The computation of Weight(λ) considers both origins of errors as

$$\begin{eqnarray}&&\mathrm{Weight}(\lambda )=\displaystyle \frac{1}{{\mathrm{error}}_{\mathrm{obs}}^{2}(\lambda )+\mathrm{Stddev}(\lambda )},\end{eqnarray} \tag{ 3 }$$

where Stddev(λ) is the standard deviation spectrum of the accepted absorption-free templates for each pixel. We repeated the measurement 500 times to derive distributions of the BAL parameters. We referred to the median value of the distribution as "the best value" of the BAL parameters, and the interval between 5% and 95% ranked values as the "90% confidence interval."

We examined whether this method can produce good estimations of BAL parameters and their uncertainties by generating fake absorbed spectra using unabsorbed spectra and given profiles, then fitting them using the above method, and then comparing the best-fitting BAL parameters with the given ones. The details are described in Appendix B. From the testing result, we can say that the 90% confidence intervals of BAL parameters obtained from our method are reliable. Throughout this paper, we have measured the BAL parameters using this method.

We can measure the BAL EWs following previous works, and we can also do that using our method. In Appendix B we tested our method and found that the 90% confidence interval of BAL EWs is also reliable. This means that when measuring the BAL EWs, our method is as good as the previous method, and thus we also used our method. In Section 3.3, we attempted to measure the EW ratio between two observations of the same object. We also used our method, though we did not test its behavior in this situation.

Quasar UV–optical spectra typically consist of power-law components representing thermal emission from the accretion disk, broad emission lines (BELs), narrow emission lines (NELs), a Balmer continuum component for the blue bump in the wavelength region bluer than 3645 Å, and blended Fe ii emission lines. We built a model in which the emission of LBQS 1206+1052 comes from three regions: the accretion disk, the broad emission line region (BELR), and the narrow emission line region (NELR), and the emission components are expressed as f_AD, f_BELR, and f_NELR hereafter. In the model, the Balmer continuum and Fe ii emissions are believed to have come from the BELR. We modeled the optical spectra of SDSS 2003, YFOSC 2012, DBSP 2014, and YFOSC 2016 by a procedure described in detail in Ji12. We first fit the emission-line-free region (2855–3010 Å, 3625–3645 Å, 4170–4260 Å, 4430–4770 Å, 5080–5550 Å, 6050–6200 Å) using a "pseudo-continuum" model consisting of a power-law component, a Balmer continuum component, a blended high-order Balmer emission line component, and an Fe ii component, by minimization of χ². The MMT 2012 spectrum does not cover emission-line-free regions; thus, we rescaled the DBSP spectrum to fit the MMT spectrum in the ranges of 6300–6450 Å and 6700–6820 Å and derived the pseudo-continuum model for MMT using the rescaled DBSP model. After subtracting the pseudo-continuum model, we applied a joint fit of the five continuum-subtracted spectra using Gaussians simultaneously by assuming the following: (1) all of the profiles of BELs and NELs are double Gaussian; (2) the profiles of all the BELs in one spectrum are identical; (3) the profiles of each NEL in all five spectra are identical; (4) the profiles of NELs from the same ion are identical; (5) the flux ratios of [N ii], [O iii], [Ne iii], and [Ne v] doublets are fixed at theoretical values. In the windows affected by absorption lines, we used the absorption-free spectra in the fitting instead of the observed spectra. The decomposition results of the optical spectra are shown in Figure 5.

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For NIR spectra, we are only concerned with the region around the He i* λ18380 line. The spectra here only contain continua, BELs, and NELs. We fit the continua phenomenologically using power laws in the emission-line-free windows of 10200–10500 Å, 11500–12400 Å, and 14200–15000 Å. The continuum-subtracted spectra around He i λ10830 were then fitted by using a model consisting of He i λ10830 BEL, Paγ BEL, and He i λ10830 NEL and by assuming that the profile of each is double Gaussian. The decomposition results of the NIR spectra are also shown in Figure 5.

In Figure 6, we plotted the normalized absorption spectra f_abs. For the optical spectra, f_abs were normalized by assuming that the absorber only covers the accretion disk and does not cover any BELR and NELR emissions. That is,

$$\begin{eqnarray}&&{f}_{\mathrm{abs}}=1+\displaystyle \frac{{f}_{\mathrm{obs}}-{f}_{\mathrm{AbsFree}}}{{f}_{\mathrm{AD}}}.\end{eqnarray} \tag{ 4 }$$

For the NIR spectra, we temporarily treated the power-law component as emission from the accretion disk and also used this equation.

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It can be clearly seen that the deepest position in the He i* λ10830 absorption trough is at a velocity of v ∼ −1400 km s⁻¹ relative to the quasar rest frame for all three observations.⁶ The features at this velocity are also seen in Mg ii, as the deepest two positions in the Mg ii trough in SDSS and DBSP spectra correspond to positions at v ∼ −1400 km s⁻¹ for the Mg ii doublet. Hα is different because the deepest position is at v ∼ −700 km s⁻¹ and absorption at v ∼ −1400 km s⁻¹ is not detected. We divided the absorption troughs into two components owing to the difference between Balmer and other lines, and we referred to the two components as the V1400 and V700 components for short, according to the blueshift velocity. It can be clearly seen that both components contribute to He i* λλ10830 and 3889 absorption troughs, while the Mg ii trough is more complicated, due to blending of the doublet. Ji12 decomposed the Mg ii trough and found that it also consists of the two components, and the V1400 component of Mg ii λ2803 is blended with the V700 component of Mg ii λ2796. Thus, we concluded that the V700 component is in Balmer, He i*, and Mg ii absorption lines, and the V1400 component is only in He i* and Mg II.

The absorption troughs in the SDSS 2003 spectrum and in follow-up spectra with time intervals of a decade show similar structures, indicating that the two components remain for over 10 years. By directly comparing the absorption troughs from different observations, we concluded that the velocities of the two components do not vary by time. On the other hand, the variability in strength is notable after normalization. The V700 component of He i* λ10830 clearly became weak from 2013 to 2015, while the V1400 component changed little. Although the optical spectra suffer from different spectral resolutions, we can quantify the variations in depths by using EWs because EW is less affected by resolution. We calculated the EW ratios relative to EW in the SDSS spectrum, which shows the deepest absorption, and the results are listed in Table 2. For the V700 component, the variances in Hα, Hβ, and He i* λ3889 (integrated in −1000 < v < 0) show the same tendency—it became weak from 2003 to 2012 and recovered in 2014 and 2016. For the V1400 component, we did not detect variance in He i* λ10830. The EW of Mg ii also decreased from 2003 to 2012 and increased in 2014, suggesting that the Mg ii of the V1400 component also has the same variability pattern as the He i* and Balmer of the V700 component, considering that the Mg ii trough is dominated by the V1400 component.

Table 2.  EW Ratios of Optical Absorption Lines in YFOSC and DBSP Spectra Relative to Those in the SDSS Spectrum and Uncertainties with 90% Confidence

	EW/EWSDSS
	Mg ii Doublet	He i λ3889	Hα	Hβ
Velocity Range	−3000 < v < 0 (for 2803)	−1000 < v < 0	−1400 < v < 0	−1400 < v < 0
MMT 201203	...		${0.19}_{-0.16}^{+0.16}$
YFOSC 201205	${0.24}_{-0.12}^{+0.07}$	${0.16}_{-0.20}^{+0.21}$	...	${0.47}_{-0.16}^{+0.18}$
DBSP 201404	${0.89}_{-0.15}^{+0.11}$	${0.62}_{-0.14}^{+0.15}$	${0.69}_{-0.24}^{+0.14}$
YFOSC 201601	${0.83}_{-0.13}^{+0.10}$	${0.54}_{-0.20}^{+0.16}$	...	${0.61}_{-0.41}^{+0.38}$

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If the absorption-line variability is due to variation in ionization state, the variance in strength of the absorption lines should be correlated with variance in continuum flux. We labeled the observation time of the eight spectral observations in the V-band light curve in Figure 2. We found that it is likely that the continuum flux during the SDSS 200303 observation is the lowest among the eight observations according to the Catalina light curve and the synthetic magnitude of the SDSS spectrum. Although not an imaging result, the synthetic magnitude is reliable because the flux calibration of the SDSS data release 7 has good quality, and because the flux is in agreement with the brightening tendency between SDSS photometry in 2002 and Catalina photometry in 2004. At the same time, all of the absorption lines are strongest in the SDSS 2003 spectrum. The highest flux recorded by the Catalina light curve was in 2013, corresponding to the TSpec 2013 spectrum, in which the V700 component of He i* λ10830 is indeed the weakest among the three TSpec spectra. This fact also reveals that the optical depth of He i* λ10830 was not large (<1) in 2013. Thus, the corresponding optical depth of the He i* λ3889 line (23 times less) should be very small. The clear detection of He i* λ3889 in the SDSS, DBSP, and YFOSC 2016 spectrum implies that the V700 component of He i* in 2013 is the weakest among all of the observations. Thus, there is an anticorrelation of the continuum fluxes and absorption depths in 2003 and 2013. We further checked this anticorrelation. The variation in EW of He i*, Balmer, and Mg ii shows the same pattern. They became weaker from 2003 to 2012 and became stronger from 2012 to 2014. On the other hand, the strengthening in continuum from 2003 to 2012 can be clearly seen in the light curve. If we adopted the magnitude value from synthetics of the DBSP spectrum, the dimming in continuum can also be found from 2012 to 2014. Though it is not a photometric result, the synthetic magnitude of the DBSP 2014 spectrum has good quality owing to two facts: one is that we observe the standard star just before the observation of LBQS 1206+1052 with close air mass, and the other is that the magnitude agrees with the decreasing tendency in 2013 in the Catalina Sky Survey light curve. In summary, we found an anticorrelation in EW of absorption lines and the continuum flux, supporting the variable ionization state model. For a further examination of this model, we will first model the absorbing troughs and obtain the ionic column densities, and then we check whether the ionic column densities agree with the photoionization model using Cloudy simulations.

4.1.1. Modeling the Absorbing Troughs

The covering conditions of absorbing gases to the central continuum source are essential for measurement of ionic column densities. As can be seen in Figure 6, the V1400 component of the He i λ10830 absorption line has negative flux if normalized using the continuum, indicating that the V1400 absorbing gas covers not only the whole accretion disk but also a part of the BELR. By normalizing using both the continuum and BELs, we concluded that the V1400 absorbing gas covers at least 60% of the BELR, and hence the size is comparable to, or larger than, the BELR. On the other hand, the V700 absorbing gas does not cover as large a fraction of the BELR as the V1400 component does. If it indeed covered 60% or more of the BELR, the Hα optical depth at the deepest position in the SDSS spectrum would be <0.45, while the Hβ optical depth would be >0.1. These two values are inconsistent considering the theoretical ratio of Hα/Hβ = 7.26. The normalized fluxes of Hα and He i* λ10830 at the velocity of ∼700 km s⁻¹ can both reach ∼0.1, indicating that the V700 absorbing gas covers at least 90% of the accretion disk. Assuming that it covers the whole accretion disk and does not cover BELR at all, we computed the optical depth ratio of Hα to Hβ to be 7.0 ± 2.1, which is consistent with the theoretical value. Thus, it is likely that the size of the V700 absorbing gas is comparable to the accretion disk and much smaller than the BELR, and hence the two absorbing gases are different in size. Considering that the V700 component has Balmer absorptions, which are not seen in the V1400 component, the physical conditions of the two absorbing gases are also different. Thus, it is likely that the two absorption gases are physically independent.

We fit the spectral data in absorption regions by assuming the following.

• 1.  
  For each absorption line in each spectrum, the velocity profile of optical depth is Gaussian for both the V1400 and V700 components.
• 2.  
  For all of the spectral lines that belong to the same ion for each component, the velocity profiles of optical depths are identical and do not vary by time.
• 3.  
  The ionic column densities are computed from the optical depth profile by

  $$\begin{eqnarray}&&{N}_{\mathrm{ion}}=\displaystyle \frac{{m}_{e}c}{\pi {e}^{2}f\lambda }\int {\tau }_{v}{dv},\end{eqnarray} \tag{ 5 }$$

  where f and λ are the oscillator strength and the wavelength of each spectral line, respectively. For ions with two or more lines in the same spectrum, the column densities are fixed.
• 4.  
  The covering conditions are the same for different ions and do not change by velocity or vary by time, while they are different for the two components. Thus, for each absorption line we have

$$\begin{eqnarray}{f}_{\mathrm{obs}}-{f}_{\mathrm{AbsFree}} & = & {f}_{\mathrm{AD}}\times (1-{f}_{\mathrm{resi}}^{\mathrm{AD}})+{f}_{\mathrm{BELR}}\\ & & \times (1-{f}_{\mathrm{resi}}^{\mathrm{BELR}}),\end{eqnarray} \tag{ 6 }$$

where ${f}_{\mathrm{resi}}^{\mathrm{AD}}$ and ${f}_{\mathrm{resi}}^{\mathrm{BELR}}$ are the residual fractions after absorption for the two emission sources, which can be expressed as

$$\begin{eqnarray}&&\left\{\begin{array}{l}\begin{array}{l}{f}_{\mathrm{resi}}^{\mathrm{AD}}=(1-{\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{AD}}+{\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{AD}}\times {e}^{-{\tau }_{{\rm{V}}700}})\\ \quad \times \,(1-{\mathrm{CF}}_{{\rm{V}}1400}^{\mathrm{AD}}+{\mathrm{CF}}_{{\rm{V}}1400}^{\mathrm{AD}}\times {e}^{-{\tau }_{{\rm{V}}1400}})\end{array}\\ \begin{array}{l}{f}_{\mathrm{resi}}^{\mathrm{BELR}}=(1-{\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{BELR}}+{\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{BELR}}\times {e}^{-{\tau }_{{\rm{V}}700}})\\ \quad \times \,(1-{\mathrm{CF}}_{{\rm{V}}1400}^{\mathrm{BELR}}+{\mathrm{CF}}_{{\rm{V}}1400}^{\mathrm{BELR}}\times {e}^{-{\tau }_{{\rm{V}}1400}})\end{array}\end{array}\right.,\end{eqnarray} \tag{ 7 }$$

where ${\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{AD}}$, ${\mathrm{CF}}_{{\rm{V}}1400}^{\mathrm{AD}}$, ${\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{BELR}}$, and ${\mathrm{CF}}_{{\rm{V}}1400}^{\mathrm{BELR}}$ are the covering factors of the V700 and V1400 absorbing gases to the accretion disk and BELR, and τ_V700 and τ_V1400 are the optical depths of the two absorbing gases. We did not consider the situation in which the absorbing gas covers the NELR because the NELR is typically too large to be covered by an absorbing cloud. The V1400 component must cover the whole accretion disk; thus, ${\mathrm{CF}}_{{\rm{V}}1400}^{\mathrm{AD}}=1$. The situation for the V700 component is more complicated: it may only cover part of the accretion disk (${\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{BELR}}=0$), or it may cover the whole accretion disk and a small part of the BELR (${\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{AD}}=1$).

Table 3.  The Best Values and 90% Confidence Intervals of the Absorption Line Parameters

		V700 component			V1400 component
Parameters		Mg II	He I*	H(n = 2)	Mg II	He I*	H(n = 2)
Line center (km s−1)		$-{671}_{-76}^{+66}$	$-{720}_{-48}^{+41}$	$-{705}_{-49}^{+46}$	$-{1412}_{-12}^{+11}$	$-{1417}_{-18}^{+17}$	—
Line width (km s−1)		${285}_{-33}^{+25}$	${281}_{-46}^{+26}$	${276}_{-59}^{+31}$	${99}_{-8}^{+6}$	${105}_{-12}^{+21}$	—
Line center (fixed) (km s−1)			$-{698}_{-33}^{+32}$			$-{1413}_{-13}^{+13}$
Line width (fixed) (km s−1)			${270}_{-28}^{+26}$			${107}_{-11}^{+13}$
column densities (1013 cm−2)	SDSS 200303	${14.6}_{-3.0}^{+6.5}$	${33.3}_{-5.3}^{+17.3}$	${6.7}_{-2.4}^{+1.8}$	${5.3}_{-0.8}^{+0.8}$	${9.6}_{-3.9}^{+3.3}$	<0.2
	MMT 201203	—	—	${1.2}_{-0.7}^{+1.1}$	—	—	<0.05
	YFOSC 201205	${2.5}_{-1.0}^{+2.1}$	${6.8}_{-3.4}^{+8.8}$	${2.2}_{-1.6}^{+2.9}$	${1.5}_{-0.4}^{+0.5}$	${6.0}_{-5.7}^{+8.8}$	<1.1
	TSpec 201302	—	<3.7	—	—	${2.6}_{-0.5}^{+0.8}$	—
	DBSP 201404	${12.2}_{-3.7}^{+9.7}$	${19.6}_{-4.5}^{+13.1}$	${4.3}_{-2.4}^{+2.2}$	${3.6}_{-1.0}^{+0.9}$	${8.0}_{-3.5}^{+3.3}$	<0.2
	TSpec 201505	—	${5.4}_{-4.3}^{+4.0}$	—	—	${3.8}_{-0.7}^{+1.0}$	—
	TSpec 201512	—	${3.7}_{-2.1}^{+3.1}$	—	—	${4.0}_{-1.0}^{+1.4}$	—
	YFOSC 201601	${13.5}_{-4.2}^{+7.0}$	${16.3}_{-5.5}^{+11.7}$	${3.3}_{-2.6}^{+3.8}$	${1.7}_{-0.9}^{+1.2}$	${8.9}_{-7.1}^{+12.5}$	<1.2

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Our model has a total of 46 free parameters, 23 for each absorbing component: line centers and line widths for three ions (Mg ii, He i*, and H(n = 2)), a total of 16 ionic column densities in eight spectra, and one covering factor. For the V700 component, the only free covering factor is ${\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{AD}}$ for the first covering situation and ${\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{BELR}}$ for the second covering situation. We simultaneously fit the eight spectra in absorption windows (−2000 to 0 km s⁻¹ for each line) using the method described in Section 3.1. The spectral resolutions are different among different observations and among different wavelengths during the same observation, which are shown in Table 1. We considered the resolution effect by convolving Gaussians to the models. We calculated the probability distributions of all the parameters and listed the best values and 90% confidence intervals in Table 3.

Table 4.  Parameters of the Absorbing Gases Obtained from Cloudy Simulations

	Parameter		V700 Absorbing Gas		V1400 Absorbing Gas
					Without Shading	With Shading
	logNH (cm−2)	21.1	21.25	21.4	20.93	21.09
	lognH (cm−3)	9.32	9.38	9.52	3.0
logU	SDSS 200303	−1.9	−1.66	−1.41
	HST/COS 2010				−1.60	−1.13
	MMT&YFOSC 2012	−1.47	−1.29	−1.12
	DBSP 201404	−1.77	−1.49	−1.25
	YFOSC 201601	−1.65	−1.4	−1.2
ΔlogU(2003 to 2012)		0.43	0.35	0.29
Distance (pc)		1.7	1.3	0.9	2800	1200

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We first set all the parameters free. Both covering situations yield the same result, that the V700 absorbing gas covers the whole accretion disk and does not cover the BELR (${\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{AD}}=1$ and ${\mathrm{CF}}_{{\rm{V}}700}^{\mathrm{BELR}}=0$), agreeing with what we had guessed from directly comparing Hα and Hβ absorption troughs in the SDSS spectrum. This is not surprising because the size of the BELR can be several orders of magnitude larger than the accretion disk. The size of the BELR of LBQS 1206+1052 can be estimated to be 6 × 10¹⁷ cm using the radius–luminosity relation of Kaspi et al. (2005) as

$$\begin{eqnarray}&&{R}_{\mathrm{BELR}}=(22.3\pm 2.1){\left(\displaystyle \frac{{L}_{5100}}{{10}^{44}\mathrm{erg}{{\rm{s}}}^{-1}}\right)}^{0.69\pm 0.05}\,\mathrm{lt}\,\mbox{--}\,\mathrm{days},\end{eqnarray} \tag{ 8 }$$

where L₅₁₀₀ = 3.0 × 10⁴⁶ erg s⁻¹ is the monochromatic luminosity at rest frame 5100 Å. The radius R_λ at which the disk temperature equals the photon energy, kT = hc/λ_rest, is given by Blackburne et al. (2011) as

$$\begin{eqnarray}{R}_{\lambda } & = & 9.7\times {10}^{15}{\left(\displaystyle \frac{\lambda }{\mu {\rm{m}}}\right)}^{4/3}{\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{10}^{9}{M}_{\odot }}\right)}^{2/3}\\ & & \times {\left(\displaystyle \frac{L}{\eta {L}_{\mathrm{edd}}}\right)}^{1/3}\mathrm{cm},\end{eqnarray} \tag{ 9 }$$

where L is the bolometric luminosity, η is the accretion efficiency (assumed to be 0.1), and ${L}_{\mathrm{edd}}$ is the Eddington luminosity. For LBQS 1206+1052, the black hole mass can be computed to be 1.9 × 10⁹ M_⊙ using the FWHM of the Hβ BEL (FWHM_Hβ ∼ 7000 km s⁻¹) and the continuum luminosity following Greene & Ho (2005) as

$$\begin{eqnarray}{M}_{\mathrm{BH}} & = & (4.4\pm 0.2)\times {10}^{6}{\left(\displaystyle \frac{{L}_{5100}}{{10}^{44}\mathrm{erg}{{\rm{s}}}^{-1}}\right)}^{0.64\pm 0.02}\\ & & \times {\left(\displaystyle \frac{{\mathrm{FWHM}}_{{\rm{H}}\beta }}{{10}^{3}\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{2}{M}_{\odot },\end{eqnarray} \tag{ 10 }$$

and the bolometric luminosity is 8L_B ∼ 2.4 × 10⁴⁶ erg s⁻¹ using the bolometric correction from Marconi et al. (2004). Then the size of the optical emission region (λ ∼ 5000 Å) can be estimated to be 6 × 10¹⁵ cm. Considering the two-order-of-magnitude difference between the sizes of the BELR and the accretion disk, the covering condition suggests that the size of the absorbing gas is larger than the accretion disk and still far smaller than the BELR. The best-fitting ${\mathrm{CF}}_{{\rm{V}}1400}^{\mathrm{BELR}}$ is also 1, indicating that the V1400 component covers the whole accretion disk and the whole BELR. As a result, we fixed the covering conditions and redid the fitting. The Gaussian centers and widths of all three ions, which are listed in Table 3, agree with each other for the V700 component, and those of the He i* and Mg ii are also inconsistent for the V1400 component. This indicates that the velocity profiles of different ions are similar; thus, we fixed the profile parameters for a better measurement of ionic column densities. The Balmer absorption of the V1400 component is not detected in all of the spectra, so we obtained an upper limit by assuming that the profile is identical to those of He i* and Mg II. The resultant ionic column densities are listed in Table 3, and the best-fit model is shown in Figure 7. As can be seen from the figure, the model reproduces the observed spectra well.

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We noticed that the He i* column densities measured from TSpec 201512 and YFOSC 201601 observations differ significantly, especially for the V700 component. Furthermore, the He i* column densities measured from NIR seem to be systematically lower than when measured from the optical. This may be due to the contribution of the dusty torus to the continuum in the NIR band. The He i* λ10830 line is at a wavelength where the emission of hot dust reaches its peak; thus, it is natural that a part of the continuum comes from hot dust. The emission region of hot dust has a larger size than the accretion disk and the BELR; thus, it is likely that the hot dust emission is not covered by the two components. Therefore, the optical depths of He i* λ10830 may be underestimated for both components. By assuming that the He i* column densities are the same in TSpec 201512 and YFOSC 201601 observations, we estimated that the residual flux of He i* λ10830 of the V700 component in the TSpec 201512 spectrum would be only ∼0.05, and it is impossible to make a precise measurement of He i* column density in this situation. Thus, we did not adopt the He i* column density from the TSpec 201512 observation. We also abandoned the value from the TSpec 201505 observation, as the situation is similar.

We plotted the column densities of Mg ii, He i*, and H(n = 2) ions as functions of observing time in Figure 8 and compared them with the V-band light curve. For the V700 component, the variations of Mg ii and H(n = 2) show the same pattern that the column densities were the highest in 2003, then decreased in 2012, and then recovered in 2014 and 2016. The pattern of He i* is also consistent if adopting the measurements from optical spectra. For the V1400 component, the pattern of Mg ii is similar, while the measurement uncertainties of He i* are too large. The variability pattern of these ionic column densities is just opposite that of the continuum.

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4.1.2. Photoionization Model

Figure 13 in Liu15 shows how the column densities of Mg ii and He i* depend on the ionization parameter U. Mg ii always decreases with increasing U. He i* decreases with increasing U when the absorbing gas is too thin to reach an ionization front, and it increases with increasing U when the gas is thick enough that the ionization front is well developed. The ionic column densities are inversely correlated with the V-band continuum in LBQS 1206+1052 for both components, in accordance with the first situation, indicating that both absorbing gases are optically thin. We noticed that the column densities of He i* and Mg ii are insensitive to H density n_H in a wide range, while H(n = 2) is sensitive to the density of the gas. We first investigate the V700 component with additional information from Balmer absorption lines. We used the photoionization code Cloudy (version 10.00; Ferland et al. 1998) to simulate the ionization process in the V700 absorbing gas. We assumed a slab-shaped geometry, unique density, homogeneous chemical composition of solar values, and a spectral energy distribution (SED) of the commonly used ionizing continuum from Mathews & Ferland (1987; MF87). The undetermined parameters are the ionization parameter U, the H density n_H, and the total Hydrogen column densities N_H. For a quick look at the general situation, we calculated a sparse grid of models with logn_H varying from 3 to 12, with logU varying from −3.5 to 2.0, and with logN_H varying from 20 to 24, and the steps of the three are 0.5 dex. The variable ionization state model assumes that only U is variable among the observations and that n_H and N_H are invariable. Thus, we check how the three ionic column densities vary as functions of ionization parameter logU. As can be seen in Figure 9, ${N}_{\mathrm{He}{\rm{I}}* }$ has an upper limit for a given N_H value, and therefore we can derive a lower limit for the N_H of ∼10²¹ cm⁻² using the maximum ${N}_{\mathrm{He}{\rm{I}}* }$ measured from the SDSS 200303 observation.

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To find the approximate photoionization solutions, we plotted the contours of the column densities of He i*, Mg ii, and H(n = 2) according to the levels of observed values in Figure 10. The observed values are selected from SDSS 200303, YFOSC 201205, DBSP 201404, and YFOSC 201601 observations. We abandoned the ${N}_{\mathrm{Mg}\mathrm{II}}$ values from the two YFOSC observations since the uncertainties are too large. For ${N}_{{\rm{H}}(n=2)}$ in 2012, the value from the MMT 201203 observation was used instead of that from YFOSC 201205 because it has a smaller uncertainty, and because we did not find variation of ${N}_{{\rm{H}}(n=2)}$ between the two epochs, which have a rest-frame time interval of only 50 days. Figure 10(a) shows that the three sets of lines from three ions roughly intersect at a position with logn_H ∼ 9 for every N_H value, supporting the results of former works that Balmer absorption lines are only detected when the density is high. For logN_H = 21, the red valid line (contour of ${N}_{\mathrm{He}{\rm{I}}* }$ in SDSS 2003 spectrum) does not occur in the region of n_H ∼ 9. It can be seen from Figure 9 that the peak value of ${N}_{\mathrm{He}{\rm{I}}* }$ depends mainly on N_H and slightly on n_H, and we found that the red valid line only occurs in the region with logn_H ∼ 9 when logN_H > 21.1. For logN_H = 21.5, the three sets of lines roughly intersect in regions of logn_H ∼ 9 and logU ∼ −1. In addition, the intersection points using ionic column densities from four observations have close n_H values (within 0.3 dex), which is in accordance with the variable ionization state model. For higher N_H values, the n_H values of intersection points from four observations differ by >0.5 dex. This implies that an upper limit of N_H could be obtained under the assumption that n_H is invariable among all of the observations.

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We then calculated a denser grid of models around the approximate solutions and searched for the photoionization solutions. We assumed that the model has six free parameters, n_H, N_H, and four U. We compared the difference between spectra predicted by the Cloudy model and the observed spectra, we calculated the χ² using the difference, and the weights are computed following the method described in Section 3.1. Only Balmer and He i* series were used because they have higher measurement accuracies relative to Mg ii for the V700 component and are less influenced by metallicity. The final solution was computed by minimizing χ². The best-fitting solution has logN_H = 21.25, logn_H = 9.38, and logU varying from −1.66 to −1.29. We cut at Δχ² = 3 and obtained 21.1 < logN_H < 21.4 and 9.3 < logn_H < 9.5, and the solutions by fixing logN_H at 21.1, 21.25, and 21.4 are listed in Table 4 and labeled in Figure 10(b).

4.1.3. Analysis of HST/COS Spectrum

The density of the V1400 component cannot be determined from the optical and NIR spectra because we only detected He i* and Mg ii absorption lines, both of which are insensitive to density (see Figure 9). Fortunately, there is an archival far-UV (FUV) spectrum of LBQS 1206+1052 taken with HST/COS in 2010, which shows abundant absorption lines in rest frame 820–1035 Å. Chamberlain & Arav (2015, hereafter CA15) analyzed the HST/COS spectrum. CA15 noticed that the deepest place in the trough has a blueshifted velocity of ∼1400 km s⁻¹, which coincides with the V1400 component. They also found that the absorption lines exhibit a profile that is skewed toward the red side of the trough. This profile is similar to that of He i* λ10830, indicating that both the V1400 and V700 components contribute to the absorption troughs. CA15 measured the density of the absorbing gas using the line ratios of N iii*/N iii and S iii*/S iii. The two components are blended in the N iii absorption trough, and meanwhile only V1400 components are detected in the S iii absorption trough; thus, the density of the V1400 component can be determined as log n_H = 3.0 ± 0.2 using S iii following CA15.

CA15 also measured the column densities of H i, N iii, O iii, O vi, S iii, and S vi and obtained log U = −1.82 and log N_H = 20.46 using the Cloudy simulation. Some of the ionic column densities from CA15 are measured by integrating the apparent optical depth (AOD) over the trough, which is mainly contributed by the V1400 component. Thus, we deduced that the ionic column densities and the photoionization solution from CA15 apply to the V1400 component. However, the results may suffer from the contamination by the V700 component. Thus, we need to examine this and measure the physical condition of the V1400 absorbing gas again.

We attempted to predict the FUV absorption spectra for the two components, in order to better understand the HST/COS spectrum. We first predicted the ionic column densities of the two components using the Cloudy simulation, in which the n_H, N_H, and U for the V1400 component are from CA15, and those for the V700 component are from our best-fitting solutions of logN_H = 21.25 and logn_H = 9.38. The V-band light curve shows that the quasar luminosity in 2010 is close to that in 2012; therefore, the U value from the MMT/YFOSC 2012 observation is adopted. The ionic column densities from Cloudy are then converted to optical depths using oscillator strengths, which are obtained from the NIST Atomic Spectra Database.⁷ We then generated absorption spectra using Gaussian optical depth profiles obtained in Section 4.1.1. The results for the two components are shown in Figure 11 for two spectral ranges, along with the observed HST/COS spectrum. As can be seen in the figure, most of the absorption troughs can find corresponding features in the predicted absorption spectra.

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However, there are contradictions between the observed and the predicted absorption spectra in the Lyβ and O vi region (red box in Figure 11). The photons in the range of 1027 Å < λ < 1032 Å are predicted to be fully absorbed by the O vi λ1031 line of the V700 component, while the observed spectrum shows a strong excess. The excess seems to have a Gaussian shape, and thus we proposed that it may be an O vi emission line. We plotted the observed spectrum in velocity spaces of C iii λ977 and O vi λ1031 in Figure 12. The red side of the C iii emission line is unabsorbed, and we can measure the redder position at half maximum at v ∼ 600 km s⁻¹, and analyses of profiles of O iii and N iii emission lines also yield similar results. On the other hand, by assuming that the excess in the O vi absorption trough is the O vi λ1031 emission line, the bluer position at half-maximum of the emission-line profile is at v ∼ −400 km s⁻¹. Thus, the FWHM of the UV emission lines is ∼1000 km s⁻¹, far narrower than that of the BELs in the optical (FWHM ∼ 6000 km s⁻¹), and still broader than that of the NELs (FWHM ∼ 500 km s⁻¹). A similar situation was seen in OI 287 (Li et al. 2015), where UV emission lines such as Lyα and C iv are narrower than Balmer BELs and broader than [O iii] NELs. This can be explained by introducing additional intermediate-width emission lines that originate in the inner face of the dusty torus, and by assuming that the UV continuum and UV BELs are suppressed by dust extinction. We plotted the SED of LBQS 1206+1052 in the UV band in Figure 13. The YFOSC 2012 spectrum was used to generate the SED together with HST/COS spectrum because the light curve shows that the quasar luminosities in the two epochs are close. We found that the continuum in the two spectra can be well fitted by a reddened quasar composite spectrum from Vanden Berk et al. (2001) by an SMC extinction curve with ${E}_{B-V}=0.07$. This implies that the continuum in the HST/COS spectrum is dust extinguished by about one order of magnitude. Therefore, it is likely that the emission lines in the HST/COS spectrum of LBQS 1206+1052 are from intermediate-width emission-line regions, just as in OI 287.

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CA15 showed their Cloudy simulation results in their Figure 3. They determined the U and N_H using the cross point of the O vi contour and other ions in U–N_H space. We argued that the apparent residual flux in the O vi trough is likely to be an emission line; thus, the measured O vi column density may not be real. Then, how should we determine the physical properties of V1400 absorbing gas? We noticed that the S vi contour also crosses with other ions. As can be seen in Figure 11 (blue box), the blue side of S vi λ944 for the V1400 component is not affected by the V700 component. Thus, we measured the S vi column density by integrating the AOD on the blue side and multiplying by 2. Now we can remeasure U and N_H using a Cloudy simulation. The settings of the Cloudy simulation are similar to those for the V700 component, except that n_H is fixed at 10³ cm⁻³. The ionic column densities measured by us are listed in Table 5, along with the values from CA15. The absorption troughs of O iii, C iii, and N iii are deep, and the measured column densities may be underestimated, due to unknown flux that is not covered by the absorbing gas, such as scattered light and emission lines. Thus, we did not adopt the column densities of these ions when searching for the photoionization solution. CA15 measured the H i column density from Lyman limit measurements, which are contaminated by the V700 component, and we did not adopt the value either. In addition, we detected weak Ar iv λλ844, 850 and C ii λ903 absorption lines for the V1400 component (purple box in Figure 11), and the column densities of Ar iv and C ii are also measured. The Cloudy simulation results are plotted in Figure 14(a), and the best-fitting solution is labeled with a black star. The ionic column densities predicted by the solution are listed in Table 5. As shown in the table, the observed and predicted column densities of S vi, S iii, Ar iv, and C ii agree within 0.3 dex.

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Table 5.  Ionic Column Densities of V1400 Component

Ion	logNion (cm−2)a		logNmodel (cm−2)b
	This Work	CA15	Without Shading	With Shading
H i	...	16.90–17.06	17.27	17.04
C ii	14.0 ± 0.3	...	14.35	14.10
C iii	...	>14.95	16.62	16.80
N iii	...	15.68 ± 0.1	16.10	16.22
O iii	...	16.26 ± 0.15	17.22	17.76
O vi	...	15.55 ± 0.1	15.94	14.17
S iii	15.1 ± 0.2	15.09 ± 0.2	14.84	14.79
S vi	15.22 ± 0.1	15.27 ± 0.1	15.24	15.18
Ar iv	15.19 ± 0.3	...	15.02	15.40
He i*	13.65 ± 0.3c	...	13.61	14.27
Mg ii	13.23–13.80d	...	13.52	13.84

Notes.

^aThe sum of the ground and excited levels for each ion. ^bThe column densities predicted by our best-fitting Cloudy model. The results are from two simulations, one not considering the shading effect (using the MF87 SED) and the other considering the shading effect (using the transmitted SED of V700 absorbing gas). ^cThe value is from three TSpec observations. ^dThe upper and lower limits are given using the measurements from SDSS 2003 and YFOSC 2012 spectra.

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Relative to CA15's solution (triangle in Figure 14(a)), our solution has a U 0.22 dex higher and an N_H 0.47 dex higher. As the contours of most ions are in the lower left to upper right direction in U–N_H space, ions with higher ionization energies, such as O vi, S vi, and Ar iv, are important to determining the solution because their contours cross with the contours of low-ionization ions. In CA15's simulation, the cross point of S vi is different from the cross point of O VI. If adopting the cross point of S vi in CA15's simulation, the solution (square in Figure 14(a)) is much closer to ours, and the difference with <0.1 dex is due to applying a different SED. The cross point of Ar iv is close to that of S vi, making the solution of using S vi more reliable.

The HST/COS spectrum shows an additional absorption-line system with a blueshift velocity of ∼200 km s⁻¹ (and hence is referred to as the V200 component hereafter), which is seen in Lyman series, C iii λ977, and N iii λ989, and the corresponding absorption lines are labeled using pink dashed lines in Figure 11.

4.1.4. Consistency between Variations in Continuum and in U

We found observational evidence against the variable covering factor model. In this model the optical depths of all of the absorption lines are invariable, and thus the change in EW is proportional to the change in the covering factor. The EW of He i* λ3889 for the V700 component in the YFOSC 201601 observation is ${0.54}_{-0.20}^{+0.16}$ (90% confidence) times the EW value in the SDSS 200303 observation. Assuming that the V700 absorbing gas covers the whole continuum in the SDSS 200303 observation, we can estimate the upper limit of the covering factor in YFSOC 201601 to be 0.7. On the other hand, another covering factor of He i* can be obtained from the He i* λ10830 absorption trough in the quasi-simultaneous 201512 TSpec observation. It can be seen from Figure 6 that the absorbing gas covers at least 80%–90% of the continuum. This fraction may be higher considering the underneath hot dust emission. Therefore, the covering factors measured from the two observations with only an 8-day interval in rest frame are not consistent if assuming that the ionic column density is invariable. We have estimated the size of the accretion disk to be ∼10¹⁵ cm. This requires a crossing velocity of ∼14,000 km s⁻¹, which is too large for an absorbing gas with a radial velocity of only 700 km s⁻¹. Moreover, if the absorbing gas moved across in such a short time, it is difficult to explain how the absorption troughs remained over 10 years.

The variation in absorption lines for the V1400 component is also strange under the assumption of this model. The covering factor of Mg ii λ2796 of the V1400 component to the continuum increased by about twice between YFOSC 201205 and DBSP 201404, while the covering factor of He i* λ10830 changed little between 2013 and 2015. One can only explain this by introducing more complicated models, such as adopting different covering factors for He i* and Mg II. However, the velocity profiles of He i* and Mg ii are nearly identical, indicating that the two ions are located in the same position, and hence it is likely that the covering factors are also the same.

The model is also difficult to understand kinetically. If the weakening of absorption lines from 2003 to 2012 is due to movement of an absorbing gas cloud, the recovery in 2014 is unusual because the cloud would not move back. If the recovery is due to the entering of a new cloud, it is difficult to explain why the velocity profiles of the two clouds show no difference. As we have reproduced all of the data using the variable ionization state model, we excluded this variable covering factor model. We conclude that the absorption-line variability in LBQS 1206+1052 is due to a change in ionization state.

We first discuss the parameters of the V700 component. The lower limit of N_H (logN_H > 21.1) was from the observed ${N}_{\mathrm{He}{\rm{I}}* }$, which is rather robust. The upper limit of logN_H < 21.4 was derived by assuming that n_H is invariable among the observations. In the process we only considered the measurement uncertainty, while the systematic errors in the photoionization simulation are not accounted for. Considering the systematic errors, the possible ranges of the parameters would be larger. The influence of uncertain metallicity is little because the BAL parameters are determined using He i* and H(n = 2), both of which are insensitive to metallicity. In addition, the ${N}_{\mathrm{Mg}{\rm{II}}}$ from the best-fit solution and from the observations are consistent by 0.3 dex, suggesting that the chemical composition of the V700 absorbing gas is similar to that of the solar one. On the other hand, the SED of the ionization continuum indeed affects the measurement of the parameters. We tested another SED, which is described in detail in Ji et al. (2015) and has a lower flux in extreme-UV and X-ray than the MF87 SED if normalized at 3000 Å. Using ${N}_{\mathrm{He}{\rm{I}}* }$, the lower limit of logN_H is 21.3, slightly larger than that using MF87 SED. The upper limit is also larger, with logN_H < 22.5, and the N_H range is also wider. The n_H is in the range of $9.4\lt \mathrm{log}{n}_{H}\lt 9.9$, and the inferred distance is in the range of 0.2–0.3 pc using a lower Q(H⁰) of 3.3 × 10⁵⁶ s⁻¹. There are no available X-ray data for LBQS 1206+1052, and the UV band suffers from dust reddening; thus, we have no observational limitation to the SED of the ionization continuum. Thus,, the uncertainty of parameters due to an uncertain SED should also be considered. Combining the results by using different SEDs, we concluded that the n_H is in the range of 10⁹–10¹⁰ cm⁻³, and the distance of the absorbing gas to the central source is in the range of 0.2–2 pc.

We then discuss the parameters of the V1400 component. The n_H is converted from n_e, which is measured using the ratio between the excited and ground states of [S iii]. [S iii] absorption lines are optically thin and hence do not suffer from uncertainty in unknown covering conditions, yet they still have a high enough S/N to ensure an accurate measurement. Thus, the measurement of n_H is reliable. The N_H and U values are from Cloudy simulations. As CA15 showed, the photoionization solution is independent of the metallicity of the gas, and the choice of SED can influence the measurement of U by up to 0.3 dex.

Since the variability is photoionization driven, the density can also be limited using the recombination timescale τ = (n_e α_r)⁻¹, where α_r is the recombination rate, which is related to the electron temperature. For a typical ionized gas, T ∼ 10⁴ K, and thus the recombination rates are 4.2 × 10⁻¹³, 4.6 × 10⁻¹³, and 1.2 × 10⁻¹² cm³ s⁻¹ for H i, He i, and Mg ii, respectively, which were obtained from Verner & Ferland (1996). For the V700 absorbing gas with n_H ∼ 10^9.4, the recombination timescales of the three ions are all less than 10⁴ s assuming ${n}_{e}=1.2{n}_{{\rm{H}}}$ for a highly ionized gas. Therefore, the variation of ion column densities can trace the continuum variability immediately for the V700 component. For the 1400 component, we can similarly estimate a recombination timescale to be ∼20 yr using n_e = 10^3.0 cm⁻³, too long to match the observation. And by assuming that the recombination timescale is <1 yr, the inferred n_e > 10^4.4 cm⁻³, higher than that measured from S iii. We noticed that for the V1400 component, only the response of Mg ii to the continuum can be seen, and we did not see the variability of He i* and other ions. Considering that the ionization energy of Mg ii (7.6 eV) is much lower than that of S iii (23.3 eV) and other ions, a possible explanation for the contradiction is that Mg ii comes from a region with higher density and thus has a shorter recombination timescale. This requires a two-phase medium for the V1400 absorbing gas, and the parameters we obtained may apply to the lower density phase.

The distance of the V1400 absorbing gas is three orders of magnitude larger than the V700 absorbing gas. Though the measurements of distances have uncertainty, we can conclude that the V1400 absorbing gas is located behind the V700 absorbing gas relative to the quasar. Thus, we needed to consider that the ionization continuum of the V1400 absorbing gas is filtered by the V700 absorbing gas. A Cloudy simulation shows that the V700 absorbing gas causes a total decrease in Q(H⁰) of 40% and that the output SED is also different than the input SED, as nearly all of the photons with 54.6 eV < E < 100 eV are absorbed (see Figure 14(b)). We refer to this effect as the "shading effect" hereafter. We made another photoionization simulation of the V1400 absorbing gas using the transmitted spectrum of the V700 absorbing gas as the input SED. The shading effect mainly causes a decrease of column densities of high-ionization ions, such as S vi, O vi, and Ar iv, and the low-ionization ions are less affected. The solution is at logU = −1.13 and logN_H = 21.09 (red star in Figure 15), which moves toward the upper right direction in U–N_H space relative to the solution without the shading effect. Considering the shading effect, the U value from the Cloudy simulation is higher and the ionization photons are reduced. Using the effective Q(H⁰) of 4.4 × 10⁵⁶ s⁻¹, the best estimation of the distance of the V1400 absorbing gas is about 1.2 kpc.

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We showed that there are three absorption-line systems in the spectra of LBQS 1206+1052 with blueshifted velocities of 1420, 700, and 200 km s⁻¹ relative to the quasar rest frame, respectively. The V700 absorbing gas has an n_H in the range of 10⁹–10¹⁰ cm⁻³. It is located at a distance of ∼1 pc from the central source, just outside of the BELR. The virialized velocity in this distance is $v\sim \sqrt{\tfrac{{{GM}}_{\mathrm{BH}}}{r}}=2000$ km s⁻¹, and thus the gas may be restricted in this region.

The V1400 absorbing gas is at a distance of ∼1.2 kpc and with an n_H of 10³ cm⁻³. The blueshifted velocity of ∼1400 km s⁻¹ indicates that it is an outflow, as it is in the line of sight of the quasar. We found a strong blue wing in the profiles of NELs of [O iii] λλ4959, 5007 and [Ne iii] λ3869, which is extended to a velocity of −2500 km s⁻¹. We measured the luminosity of [O iii] λ5007 and [Ne iii] λ3869 in a velocity range from −2000 to −1000 km s⁻¹ to be 6 × 10⁸ L_⊙ and 6 × 10⁷ L_⊙, respectively. The distance and density of the V1400 absorbing gas are both similar to those of the NELR, where the blue wing of NELs may originate, and the blueshifted velocities of the V1400 absorbing gas and the blue wing are also consistent. These similarities suggest a link between the blue wing of NELs and the V1400 absorbing gas. Thus, we calculated the outflow rate in the kiloparsec scale by assuming that the outflow seen in the blue wing is formed by a layer of gas clouds with similar distances and properties to those of the V1400 absorbing gas. For this purpose we first simulated the emission-line spectrum of the layer by assuming a spherical shell of gas with a radius of 1 kpc, n_H of 10³ cm⁻³, and radial H column density of 10^21.09 cm⁻². We used the MF87 SED instead of the transmitted SED of the V700 absorbing gas. The results show that the layer of outflowing gas can produce enough of the [O iii] and [Ne iii] emission lines measured above if the global covering factor is >10⁻³, the mass outflow rate is estimated to be 0.3 M_⊙ yr⁻¹, and the inferred kinetic outflow rate is 1.5 × 10⁴¹ erg s⁻¹. The total mass outflow rate in this distance may be several times higher considering those gases with lower or higher velocities, and the possible gases in the opposite direction, which are probably obscured by the dusty torus. The estimation assumes that all of the gases in this region have the same density as the V1400 absorbing gas, and considering the typical density in the NELR of 10²–10⁴ cm⁻², the mass outflow rate may have an uncertainty of 1 dex.

The V200 absorbing component shows too few lines, and we cannot obtain a good estimation on the properties of the absorbing gas. We attempted to set a constraint on its properties using the nondetection of several lines. The nondetection of N iii λ991 can set an upper limit of the n_H as 10² cm⁻³. The nondetection of the high-ionization line S vi λ944 suggests either a lower U in the V200 absorbing gas than in the V1400 absorbing gas or a further decrease in hard photons due to the shading effect of the V1400 absorbing gas, both of which indicate a larger distance of the V200 absorbing gas relative to the V1400 absorbing gas. The lower blueshift velocity also implies that the V200 absorbing gas is in an outer region.

We found extended emission-line regions (EELRs) around LBQS 1206+1052 from the long-slit optical spectra. The EELRs were found in MMT 201203, YFOSC 201205, DBSP 201404, and YFOSC 201601 spectra with different position angles of 21, 0, 24, and 90°, respectively. [O iii] λλ4959, 5007, Hα, Hβ, [Ne iii] λ3869, and [O ii] λ3727 emission lines were seen for the EELRs. The highest flux of the extended emission-line feature was recorded in the YFOSC 2012 spectrum with a long slit in the N–S direction. We plotted the two-dimensional spectral image in Figure 16. The brightest position is at 2.8 (15 kpc in projection) north of the quasar, and the EELR extends for a maximum distance of ∼5''. After subtracting the contribution of the traditional NLR, the measured extended [O iii] luminosity is 1.1 × 10⁴³ erg s⁻¹, and the total luminosity is higher considering that this luminosity is only extracted from a slit with 18 width. This luminosity is very high among the EELRs, e.g., the highest extended [O iii] luminosity recorded in Fu & Stockton (2009) is 1.0 × 10⁴³ erg s⁻¹. Assuming that the density of the EELR is similar to those measured by Fu & Stockton (2009), the mass of the gas can be estimated to be 3 × 10⁶ M_⊙ using Hβ luminosity. The extended [O iii] feature shows a radial velocity difference relative to the quasar rest frame on both sides, and we measured a redshift velocity of ∼100 km s⁻¹ on the north side. We have seen outflows in the kiloparsec scale with enough mass and a high enough velocity to form a structure with a size of 15 kpc. If the EELR was formed by a similar outflow in the past, the dynamic timescale can be estimated to be $\sim 1.5\times {10}^{8}\,\mathrm{yr}$ using the size and an expanding velocity of ∼100 km s⁻¹, which is close to the lifetime of AGNs (e.g., Marconi et al. 2004). Therefore, we presented an overall scenario of outflows in LBQS 1206+1052 that the quasar started to drive outflows when it was born ∼10⁸ yr ago, and continuously generated strong outflows until at least ∼10⁶ yr ago, which is the dynamic timescale of the V1400 outflow. A detailed analysis of the EELR is beyond the scope of this work. Future integral field spectrographic observations are needed to better understand the large-scale outflow in LBQS 1206+1052.

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Changes in ionization state and movement of absorbing gas are the two best origins of absorption-line variability. To date, no one can unambiguously say which is more important among BAL quasars. He i* and Balmer multiplets are powerful in directly determining covering conditions and measuring ionic column densities. Therefore, follow-up observations of He i* BAL quasars and Balmer BAL quasars can distinguish the two possible origins in these quasars, and examples are presented in Shi et al. (2016b) and this work. He i* absorption lines exist in nearly all LoBAL quasars; thus, follow-up observations of a sample of He i* BAL quasars can tell us the fraction of those that show variable ionic column densities and those that show variable covering factors. In this way we can make clear the origin of absorption-line variability in LoBAL quasars.

Balmer BAL quasars are rare but important because they trace high-density media. We need to measure the properties of absorbing gases in Balmer BAL quasars to better understand this rare type of BAL and high-density media around quasar nuclei. Typically column densities of three ions are needed to obtain the basic parameters, such as n_H, N_H, and U. For example, objects studied by Zhang et al. (2015) and Shi et al. (2016b, 2016a) are iron LoBALs, and they used Balmer, He i*, and excited states of Fe ii to calculate all three parameters. We show in this work that by taking follow-up observations, we can limit the parameters using only Balmer and He i*. Considering that all known Balmer BALs show corresponding He i*, this means that the density and position of absorption media can be determined for most of the Balmer BAL quasars. Thus, we propose that follow-up observations of Balmer BAL quasars are essential to better understand this rare population, especially those that are not iron LoBALs.