HST/COS Observations of Quasar Outflows in the 500–1050 Å Rest Frame. II. The Most Energetic Quasar Outflow Measured to Date

We model the unabsorbed emission of the two different epochs separately following the approach of Chamberlain & Arav (2015), Miller et al. (2018), and Xu et al. (2018). The models include two components: (1) a continuum that is represented by a power law, and (2) strong emission lines, such as O v and Ne viii, which are fitted with one or more Gaussian profiles. The adopted emission model for the 2017 epoch is shown as the solid red line in Figure 1.

The COS EUV500 spectrum of SDSS J1042+1646 shows a variety of absorption features due to the interstellar medium (ISM) within our galaxy, intervening Lyα forest systems, and quasar outflow absorption features at different velocities. We identify five kinematically distinct outflow systems (S1–S4, where S1 has two components: S1a and S1b, see Table 2). The full, dereddened spectrum is shown in Figure 1. For the 2017 epoch, we marked the strong absorption lines related to these five outflow systems with colored dashed lines (system 1a and 1b are merged for simplicity, see Section 4.1).

The main method to analyze AGN outflows involves the following steps: (1) identifying outflow systems at distinct velocities; (2) measuring ionic column densities (N_ion) of their absorption troughs using three standard methods, i.e., apparent optical Depth (AOD), partial covering (PC), and power law (PL); and (3) comparing these N_ion with the predictions from photoionization models to determine the physical properties for each outflow (e.g., Arav et al. 2001, 2012, 2018; Hamann et al. 2001; Borguet et al. 2012a, 2013; Chamberlain & Arav 2015; Xu et al. 2019). The AOD method assumes that at every velocity, the outflow completely and homogeneously covers the emission source (see, e.g., Savage & Sembach 1991). The PC method assumes a constant optical depth over a fraction of the emission source for every velocity (see, e.g., Edmonds et al. 2011). The PL method assumes the outflow at each velocity completely covers the emission source but has a varying optical depth across the source in the form of a power law (see, e.g., Arav et al. 2005).

For most of the previous works, the diagnostic absorption lines were within the λ_rest > 1050 Å. The above method works well in this range since there is a relatively small number of absorption troughs (mainly Lyα, C iv, N v, Si iv, in rare cases P v, and S iv). Blending of these absorption troughs between different outflow systems is minimal to moderate in most of the cases.

This analysis method is inadequate for the EUV500 band since the EUV500 band includes outflow troughs from ∼70 individual transitions. The atomic properties for these detected transitions are shown in Table 3 and the ionic transitions observed in SDSS J1042+1646 are marked in red. With more troughs and multiple outflow systems, trough blending is more severe than in the λ_rest > 1050 Å range, especially when the absorption troughs are wide (e.g., see the panel 2 in Figure 1). Therefore, it is difficult to measure N_ion directly for most of the observed troughs in the EUV500. Similarly, it is impractical to measure upper limits for all possible transitions (∼850 are within the wavelength range covered in that data alone).

Table 3.  Atomic Data for Observed Transitions in EUV500 Range

Iona	$\lambda$ b	Elowc	fd	IPe	log(${n}_{{\rm{e}},\mathrm{crit}}$)f
	(Å)	(cm−1)		(eV)	log(cm−3)
H i	937.803	0.00	0.008	13.60	⋯
H i	949.743	0.00	0.014	13.60	⋯
H ig	972.537	0.00	0.029	13.60	⋯
H i	1025.72	0.00	0.079	13.60	⋯
C iii	977.020	0.00	0.759	47.89	⋯
N iii	684.998	0.00	0.135	47.45	⋯
N iii	685.515	0.00	0.270	47.45	⋯
N iii*	685.817	174.4	0.320	47.45	3.3
N iii*	686.336	174.4	0.069	47.45	3.3
N iii	763.334	0.00	0.084	47.45	⋯
N iii*	764.351	174.4	0.081	47.45	3.3
N iii	989.799	0.00	0.123	47.45	⋯
N iii*	991.511	174.4	0.122	47.45	3.3
N iv	765.147	0.00	0.611	77.47	⋯
O iii*	599.590	20273.27	0.292	77.47	5.9
O iii	702.337	0.00	0.134	54.93	⋯
O iii*	702.900	113.2	0.135	54.93	3.1
O iii*	703.854	306.2	0.136	54.93	3.7
O iii	832.929	0.00	0.106	54.93	⋯
O iii*	833.749	113.2	0.106	54.93	3.1
O iii*	835.289	306.2	0.104	54.93	3.7
O iv	608.397	0.00	0.067	77.41	⋯
O iv*	609.829	385.9	0.067	77.41	4.1
O iv	787.710	0.00	0.111	77.41	⋯
O iv*	790.199	385.9	0.110	77.41	4.1
O v	629.732	0.00	0.512	113.90	⋯
O v* J = 1	758.677	82078.6	0.080	113.90	–h
O v* J = 0	759.442	81942.5	0.191	113.90	⋯
O v* J = 1	760.227	82078.6	0.048	113.90	⋯
O v* J = 2	760.446	82385.3	0.143	113.90	⋯
O v* J = 1	761.128	82078.6	0.064	113.90	⋯
O v* J = 2	762.004	82385.3	0.048	113.90	⋯
O vi	1031.912	0.00	0.133	138.12	⋯
O vi	1037.613	0.00	0.066	138.12	⋯
Ne iv	541.128	0.00	0.055	97.11	⋯
Ne iv	542.074	0.00	0.110	97.11	⋯
Ne iv	543.884	0.00	0.170	97.11	⋯
Ne v	568.424	0.00	0.110	126.21	⋯
Ne v*	569.828	411.2	0.109	126.21	4.3
Ne v*	572.335	1109.5	0.114	126.21	4.9
Ne vi	558.603	0.00	0.092	157.93	⋯
Ne viii	770.409	0.00	0.102	239.09	⋯
Ne viii	780.324	0.00	0.050	239.09	⋯
Na ix	681.720	0.00	0.092	299.90	⋯
Na ix	694.150	0.00	0.045	299.90	⋯
Mg x	609.793	0.00	0.084	367.50	⋯
Mg x	624.941	0.00	0.041	367.50	⋯
Al xi	550.030	0.00	0.077	442.00	⋯
Al xi	568.120	0.00	0.037	442.00	⋯
Si xii	499.406	0.00	0.072	523.00	⋯
Si xii	520.665	0.00	0.034	523.00	⋯
S iv	657.319	0.00	1.130	47.30	⋯
S iv*	661.396	951.4	1.020	47.30	4.8
S iv*	661.455	951.4	0.118	47.30	4.8
S iv	744.904	0.00	0.249	47.30	⋯
S iv	748.393	0.00	0.459	47.30	⋯
S iv*	750.221	951.4	0.597	47.30	4.8
S iv*	753.760	951.4	0.131	47.30	4.8
S iv	809.656	0.00	0.118	47.30	⋯
S iv*	815.941	951.4	0.085	47.30	4.8
S v	786.468	0.00	1.360	72.68	⋯
S vi	933.378	0.00	0.436	88.05	⋯
S vi	944.523	0.00	0.215	88.05	⋯
Ar iv	850.605	0.00	0.043	59.81	⋯
Ar v	705.353	0.00	0.061	75.04	⋯
Ar v	822.174	0.00	0.520	75.04	⋯
Ar vi	544.730	0.00	0.218	91.01	⋯
Ar vi	548.900	0.00	0.433	91.01	⋯
Ar vi	754.930	0.00	0.071	91.01	⋯
Ar vi*	767.065	2207.10	0.488	91.01	6.1
Ar vii	585.748	0.00	1.210	124.40	⋯
Ar viii	700.240	0.00	0.375	143.45	⋯
Ar viii	713.801	0.00	0.180	143.45	⋯
Ca iv	655.998	0.00	0.022	67.15	⋯
Ca v	637.917	0.00	0.014	84.43	⋯
Ca v	646.534	0.00	0.040	84.43	⋯
Ca v*	651.531	3275.6	0.053	84.43	6.3
Ca vi	629.602	0.00	0.016	108.78	⋯
Ca vi	633.844	0.00	0.032	108.78	⋯
Ca vi	641.904	0.00	0.049	108.78	⋯
Ca vii	624.385	0.00	0.058	127.70	⋯
Ca vii*	639.150	4071.4	0.066	127.70	7.5
Ca viii	582.845	0.00	0.078	147.40	⋯
Ca viii*	597.935	4308.3	0.063	147.40	6.9
Ca x	557.765	0.00	0.326	211.30	⋯
Ca x	574.010	0.00	0.160	211.30	⋯

Notes.

^aIons with one or more troughs detected in outflows observed in HST GO-14777. ^bRest wavelength of observed transitions. ^cLower-level energy of these transitions from the National Institute of Standards and Technology (NIST) database (Kramida et al. 2018), except for Ar vi* λ767.06, which is from Verner et al. (1996). ^dTransition's oscillator strengths from the NIST database, except for Ar v, Ar vi, and Ca iv-Ca viii, which are from Fischer et al. (2006; see details in Paper V). ^eIonization potential, which gives the energy required to ionize the element to the next stage of ionization (Allen 1977). ^fThe logarithm of the critical electron number density for the excited transitions. The ${{\rm{n}}}_{{\rm{e}},\mathrm{cirt}}$ values are from CHIANTI version 7.1.3 with assuming a temperature of 20,000 K (Landi et al. 2013). ^gThe ionic transitions that are observed in SDSS J1042+1646 are shown in bold. ^hWe discuss the O v* multiplet in Section 4.2.3.

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For these reasons, we developed a Synthetic Spectral Simulation method (SSS), which allows us to fit the multitude of troughs and determine the photoionization solutions more efficiently and accurately. While SSS may appear to be superficially similar to the spectral synthesis code SimBAL (Leighly et al. 2018), these two methods are philosophically quite different and to date have been applied to different rest-wavelength bands. The main analyzing steps of SSS are:

• (1)  
  Instead of directly measuring ${N}_{\mathrm{ion}}$ of each absorption trough, we only measure the uncontaminated absorption troughs. For doublet transitions that are not heavily saturated, we obtain N_ion measurements using the PC method described in Arav et al. (2008). For saturated transitions, we use the AOD N_ion and treat them as lower limits. For singlet transitions with a maximum optical depth, ${\tau }_{\max }$, greater than 0.5, we treat the AOD N_ion as lower limits. For absorption troughs with ${\tau }_{\max }$ < 0.05, we determine the AOD N_ion as upper limits. For singlet transitions with 0.05 < ${\tau }_{\max }$ < 0.5 and where the outflow shows other absorption troughs with $\tau \gt 2$ from ionic transitions with similar ionization, we treat the singlets' AOD N_ion as measurements since they are minimally affected by saturation effects (<10%).
• (2)  
  We then use these N_ion as a basis to determine a preliminary photoionization solution (PI₁). Photoionized plasma in an AGN outflow is characterized by the total hydrogen column density, ${N}_{{\rm{H}}}$, and the ionization parameter, ${U}_{{\rm{H}}}$, where

  $$\begin{eqnarray}&&{U}_{{\rm{H}}}\,=\,\displaystyle \frac{{Q}_{{\rm{H}}}}{4\pi {R}^{2}{n}_{{\rm{H}}}c},\end{eqnarray} \tag{ 1 }$$

  ${Q}_{{\rm{H}}}$ is the source emission rate of hydrogen ionizing photons, R is the distance of the outflow from the central source, ${n}_{{\rm{H}}}$ is the hydrogen number density (for a highly ionized plasma, ${n}_{{\rm{H}}}$ ≃ 0.8 ${n}_{{\rm{e}}}$), and c is the speed of light.We run the spectral synthesis code Cloudy (version c17.00; Ferland et al. 2017) to generate grids of photoionization simulations. We assume a spectral energy distribution (SED) and a metallicity (e.g., Arav et al. 2013, and see elaboration in Section 4.1.2). We vary log(${U}_{{\rm{H}}}$) between −3.0 and 3.0 and log(${N}_{{\rm{H}}}$) between 17.0 to 24.0 (hereafter, log(${N}_{\mathrm{ion}}$) is in units of log(cm⁻²)) in steps of 0.05 dex. At each grid point, Cloudy predicts the N_ion for all ions in its database. For each unblended absorption trough from a given ionic transition, we fit their optical depth profile in velocity space by a Gaussian profile as:

  $$\begin{eqnarray}&&\tau (v)\,=\,\displaystyle \frac{A}{\sigma \sqrt{2\pi }}\times \exp \left(\displaystyle \frac{{\left(v-{v}_{c}\right)}^{2}}{2{\sigma }^{2}}\right),\end{eqnarray} \tag{ 2 }$$

  where $\tau (v)$ is the optical depth profile of the absorption trough, $v$ is the velocity, A is the scaling factor, σ is the velocity dispersion, and v_c is the velocity centroid of the Gaussian profile. $\tfrac{A}{\sigma \sqrt{2\pi }}$ is the maximum τ of the trough from the model. For each outflow system, we find the best v_c and σ by fitting the detected unblended absorption troughs.For each ion, A in Equation (2) is scaled according to the predicted value of N_ion based on PI₁ (e.g., Savage & Sembach 1991; Edmonds et al. 2011):

  $$\begin{eqnarray}&&\begin{array}{l}{N}_{\mathrm{ion}}=\displaystyle \int N(v){dv}\\ \qquad =\,\displaystyle \int \displaystyle \frac{3.8\times {10}^{14}}{f\cdot \lambda }\cdot \displaystyle \frac{A}{\sigma \sqrt{2\pi }}\times \exp \left(\displaystyle \frac{{\left(v-{v}_{c}\right)}^{2}}{2{\sigma }^{2}}\right){dv},\end{array}\end{eqnarray} \tag{ 3 }$$

  where $N(v)$ is the velocity distribution of N_ion (cm⁻² km⁻¹ s), $f$ is the oscillator strength of the corresponding ionic transition, and λ is the rest wavelength of the transition.
• (3)  
  We assume that all troughs in a given outflow system can be modeled using a Gaussian $\tau (v)$ function (see Equation (2)) with the same v_c and σ determined from the unblended absorption troughs of each outflow system. We vary A to match the N_ion predicted from PI₁, creating a full, AOD optical depth model for the entire observed spectrum. This model is then used to produce a synthetic spectrum that we overlay on top of the data. Since PI₁ has a minimal number of constraints (no constraints from blended troughs and maybe a few upper limits), there could be predicted troughs that conflict with the data. Therefore, we first look for predicted troughs that violate the ${\tau }_{\max }$ upper limit threshold (discussed in step (1) above) within the continuum portion of the data so that we can measure additional upper limits. For example, PI₁ for S1a did not include the upper limit from O iii. Inspection of the continuum region around the O iii 833, O iii* 834, and O iii* 835 transitions marked in Figure 1 showed predicted troughs from PI₁ that were not supported by the data (${\tau }_{\max }$ exceeded 0.05 for the strongest transitions at those wavelengths). Additional models are then created using ${U}_{{\rm{H}}}$ and ${N}_{{\rm{H}}}$ values that are on the boundary of the 1σ contour for PI₁ and inspected to ensure that all upper limits are found.
• (4)  
  A new photoionization solution, PI₂, is determined for each outflow, including any newly measured upper limits, and another synthetic spectrum is created. As an example, for S1a this resulted in a decrease in ${N}_{{\rm{H}}}$ by 0.1 dex and an increase in ${U}_{{\rm{H}}}$ by 0.03 dex for the high-ionization phase (HP, compared to PI₁) and no change in the VHP (see Section 4.1.2). The blended troughs are then inspected for regions where none of the outflows have predicted troughs that can account for the observed absorption (none were found in these data). For such instances, the 1σ contour of PI₂ is probed for all outflows like what was done is step (3), and if only one outflow trough is found that can match the absorption, a new lower limit (or in rare cases involving doublets, a measurement) can be made.
• (5)  
  A final solution (PI) is then created from all measurements and limits. As a final check, the unblended troughs yielding the measurements that produced PI₁ are visually inspected to ensure that there are not any contaminating troughs that would make the measurements unreliable. As an example of the final results, we show the overall fit to the data (see Figure 2), where we use the SSS solutions derived in Sections 4.1–4.3. The colored dashed lines are for different outflow systems, while the solid red lines are the overall model achieved by summing all outflow systems.
• (6)  
  To determine R, we use troughs from density sensitive transitions to obtain ${n}_{{\rm{e}}}$ (e.g., Hamann et al. 2001; Korista et al. 2008; Borguet et al. 2012a; Arav et al. 2013; Xu et al. 2019). We vary the ${n}_{{\rm{e}}}$ of the outflow systems to fit the troughs of transitions from excited states (see Section 4.2.3 as an example). Overall, the SSS is a three-dimensional model in the parameter space of ${U}_{{\rm{H}}}$, ${N}_{{\rm{H}}}$, and ${n}_{{\rm{e}}}$. The detailed analysis for each outflow system is shown step by step in Section 4, and we discuss the strengths and caveats of this method in Section 6.

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4.1.1. Kinematics and N_ion Determinations

S1 has strong absorption troughs from both high-ionization species, such as O iii, O iv, and Ca vi; and very high-ionization species, including Na ix, Mg x, and Ne viii. In Figure 3, we show the kinematics of the absorption troughs for both the 2011 and 2017 epochs in green and purple, respectively. The troughs from −7000 km s⁻¹ to −4000 km s⁻¹ show double-minima features, which are most apparent in the Na ix-b, Ar vii, and Ar viii-b (hereafter, the "-b" or "-r" suffix stands for the shorter (bluer) or longer (redder) wavelength component of doublet transitions, respectively). Since these two features appear at the same velocity in several troughs, we divide S1 into two components, 1a and 1b, which are centered at −4950 km s⁻¹ and −5750 km s⁻¹, respectively. For each individual ion, we report the measured N_ion for the 2017 epoch in Table 4.

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The N_ion measurements used for the initial ${U}_{{\rm{H}}}$ and ${N}_{{\rm{H}}}$ solution are from the Na ix and Ar viii doublet transitions, and they are determined in the following ways. (1) For the Na ix doublets in component 1b, we assume each trough is symmetric since the troughs are well fitted with Gaussian profiles (see Figures 2 and 3) and solve for N_ion using the PC equations on the unblended high-velocity wing. We then double the value to obtain the measurement. (2) Similarly, for the Ar viii doublet in components 1a and 1b, the Ar viii-r is contaminated by two intervening systems. Therefore, the unblended half of the troughs are used to solve the PC equations. Then, we double the values for the N_ion measurements. (3) The Na ix-r in component 1a is blended with the Ar viii-b trough from S2. If no other information is available, we treat AOD N_ion value derived from the Na ix-b as a lower limit. However, the Ar viii doublet of component 1a is not saturated and is deeper than the Na ix-b absorption, while Ar viii and Na ix have similar IPs. Therefore, we can safely treat the AOD N_ion value derived from the Na ix-b as a measurement.

Given the signal-to-noise ratio of the data and different spectral resolution of the observations, the absorption troughs are consistent with no variation between the two epochs for most of the ions. An exception is the low-velocity wing of the Ar viii-r absorption trough. However, the entire Ar viii-b troughs are consistent with no variations between the 2011 and 2017 epochs. Therefore, the deviation in Ar viii-r is not intrinsic to the outflow system and may be due to calibration issues.

Ca vi has three transitions at 629.60 Å, 633.84 Å, and 641.90 Å, where their $f$ ratios are almost 1:2:3, respectively. Ca vi λ629.60 and λ633.84 are not measurable, since the former coincides with the strong O v λ629.73 and the latter is blended with two intervening systems. However, we observed shallow absorption troughs from Ca vi λ641.90, i.e., ${\tau }_{\max }$ < 0.2. Therefore, the AOD N_ion derived will be close to the actual N_ion value (see elaborations in Section 2.9 of Leighly et al. 2011 and Section 5.4 of Arav et al. 2013). Thus, we treat the AOD N_ion from the absorption trough of Ca vi λ641.90 as a measurement. Similarly, for S iv λ657.32, we are able to measure the AOD N_ion of it for both component 1a and 1b. We treat them as N_ion measurements since they have ${\tau }_{\max }\lt 0.3$.

The strongest two observable transitions from O iii are at 702.34 Å and 832.93 Å, and both are consistent with no absorption. We get an upper limit on N_ion for O iii from the AOD measurement of the stronger $f$ transition at 702.34 Å. Since oxygen is the most abundant metal, the non-detection of O iii hints that none of the doubly ionized species would be strong enough to be detected in our spectrum. Indeed, the troughs from N iii are consistent with no absorption.

The other ionic transitions are either saturated or undetected. Therefore, the AOD N_ion for these two types are treated as lower and upper limits, respectively.

4.1.2. SSS Models and Photoionization Solutions

After we determined N_ion for unblended troughs, we follow the SSS method in Section 3.3 to get the best-fitting photoionization model for all observed troughs. To account for systematics in the unabsorbed emission model, the adopted N_ion lower limits assume lower errors of 20%, and N_ion upper limits assume upper errors of 20%. We assume the solar metallicity (Grevesse et al. 2010) and the HE0238 SED (Arav et al. 2013). This SED is based on observations of quasar HE0238–1904 in a similar rest-frame wavelength range to our object (Arav et al. 2013). For the observed data (570–1000 Å rest frame), the ratio of the HE0238 SED with the SDSS J1042+1646 continuum is constant to within ±10%. The best-fitting model is shown as the black solid lines in Figure 3. Absorption troughs from components 1a and 1b are plotted separately as blue and red dotted lines. The ratios of measured N_ion to the model predicted N_ion are presented in the fourth column in Table 4.

Arav et al. (2013) demonstrated that detections of both the very high-ionization troughs (e.g., Ne viii and Mg x) and high-ionization troughs (e.g., O iv) in the same outflow state two ionization phases for the absorber. We find the same situation in all of the outflow systems discussed here. Figure 4 shows the models' corresponding photoionization solution. For component 1a (see top panel of Figure 4), the VHP is marked as the red cross and is mainly constrained by the N_ion measurements of Na ix and Ar viii. However, this VHP underestimates the observed N(S iv) by over a factor of 1000. Moreover, if we shift this VHP vertically up to match the N(S iv) curve at log(${N}_{{\rm{H}}}$) = 22.78, the solution will overpredict the N(Ar viii) by a factor of 13 and N(Ca vi) by a factor of 22. Therefore, a pure VHP solution is unable to produce all of the observed ${N}_{\mathrm{ion}}$. The HP is marked by the blue cross and produces the observed N(S iv) and is constrained by the ${N}_{\mathrm{ion}}$ upper limit of O iii. However, this HP produces negligible amounts of the observed N(Ar viii) and N(Na ix). Therefore, we invoke a two-phase ionization solution. The VHP has log(${N}_{{\rm{H}}}$) = ${22.37}_{-0.12}^{+0.19}$ and log(${U}_{{\rm{H}}}$) = ${0.42}_{-0.09}^{+0.16}$, and the HP has log(${N}_{{\rm{H}}}$) = ${20.39}_{-0.58}^{+0.40}$ and log(${U}_{{\rm{H}}}$) = −0.98${}_{-0.30}^{+0.17}$. The N_ion upper limits from N iii, S v, and Ar v, and the lower limits from Ne viii, Mg x, and Ca viii are consistent with this two-phase solution and omitted for clarity's sake.

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Similarly, component 1b (see the bottom panel of Figure 4), has a VHP at log(${N}_{{\rm{H}}}$) = ${22.51}_{-0.21}^{+0.27}$ and log(${U}_{{\rm{H}}}$) = ${0.54}_{-0.16}^{+0.24}$, and an HP at log(${N}_{{\rm{H}}}$) = ${20.52}_{-0.34}^{+0.36}$ and log(${U}_{{\rm{H}}}$) = −0.93${}_{-0.18}^{+0.17}$. We discuss and compare the two ionization phase solutions to former studies in Section 6.1.

4.1.3. Determinations of n_e from S iv and S iv*

The most robust way for determining the distance, R, from the ionizing source of an absorption outflow is to use the troughs from ionic excited states. The ratio between the N_ion from excited and ground states, e.g., N(S iv*)/N(S iv), yields ${n}_{{\rm{e}}}$ for an outflow, and combined with the value of ${U}_{{\rm{H}}}$, R can be determined (see Equation (1), e.g., Borguet et al. 2013; Chamberlain et al. 2015; Arav et al. 2018; Xu et al. 2018, 2019).

For component 1a, we observed the absorption troughs from the strongest S iv transition at 657.32 Å and the corresponding excited state at 661.40 Å both with oscillator strengths, $f$ ∼1.18. For the 2017 data, we show our best-fitting SSS model for the S iv region in Figure 5. We clearly have a deeper feature in the S iv λ657.32 region than in the S iv* λ661.40 region for component 1a. This yields log[N(S iv)] = ${14.19}_{-0.13}^{+0.10}$ and log[N(S iv*)] = ${13.35}_{-0.12}^{+0.11}$. Following the same method described in Section 2 of Xu et al. (2019), we derive log(${n}_{{\rm{e}}}$) = ${3.68}_{-0.25}^{+0.18}$ for component 1a (hereafter, log(${n}_{{\rm{e}}}$) is in units of log(cm⁻³)).

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Similarly, for component 1b, the absorption trough from S iv λ657.32 shows a deeper feature than S iv* λ661.40, while the latter cannot be much deeper than the current modeling due to the flux level on the two shoulders (see Figure 5). We get log[N(S iv)] = ${13.93}_{-0.13}^{+0.14}$ and log[N(S iv*)] = ${13.21}_{-0.13}^{+0.10}$. This leads to log(${n}_{{\rm{e}}}$) = ${3.78}_{-0.26}^{+0.23}$, which is consistent with the ${n}_{{\rm{e}}}$ result for component 1a within the errors. This strengthens the possibility that both outflows originate from the same absorber. After we determine ${n}_{{\rm{e}}}$ for the outflows, R can be derived (see Section 5).

S2 also shows absorption troughs from both high- and very high-ionization species. Moreover, S2 has deep absorption troughs near its expected O v* multiplet region. We begin by determining the N_ion and constructing the photoionization solutions. Following that, we model the O v* regions and derive the constraints for ${n}_{{\rm{e}}}$ and R.

4.2.1. Kinematics and N_ion Determinations

We show the strong absorption troughs for S2 in Figure 6, where the 2011 and 2017 epochs are shown in green and purple colors, respectively. The data is consistent with no variability between the 2011 and 2017 epochs. We report the measured N_ion in Table 4 and discuss them in detail here.

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Similar to S1, we adopt the PC method and get N_ion measurements from the unblended and well-separated Na ix and Ar viii doublets. The Ne viii and Mg x doublet troughs are black at their deepest points, so their AOD N_ion from the red component are taken as lower limits. For the Ca vi triplet, the absorption trough from Ca vi at 629.60 Å and 633.84 Å are blended with the Galactic Lyα region, while the Ca vi λ641.90 shows similar but shallower trough features as the Na ix doublet. After modeling out the contamination of intervening systems (i.e., at v = −7050, −7320, and −7720 km s⁻¹) by narrow Gaussian profiles, the AOD N_ion value from the Ca vi λ641.90 is treated as a measurement. The absorption troughs from other ion transitions are either lower or upper limits and are reported in Table 4. The lack of detection from O iii and lower IP ions demonstrates that this is not a low-ionization BALQSO.

4.2.2. SSS Models and Photoionization Solutions

We present the best-fitting SSS model as the black solid line in Figure 6 for each trough and the corresponding photoionization solution in Figure 7. Similar to S1, all of the observed troughs are well fitted by a two-phase photoionization solution. The VHP is constrained mainly by the N_ion measurements from Na ix and Ar viii, and is supported by the N_ion from Ca vi. This yields log(${N}_{{\rm{H}}}$) = ${22.40}_{-0.10}^{+0.12}$ and log(${U}_{{\rm{H}}}$) = ${0.4}_{-0.06}^{+0.12}$. The HP is constrained by the upper limit from S iv, measurement of Ca vi, and the lower limits from O iv and N iv. This yields log(${N}_{{\rm{H}}}$) = ${20.79}_{-0.34}^{+0.32}$ and log(${U}_{{\rm{H}}}$) = −0.60${}_{-0.14}^{+0.17}$. Other ions from S2 that are not shown in Figure 7 are consistent with the solutions.

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4.2.3. Determination of n_e from the O v* Multiplet

The O v* transitions near 760 Å are the isoelectronic sequence of the C iii* transitions near 1175 Å, which are sensitive to a wide range of ${n}_{{\rm{e}}}$ (Gabel et al. 2005; Borguet et al. 2012b; Arav et al. 2015; Leighly et al. 2018). Our HST program shows the first clear detection of O v* absorption troughs in an AGN outflow, in both quasar SDSS J1042+1646 and PKS 0352-0711 (Paper V). For the O v* multiplet, there are six (J–J') components of the 2s2p³P_J−2p^{2 3}P${}_{{J}^{{\prime} }}$ multiplet between 758.7 Å and 762.0 Å (Doyle et al. 1983; Keenan et al. 1994). However, they are very rare to be observed in either emission or absorption. Previously, the only extra-terrestrial detections of O v* were in solar spectra. The O v* multiplet has been resolved as emission lines by the Harvard S-055 EUV spectrometer on board Skylab (Doyle et al. 1983; Keenan et al. 1994) and more recently by the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) on board the Solar and Heliospheric Observatory (SOHO) (O'Shea et al. 2000).

In the upper panel of Figure 8, the ratio of each J level's population to that of the ground state is plotted as a function of ${n}_{{\rm{e}}}$. In the bottom panel, we show the population ratios between different J levels versus ${n}_{{\rm{e}}}$. When log(${n}_{{\rm{e}}}$) < 5, the level population of ${{\rm{O}}{{\rm{V}}}^{* }}_{J=0}$, i.e., n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=0}$), dominates, and n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=1}$) and n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=2}$) keep increasing as ${n}_{{\rm{e}}}$ grows in this region. In the log(${n}_{{\rm{e}}}$) range between 5 and 9, n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=2}$) > n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=0}$) > n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=1}$). n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=0}$) is populated quickly for high ${n}_{{\rm{e}}}$, and finally reaches equilibrium at log(${n}_{{\rm{e}}}$) > 12, where n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=2}$)> n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=1}$) > n(${{\rm{O}}{{\rm{V}}}^{* }}_{J=0}$).

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We observed significant absorption troughs at the expected locations of the O v* transitions. The best-fitting photoionization solution from SSS model predicts that the total log[N(O v)] = 17.02 cm⁻², with the ratio of contributions from the HP and VHP as ∼1:2. The Cloudy predicted temperature for the HP and VHP are around T_low = 21,000 K and T_high = 44,000 K, respectively. Due to the strong temperature dependence of n(O v*)/n(O v), the VHP produces 20 times more N(O v*)/N(O v) compared to the HP. Overall, most (∼97.5%) of the O v* observed in the spectrum is from the VHP.

In order to fit the observed O v* region, we adopt the model predicted value for N(O v) and temperature T_high. We vary log(${n}_{{\rm{e}}}$) from 5 to 13, in steps of 0.1 dex and show some of the fits to this range in Figure 9. The black and gray histograms are the normalized flux and error for the 2017 epoch, respectively. The red dashed lines are the models for the O v* multiplet with the corresponding J values. The vertical line below each J value indicates the relative $f$ of the line. We note that there are several "contaminations" from intervening systems at 1466.5 Å, 1469.0 Å and 1470.0 Å.

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Despite all of the intervening systems, we can still estimate ${n}_{{\rm{e}}}$ as shown in Figure 9. The lower limit is determined at log(${n}_{{\rm{e}}}$) = 5.5, where the model clearly underestimates the data by more than 1σ (see panel 1 and 2). The upper limit is determined to be log(${n}_{{\rm{e}}}$) = 6.3, where the model overestimates the data (see panel 4). We get the best fit when log(${n}_{{\rm{e}}}$) = 5.8. Therefore, log(${n}_{{\rm{e}}}$) = ${5.8}_{-0.3}^{+0.5}$.

Besides O v*, we observed troughs from other density sensitive transitions. However, they are either situated in a saturated region (Ne v* λ572.33 and O iv* λ790.20), or too weak to form a significant trough (S iv* λ661.40 and the corresponding S iv at 657.32 Å). From the best-fitting photoionization solution model with the above-determined ${n}_{{\rm{e}}}$, we are able to predict absorption troughs that are consistent with the data in the expected regions of these transitions.

S3 also shows absorption troughs from both high- and very high-ionization species. We show the data and the best-fitting SSS models in Figure 10. For the O iv + Mg x-b region, the blue dotted lines are for the O iv λ608.340 and O iv* λ609.83 troughs while the red dotted line is for the Mg x λ609.79 trough. For the Ca vii + Mg x-r region, the cyan and red dotted lines are for the Ca vii λ624.28 and Mg x λ624.94 troughs, respectively. These two regions fall in the gap of the HST/COS G140L grating in the 2011 epoch. For the Ar viii-r and Ar vi region, their modeled troughs are shown as orange dotted lines. The Ar viii-r trough is consistent with the shallow observed absorption and is contaminated by the Ar viii λ700.24 trough from S1a (centered at −10,600 km s⁻¹ in the top-right panel of Figure 10). Therefore, the AOD ${N}_{\mathrm{ion}}$ from the Ar viii-r trough is treated as an upper limit. The higher velocity wing of the Ar vi λ754.93 trough is contaminated by the Ne viii λ780.32 trough from S4, while S4 shows variability between the 2011 and 2017 epochs. We discuss this variability in Paper IV.

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We report the measured ${N}_{\mathrm{ion}}$ in Table 4 and the best-fitting photoionization solution from the SSS model in Figure 11. All observed outflow absorption troughs are well fitted by a two-phase ionization model. The observed amount N(Ca vii) originates from both the HP and VHP, with a ratio of ∼1:3, respectively. Therefore, Ca vii gives constraints to both phases. The HP yields log(${N}_{{\rm{H}}}$) = ${20.69}_{-0.28}^{+0.34}$ and log(${U}_{{\rm{H}}}$) = −0.67${}_{-0.31}^{+0.21}$. This solution is constrained by the O iv and Ar vi troughs, as well as the Ca vii trough. The VHP gives log(${N}_{{\rm{H}}}$) = ${21.54}_{-0.18}^{+0.17}$ and log(${U}_{{\rm{H}}}$) = ${0.09}_{-0.07}^{+0.08}$. This solution is constrained mainly by the measured N_ion of the Mg x doublet and Ca vii, and the upper limit of Ar viii. Comparing between the 2011 and 2017 epochs, the troughs of S3 show no variations.

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We do not observe measurable absorption troughs from density diagnostic transitions for S3. Therefore, the ${n}_{{\rm{e}}}$ of S3 is undetermined.

6.1.1. Prevalence of Outflows with a VHP

6.1.2. Volume Filling Factor

Kinematic similarities (both velocity and width centroid) between troughs from the HP and the VHP suggest that these two phases are co-spatial. For each phase (HP or VHP), the volume is proportional to ${N}_{{\rm{H}}}$/${n}_{H}$, and the ${n}_{H}$ ratio between the HP and the VHP is given by ${U}_{{\rm{H}},{VHP}}/{U}_{{\rm{H}},{HP}}$. Therefore, the volume filling factor between the two phases is defined as (see Section 8.1 in Arav et al. 2013):

$$\begin{eqnarray}&&{f}_{V}\equiv \displaystyle \frac{{V}_{{HP}}}{{V}_{{VHP}}}\,=\,\displaystyle \frac{{N}_{{\rm{H}},{HP}}}{{N}_{{\rm{H}},{VHP}}}\times \displaystyle \frac{{U}_{{\rm{H}},{HP}}}{{U}_{{\rm{H}},{VHP}}}\end{eqnarray} \tag{ 6 }$$

where V is the volume of the outflows, and the subscripts HP and VHP denotes the HP and VHP, respectively. For the outflows in quasar HE0238–1904, the VHP has log(${U}_{{\rm{H}}}$) 2–3 dexes higher and log(${N}_{{\rm{H}}}$) 2–2.5 dexes higher than the HP. Therefore, the HP is inferred to have log (${f}_{V}$) ∼ −4 to −6 compared to the VHP. Thus, Arav et al. (2013) reached the conclusion that the VHP carries much more material than the HP and is closer to the situation seen in X-ray warm absorbers (e.g., Netzer et al. 2003; Gabel et al. 2005). We show the ${f}_{V}$ values for the outflows in SDSS J1042+1646 in Table 5.

6.1.3. Comparisons with Warm Absorbers

Since we have multiple outflow systems along the line of sight at different distances, the inner outflows would absorb photons from the central AGN and could change the SED incident on the outer outflows. This is called the "Shading Effect" (Sun et al. 2017) and here we quantify its effect on our derived photoionization solutions. We show our results when the outflow is directly exposed to the HE0238 SED in the first part of Table 5. Outflow S2 has a smaller R compared to the other systems, and its high ${N}_{{\rm{H}}}$ could significantly affect the SED seen by other outflows. Therefore, we test the shading covered by S2 here and compare it to the original results using the unshaded HE0238 SED.

Our model predicts that S2 has two ionization phases. We input the HE0238 SED and calculate the transmitted SED after passing through S2's VHP and HP to get ${\mathrm{SED}}_{\mathrm{Tran}.\mathrm{VHP}}$ and ${\mathrm{SED}}_{\mathrm{Tran}.\mathrm{HP}}$, respectively. We show these two transmitted SEDs in the top panel of Figure 12 as blue and red lines, respectively. The unshaded HE0238 SED is plotted as the solid black line. The ${\mathrm{SED}}_{\mathrm{Tran}.\mathrm{VHP}}$ shows a reduction of flux ∼0.3 dex near the He ii edge; and further reduction of flux ∼1 dex from 100 eV to 1 keV, which is mainly caused by metal absorptions. The ${\mathrm{SED}}_{\mathrm{Tran}.\mathrm{HP}}$ has a minimal reduction while the largest change is ∼0.1 dex near the He ii edge. To check the total "Shading Effect", we test the scenario where ${\mathrm{SED}}_{\mathrm{Tran}.\mathrm{VHP}}$ is incident on the HP of S2. As shown in the bottom panel of Figure 12, considering the shading from both phases (purple lines) only affects the SED by an additional 10% compared to the ${\mathrm{SED}}_{\mathrm{Tran}.\mathrm{VHP}}$ (blue lines in the top panel).

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We use these transmitted SEDs as the input SEDs to generate new grids of models with Cloudy. Based on these models and the same method reported in Section 4, we find new photoionization solutions for the shaded systems S1a, S1b, and S3. We then calculate new Q_H values using the transmitted SEDs and calculate the outflows' R, and energetics accordingly (see Equations (1), (4), (5)). We compare these solutions to the unshaded results in Table 5, where the second part of the Table is for the photoionization solutions from ${\mathrm{SED}}_{\mathrm{Tran}.\mathrm{VHP}}$. We find that when considering the "Shading Effect" with the ${\mathrm{SED}}_{\mathrm{Tran}.\mathrm{VHP}}$, we get a larger log(${U}_{{\rm{H}}}$) by ∼0.3–1.0 dex and a larger log(${N}_{{\rm{H}}}$) by ∼0.1–0.5 dex. This is because the shading of S2 decreases the amount of hydrogen ionizing photons, so a higher ${U}_{{\rm{H}}}$ is needed to keep a similar ionization state as the unshaded case. The new ${U}_{{\rm{H}}}$ and ${N}_{{\rm{H}}}$ values lead to a decrease of ∼0.1 dex in R, $\dot{M}$ and $\dot{{E}_{k}}$.

As shown in Section 1, significant AGN feedback typically requires high $\dot{{E}_{k}}$, where ${{\rm{\Gamma }}}_{\mathrm{Edd}}$ is at least 0.5 (Hopkins & Elvis 2010) or 5% (Scannapieco & Oh 2004). Equations (4) and (5) show that $\dot{M}$ and $\dot{{E}_{k}}$ are linearly dependent on the solid angle subtended by the outflows around the source (4 $\pi {\rm{\Omega }}$). Since there are no direct spectroscopic determinations for Ω, the common approach is to use the detection frequency of outflows in surveys as a proxy. In SDSS J1042+1646, the most energetic outflow is S1b. Based on our analysis results, $\dot{M}$ and $\dot{{E}_{k}}$ are given by:

$$\begin{eqnarray}&&\dot{M}\simeq {\rm{\Omega }}\times 8600\ {M}_{\odot }\ {\mathrm{yr}}^{-1}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{\dot{E}}_{k}\simeq {\rm{\Omega }}\times 2.5\times {10}^{47}\ \mathrm{erg}\ {{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 8 }$$

Multiple surveys have been done to find that C iv BALs appear in approximately 20% of all quasars (e.g., Hewett & Foltz 2003; Dai et al. 2008, 2012; Gibson et al. 2009; Allen et al. 2011). The outflows reported here are consistent with C iv BALs since we observed absorption troughs from O iv λ787.71, which has a similar IP to C iv λ1548.19. Moreover, the populations of C iv and O iv are similar over a broad range of ${U}_{{\rm{H}}}$ (see Figure 12 in Muzahid et al. 2013). Also, using the classification scheme in Paper I and the widths of their Ne viii absorption trough widths in Table 2, all of the outflows here are BALs except for S3, which is a mini-BAL. Therefore, Ω of these outflows should be similar to that assumed for C iv BAL outflows. Thus, we adopt an Ω = 0.2 and this lead to $\dot{M}$ = 4300 ${M}_{\odot }\ {\mathrm{yr}}^{-1}$ and ${\dot{E}}_{k}$ = ${10}^{46.7}$ erg ${{\rm{s}}}^{-1}$ for outflow S1b. These are the largest $\dot{M}$ and ${\dot{E}}_{k}$ reported for quasar outflows to date.

The former records are $\dot{M}$ ∼ 3500 M_⊙ yr⁻¹ (Maiolino et al. 2012) and $\dot{{E}_{k}}$ ∼ ${10}^{45.9}$ erg s⁻¹ (Chamberlain et al. 2015). Moreover, S1b has an ${\dot{E}}_{k}$ ∼ 20% of its ${{\rm{L}}}_{\mathrm{Edd}}$. With this high ${{\rm{\Gamma }}}_{\mathrm{Edd}}$, S1b can be the dominate sources of energy for AGN feedback in the host galaxy of SDSS J1042+1646 (Scannapieco & Oh 2004).

Similarly, for component 1a, this yields R = ${840}_{-300}^{+500}$ pc, $\dot{M}$ = ${2800}_{-800}^{+200}$ M_⊙ yr⁻¹, and log($\dot{{E}_{k}}$) = ${46.4}_{-0.1}^{+0.1}$ erg s⁻¹. Combining S1a and S1b, outflow S1 has an $\dot{{E}_{k}}$ close to ${10}^{47.0}$ erg s⁻¹ and ${{\rm{\Gamma }}}_{\mathrm{Edd}}$ close to 30%.

AGN outflows can exhibit the super solar metallicity (SSM; e.g., Gabel et al. 2006; Arav et al. 2007). Paper V discusses the quantitative effects of SSM on the inferred parameters for outflows observed in the EUV500. Unlike the case shown in Paper V, the photoionization solutions of S1, S2, and S3 in SDSS J1042+1646 are consistent with the solar metallicity. To estimate the effects of possible SSM on S1, S2, and S3, we follow approach from Paper V and compute the analysis results for two metallicity values: solar (${Z}_{\odot }$) and 4.7 times solar (4.7 ${Z}_{\odot }$). For outflow system 1 and 2, the results based on 4.7 ${Z}_{\odot }$ leads to a decrease of distance by up to 30% and decreases of $\dot{M}$ and ${\dot{E}}_{k}$ by up to a factor of six. However, the goodness of the fit (determined by their ${\chi }^{2}$) for all models is comparable, so the fits cannot provide a metallicity constraint.