The UVES data of J1439-0106 was collected as part of the programs 081.B-0285(A) and 083.B-0604(A), and has been added to the SQUAD data base complied by Murphy et al. ( 2019 ). From the normalized spectrum, we identify two distinct absorption outflow systems, which we label here as the mini broad absorption line (mini-BAL) system S1, and the narrow absorption line (NAL) system S2 of which we find S1 suitable for our analysis thanks to the presence of excited state absorption troughs.

This paper is structured as follows. Section 2 describes the observation of J1439-0106, as well as the method we used to retrieve its spectral data. Section 3 discusses the measurement of ionic column densities of S1, as well as the determination of N H , U H , and n e . Section 4 shows the resulting calculation of Ṁ and Ė k , as well as its ratio with L Edd . Section 5 provides a discussion of these results, as well as a comparison with previous work. Section 6 summarizes and concludes the paper. We adopt a cosmology of h = 0.696, m = 0.286, and = 0 . 714 (Bennett et al. 2014 ). We use the Python astronomy package Astropy (Astropy Collaboration et al. 2013, 2018 ) for cosmological calculations. The combined spectral data, co v ering wav elengths between 3284-9466 Å, was normalized by the quasar's continuum and emission, and added to the SQUAD data base by Murphy et al. ( 2019 ). The spectrum is shown in Fig. 1 . The object was also observed in 2002 May 15, as part of the Sloan Digital Sky Survey (SDSS) (Abazajian et al, 2004 ), the spectrum of which we use to calibrate the flux shown in Fig. 1 , as well as find the bolometric and Eddington luminosities of the quasar.

From the UVES spectrum, we identify two different absorption outflow systems, mini-BAL S1 ( v ≈ -1550 km s -1 ), and NAL S2 ( v ≈ -2750 km s -1 ). We focus on S1 in the analysis of this paper, Downloaded from https://academic.oup.com/mnras/article/516/1/100/6665942 by Virginia Polytechnic Institute and State University -Main Library user on 21 June 2023 as it shows troughs of several Fe II excited lines, allowing us to find the outflow distance from the source, and by extension, the mass flow rate.

Finding the ionic column densities ( N ion ) of S1 is crucial to determine the energetics parameters of the outflow system. In order to measure the column densities, we use the systemic redshift of the quasar to convert the spectrum from wavelength space to velocity space, as shown in Fig. 2 . We then use two different methods to find the ionic column densities, assuming either an apparent optical depth (AOD) of a uniform outflo w (Sav age & Sembach 1991 ), or partial co v ering (PC) based on a v elocity dependent co v ering factor (Barlow, Hamann & Sargent 1997 ;Arav et al. 1999a , b ).

The AOD method and PC method have different advantages o v er one another with the PC method being particularly more helpful in finding more accurate column densities for ions with absorption doublets or multiplets, while the AOD method yields lower limits to the column densities (de K ool, K orista & Arav 2002 ;Arav et al. 2005 ;Edmonds et al. 2011 ;Borguet et al. 2012a ). The differences Fe II * 862 7 + 1 -1

Fe II * 1873 100 + 10 -10

between the two methods is explained in further detail in Section 3.1 of Byun et al. ( 2022 ). We choose our integration range for each ion based on the visibility of absorption troughs, as shown in Fig. 2 . In cases the red and blue troughs of a doublet are blended (e.g. C IV ), we choose a range in which the red and blue troughs are not o v erlapping in order to gain a lower limit of the column density. The measured column densities are shown in Table 1 . Note that we add a 20 per cent error in quadrature to account for the uncertainty in the continuum model (Xu et al. 2018 ).

With the ionic column densities found, we can use these measurements to find the hydrogen column density ( N H ) and ionization parameter ( U H ) of S1 (e.g. Xu et al. 2019 ;Miller et al. 2020a ;Byun et al. 2022 , Walker et al., in preparation). We use the spectral synthesis code Cloudy (Ferland et al. 2017 , version c17.00) to create a grid of simulated models based on varying values of N H and U H , using the spectral energy distribution (SED) of quasar HE0238-1904 (hereafter HE0238) (Arav et al. 2013 ). Via χ 2 analysis, we find the model with ionic column densities that best match the measured v alues, as sho wn in Fig. 3 . We use two different grids based on metallicity values solar and super-solar ( Z = 4. 68 Z Ballero et al. 2008 ;Miller et al. 2020b ) to find two different solutions, as previous studies show that the metallicities of outflows are between Z and 5 Z (e.g. Gabel, Arav & Kim 2006 ;Arav et al. 2007 ;Miller et al. 2020b ). The values of N H and U H are shown in Table 2 .

Finding the distance of the outflow from its source is crucial to finding the mass flow rate, and by extension, the kinetic luminosity. This is done by finding the electron number density ( n e ), which is measured by taking the ratios between excited and ground state column densities of ions (e.g. Moe et al. 2009 ;Byun et al. 2022 ). The CHIANTI 9.0.1 Data base (Dere et al. 1997 ;Dere et al. 2019 ) models, the n e dependent ratios between different energy states based on collisional excitation, and can be used to find the value of n e from measured column densities. S1 shows absorption lines of five different excited states, as well as the ground state, of Fe II , and we find n e by finding the ratios between these excited states and the resonance state ( N ( Fe II * ) /N ( Fe II )), as shown in Fig. 4 . While we find troughs of Si II and Si II * , they are unreliable for finding n e due to the saturation of the troughs (see plot i in Fig. 2 ). We find the weighted mean of the log n e values measured using the different excited states via the linear model method described by Barlow ( 2003 ). This yields a value of log n e = 3 . 4 + 0 . 1 -0 . 1 .

The distance of the outflow from the quasar can be found based on the definition of the ionization parameter:

where Q H is the emission rate of hydrogen ionizing photons, R is the distance from the source, c is the speed of light, and n H is the hydrogen number density. Once we find Q H , we can use the values of U H and n e found in Section 3 to find R , as n e ≈ 1.2 n H in highly ionized plasma (Osterbrock & Ferland 2006 ). We find the value of Q H as follows, as per previous works (e.g. Miller et al. 2020a ;Byun et al. 2022 , Byun et al., in preparation;Walker et al., in preparation). We scale the SED of HE0238 to match the continuum flux of J1439-0106 at observed wavelength λ = 6500 Å, from the SDSS observation of 2002 May 15, ( F λ = 8 . 49 + 0 . 64 -0 . 64 × 10 -17 erg s -1 cm -2 Å -1 ). We then inte grated o v er the SED for energies o v er 1 Ryd, resulting in Q H = 5 . 3 + 0 . 4 -0 . 4 × 10 56 s -1 . Once the distance is found, we can find the mass flow rate ( Ṁ ) and kinetic luminosity ( Ė k ) as shown in the following (Borguet et al. 2012a ):

where is the fraction of the solid angle co v ered by the outflow, μ = 1.4 is the molecular weight, m p is the mass of a proton, and v is the outflow velocity. We assume = 0.2 based on ratio of quasars with C IV BALs reported by Hewett & Foltz ( 2003 ). When propagating the uncertainties of the parameters, we take into account the positive correlation between U H and N H in the photoionization solutions (see Fig. 3 ) to a v oid o v erestimating our errors (see Walker et al. (in preparation) for a detailed explanation). The values found for Ṁ and Ė k are in Table 2 .

In order to be a major contributor to AGN feedback, S1 needs to have a kinetic energy of at least ∼0 . 5 per cent (Hopkins & Elvis 2010 ) or perhaps as much as ∼5 per cent (Scannapieco & Oh 2004 ) of the quasar's Eddington luminosity ( L Edd ), depending on the theoretical model. To find L Edd , we follow the method by Byun et al. ( 2022 ), Woo & Park ( 2019 ) to find the mass of the black hole. As there is Fe II emission in the region of Mg II emission, we use the Fe II template by Tsuzuki et al. ( 2006 ) and run a best-fitting algorithm to match the template to the spectrum, following Woo et al. ( 2018 ).

The resulting black hole mass is M BH = 7 . 05 + 2 . 68 -2 . 03 × 10 8 M with a corresponding Eddington luminosity of L Edd = 8 . 89 + 3 . 38 -2 . 56 × 10 46 erg s -1 . The Eddington ratio of the outflow ranges from 0 . 099 + 0 . 12 -0 . 05 per cent (for solar metallicity) to 0 . 023 + 0 . 053 -0 . 018 per cent (for super-solar metallicity), which is below the threshold for AGN feedback contribution.

We have found the value of n H of S1 based on the ratios between the column densities of excited state and resonance state Fe II . This has notably done by Korista et al. ( 2008 ) for the outflow of the quasar NVSS J235953-124148. The log n e values from the different energy states in Fig. 4 are in agreement within ∼0.2 dex, which is comparable to the agreement shown in fig. 3 of Korista et al. ( 2008 ), showing that the ratios between Fe II energy states can be consistently used to probe the n e value and the distance of an outflow from its source.

We have identified two outflow systems from the VLT/UVES spectrum of the quasar SDSS J1439-0106, the mini-BAL S1, and the NAL S2. After measuring the column densities of the ions identified in S1, we used these measurements to find the N H and U H values of S1 via photoionization analysis using models of both solar and super-solar metallicity (see Fig. 3 ).

With the abundance ratios between five different excited states of Fe II and the resonance state, we found the electron number density of (a) (b)