# THE X-RAYS WIND CONNECTION IN PG 2112+059

C. Saez 1, W. N. Brandt2, F. E. Bauer3,4,5, G. Chartas6, T. Misawa7, F.
Hamann8, and S. C. Gallagher9
1Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago,
Chile
2 Department of Astronomy and Astrophysics, 525 Davey Lab, The Pennsylvania
State University, University Park, PA 16802, USA
3 Instituto de Astrofísica and Centro de Astroingeniería, Facultad de Física,
Pontificia Universidad Católica de Chile, Casilla 306,
Santiago 22, Chile
4 Millennium Institute of Astrophysics (MAS), Nuncio Monseñor Sótero Sanz 100,
Providencia, Santiago, Chile
5 Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, Colorado
80301 https://orcid.org/0000-0002-8686-8737
6 Department of Physics and Astronomy, College of Charleston, Charleston, SC
29424, USA
7 School of General Education, Shinshu University, 3-1-1 Asahi, Matsumoto,
Nagano 390-8621, Japan
8 Department of Physics & Astronomy, University of California, Riverside, CA
92507, USA
9 Department of Physics and Astronomy and Institute for Earth and Space
Exploration, The University of Western Ontario, London,
ON, N6A 3K7, Canada

###### Abstract

We study the connection between the X-ray and UV properties of the broad
absorption line (BAL) wind in the highly X-ray variable quasar PG 2112+059 by
comparing _Chandra_ -ACIS data with contemporaneous UV _HST_ /STIS spectra in
three different epochs. We observe a correlation whereby an increase in the
equivalent-widths (EWs) of the BALs is accompanied by a redder UV spectrum.
The growth in the BALs EWs is also accompanied by a significant dimming in
soft X-ray emission ($\lesssim 2\,\text{keV}$), consistent with increased
absorption. Variations in the hard X-ray emission ($\gtrsim 2\,\text{keV}$)
are only accompanied by minor spectral variations of the UV-BALs and do not
show significant changes in the EW of BALs. These trends suggest a wind-shield
scenario where the outflow inclination with respect to the line of sight is
decreasing and/or the wind mass is increasing. These changes elevate the
covering fraction and/or column densities of the BALs and are likely
accompanied by a nearly contemporaneous increase in the column density of the
shield.

###### keywords:

techniques: spectroscopic — X-rays: galaxies — galaxies: active — quasars:
absorption lines — galaxies: individual: PG 2112+059.

††pagerange: THE X-RAYS WIND CONNECTION IN PG
2112+059–LABEL:lastpage††pubyear: 2020

##  1 Introduction

It is well established that, with exception of dwarf galaxies, every galaxy
should have a supermassive black hole (SMBH) with black hole masses ($M_{\rm
BH}$) of $10^{6}M_{\odot}\lesssim M_{\rm BH}\lesssim 10^{10}M_{\odot}$ in
their centers (e.g., Mezcua et al., 2018; Kormendy & Ho, 2013). Active
Galactic Nuclei (AGN), which in their brightest states become quasars111A
quasar is defined as a “bright AGN” with $M_{B}<-23$ or $L_{\rm B}\gtrsim
10^{44}\,\hbox{erg~{}s${}^{-1}$}$; (Schmidt & Green, 1983) , in brief (of the
order of $10^{7}$ years; Haehnelt & Rees, 1993) and powerful duty cycles are
thought to regulate SMBH growth (Soltan, 1982). AGN should also transport
energy from the SMBH to their surrounding host galaxy (e.g, Fabian, 2012)
through various feedback mechanisms, including jets and quasar winds (or
accretion disk winds). These two mechanisms are key ingredients to explain the
regulation of galaxy evolution, and the origin of known observational
relationships between the SMBH masses and bulge properties in nearby galaxies
(e.g., Hopkins et al., 2006; Somerville et al., 2008; Kormendy & Ho, 2013).

Evidence of winds is observed in the ultra-violet (UV) rest-frame spectra in a
fraction of quasars ($\sim 20\%$, e.g., Hewett & Foltz, 2003; Gibson et al.,
2009) through ionized broad absorption lines (BALs). These spectral features
with broadening above $2000$ km s-1 (Weymann et al., 1991) appear as
absorption with blueshifted velocity offsets of $2,000$ to $30,000$ km s-1
from the line rest-frame. Depending on the ionization state of the wind, BAL
quasars are divided into at least two categories (e.g. Hall et al., 2002):
high-ionization BAL quasars (HiBALs) and low-ionization BAL quasars (LoBALs).
HiBALs show absorption features from O vi, N v, and C iv lines. LoBALs are
characterized to have high-ionization absorption plus absorption from Al iii,
C ii and/or Mg ii lines.

Observations and theory suggest that quasar BAL features are an orientation
effect (e.g., Murray et al., 1995; Risaliti & Elvis, 2010; Filiz Ak et al.,
2014), and thus these outflows should be intrinsic to every quasar. Models
predict that BALs originate from the accretion disk in funnel shaped
structures at distances of $10^{2}-10^{3}R_{S}$ (where $R_{S}=2GM_{\rm
BH}/c^{2}$ is the Schwarzschild radius) from their central SMBH (e.g., Murray
et al., 1995; Proga et al., 2000). In contrast, larger distances of
$10^{3}-10^{7}R_{S}$ are inferred from the BAL observational signatures (e.g.,
de Kool et al., 2001; Hall et al., 2011; Arav et al., 2013). Similar distance
estimates are found for narrow absorption lines (NAL) and mini-BALs quasars
(e.g., Misawa et al., 2016; Xu et al., 2019). Therefore, UV outflows could be
observed far from their origin or a revision on their models is needed. BAL
quasars also tend to show particularly distinctive weak X-ray emission (e.g.,
Gibson et al., 2009), which has been attributed to absorption (e.g., Page et
al., 2017) and/or intrinsically weak emission (e.g., Luo et al., 2014).

The growing evidence from BAL quasar spectral features from UV to X-rays has
motivated many models. These models postulate that outflows are launched in
funnel shaped structures driven by radiation and/or magnetic forces from the
accretion disk (e.g., Murray et al., 1995; Proga et al., 2000; Fukumura et
al., 2010). In view of these models, BALs correspond to lines of sight that
are intercepting these structures. Additionally, the weak X-ray emission could
be a product of absorption from the inner parts $\lesssim 100\,R_{S}$ of the
medium that is not accelerated enough to be expelled to the inter galactic
medium (IGM; failed wind). There could be also a highly ionized part of the
wind accelerated to relativistic speeds $\gtrsim 0.1c$ (with $c$ the speed of
light) and showing spectral signatures in the X-ray through highly ionized Fe
xxv and Fe xxvi BAL lines (e.g., Chartas et al., 2002, 2003; Saez & Chartas,
2011; Hamann et al., 2018).

The HiBAL quasar PG 2112+059 with $z=0.459$ (Monroe et al., 2016) and
$M_{V}=-27.3$ is one of the most luminous PG quasars. It has been observed in
X-rays from 1991-2007 by various X-ray missions, including _ROSAT_ , _ASCA_ ,
_XMM-Newton_ , and _Chandra_. In these observations, PG 2112+059 has shown
typical BAL X-ray weakness and order of magnitude X-ray flux changes over
periods of time as short as 6 months (Saez et al., 2012). The physical model
that leads to the observed X-ray emission is not well understood. It could be
a reflection-type model (e.g., Schartel et al., 2010) or a complex absorption
model (e.g., Gallagher et al., 2004; Saez et al., 2012). In this work, our
main goal is to analyze the connection between the strong X-ray variability of
PG 2112+059 and the physical properties that the associated BAL winds present
in the UV. Through this kind of joint analysis, we are aiming to better
understand the mechanisms that create these winds. Throughout this paper,
unless stated otherwise, we use cgs units, errors are quoted at the 1$\sigma$
level, and we adopt a flat $\Lambda$-dominated universe with
$H_{0}=70~{}\hbox{km~{}s${}^{-1}$}\;{\rm Mpc^{-1}}$, $\Omega_{\Lambda}=0.7$,
and $\Omega_{M}=0.3$.

Figure 1: _HST_ UV spectra of PG 2112+059 illustrating the presence of O vi, N
v, and C iv BALs. The upper, middle and lower panel correspond to epochs 1, 2
and 3, respectively. The green and black curves indicate the G140L and G230L
grating spectra, while, the red and blue curves are the fitted spectral model
in the extreme-UV and far-UV (EUV and FUV) wavelength bands (see §2.3) with
thickness given by the 1$\sigma$ confidence region and the dotted line is the
spectral error. The gray areas are the wavelength ranges where continua fits
are performed.

##  2 METHODOLOGY

###  2.1 Observations

Table 1: Log of _Chandra_ observations of PG 2112+059

|  | exp. time |  | rate |
---|---|---|---|---|---
obs. date | obs. id | (ks) | counts | (10-3 s-1) | Ref.a
2002/09/01 (Epoch 1) | 3011 | 56.9 | $829_{-29}^{+30}$ | 14.6$\pm$0.5 | 1
2014/12/20 (Epoch 2) | 17553 | 18.2 | $62_{-8}^{+9}$ | 3.4$\pm$0.5 | 2
2015/08/29 (Epoch 3) | 17148 | 18.3 | $140_{-12}^{+13}$ | 7.6$\pm$0.7 | 2

All observations utilize the ACIS-S3 detector. The counts and rates are from
background-subtracted source photon counts in the _Chandra_ full-band (0.5–8
keV). The exposure times, photon counts, and rates are obtained after
screening the data. The errors on the source counts were computed by
propagating the asymmetric errors on the total and background counts using the
approach of Barlow (2004). The total and background count errors were
estimated from Tables 1 and 2 of Gehrels (1986).

a References: (1) Gallagher et al. (2004); (2) This work.

Table 2: Log of _HST_ STIS observations of PG 2112+059

|  | exp. time |  |  |  |  |
---|---|---|---|---|---|---|---
obs. date | prop. id | (s) | instrument | grating | wave-range | ra | Ref.b
2002/09/01 (Epoch 1) | 9277 | 1100 | FUV-MAMA | G140L | 1150$-$1730 | 1223 | 1
2002/09/01 (Epoch 1) | 9277 | 900 | NUV-MAMA | G230L | 1570$-$3180 | 767 | 1
2014/12/18 (Epoch 2) | 13948 | 1095 | FUV-MAMA | G140L | 1150$-$1730 | 1222 | 2
2014/12/18 (Epoch 2) | 13948 | 920 | NUV-MAMA | G230L | 1570$-$3180 | 767 | 2
2015/09/11 (Epoch 3) | 13948 | 1095 | FUV-MAMA | G140L | 1150$-$1730 | 1222 | 2
2015/09/11 (Epoch 3) | 13948 | 920 | NUV-MAMA | G230L | 1570$-$3180 | 767 | 2

The STIS observations utilize the following gratings: G140L for the FUV-MAMA
and G230L for the NUV-MAMA configurations.

a The spectral resolution ($R=\lambda/\Delta\lambda$) is calculated at the
central wavelength of each configuration, i.e. at 1425 Å and 2376 Å for the
FUV-MAMA and NUV-MAMA configurations, respectively.

b References: (1) Gallagher et al. (2004); (2) This work.

In this work, we analyze two $\sim 20$ ks _Chandra_ observations each with a
contemporaneous _HST_ STIS spectrum, performed in 2014–2015 and separated by
approximately nine months. These new observations are compared with a nearly
simultaneous archival _Chandra_ -_HST_ observation from 2002 (analyzed in
Gallagher et al., 2004).222Details about the motivation of these observations
can be found at Saez et al. (2016). Each _Chandra_ observation was performed
within $\sim$10 days of an _HST_ observation. During the _Chandra_ -_HST_ time
gap although there could be X-ray spectral variability, this should not be
important when compared to long term ($\gtrsim 6$ months) spectral
variability. Based on the existing constraints for PG 2112+059 we expect that
any significant X-ray spectral variability (relevant for this study) should be
on time scales $\gtrsim 1$ month. For instance, in the period between May 3
and November 5 of 2007 PG 2112+059 has 4 _XMM-Newton_ observations each with
at least 500 0.3–10 keV counts (see Saez et al., 2012, for details). During
this period, no significant variability was detected (at a 99% level), such
that any potential flux variations were less than 20%. Additionally, on time
scales $\lesssim 1$ month, it is expected that fractional changes in the
normalized continuum flux removed by absorption should be $\lesssim 10$% in
the UV BALs (e.g., Capellupo et al., 2013). On time scales longer than a month
the fraction of the normalized flux removed by absorption could change more
dramatically in BALs. As we do not expect strong variability either in the
X-ray flux or in the UV BALs absorption profiles in scales $\lesssim 1$ month,
hereafter, we will refer to each contemporaneous _Chandra_ -_HST_ observation
time-ordered epoch as 1, 2 or 3. Details about the dates and most important
characteristics of these three sets of _Chandra_ -_HST_ spectra can be found
in Table 1 for the _Chandra_ observations and in Table 2 for the _HST_
observations.

The _Chandra_ observations were reduced using the standard software CIAO
version 4.12 provided by the _Chandra_ X-ray Center (CXC). For each epoch, we
reprocessed the datasets through the chandra_repro script to obtain the latest
calibration. Source and background spectra and associated products were
extracted using the CIAO script specextract from a circular region with an
aperture radius of 4″ and an annular source-free region with an inner radius
of 6″ and an outer radius of 24″, respectively. The numbers of background-
subtracted counts in the source regions at energies of 0.5–8 keV and some
details about the _Chandra_ observations are presented in Table 1.

The _HST_ spectra were reduced with the standard STIS pipeline, and the
resulting spectra are expected to have a flux calibration at the $\sim 5$%
level of precision (Bostroem & Proffitt, 2011). The _HST_ STIS spectra span a
wavelength range of 1570–3180 Å which in the rest frame of PG 2112+059 sample
several important BAL features such as O vi, Ly$\alpha$, N v, Si iv, and C iv.
In each _HST_ observation epoch, the exposure was $\sim 1100$ s and $\sim 900$
s for the G140L and G230L gratings, respectively, (see Table 2) both with a
$52\arcsec\times 0\aas@@fstack{\prime\prime}2$ slit. The spectra have
dispersions on average of $\approx 0.58$ Å and $\approx 1.54$ Å per pixel for
the G140L and G230L gratings, and resolving powers of $R\approx 1220$ and
$R\approx 770$ at the grating central wavelengths of 1425 Å and 2376 Å,
respectively. The G140L and G230L grating spectra overlap in the range
1570–1730 Å. In this wavelength overlap region, as a product of the
calibration, each grating spectra show decreasing signal-to-noise ratios (S/N)
per pixel at their respective endpoints. Therefore, for our analysis, we
select a limiting wavelength of 1700 Å ($\approx 1170$ Å in the rest-frame of
PG 2112+059) as the end of the G140L spectrum and beginning of the G230L
spectrum. This wavelength is approximately where both gratings reach the same
S/N in wavelength bins of comparable sizes. In each observation, the S/N in
the continuum is on average $\approx 10$ (19) per pixel with a standard
deviation of $\approx 3$ (5) for the G140L (G230L) grating. The full reduced
and dereddened _HST_ spectrum of PG 2112+059 at each epoch is presented in
Figure 1. The dereddening has been obtained by assuming a Galactic extinction
of $E(B-V)=0.0904$ (from Schlegel et al., 1998), equivalent to $N_{H}\approx
6\times 10^{20}\,$cm-2 (e.g., Güver & Özel, 2009), where $N_{\rm H}$ is the
total (neutral an ionized) hydrogen column density. The reddening model used
here and hereafter is that of Pei (1992).

Table 3: _Chandra_ X-ray spectral fits statistics  |  $C$-statistic/dof |
---|---|---
epoch | APL | WADR |  $p$-values
1 | 504.0/509 | 459.7/508 | 0.000
2 | 235.8/509 | 231.1/508 | 0.007
3 | 374.9/509 | 365.7/508 | 0.002
Table 4: _Chandra_ X-ray spectral fits parameters of the WAPLR model

epoch | ${N}_{\rm H}$ | log $\xi$ | normPL | normR
---|---|---|---|---
(1) | (2) | (3) | (4) | (5)
1 | 12$\pm$ 2 | 2.14$\pm$0.03 | 6.4$\pm$1.0 | 14.6$\pm$5.5
2 | 64$\pm$ 42 | 3.02$\pm$1.49 | 1.4$\pm$0.3 | 13.9$\pm$7.7
3 | 16$\pm$ 2 | 1.95$\pm$0.03 | 7.5$\pm$1.4 | 1.6$\pm$5.3

Col. (1): Observation Epoch. Col. (2): Column density in units of $10^{22}$
cm-2. Col. (3): Logarithm of the ionization parameter $\xi=L/n\,r^{2}$, as
defined in xspec. Col. (4–5): Normalizations of the continuum power-law and
the reflection model (pexmon). Both normalizations are in units of
$10^{-5}\,{\rm counts\>\,cm^{-2}\,s^{-1}\,keV^{-1}}$.

Figure 2: Folded (upper panel) and unfolded (lower panel) _Chandra_ spectra of
PG 2112+059. The solid histograms indicate the best-fitting WAPLR model to
each observation. The light gray, gray, and black colors are associated with
epochs 1, 2 and 3, respectively. In each observation a grouping with a minimum
10 counts per bin has been used.

###  2.2 X-ray analysis

Given that both of our new _Chandra_ observations of PG 2112+059 have very
modest count statistics, we performed fits in the 0.5–8 keV band using the
$C$-statistic (Cash, 1979) in xspec (Arnaud, 1996). Additionally, in all the
X-ray models used here Galactic absorption with total hydrogen column density
of $\hbox{${N}_{\rm H}$}=6.0\times 10^{20}$ cm-2 is assumed (Kalberla et al.,
2005). We use unbinned data and thus the $C$-statistic may not be appropriate
to utilize when performing background subtraction. For this purpose, we fit
the background spectra with a flat response using the cplinear model (Broos et
al., 2010). The background model is scaled and subtracted when we fit the
source spectra. Our new X-ray observations were designed to provide flux
constraints, and with this goal we use a model that is simple and at the same
time provides good fits to our observations.

To fit the _Chandra_ spectra, we select a model used in Schartel et al. (2010)
consisting of a continuum power law and an ionized reflection component, these
both pass through a warm absorber. Hereafter we will refer to this model as
the warm-absorbed power-law and reflection model (WAPLR; xspec model
phabs*zxipcf*(pow+pexmon)). To avoid overfitting our spectra we fixed many of
the parameters that describe the WAPLR model333For the warm absorber (xspec
model zxipcf), we fix the covering fraction to 1. For the continuum power-law
model (xspec model pow), we fix the photon index to 1.9. The value of
$\Gamma=1.9$ is close to an average value of the photon index for quasars
(e.g., Reeves & Turner, 2000; Saez et al., 2008; Nanni et al., 2017). For the
reflection model (xspec model pexmon), we fix the incident power-law photon
index to 1.9, the cutoff energy to 150 keV, the scaling factor for reflection
to $-1$ (no direct emission, only reflected component), the inclination angle
to $45^{\circ}$, and we assume solar abundances. , leaving 4 degrees of
freedom: the normalization of the continuum power-law (${\rm norm_{PL}}$), the
normalization of the reflection component (${\rm norm_{R}}$), and the column
density (${N}_{\rm H}$) and the logarithm of ionization parameter (as defined
by xspec; $\log\xi$) of the warm absorber.

The selection of the WAPLR model over a simpler model like the absorbed power-
law model (APL;444The APL model consist on a power-law with an intrinsic
neutral absorber component, and thus it has 3 degrees of freedom: the
normalization and photon index of the power-law, and the hydrogen column
density (${N}_{\rm H}$) of the redshifted absorber. xspec model
phabs*zphabs*pow) is based on evidence of spectral complexity that includes
the presence of a reflection component in previous PG 2112+059 high S/N
spectra (e.g., Schartel et al., 2010; Saez et al., 2012). Additionally, the
WAPLR model is a good representation of the data in past _XMM-Newton_
observations of PG 2112+059 (Schartel et al., 2007, 2010), and provides
significant improvements over the fits of an APL model over Epochs 1–3 (see
next paragraph). In Figure 2 we present the _Chandra_ spectra with their
respective WAPLR fits. As this figure shows, the WAPLR model reproduces the
significant Fe K$\alpha$ emission feature at rest-frame energies $\sim
6.4~{}{\rm keV}$ (feature at $\sim 4.4$ keV in Figure 2) found in Epoch 1
(Gallagher et al., 2004).

In Epochs 1–3 we check that the WAPLR model shows an improvement in the fits
(lower values of $C$-statistic; see Table 3) when compared with the APL model.
We test these fit improvements by using a modified version of the likelihood
ratio test (LRT) routine provided by the xspec
package.555https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node124.html.
Using this routine we generate 1000 Monte Carlo simulated spectra from the
fits of the APL model. These simulated spectra are fitted with both the APL
and WAPLR models to generate a table of $\Delta C$, where $\Delta C$ is the
difference between values of the $C$-statistic obtained with the APL and the
WAPLR model. The $p$-values correspond to the fraction of fits where $\Delta
C>\Delta C_{\rm obs}$, where $\Delta C_{\rm obs}$ is the observed value of
$\Delta C$. From the simulated data, in Epochs 1 and 3 we check that the WAPLR
provides a significant improvement over the fit with the APL model ($p\lesssim
0.002$) (see Table 3). We also find in Epoch 2 a significant improvement on
the fits (with $p\approx 0.007$), albeit, this observation might not have
enough counts to be reliable in differentiating between model fits. The best-
fitted parameters and fluxes obtained from the WAPLR model are presented in
Tables 4 and 5. Hereafter (if not stated otherwise), we assume that any X-ray
parameter estimated from spectral fits is obtained from WAPLR model using the
$C$-statistic.

Table 5: X-ray fluxes and Luminosities of PG 2112+059

epoch | $f_{0.5-2}$ | $f_{2-8}$ | $f_{0.5-8}$ | $f_{\rm 2keV}$ | $\Gamma_{\rm eff}$ |  HR | ${\rm log}\,L_{\rm 2keV}$ | log $L_{2-10}$
---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
1 | 3.2$\pm$0.2 | 16$\pm$ 1 | 19$\pm$ 1 | 5.5$\pm$0.4 | 0.85$\pm$0.08 | 0.21$\pm$0.04 | 25.47$\pm$0.03 | 44.07$\pm$0.03
2 | 1.1$\pm$0.5 | 4$\pm$ 2 | 5$\pm$ 3 | 1.5$\pm$0.7 | 1.00$\pm$0.61 | 0.15$\pm$0.14 | 24.90$\pm$0.21 | 43.48$\pm$0.17
3 | 1.2$\pm$0.2 | 13$\pm$ 2 | 14$\pm$ 2 | 2.5$\pm$0.3 | 0.29$\pm$0.14 | 0.43$\pm$0.08 | 25.12$\pm$0.06 | 43.96$\pm$0.06

X-ray fluxes, luminosities and total hydrogen column densities are corrected
for Galactic absorption assuming $\hbox{${N}_{\rm H}$}=6.0\times 10^{20}$ cm-2
(Kalberla et al., 2005) and are obtained from the best-fitting parameters for
a WAPLR model (xspec model phabs*zxipcf*[pow+pexmon]). Col. (1): Observation
Epoch. Cols. (2–4): Observed fluxes in the 0.5–2 keV, 2–8 keV, and 0.5–8 keV
bands in units of $10^{-14}$ erg cm-2 s-1. Col. (5): Observed flux densities
at rest-frame 2 keV in units of $10^{-32}$ erg cm-2 s-1Hz-1. Col. (6): X-ray
effective photon index $\Gamma_{\rm eff}=-\alpha_{x}+1$ obtained from the
ratio of of 2–8 keV to 0.5–2 keV flux assuming power-law spectra
($f_{\nu}\propto\nu^{\alpha_{x}}$). Col. (7): Hardness ratio, corrected due to
time-dependent loss of _Chandra_ -_A_ CIS sensitivity (see §3 for details).
(10) Logarithm of the monochromatic luminosity at rest-frame 2 keV. (11)
Logarithm of the luminosity at rest-frame 2–10 keV.

###  2.3 UV Continuum Fit and Normalization

To describe the C iv BAL, we fit the _HST_ /UV continuum in three relatively
line-free (RLF) windows at rest-frame wavelengths in the far-UV band (FUV;
$>1200$ Å) of PG 2112+059: 1280–1300 Å, 1700–1800 Å, and 1950–2200 Å. These
RLF windows were selected in a similar fashion as Gibson et al. (2009), with a
small difference in the first RLF window. For this window, the lower
wavelength limit is 1280Å (instead 1250Å) in order to avoid the broad
Ly$\alpha$+N v emission line. Additionally, the upper limit is 1300Å (instead
1350Å) in order to avoid a possible BAL Si iv region. The continuum in the
extreme-UV (EUV) band ($<1200$ Å) is expected to have thermal signatures of
the accretion disk (i.e., big-blue-bump features; e.g. Telfer et al., 2002;
Zheng et al., 1997) and to exhibit significant unaccounted attenuation mainly
due to the Lyman forest666It is a product of intervening lines Ly$\alpha$
1216, Ly$\beta$ 1026 and the depression of the continuum at wavelengths close
to the Lyman break limit (at 912 Å). Individual intervening H i absorption
have been identified in high-resolution UV observations of quasars at $z\sim
0.3$ (see e.g., Lehner et al., 2007). Additionally, in quasars at $z\gtrsim
0.3$ it is expected attenuation of the continuum $\sim 10\%$ at wavelengths
nearby the Lyman break limit (approximately in the range [800–900] Å) (e.g.,
Zheng et al., 1997)., i.e., the integration of H i absorption features coming
from intervening media. At the redshift of PG 2112+059 we expect that these
features show approximately in the wavelength range [800–1200]. Therefore, to
study the O vi and N v BALs, we independently characterize the EUV band
through two RLF windows: 940–950 Å, and 1110–1140 Å. The use of the 940–950 Å
window is to constrain the fitted continua to be close to the spectra at a
wavelength $\sim 945$ Å. This wavelength, as seen from Figure 1, should be
close to the blue end of the O vi BAL region (see, for example, Moravec et
al., 2017). Additionally, the 1110–1140 Å window is coincident with the blue
end of the N v BAL. The RLF windows used to fit the FUV (above 1200Å) and EUV
(below 1200Å) bands are shown in Figure 1 as gray areas.

The selected RLF windows described in the last paragraph are fitted using a
least-squares sigma-clipping method, discarding data that deviate by greater
than 3$\sigma$ from the model. In the FUV band, to estimate the continua, we
use a model composed of a power-law intrinsically reddened. There are only
three parameters in this model: power-law normalization, the power-law
spectral index, and the magnitude of intrinsic reddening E(B-V). Given that
there is degeneracy between the UV emission continuum shape and E(B-V), we do
not physically interpret the fitted values of the intrinsic reddening.
Additionally, in the FUV band, we also performed fits using a unreddened
(unabsorbed) power-law. These fits were used to estimate the steepness of the
spectra through the spectral index $\alpha_{FUV}$, the monochromatic fluxes at
2000 Å, and to extrapolate monochromatic fluxes at 2500 Å; all these
parameters are listed in Table 6. For the EUV band, given the reduced
wavelength range of the fitting regions, a simple, unreddened power-law were
used. The monochromatic fluxes at 950 Å and the spectral indexes
$\alpha_{EUV}$ obtained with these fits are also found in Table 6. Note that
all spectral indexes presented in Table 6 are in frequency units.777A power
law continuum is expressed in frequency units as $f_{\nu}\propto\nu^{\alpha}$
where $\alpha$ is the spectral index. A power-law continuum in frequency units
$f_{\nu}\propto\nu^{\alpha}$ is a power-law continuum in wavelength units
$f_{\lambda}\propto\lambda^{\alpha_{\lambda}}$ with
$\alpha_{\lambda}=-(\alpha+2)$. The BAL features obtained by subtracting the
fitted continuum still have second order deviations near their borders caused
by strong broad emission lines (ELs). To mitigate this, the strongest emission
lines (i.e., C iv, Si iv, Ly$\alpha$+N v, and O vi; ELs) were fitted using
Voigt profiles, and the resulting fitted model spectra (continuum+ELs), which
is assumed to be absorbed by the BALs, can be seen in Figure 1. This figure
highlights that there is no significant Si iv BAL feature observed at any
epoch.

Table 6: UV properties of PG 2112+059

epoch | $f_{950}$ | $f_{2000}$ | $f_{2500}$ | $AB_{2500}$ | ${\rm log}\,L_{2500}$ | $\alpha_{EUV}$ | $\alpha_{FUV}$ | $\alpha_{\rm ox}$ | $\Delta\hbox{$\alpha_{\rm ox}$}$
---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
1 | 0.83$\pm$0.05 | 1.56$\pm$0.08 | $1.79\\!\pm\\!0.09$ | 15.77$\pm$0.06 | 30.98$\pm$0.02 | $-0.82\\!\pm\\!0.13$ | $-0.62\\!\pm\\!0.03$ | $-2.12\\!\pm\\!0.02$ | $-0.48$
2 | 0.51$\pm$0.04 | 1.86$\pm$0.09 | $2.39\\!\pm\\!0.12$ | 15.45$\pm$0.06 | 31.11$\pm$0.02 | $-2.31\\!\pm\\!0.16$ | $-1.15\\!\pm\\!0.03$ | $-2.38\\!\pm\\!0.08$ | $-0.73$
3 | 0.68$\pm$0.05 | 2.17$\pm$0.11 | $2.62\\!\pm\\!0.13$ | 15.35$\pm$0.05 | 31.15$\pm$0.02 | $-2.40\\!\pm\\!0.14$ | $-0.85\\!\pm\\!0.03$ | $-2.31\\!\pm\\!0.02$ | $-0.66$

Details about this table are provided in §2.3. Rest-frame Monochromatic fluxes
(Cols. 2–4) are obtained from continuum fits of dereddened spectra using the
Galactic extinction given by $E(B-V)=0.0904$ (from Schlegel et al., 1998) and
are in units of $10^{-26}$ erg cm-2 s-1Hz-1. Errors in monochromatic fluxes
are obtained by adding in quadrature the 1$\sigma$ errors associated with
continuum fits with the expected 5% errors associated with flux calibration
(Bostroem & Proffitt, 2011). Col. (1): Observation Epoch. Col. (2): Rest-frame
monochromatic flux at 950 Å. Col. (3): Rest-frame monochromatic flux at 2000
Å. Col. (4): Rest-frame monochromatic flux at 2500 Å. Col. (5): Rest-frame
Monochromatic AB magnitude at 2500 Å. Col. (6): Logarithm of monochromatic
luminosity at rest-frame wavelength 2500 Å. Col. (7): Power-law UV index at
the extreme-UV (EUV; $<1200$ Å). Col. (8): Power-law UV index at the far-UV
(FUV; $>1200$ Å). Col. (9): Galactic absorption corrected optical-to-X-ray
power-law slope $\hbox{$\alpha_{\rm ox}$}=0.384\,{\rm log}(f_{\rm
2keV}/f_{2500\textup{\AA}})$. No correction for intrinsic reddening or
absorption has been made. Col. (10): The difference between the measured
$\alpha_{\rm ox}$ value and the predicted $\alpha_{\rm ox}$ for radio quiet
quasars, based on the Just et al. (2007) relation: $\hbox{$\alpha_{\rm
ox}$}=-0.140\,{\rm log}L_{2500\textup{\AA}}+2.705$.

Figure 3: Logarithm of the observed flux in the _Chandra_ soft (0.5–2 keV),
hard (2–8 keV), and full (0.5–8 keV) bands in units of $10^{-14}$ erg cm-2 s-1
versus modified Julian date for each _Chandra_ observation of PG 2112+059. The
shaded area corresponds to the expected range of X-ray fluxes obtained
assuming a typical $\hbox{$\alpha_{\rm ox}$}=0.384\times{\rm log}[L_{\rm
2keV}/L_{2500}]$ (see Table 5 of Steffen et al., 2006) and a power-law
spectrum with $\Gamma=1.9$. The horizontal dotted line corresponds to the
best-fit brightest flux ever obtained (in 1999 with ASCA, MJD$=51481$). The
light gray, gray and black colors are associated with epochs 1, 2 and 3,
respectively.

##  3 Results

In this section, we test the significance of the variability of different
spectral (UV and X-ray) parameters between two epochs. In order to do this, we
calculate the $\chi^{2}$ statistic assuming that the data points are the
estimated parameter (with their respective 1$\sigma$ errors), and the model is
a constant obtained from the best fit. The $\chi^{2}$ value provides a
statistical test of the null hypothesis that the parameter value of each epoch
is equal to its best-fitted value. This model has one parameter to fit two
data points, thus the $\chi^{2}$ value follows a $\chi^{2}$-distribution with
one degree of freedom. From hereafter, we refer to a significant (marginal)
change of a parameter between two epochs, when the null hypothesis probability
is less than 0.01 (between 0.05 and 0.01). The soft X-ray fluxes (i.e., at
energies up to 2 keV) in Epoch 1 are significantly larger than those in the
other epochs (see Table 5). Additionally, when Epochs 2 and 3 are compared,
although soft X-ray fluxes do not show significant variation, the hard flux
presents a marked increase (see Figures 2–3 and Table 5). We also find
hardening in the X-ray spectra when Epoch 1 is compared with Epoch 3 with a
significant increase in the hardness-ratio (hereafter HR888Hardness ratio
defined as HR=(Hc-Sc)/(Hc+Sc); where Hc and Sc are the source counts in the
hard band (2–8 keV) and soft band (0.5–2 keV) respectively. In the values of
HR presented in Table 5, the counts have been corrected due to time-dependent
loss of _Chandra_ -_A_ CIS sensitivity by using the effective area of Epoch 3
as reference. ) as seen in Table 5. As compared to the X-rays, the UV continua
show only minor variations (see Figure 1 and Table 6), and thus, the
multiwavelength changes (measured by $\alpha_{\rm ox}$) between Epoch 1 and
the other epochs, are mainly the product of the significant variation in the
soft X-ray flux. Additionally, a significantly redder UV spectrum is observed
when Epoch 1 is compared with Epochs 2-3 (see $\alpha_{EUV}$ and
$\alpha_{FUV}$ in Table 6).

Figure 4: Normalized flux in the O vi BAL region. The light gray, gray and
black colors histograms are the STIS spectra observed in epochs 1, 2 and 3,
respectively. The lower curve correspond to errors at the 68% confidence
level. The three vertical dotted lines indicate line of sight outflow
velocities of $-21900$,$-13800$ and $-7500$ km s-1 around local minima
respectively. The dashed and dot-dashed curves correspond to blue-shifted
(blue-shift velocity of 16000 km s-1) partially covered ($C_{f}=0.8$)
absorption profiles obtained from cloudy runs with $\log U=-0.8$, turbulent
velocity 6500 km s-1 and column densities $\hbox{log~{}$N_{\rm H}$}=20.1$ and
$\hbox{log~{}$N_{\rm H}$}=20.5$ respectively. Figures 4–6 are obtained using
boxcar smoothing over 13 pixels for the G140L spectra and 7 pixels for the
G230L spectra.  Figure 5: Normalized flux in the Ly$\alpha$-N v BAL region
(see legend of Figure 4 for more details).  Figure 6: Normalized flux in the C
iv BAL region (see legend of Figure 4 for more details).

The observed BALs in the _HST_ spectra are mainly due to the O vi, N v, and C
iv line doublets, albeit there are other absorption lines as well that could
have secondary contributions in the observed BALs (see §4.1 for details).
Hereafter, unless otherwise stated, we assume that the zero velocity for each
ion is the absorbing line laboratory wavelength for the blue component of the
doublets given by Verner et al. (1994). These wavelengths are 1031.9 Å (O vi),
1238.8 Å (N v), and 1548.2 Å (C iv). Using the fitted model spectra
(continuum+ELs) described in §2.3 we obtain the normalized spectra around the
O vi, N v, and C iv BALs as shown in Figures 4–6 . In general, for all the
BALs observed, Epochs 2 and 3 show more conspicuous absorption than Epoch 1.
Additionally, the spectral differences are most pronounced when comparing
either Epoch 2 or 3 with Epoch 1. Epochs 2 and 3 show strong differences with
Epoch 1 that are concentrated at $\approx 960$ Å and $\approx 990$ Å for the O
vi BAL, at $\approx 1150$ Å and $\approx 1190$ Å for the N v BAL, and at
$\approx 1440$ Å and $\approx 1480$ Å for the C iv BAL. For every ion, when
Epoch 2 or 3 are compared with Epoch 1, the zones of variability are more
intense at velocities $\approx-22000\>\hbox{km~{}s${}^{-1}$}$ and
$\approx-13000\>\hbox{km~{}s${}^{-1}$}$. Epochs 2 and 3 show small differences
between each other that seem to be more marked at $\approx 990/1010$ Å
($\approx-12000/-7000\>\hbox{km~{}s${}^{-1}$}$), $\approx 1180$ Å
($\approx-14000\>\hbox{km~{}s${}^{-1}$}$) and $\approx 1460$ Å
($\approx-17000\>\hbox{km~{}s${}^{-1}$}$) for the O vi, N v, and C iv BALs,
respectively. The normalized spectra also show a reasonable level of
consistency when observed as a function of velocity. For example, the BALs in
Epoch 1 appear as relatively featureless profiles in the range of velocities
between $-25000$ to $-5000$ km s-1. On the other hand, the absorption profiles
of Epochs 2 and 3 seem to share similar distinguishable features centered at
speeds $\sim-22000$, $\sim-14000$ and $\sim-8000$ km s-1 respectively (see
vertical dotted lines in Figures 4–6). As a separate note, an _HST_ FOS
observation performed in 1992 shares qualitative spectral similarities with
Epochs 2 and 3. In this observation the UV spectral slope of PG 2112+059 was
redder, and the EWs of the BALs were greater when compared with Epoch 1 (see
Fig. 4 of Gallagher et al., 2004).

Table 7: Equivalent widths of UV BALs

| equivalent-widths | equivalent-width ratios
---|---|---
epoch | O vi | N v | C iv | ${\hbox{O {\sc vi}}}/{\hbox{C {\sc iv}}}$ | ${\hbox{N {\sc v}}}/{\hbox{C {\sc iv}}}$ | ${\hbox{N {\sc v}}}/{\hbox{O {\sc vi}}}$
(1) | (2) | (3) | (4) | (5) | (6) | (7)
1 | 10.5$\pm$1.1 | 16.6$\pm$1.4 | 12.9$\pm$1.2 | 0.81$\pm$0.11 | 1.28$\pm$0.16 | 1.57$\pm$0.21
2 | 17.6$\pm$0.9 | 27.8$\pm$1.0 | 29.0$\pm$1.4 | 0.61$\pm$0.04 | 0.96$\pm$0.06 | 1.58$\pm$0.10
3 | 19.7$\pm$0.9 | 27.3$\pm$1.1 | 30.0$\pm$1.1 | 0.66$\pm$0.04 | 0.91$\pm$0.05 | 1.39$\pm$0.09

Equivalent Widths (EW) and their errors are obtained from equations 2 and 3 of
§3 Col. (1): Observation Epoch. Cols. (2–4): Equivalent widths (in Å) of O vi,
N v and C iv BALs. Cols. (5–7): Equivalent width ratios.

The equivalent width (EW) of an absorption feature is defined as:

${\rm EW}=\int(1-f(\lambda))d\lambda,$ (1)

where $f(\lambda)$ is the normalized spectra. This is obtained by adding each
pixel contribution through (Kaspi et al., 2002):

${\rm EW}=\sum_{i}\left(1-\frac{F_{i}}{F_{C}}\right)B_{i},$ (2)

where $i$ runs through every pixel, $F_{i}$ is the flux in the $i$th pixel,
$B_{i}$ is the pixel width (in Å), and $F_{C}$ is the continuum flux.
Additionally the EW error is calculated by expanding the errors of the flux in
each pixel and the error of the continua, thus obtaining:

$\Delta{\rm EW}=\sqrt{\left(\frac{\Delta
F_{C}}{F_{C}}\sum_{i}\frac{B_{i}F_{i}}{F_{C}}\right)^{2}+\sum_{i}\left(\frac{B_{i}}{F_{C}}\Delta
F_{i}\right)^{2}}.$ (3)

For each of the three BAL features (i.e., O vi, N v, and C iv), valid pixels
for EW calculations are those in the range of blueshifted velocities of $3000$
to $25000$ km s-1, using as reference the wavelength of the O vi 1032, N v
1239, and C iv 1548 blue doublets, respectively. Since the Si iv BAL is not
observed, we obtain EW upper limits by multiplying by 2.3 the EW error (upper
limit at the $\approx 99$% confidence level), which is obtained assuming
$F_{i}=F_{C}$ in equation 3 and the wavelength of the blue doublet of the Si
iv 1394 as the reference. These EW upper limits are $\sim 4$ Å for every
observation.

For each epoch, the EWs and EW ratios of the observed BALs in the rest-frame
of PG 2112+059 are presented in Table 7. From this table, we infer that there
is no significant overall difference (within the errors) between the EWs
obtained in Epochs 2 and 3. However, Epoch 1 shows weaker EWs in every
observed BAL feature when compared either with Epochs 2 or 3 (see Table 7). We
do not find any significant change in the EWs ratios between epochs.

Table 8: Spectral properties of BAL features

|  O vi (1031.9 Å) |  N v (1238.8 Å) |  C iv (1548.2 Å)
---|---|---|---
epoch | $v_{\rm min}$ | $v_{\rm max}$ | $v_{\rm mean}$ | $BI$ | $v_{\rm min}$ | $v_{\rm max}$ | $v_{\rm mean}$ | $BI$ | $v_{\rm min}$ | $v_{\rm max}$ | $v_{\rm mean}$ | $BI$
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13)
1 | $-5222$ | $-23136$ |  $-14391$$\pm$2009 | 1594$\pm$242 | $-10094$ | $-24749$ |  $-16527$$\pm$1960 | 2136$\pm$199 | $-10595$ | $-23336$ |  $-16038$$\pm$1808 | 1046$\pm$105
2 | $-5326$ | $-25748$ |  $-16110$$\pm$996 | 3900$\pm$226 | $-6420$ | $-25039$ |  $-16952$$\pm$799 | 5414$\pm$154 | $-6381$ | $-25761$ |  $-16520$$\pm$958 | 4626$\pm$213
3 | $-5127$ | $-23908$ |  $-14974$$\pm$907 | 4472$\pm$210 | $-6199$ | $-24767$ |  $-16306$$\pm$844 | 5241$\pm$182 | $-6417$ | $-27129$ |  $-15951$$\pm$686 | 4688$\pm$173

The units of (2–13) are km s-1. Col. (1): Observation Epoch. Cols. (2–13):
$v_{\rm min}$, $v_{\rm max}$, $v_{\rm mean}$ and BI for O vi (Cols. 2–5), N v
(Cols. 6–9) and O vi (Cols. 10–13).

We obtain the balnicity index (hereafter BI) using the standard approach of
Weymann et al. (1991), i.e., through:

$BI=\int_{3000}^{25000}\left(1-\frac{f(-v)}{0.9}\right)Cdv,$ (4)

where $f(v)$ is the normalized spectrum at velocity $v$ in km s-1 in the rest
frame. The BIs starts to count from blueshifted velocities greater than 3000
km s-1 and $C$ is equal to zero unless the absorption depth in the normalized
spectrum is greater than 10% for an span of at least 2000 km s-1.999The values
of BI range from 0 (for non-BAL features) to 20000 km s-1. As in the case of
the EW, blueshifted velocities above 25000 km s-1do not count for the BI
calculations. The velocity ranges where we find BAL absorption are $v_{\rm
min}$ and $v_{\rm max}$, and we assume that this absorption is present when
the spectrum falls below 10% of the continuum level. For each ion, the
calculations of BI, $v_{\rm min}$, and $v_{\rm max}$ are obtained using boxcar
smoothing over 13 pixels for the G140L spectra and 7 pixels for the G230L
spectra (see Table 8). Since the BI index is a modification of the EW, we
properly modify equations 2 and 3 to obtain BIs with their errors. We also
calculate a mean velocity of each BAL given by

$\text{$v_{\rm mean}$}=-\frac{\displaystyle\
\int_{3000}^{25000}(1-f(-v))vdv}{\displaystyle\
\int_{3000}^{25000}(1-f(-v))dv},$ (5)

where $f(v)$ is the normalized spectrum. The calculations of $v_{\rm mean}$
with their error were obtained adding each pixel contribution in a similar
fashion as was done when obtaining the EWs. As shown in Table 8, the BIs show
similar tendencies as the EWs, and based on the C iv line, PG 2112+059 BIs
range between 1000–4700 km s-1. This range of BIs is consistent with a BI of
$\approx 2980$ km s-1obtained by Brandt et al. (2000) on a FOS/HST observation
of PG 2112+059 performed in 1992. Additionally, from Table 8, although some
variations of $v_{\rm min}$ and $v_{\rm max}$ are observed, these seem to be
associated with changes in the optical depth and not with dynamical variations
of the wind. This statement is confirmed by the mean velocity of the outflow
($v_{\rm mean}$), which does not show any significant variations either when
we compare between BAL features or observations (as seen in Table 8).

##  4 Analysis and Discussion

In this section, we analyze possble physical scenarios that could explain our
results. In §4.1 we introduce a photoionization model that attempts to
constrain basic physical properties of the UV outflow (e.g., the ionization
state and hydrogen column density) based on the ranges of the EW and EW ratios
presented in the last section. For this subsection, an optically thin BAL
medium fully covering the central source is assumed. In §4.2 we analyze an
extension §4.1 by incorporating the covering fraction in the modeling of the
UV wind. Finally, in §4.3 we discuss the possible connection between the
decrease in the soft X-ray emission and the increase in the BAL EWs found in
Epochs 1–3.

###  4.1 cloudy simulations

Under the assumption that the absorbing gas producing the BAL features
observed and analyzed in §3 have a common origin, we use cloudy (version
C17.vr; Ferland et al., 2017) to analyze the observed equivalent widths and
ratios found in Table 7. We perform cloudy simulations assuming a point source
AGN-type spectrum incident to an optically thin media. The spectral energy
distribution (SED) of the point source spectrum is the agn cloudy
model.101010For more details on the agn cloudy model see Korista et al.
(1997). The specific cloudy command used was AGN 5.5 -2.2 -0.5 0  in which 5.5
is the logarithm of the temperature of the big blue bump, $-2.2$ is
$\alpha_{\rm ox}$, $-0.5$ is the low energy slope of the big blue bump
$\alpha_{UV}$, and 0 is the X-ray slope $\alpha_{x}$ (where
$\alpha_{x}=-\Gamma+1$). These parameters have been chosen to approximately
fit the spectral energy distribution of past and current observations of the
X-ray and UV spectra of PG 2112+059 (see Fig. 7). The absorbing medium is
given by a layer with total hydrogen column density of $\hbox{${N}_{\rm
H}$}=10^{13}~{}\hbox{cm${}^{-2}$}$ fully covering the central source, with
solar abundances and a fixed hydrogen density of $n_{\rm
H}=10^{8}~{}\hbox{cm${}^{-3}$}$. The chosen value of $n_{\rm H}$ can be varied
by at least three orders of magnitude without producing any noticeable effect
on the results of our simulations (see e.g. Hamann, 1997). The value of
${N}_{\rm H}$ is chosen in order that the medium is “thin enough" so the most
prominent lines that could form BALs have optical depths $\tau_{0}$ in their
centers which are significantly less than unity.

The cloudy simulations have been performed varying the values on the
ionization parameter of the absorbing layer. The ionization parameter is the
ratio of hydrogen ionizing photon density to hydrogen density, i.e.:

$U=\frac{Q_{\rm H}}{4\pi r^{2}n_{\rm H}c},$ (6)

where $n_{H}$ is the total hydrogen density. $Q_{H}$ is the rate of hydrogen
ionizing photons emitted by the central object given by:

$Q_{\rm H}=\int_{\nu_{Ry}}^{\infty}\frac{L_{\nu}d\nu}{h\nu},$ (7)

where $\nu_{Ry}$ is the frequency for photons with energies of 1 Rydberg
($Ry$).111111Equation 7 shows that $Q_{\rm H}$ depends on the SED of the
central object above $1\,Ry$.

Figure 7: SED used for our cloudy simulations. For reference we plot
photometric data from: _XMM-Newton_ Optical Monitor (circles; from Schartel et
al., 2007), 2MASS/CTIO (squares; from Skrutskie et al., 2006), _GALEX_
(diamonds; from Bianchi et al., 2014), and our observations (with triangles
for Epoch 1 and inverted triangles obtained from the weighted mean X-ray and
UV fluxes from Epoch 2 and 3 in Tables 5 and 6).

In the optically thin regime for a fixed value of the ionization parameter and
metallicity, the equivalent-width of an absorption line associated to the ion
$j$ of column density $N_{j}$ should satisfy:

${\rm EW}\propto N_{j}\propto\hbox{${N}_{\rm H}$}.$ (8)

In particular, $N_{j}$ can be obtained through the following expression:

$N_{j}\approx\frac{m_{e}c^{2}}{\pi e^{2}f\lambda_{0}^{2}}{\rm EW},$ (9)

where $f$ is the oscillator strength and $\lambda_{0}$ is the laboratory
wavelength of an absorption line associated to the ion $j$. Additionally, for
Gaussian line profiles the optical depth at the line center of an absorption
line produced by an ion $j$ is:

$\tau_{0}\approx\frac{{\rm EW}\,c}{\sqrt{\pi}\,b\,\lambda_{0}},$ (10)

where $b=\sqrt{2kT/m_{j}}$ is the most probable thermal velocity. If we assume
that the BALs are the added contribution of blue-shifted optically thin
layers, our model can be properly scaled to represent the BAL medium. From the
curves presented in Figures 4–6, if we assume $C_{f}=1$ we confirm that the
BAL medium maximum optical depth is $\tau_{\lambda}(\rm max)\lesssim 0.5$, and
thus, we expect that our model can be used to estimate the ionization state
and column density of the ions that produce the BALs. By comparing these ion
column densities with those obtained in our cloudy runs (with log $N_{\rm
H}$=13), through equations 8 and 9, we can also extrapolate column densities
of other ions or elements that do not necessarily have observed spectral
signatures (for example ${N}_{\rm H}$). For partially covered outflows
($C_{f}<1$), which are commonly seen in BAL quasars (see e.g., Arav et al.,
1999; Dunn et al., 2012; Leighly et al., 2019), our model can be extended to
provide useful insights into the ionization and column densities of the wind
as described in §4.2.

Figure 8: Upper panel: Logarithm of line-center optical depths versus
logarithm of the ionization parameter. Middle panel: Logarithm of the
equivalent width versus logarithm of the ionization parameter. Lower panel:
Logarithm of the combined equivalent width (EW) versus logarithm of the
ionization parameter for line blending BAL regions. In the upper and middle
panels the lines marked correspond to the most prominent lines that are likely
found in the BALs of the HST/STIS spectra. In all the panels the dotted, dash-
dotted, dashed and full lines indicate lines belonging to the $\rm OVI_{b}$,
$\rm NV_{b}$, $\rm SiIV_{b}$ and $\rm CIV_{b}$ blends, respectively (see main
text for more details). In the lower panel in a whiter tone the combined EW of
the O vi 1032,1038 (dotted-line), N v 1239,1243 (dash-dotted) line doublets
are marked. This figure is generated through cloudy simulations of a point
source AGN spectrum incident on an optically thin layer with a column density
of $10^{13}\,\hbox{cm${}^{-2}$}$. Figure 9:  Logarithm of the equivalent width
ratios of two line blends versus logarithm of the ionization parameter. Upper
panel: The dotted, dash-dotted, and full lines indicate the $\rm
OVI_{b}/CIV_{b}$, $\rm NV_{b}/CIV_{b}$, and $\rm NV_{b}/OVI_{b}$ EWs ratios,
respectively. The red, green and blue horizontal bands represent the observed
ranges of (in all Epochs) $\rm OVI_{b}/CIV_{b}$, $\rm NV_{b}/CIV_{b}$, and
$\rm NV_{b}/OVI_{b}$ ratios (from Table 7). Lower panel: the dotted, dash-
dotted, and full lines indicate the $\rm SiIV_{b}/OVI_{b}$, $\rm
SiIV_{b}/NV_{b}$, and $\rm SiIV_{b}/CIV_{b}$ EWs ratios respectively. The red,
green and blue downward arrows mark the maximum $\rm SiVb/OVI_{b}$, $\rm
SiVb/NV_{b}$ and $\rm SiVb/CIV_{b}$ EW ratio upper limits in our observations.
Both panels are generated through cloudy simulations of a point source AGN
spectrum incident on an optically thin layer with a column density of
$10^{13}\hbox{cm${}^{-2}$}$. The vertical dotted-line band marks the expected
$\log U$ range of the BAL medium (see §4.1).

The absorption lines that we analyze are those that have significant
signatures in the wavelength range of the _HST_ /STIS spectrum. Additionally,
these lines must cover the ionization states where the C iv lines are
significant. The most important of these lines are the O vi 1032,1038, N v
1239,1243, Si iv 1394,1403 and C iv 1548,1551 doublets. There are other lines
that should have signatures in the spectral and ionization ranges of
consideration; these are the Ly$\alpha$ 1216, Ly$\beta$ 1026, and the Si iii
1207 lines. Given the wavelengths of these lines, we likely expect to find
four blended sets of lines that could form BALs in our observations. The
first, identified as the $\rm OVI_{b}$ blend is produced by the Ly$\beta$ line
and the O vi doublet. The second blend, identified as the $\rm NV_{b}$ blend
is produced by the Ly$\alpha$, Si iii lines and the N v doublet. Finally, the
third and fourth, identified as the $\rm SiIV_{b}$ and $\rm CIV_{b}$ blends
are produced by the Si iv and C iv doublets, respectively.

In Figure 8 we show the optical depth at the line center $\tau_{0}$ (upper
panel) and EW (middle panel) as a function of ionization parameter for the
blue line of the O vi, Si iv, N v and C iv doublet with the Ly$\alpha$,
Ly$\beta$, and the Si iii lines. In the lower panel of Figure 8 we show the
logarithm of the added EWs of each line blend. To differentiate between line
blends, in Figure 8 each line in a particular blend is marked with a
distinctive line style. The upper panel of this figure shows that all the
lines have values of $\tau_{0}$ well below unity, thus confirming the fact
that we are analyzing optically thin lines. For our set of parameters, Figure
8 indicates the ionization ranges where each line is contributing to
potentially form a BAL. As we see in §3, our observations show prominent C iv
BAL signatures with no evidence of Si iv BAL features. Thus, if the BALs are
produced by a medium with a narrow range of ionization states, we expect that
$\log U\gtrsim-1$. Additionally, we expect that $\log U\lesssim 1$ in order to
be able to observe a significant C iv BAL or N v BAL as compared to the O vi
BAL . Therefore, in general we expect an outflow with $-1\lesssim\log
U\lesssim 1$, although a more refined ionization parameter range is obtained
from analyzing the EW ratios as described in the following paragraphs. In this
ionization parameter range a comparison of the middle and lower panels in
Figure 8 confirms that the most prominent lines producing BALs in our
observations are the blue components of C iv, O vi and N v doublets.

In Figure 9 the logarithms of the EW ratios of two different line blends as a
function of $U$ are shown. The curves in the upper panel of Figure 9
correspond to ratios between the EWs of blends that could produce the observed
BALs (i.e., OVIb, NVb, and CIVb blends). Additionally, the curves in the lower
panel correspond to ratios between the EWs of the SiIVb blend and the OVIb,
NVb, and CIVb blends, respectively. In the upper panel of Figure 9 we have
marked horizontal bands that correspond to the maximum and minimum EW ratios
obtained from Table 7. A simple observation of these bands indicates that
there is no particular value of the ionization parameter that produces all the
observed ratios in Table 7. Additionally, the upper panel of Figure 9 shows
that the observed values of the $\rm NV_{b}$/$\rm CIV_{b}$ EW ratios are below
the full-line curve. Thus, the discrepancies between our model and the
observed EW ratios might be due to unknown complexity of the outflow, like
variations from solar abundances of Oxygen, Nitrogen and Carbon and/or
gradients in the ionization state through the outflow. There could also be
discrepancies due to the assumption of optical thinness of our model, although
we expect these should not be important as described in §4.2.

The fact that the observed NVb/CIVb EW ratios are lower than expected from our
model might be attributed to subsolar N/C abundance ratios as observed in
quasar HE 0141–3932 (Reimers et al., 2005). Since we cannot observe individual
lines in the outflow and thus cannot estimate the relative abundances of O, N
and C, in order to estimate a range for the ionization parameter of the wind,
we add an error of 0.3 dex in the logarithm of the observed EW ratios. This
error is close to what is expected from the dispersion of relative abundances
of O, N and C in extragalactic H ii regions at nearly solar metallicities
(e.g., Esteban et al., 2009; Berg et al., 2016). Based on the expanded error
bands in the EW ratios, we obtain from the curves in Figure 9 that
$-1.2\lesssim\log U\lesssim-0.7$, $-1.8\lesssim\log U\lesssim-0.2$, and
$-1.1\lesssim\log U\lesssim-0.5$ from the O vi/C iv, N v/C iv and N v/O vi
ratios, respectively. Additionally, by comparing the observed Si iv ratios
upper limits with the curves in the lower panel of Figure 9, we obtain $\log
U\gtrsim-1.1$, and thus, we expect a range of the ionization outflow parameter
$-1.1\lesssim\log U\lesssim-0.7$. Assuming that the ionization parameter is
uniformly distributed in $[-1.1,-0.7]$ , and using the tables generated by our
cloudy simulations, we obtain logarithms of relative abundance ratios with
respect to hydrogen of $-4.21\pm 0.14$, $-4.40\pm 0.05$, $-4.51\pm 0.12$ for O
vi, N v and C iv respectively. From equations 8 and 9, the abundance ratios
obtained can be used to estimate (from the O vi, N v, and C iv ion column
densities) the BALs hydrogen column densities.

Using the observed EW of each BAL in Table 7 we obtain an approximation of the
column densities of the O vi, N v, and C iv ions through equation 9. For this
we assume that the EW of each observed BAL is produced by the added EWs of the
O vi, N v, and C iv doublets respectively.121212For a line doublet the ion
column density $N_{j}$ can be obtained from:
$N_{j}\approx\frac{m_{e}c^{2}}{\pi
e^{2}(f_{b}\lambda_{b}^{2}+f_{r}\lambda_{r}^{2})}{\rm EW},$ where $b$ and $r$
stands for parameters of the blue and red doublet respectively.  Additionally,
from the estimated relative abundances of ions with respect to hydrogen we
estimate ${N}_{\rm H}$ column densities from each ion, which are shown in
Table 9. As this table indicates, the medium that produces the BALs has
$\hbox{log~{}$N_{\rm H}$}\sim 20$ in Epoch 1 and its column density increases
by $\approx 0.3$ dex from Epoch 1 to Epochs 2-3.

Table 9: Observed column densities of UV BALs

| logarithm of ion column densities | logarithm of h column densities
---|---|---
epoch | O vi | N v | C iv | O vi | N v | C iv
(1) | (2) | (3) | (4) | (5) | (6) | (7)
1 | 15.75$\pm$0.04 | 15.72$\pm$0.04 | 15.33$\pm$0.04 | 19.96$\pm$0.15 | 20.11$\pm$0.06 | 19.84$\pm$0.13
2 | 15.97$\pm$0.02 | 15.94$\pm$0.01 | 15.68$\pm$0.02 | 20.19$\pm$0.14 | 20.34$\pm$0.05 | 20.20$\pm$0.12
3 | 16.02$\pm$0.02 | 15.93$\pm$0.02 | 15.69$\pm$0.01 | 20.23$\pm$0.14 | 20.33$\pm$0.05 | 20.21$\pm$0.12

Col. (1): Observation Epoch. Cols. (2–4): Logarithm of ion column densities
(in cm-2) obtained using equation 9 from the equivalent widths (EWs) of the O
vi, N v and C iv BALs. Cols. (5–7): Logarithm of hydrogen column densities as
obtained from columns (2–4) and the ion abundances ratios with respect to
hydrogen estimated by our thin layer cloudy model (as described in §4.1).

Equation 6 can be used to obtain $r_{UV}$, the distance from a central
emitting source to the observed UV BAL wind. In view of our observations, we
assume that $-1.1\lesssim\log U\lesssim-0.7$ and $Q_{H}=5.6\times
10^{56}~{}{\rm s}^{-1}$ from the SED obtained in Figure 7. Additionally, based
on observations of BALs, mini-BALs and NALs, the electron density of the
outflow $n_{e}$ should lie between $3\lesssim\log n_{e}\lesssim 10$ (e.g., de
Kool et al., 2001; Hamann et al., 2011; Misawa et al., 2016; Xu et al., 2019),
with $n_{\rm H}\approx n_{e}$.131313Assuming that the BALs have solar
metallicities and totally ionized $n_{e}\approx 1.2\,\hbox{$n_{\rm H}$}$.
Based on these assumptions $r_{UV}$ is within $[10^{3}-10^{7}]R_{S}$
($[0.1-1000]~{}{\rm pc}$), where $R_{S}$ is obtained assuming a black hole
mass of $M_{\rm BH}\approx 10^{9}M_{\odot}$ (Vestergaard & Peterson, 2006).

###  4.2 Optical Depth Fits

In this section, we estimate the BAL ion column densities by performing fits
on the optical depths. This is done in order to analyze outflows that are not
necessarily optically thin nor are totally covering the central source. The
fits are performed by first transforming the normalized spectra to an optical
depth profile as a function of wavelength ($\tau_{\lambda}$). The optical
depth BAL profiles, assumed to be produced by the O vi, N v, and C iv line
doublets (as in §4.1), are deblended using the methodology described in
Junkkarinen et al. (1983). Using this approach the $\tau_{\lambda}$ profile is
transformed to a single line with an oscillator strength of
$f_{*}=f_{b}+f_{r}$ and a laboratory wavelength given by
$\lambda_{*}=(f_{b}\lambda_{b}+f_{r}\lambda_{r})/(f_{b}+f_{r})$, where $f_{b}$
($f_{r}$) is the oscillator strengths of the blue (red) doublet and
$\lambda_{b}$ ($\lambda_{r}$) is the laboratory wavelengths of the blue (red)
doublet. Once deblended, each BAL profile is fitted as function of velocity
using Gaussian profiles i.e.,

$\tau_{v}=\tau_{0}\exp(-((v-v_{0})/b)^{2}),$ (11)

where $\tau_{0}$ is an estimation of the maximum optical depth of the profile.
The ion column density of a single line absorption profile can be obtained
from the optical depth velocity profile through the following expression:

$N_{j}=\frac{m_{e}c}{\pi e^{2}f_{*}\lambda_{*}}\int\tau_{v}\,dv,$ (12)

where $\int\tau_{v}\,dv=\sqrt{\pi}\,\tau_{0}\,b$ for a Gaussian profile.
Therefore, using equation 12 we show in Table 10 the column densities of the O
vi, N v and C iv ions using Gaussian fits on the optical depth profiles of
each observation. Additionally, in Table 10, we show the estimated hydrogen
column densities using the relative ion abundance ratios with respect to the
hydrogen obtained in §4.1. For $C_{f}=1$, the results in Table 10 (as
expected) are very similar to those of Table 9. For $C_{f}<1$, which is the
case of an absorber partially covering the emitting source, the observed and
true optical depths of an absorption line are obtained from:

$\exp(-\tau_{\lambda}^{\rm obs})=(1-C_{f})+C_{f}\exp(-\tau_{\lambda}^{\rm
true}).$ (13)

Since $\tau_{\lambda}^{\rm true}$ grows monotonically with column density, in
absence of constraints on the column density, the assumption of $C_{f}=1$
results in column densities that are lower limits. In Table 10 we have
performed again Gaussian fits to the deblended ionic profiles but now with
$C_{f}=0.8$ and 0.6. The case of $C_{f}=0.6$ is a rough estimate of the
minimum value expected from Epochs 2 and 3.141414It is expected that
$C_{f}\geq 1-f_{\rm min}$ were $f_{\rm min}$ is the minimum normalized
residual flux from an absorption trough (e.g., Crenshaw et al., 2003). From
Table 10, as expected, the column densities and maximum optical depths
($\tau_{0}$) vary approximately inversely proportional with $C_{f}$.
Additionally, from this table, we conclude that for a given BAL profile if
$C_{f}$ is close to its expected minimum then $\tau_{0}\gtrsim 1$. For this
particular case, i.e. of saturated line profiles, our model might not give
reliable estimates of $U$ and/or ${N}_{\rm H}$.

The approach used to describe the UV BAL winds in §4.1 and this section is
mainly based on constraining the medium ionization parameter and describing
ion column densities of each BAL. This methodology, although simple should
give us reliable constraints on the expected column densities and the
ionization state of the wind. To clarify this better, we generate two cloudy
runs motivated by the optical depth Gaussian fits in the case of $C_{f}=0.8$.
Both runs are from a layer with solar abundance, with ionization parameter at
the illuminated face $\log U=-0.8$, and turbulent velocity $v_{\rm
turb}=6500~{}\hbox{km~{}s${}^{-1}$}$. The difference in the runs are the
chosen values of column densities which are $\hbox{log~{}$N_{\rm H}$}=20.1$
and $\hbox{log~{}$N_{\rm H}$}=20.5$ respectively. The chosen value of $U$ is
within the expected for the UV BAL medium, $v_{\rm turb}$ is close to the
average value of the estimated velocity dispersions of the Gaussian fits ($b$
parameter in equation 11), and the values of log $N_{\rm H}$ are close to the
average values estimated for Epoch 1 and Epochs 2-3 (for $C_{f}=0.8$ in Table
10). The absorption spectra from these cloudy runs are then corrected for
partial covering (using equation 13 with $C_{f}=0.8$) and blue-shifted with a
blue-shifted velocity of 16000 km s-1. This velocity is close to the average
Gaussian central velocities ($v_{o}$ in equation 11) obtained from the fits.
The resulting absorption profiles are shown in Figures 4–6. By comparing these
curves with the observed profiles, and given the simplicity of our model
assumptions, we find a good agreement with the observations. Note that similar
absorption profiles to those presented in Figures 4–6 can be obtained for the
case of $C_{f}=0$ and $C_{f}=0.6$. The use of more sophisticated
photoionization models (e.g., Leighly et al., 2018, 2019) requires a clearer
definition of the continuum at rest-frame wavelengths $\lesssim 1200$ Å, and
additional evidence of spectral features (not found in this work) that could
provide tighter constraints in the covering fraction and/or the chemical
abundance of the BALs medium.

Table 10: Column densities and maximum optical depths from deblended Gaussian
fits to BAL optical depth profiles

| logarithm of ion column densities | logarithm of h column densities | Fitted values of $\tau_{0}$
---|---|---|---
epoch | O vi | N v | C iv | O vi | N v | C iv | O vi | N v | C iv
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
| covering fraction Cf= 1.00
1 | 15.83$\pm$0.04 | 15.72$\pm$0.04 | 15.38$\pm$0.02 | 20.04$\pm$0.15 | 20.12$\pm$0.06 | 19.89$\pm$0.12 | 0.23$\pm$0.01 | 0.32$\pm$0.02 | 0.24$\pm$0.01
2 | 16.11$\pm$0.05 | 16.02$\pm$0.03 | 15.79$\pm$0.03 | 20.32$\pm$0.15 | 20.42$\pm$0.06 | 20.30$\pm$0.12 | 0.38$\pm$0.02 | 0.62$\pm$0.03 | 0.56$\pm$0.02
3 | 16.12$\pm$0.04 | 16.00$\pm$0.03 | 15.81$\pm$0.03 | 20.33$\pm$0.15 | 20.40$\pm$0.06 | 20.32$\pm$0.12 | 0.46$\pm$0.03 | 0.61$\pm$0.03 | 0.53$\pm$0.02
| covering fraction Cf= 0.80
1 | 15.93$\pm$0.05 | 15.84$\pm$0.04 | 15.49$\pm$0.02 | 20.14$\pm$0.15 | 20.24$\pm$0.07 | 20.00$\pm$0.12 | 0.30$\pm$0.02 | 0.42$\pm$0.03 | 0.31$\pm$0.01
2 | 16.23$\pm$0.05 | 16.15$\pm$0.03 | 15.92$\pm$0.03 | 20.44$\pm$0.15 | 20.55$\pm$0.06 | 20.43$\pm$0.12 | 0.51$\pm$0.03 | 0.85$\pm$0.05 | 0.76$\pm$0.03
3 | 16.24$\pm$0.05 | 16.14$\pm$0.03 | 15.93$\pm$0.03 | 20.45$\pm$0.15 | 20.54$\pm$0.06 | 20.44$\pm$0.12 | 0.62$\pm$0.04 | 0.84$\pm$0.05 | 0.72$\pm$0.03
| covering fraction Cf= 0.60
1 | 16.08$\pm$0.05 | 15.99$\pm$0.04 | 15.63$\pm$0.02 | 20.29$\pm$0.15 | 20.39$\pm$0.07 | 20.14$\pm$0.12 | 0.42$\pm$0.03 | 0.61$\pm$0.04 | 0.44$\pm$0.01
2 | 16.40$\pm$0.06 | 16.37$\pm$0.04 | 16.10$\pm$0.03 | 20.61$\pm$0.15 | 20.77$\pm$0.07 | 20.61$\pm$0.12 | 0.77$\pm$0.05 | 1.43$\pm$0.10 | 1.22$\pm$0.05
3 | 16.42$\pm$0.05 | 16.35$\pm$0.04 | 16.12$\pm$0.03 | 20.63$\pm$0.15 | 20.75$\pm$0.07 | 20.63$\pm$0.12 | 0.99$\pm$0.07 | 1.44$\pm$0.11 | 1.20$\pm$0.07

Col. (1): Observation Epoch. Cols. (2–4): Logarithm of ion column densities
(in cm-2) obtained using equation 12 on optical dephs obtained through
Gaussian fits of the deblended optical depth profiles of the O vi, N v and C
iv BALs. Cols. (5–7): Logarithm of hydrogen column densities as obtained from
columns (2–4) and the ion abundances ratios with respect to hydrogen as
described in §4.1. Cols. (8–10) maximum optical depth from Gaussian fits of
the deblended optical depth profiles of the O vi, N v and C iv BALs.

###  4.3 Is there a Connection between variability of the BALs and the X-rays?

With a limited sample of observations, we are not able to establish any
conclusive argument regarding an X-ray wind connection in PG 2112+059.
However, our analysis has revealed some trends that could shed light on what
to expect for future observations. The most relevant tendency shown in our
observations is that a weakening in the soft X-ray flux could be associated
with an increase of the EW of the BALs (see Figures 3–6). The mean velocities
of the BALs did not change significantly in our observations; thus, we do not
find evidence that the X-rays are connected with the acceleration mechanism of
the UV wind.

If the BALs are produced from an optically thin medium, fully covering the
central source, the increase in the EW could be due to a growth in the column
density of the wind, which doubled between Epoch 1 and Epochs 2-3 (as seen in
§4.1 and §4.2). Therefore, a weakening in the X-rays could be associated with
a more massive outflow. In the case of a partially covered outflow, the EW
increase of the BALs might be also linked to a growth in the covering fraction
of the wind. As noted in §3 the increase in EW of the BALs is also associated
with a redder UV spectra as measured by $\alpha_{EUV}$ and $\alpha_{FUV}$ (see
Table 6). This change of the UV spectra may be related to a decrease of the
wind inclination with respect to the line of sight (Baskin et al., 2013). A
redder UV spectrum might also be a consequence of an increase in the column
density (mass) of the outflow. The combined effect of a more massive and/or
less inclined wind might produce an increase in the covering fraction and/or
the column density. Note that if the UV wind is partially covering the central
source, then the BAL column densities of $\hbox{log~{}$N_{\rm H}$}\sim 20$
obtained in §4.1 are interpreted as lower limits (see Table 10).

Epoch 2 corresponds to the weakest state ever recorded in X-rays. The
variability in the X-rays between Epoch 1 and Epoch 2-3 could be interpreted
as an increase in the column density of the shield (see Table 4).
Unfortunatelly, our new X-ray observations have low S/N, and thus, they are
not sufficient to give any conclusive statement. From Saez et al. (2012), when
comparing past X-ray observations of PG 2112+059, Epoch 1 is close to average
X-ray brightness. Additionally, in the _ASCA_ observation performed in 1999
(hereafter identified as Epoch 0; Gallagher et al., 2001), which corresponds
to the brightest X-ray observation registered, the 0.5–2 keV X-ray flux is
approximately 10 times greater than that of Epoch 1 (see Figure 3). For the
brightest X-ray observation, a simple absorbed power law model with
$\hbox{log~{}$N_{\rm H}$}\sim 22$ gives a plausible fit to the data (Gallagher
et al., 2001; Saez et al., 2012). In conclusion, a shielding layer with a
varying log $N_{\rm H}$ from $\sim\,22.0$ to $\sim\,23.0$ might at least
explain in part the strong X-ray variability that this source has. The premise
of a shield layer with varying column density is also reinforced by the
observed values of the 2 keV rest-frame monochromatic fluxes of PG 2112+059.
To demonstrate this, we assume that the intrinsic (unabsorbed) monochromatic
flux at 2 keV is $f_{\rm 2keV}\approx 11\times
10^{-31}\hbox{erg~{}cm${}^{-2}$~{}s${}^{-1}$}$, which is obtained assuming
that the 2500 Å luminosity is given by the weighted average of Epochs 1–3 and
the 2 keV luminosity is from equation 3 of Just et al. (2007). We further
assume that every X-ray observation is a product of an APL model with a
varying column density and a fixed photon index ($\Gamma=1.9$). Therefore,
with $f_{\rm 2keV}\approx 8\times
10^{-31}\hbox{erg~{}cm${}^{-2}$~{}s${}^{-1}$}$ for the brightest X-ray
observation (Epoch 0; see Table 9 from Saez et al., 2012), and the
monochromatic 2 keV rest-frame fluxes in Table 5, we estimate
$\hbox{log~{}$N_{\rm H}$}\approx 22.0$, 22.8 and 22.9 for Epoch 0, Epoch 1 and
Epoch 2-3, respectively. As described in §2.2, we expect the X-ray absorption
of PG 2112+059 is more complex than that obtained from an APL model. However,
under the assumption that the intrinsic X-ray emission does not vary
significantly, the APL model should provide good approximations to the column
densities that produce the observed changes in soft X-ray emission.

In the wind-shield scenario (Murray et al., 1995; Gallagher & Everett, 2007),
the UV wind is attributed to the outermost portions of the wind while the
X-ray shield to the innermost zones of the wind. As stated in §4.1, the UV
wind should be at distances from the central source of $r_{\rm UV}\gtrsim
1000R_{S}$. Given the X-ray variability found between Epochs 2 and 3 of
$\sim\\!5$ months in the rest-frame, and assuming a dynamic shield, a coherent
light crossing time argument gives a distance to the central source of $r_{\rm
X}\lesssim 1000R_{S}$ (where $M_{\rm BH}\approx 10^{9}M_{\odot}$ is assumed;
Vestergaard & Peterson, 2006). Thus, we expect that the absorption in X-rays
is produced by a different medium than that producing the UV BAL features.
Based on other observations of BAL quasars, we might expect X-ray variability
associated to shield signatures on time scales shorter than 5 months in the
rest-frame (e.g., Chartas et al., 2009; Reeves et al., 2020). Under a wind-
shield scenario interpretation, a change in the inclination and/or mass of the
wind could produce an increment in the column density and/or the covering
fraction. Associated to these changes, we also expect a nearly contemporaneous
effect in the inner zone of the wind, as observed with a likely increase in
the column density of the shield after Epoch 1. In our observations, we do not
detect significant changes in the EW ratios of the observed BALs, and thus, we
cannot establish if the increase in EWs is associated with changes in the
ionization state of the wind. If we assume a shielded wind-scenario in an
observation where the X-ray emission flux rises to a close to brightest state,
we likely expect less massive winds and changes in the incident SED that could
indicate variation in the ionization state of the wind (i.e., variability in
the EW ratios).

Based on this analysis, it would be fundamental to perform a multi-wavelength
monitoring campaign of this source to confirm or reject the trends found in
this work. At this time, it is not possible to elucidate if a complex
absorption or simply an intermittent X-ray source is producing the strong
variability that this source shows. This dilemma might be resolved with long
exposure _NuSTAR_ observations, in order to further constrain the model
associated with the fast and dramatic X-ray variability of PG 2112+059. As
described in this work, albeit our results are preliminary, a shielded wind
model seems to give a plausible explanation to our _HST_ /_Chandra_ spectra.

##  5 Summary and Conclusions

In this work, we analyze three sets of _Chandra_ observations each with a
contemporaneous _HST_ STIS spectra (Epochs 1–3) of PG 2112+059. Epoch 1 was
performed in 2002, while Epochs 2 and 3 were performed in 2014–2015 and
separated by approximately nine months. Our main conclusions are the
following:

  1. 1.

There is significant X-ray spectral hardening between Epoch 1 and Epoch 3. The
soft X-ray flux ($\lesssim\\!2$ keV) does not change significantly between
Epochs 2 and 3. Additionally, the 0.5–2 keV flux is reduced by approximately
one third when Epoch 1 is compared either with Epoch 2 or Epoch 3.

  2. 2.

The _HST_ UV spectra exhibit BAL features that are likely associated with the
O vi 1032,1038, N v 1239,1243, and C iv 1548,1551 doublets. These
observations, in general show that Epoch 1 is significantly distinct from
either Epoch 2 or Epoch 3. Additionally, Epoch 3 has only minor changes in
relation to Epoch 2. When Epoch 1 is compared with Epochs 2-3, the EWs of the
BALs are found to increase and the UV spectral slope becomes redder.

  3. 3.

Under the assumption that BALs are produced by an optically thin medium fully
covering the source, we estimate hydrogen column densities of $\sim
10^{20}\hbox{cm${}^{-2}$}$ for Epoch 1 that increase by a factor of
approximately two for Epoch 2-3. If the medium is partially covered
($C_{f}<1$), the outflow column densities obtained assuming $C_{f}=1$ become
lower limits and the covering fraction might be also contributing to the
changes of EWs. In conclusion, the increasing EWs can be explained by an
increase in column densities and/or covering fractions. These changes
accompanied by a redder UV spectrum might be indicating a decrease in the
inclination of the outflow along the line of sight and/or an increase in the
wind mass. The EW ratios of the C iv, N v, and O vi BALs do not change
significantly between observation Epochs, implying that the BALs medium
ionization parameter is stable.

  4. 4.

The decrease in the soft ($\lesssim 2$ keV) X-ray flux, that is produced
between Epoch 1 and Epoch 2-3, is possibly associated with an increase in the
absorption of the shield. This growth is close to contemporaneous with
increments of the BALs EWs.

The analysis of the X-ray/UV spectra of PG 2112+059, provide support for the
wind-shield scenario model of BAL winds. A future multiwavelength long-term
monitoring campaign of this source in combination with a more sophisticated UV
spectral analysis (e.g., with SimBAL; Leighly et al., 2018) would be of
interest to confirm or reject the conclusions obtained here.

##  6 Acknowledgements

Support for this work was provided by the National Aeronautics and Space
Administration through Chandra Award Number GO5-16119X issued by the Chandra
X-ray Observatory Center, which is operated by the Smithsonian Astrophysical
Observatory for and on behalf of the National Aeronautics Space Administration
under contract NAS8-03060. Support for Program number HST-GO-13948.001-A was
provided by NASA through a grant from the Space Telescope Science Institute,
which is operated by the Association of Universities for Research in
Astronomy, Incorporated, under NASA contract NAS5-26555. We acknowledge
support from ANID grants CATA-Basal AFB-170002 (FEB), FONDECYT Regular 1190818
(FEB), 1200495 (FEB) and Millennium Science Initiative Program - ICN12_009
(FEB). This work was partially supported by JSPS KAKENHI Grant Number
21H01126. SCG acknowledges support from the Natural Science and Engineering
Research Council of Canada.

##  7 Data Availability

The scientific results reported in this article are based on publicly
available observations made by the Chandra X-ray Observatory and the Hubble
Space Telescope (_HST_). The list of _Chandra_ observations IDs (ObsIDs) are:
3011, 17148, and 17553.151515Downloadable from https://cxc.harvard.edu/cda/
Additionally, the _HST_ observations are from Proposal IDs 13948 and
9277.161616Downloadable from: https://archive.stsci.edu/

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