The Baryonic Content of Galaxies Mapped by MaNGA and the Gas Around Them

Our sample consists of 14 nearby galaxies (at z < 0.1) mapped in the SDSS/MaNGA survey with UV-bright quasars/active galactic nuclei (AGNs) at impact parameters between 0 and 140 kpc from the galactic centers. The targeted quasars have GALEX FUV mag < 19.5, and their impact parameters range from 0–25 times the effective radii of the corresponding MaNGA galaxies. For 1-635629, a bonus galaxy covered in the same setting as 1-180522, the impact parameter is 38.7 R_e .

We performed HST COS spectroscopy for these quasars/AGNs, as described in Section 2.2. The targets are listed in Table 1. We divide the targets into two groups by the value of impact parameter. The first group contains four objects with zero impact parameter, because in these cases we observed the central source, hereafter referred to as AGNs (see Figure 1). In these cases, the absorbing gas can be at any distance from the central source along the line of sight, and could potentially be associated with the central engine. Physical conditions in the absorbing gas in such cases can be very different from those in the CGM and ISM. The objects in the second group have nonzero impact parameters (more than 20 kpc) and likely probe gas related to the CGM of the galaxies (see Figure 2). In two cases (J2130−0025 and J0838+2453), the quasar sight lines cross two galaxies at different impact parameters and redshifts.

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Table 1. Physical Properties of the Sample of MaNGA Galaxies and Background Quasars

MaNGA	zgal	$\mathrm{log}{M}_{\star }$	SFR	log sSFR	Dn (4000) a	Quasar	zquasar	Imp Par.	Re	b/Re
ID		(M⊙)	(M⊙ yr−1)	(yr−1)				(b) (kpc)	(kpc)
1-71974	0.03316	10.30	1.72	−10.06	1.30	J0755+3911	0.0332	0	4.9	0
1-385099 b	0.02866	10.69	0.20	−11.38	1.54	J0838+2453	0.0287	0	5.4	0
12-192116	0.02615	8.80	0.59	−9.03	1.22	J1338+2620	0.0261	0	3.3	0
1-594755	0.03493	10.78	N/A	N/A	1.23	J1653+3945	0.0349	0	1.3	0
1-575668	0.06018	11.02	N/A	N/A	1.87	J1237+4447	0.4612	39	10.6	3.8
1-166736	0.01708	8.98	0.08	−10.07	1.31	J0950+4309	0.3622	23	3.4	6.9
1-180522 b	0.02014	9.31	0.55	−9.56	1.26	J2130−0025	0.4901	34	4.1	8.5
1-561034	0.09008	10.86	N/A	N/A	1.86	J1709+3421	0.3143	75	6.0	12.8
1-585207 b	0.02825	10.09	N/A	N/A	1.93	J0838+2453	0.0287	37	2.4	15.5
1-113242	0.04372	10.88	N/A	N/A	2.14	J2106+0909	0.3896	116	5.5	22.9
1-44487 b , c	0.03157	10.47	1.34	−10.34	1.74	J0758+4219	0.2111	136	6.2	22.6
1-44487 b , c	0.03174	N/A	N/A	N/A	N/A	J0758+4219	0.2111	137	N/A	N/A
1-564490	0.02588	10.15	2.60	−9.73	1.27	J1629+4007	0.2725	132	5.7	23.8
1-635629 c	0.01989	9.56	1.26	−9.45	1.34	J2130−0025	0.4901	66	1.7	38.7

Notes.

^a The 4000 Å break (D_n (4000)) was measured between 1 < R/R_e < 1.5 to avoid the AGN contamination. ^b Quasar–galaxy pairs have the same quasar sight lines. ^c The case of merged galaxies. N/A—not applicable, or not available.

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Our sample of 11 quasars was observed with HST COS under program ID 16242 (PI V. Kulkarni) during 2020 September–December. These observations are summarized in Table 2. The FUV channel of COS was used in TIME-TAG mode. The G130M FUV grating and the 25 Primary Science Aperture were used. The grating was centered at 1222 and 1291 Å to cover the absorption lines of interest. This leads to a resolving power across the dispersion axis of R ∼ 10,000–18,000. The grating settings were optimized so that the key lines do not fall in the gaps in the wavelength coverage or in geocoronal emission lines. Target acquisitions were performed using the ACQ/IMAGE modes, after which 3–11 exposures ranging from 515–1339 s each were obtained for each target.

Table 2. HST COS Observing log

Quasar	zquasar	R.A.	Decl.	Date	COS Setting	${T}_{\exp }$ a	S/N b
		(J2000.0)	(J2000.0)			(s)
J0755+0311	0.0332	118.85	39.18	2020 Sep 11	G130M/1291	2192	13.5
J0758+4219	0.2111	119.58	42.32	2020 Sep 6	G130M/1222	2147	5.3
J0838+2453	0.0287	129.55	24.89	2020 Oct 29	G130M/1222	7436	7.4
J0950+4309	0.3622	147.56	43.15	2020 Nov 27	G130M/1222	15254	9.4
J1237+4447	0.4612	189.39	44.79	2020 Dec 16	G130M/1222	4986	9.9
J1338+2620	0.0261	204.51	26.34	2020 Dec 17	G130M/1222	2062	4.5
J1629+4007	0.2725	247.26	40.13	2020 Sep 2	G130M/1222	7631	10.4
J1653+3945	0.0349	253.47	39.76	2020 Oct 8	G130M/1222	2086	13.7
J1709+3421	0.3143	257.49	34.36	2020 Sep 3	G130M/1291	9592	12.0
J2106+0909	0.3896	316.71	9.16	2020 Oct 10	G130M/1222	7376	4.5
J2130−0025	0.4901	322.59	−0.43	2020 Sep 12	G130M/1222	19310	7.8

Notes.

^a The total integration time (summed over all exposures). ^b The signal-to-noise ratio (S/N) was calculated at 6 pixel binning at ≃1250 Å.

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For a majority of the targeted galaxies, we clearly detect strong absorption lines of H i, Si ii, and Si iii at redshifts close to the galactic redshifts (within ±200 km s⁻¹). Since there are no other galaxies at these redshifts around the quasar sight lines (within ∣z_photom − z_gal∣ < 0.05 and ∼100 kpc and down to SDSS magnitude r ≃ 22), our HST COS spectra probe the CGM of the selected MaNGA galaxies. ¹¹ The profile fits to the HST COS absorption line data and the measurements of column densities are presented in detail in Appendix B.

2.2.1. Data Reduction and Spectral Extraction

2.2.2. Spectral Analysis

For each quasar/AGN, we analyzed the absorption systems at the redshifts of associated MaNGA galaxies. Figure 3 shows examples of our analysis for the four galaxies shown in Figure 2. Fits for the remaining sight lines are shown in Appendix B. To perform this analysis, we used a custom modification of the Voigt profile fitting code ¹² to derive the redshifts, column densities, and Doppler parameters of velocity components for H i, N i, O i, Ar i, and various low-ionization (Si ii, S ii, C ii, N ii, and Fe ii) and high-ionization (Si iii, Fe iii, N v, and O vi) metal absorption lines. The wavelengths and oscillator strengths for these transition were taken from Morton (2003). Further details about this code and examples of its usage can be found in Balashev et al. (2017, 2019).

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For each absorption line (except the case of damped H i Lyα described below), we derived the local continuum using a B-spline interpolation matched on the adjacent unabsorbed spectral regions. The spectral pixels used to constrain the fit were selected visually. The number of velocity components was also defined visually and increased in case of remaining structure in the residuals. Since our spectra have low signal-to-noise ratio (S/N ∼1–10) and given medium spectral resolution (∼20 km s⁻¹), we cannot resolve the velocity structure in detail. Therefore, the redshifts and Doppler parameters were tied for all species for each velocity component. The fit to each absorption lines was calculated by the convolution of the synthetic spectrum with the COS line spread function (LSF) chosen for the appropriate COS setting. ¹³ For weak lines, we present measurements of column densities where possible, and 3σ upper limits in cases of nondetections.

The H i column density was measured from the Voigt profile fit to the Lyα line. ¹⁴ For most of our spectra, the H i line is not damped (with N(H I) ≤ 10¹⁸ cm⁻²) and corresponds to the linear or flat parts of the curve of growth. In these cases, the number of components and b-values should be accurately constrained. Therefore, the number of components was defined visually from fitting to the profiles of associated metal lines (Si ii, Si iii, and C ii), and increased in case of remaining structure in the residuals. The range of b-parameters was constrained to 15–100 km s⁻¹ (the values of b-parameters measured for H i absorbers at z ≤ 1 in the COS CGM Compendium (Lehner et al. 2018), where H i lines were fitted using several transitions in the Lyman series). Then the redshift, b-parameter, and H i and metal column densities for each component were varied together using the AffineInvariantMCMC sampler by MADS ¹⁵ to obtain the posterior probability density function (PDF) of the fitting parameters. The column density of H i and metals and the b-parameters can be rather uncertain for individual components that are blended; however, the total column densities summed over the components are usually well constrained (with uncertainty ∼0.3 dex). We demonstrate the posterior PDF of fitting parameters for systems shown in Figure 3 in Appendix B, along with comments to fits for individual systems.

For one case, the galaxy J1338+2620, the absorption Lyα line shows damping wings and is located close to the galaxy Lyα emission line. An interesting feature of this spectrum is that both the emission Lyα line and absorption Lyα line are shifted relative to their expected positions. The emission Lyα line is redshifted by 150 km s⁻¹ with respect to the galactic redshift derived by positions of other emission lines (Hα, Hβ, S ii, N ii, and O iii) seen in the SDSS spectrum. The emission lines are very narrow ∼300 km s⁻¹ (similar to those for type II Seyfert galaxies), which allows the redshift to be well constrained. The Lyα absorption line has a broad core (∼300 km s⁻¹ wide), and its center is blueshifted by −150 km s⁻¹ with respect to the strongest component of the metal absorption lines (Si ii, S ii, and O i). Additionally we detect a decrease of the local continuum near the Lyα absorption and Lyα emission lines, which is consistent with the presence of the damped Lyα (DLA) absorption line with broad damping wings and high H i column density (10^20.3 cm⁻²). However, such an H i Lyα line is expected to have a broad bottom ∼600 km s⁻¹, twice the observed value. We believe this situation is similar to studies of proximate DLA absorption systems in quasar spectra, which work as a natural coronagraph for the Lyα emission from the accretion disk, while the leaking Lyα emission remains partially blended in the wings of the DLA system (see, e.g., Noterdaeme et al. 2021). In this case we simultaneously fitted both the absorption profile and the unabsorbed quasar continuum.

We consider two potential ways to fit the Lyα line in this spectrum: (i) it could be a sub-DLA system that covers the Lyα emission line only partially. In this case, the local continuum was modeled as the sum of a smooth component and a Gaussian emission line. The smooth component represents the flat part of the quasar continuum and was reconstructed locally by fitting with a B-spline interpolation. The Lyα emission line was fitted by a Gaussian function centered on the redshift of the quasar. The H i Lyα absorption line was fitted by the sum of four velocity components, whose redshifts were tied to the redshifts of the velocity components in metal absorption lines (O i, Si ii, S ii, Fe ii, and Si iii). A detailed fit to metal lines is provided in Appendix B. In this case, we derive the total H i column density (10^19.2±0.1 cm⁻²), and the best fit is shown in the top panel of Figure 4. We note, however, that (i) we needed to decrease the continuum level manually in the vicinity of the sub-DLA system, and (ii) the strongest H i component (10^19.2±0.1) is shifted to −150 km s⁻¹ relative to the strongest component in the metal absorption lines.

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The second possibility is a combination of a broader, more damped Lyα absorption line and leaked Lyα emission. The damped Lyα line was centered at the redshift of the strongest metal component at z = 0.026043. The profile of the leaked Lyα emission is non-Gaussian; therefore, it was fitted by a sum of three Gaussian lines. In this case, we derive the H i column density 10^20.2±0.1 cm⁻². The fit is shown in the middle panel of Figure 4. The absorption Lyα line is broad (∼600 km s⁻¹) and likely covers the emission Lyα line from the galactic center completely. In the bottom panel, we also show the fit by a model, where the galaxy Lyα emission line at the quasar redshift is added to the fit. However, the difference in the fit profile and the derived H i column density is small, compared to the fit (middle panel) without including the galaxy Lyα emission (∼0.1 dex).

The advantage of the fitting approach including the leaked Lyα emission is that (i) it can describe the decrease of the local continuum near the Lyα absorption without manual modification of the smooth B-spline fit and (ii) the redshift of H i component matches the redshift of the strongest metal components well. Therefore we adopt the column density of H i for this system to be 10^20.2±0.1 cm⁻².

The MaNGA (Bundy et al. 2015) survey is one of the three main components making up SDSS-IV (Blanton et al. 2017). Completed in 2020 June, MaNGA made integral field unit (IFU) spectroscopic observations of just over 10,000 galaxies using the 2.5 m Sloan Telescope at Apache Point Observatory (Gunn et al. 2006). These galaxies were selected from the extended version of the NASA-Sloan Atlas (NSA; Blanton et al. 2017; Wake et al. 2017) to be in the redshift range of 0.01 < z < 0.15 and have an approximately flat number density distribution as a function of stellar mass between 10⁹ and 10¹² M_⊙. The targets were further chosen so that they could be covered by the MaNGA IFU bundles out to either a radius of 1.5 or 2.5 times the effective radius (R_e ). Full details of the MaNGA sample selection are given in Wake et al. (2017).

The 17 MaNGA IFU bundles are hexagonal in shape with sizes in the range 12"–32" matched to the typical angular size distribution of the target sample of galaxies. In addition, there are 12 seven-fiber mini-bundles that are placed on flux calibration stars, and 92 single fibers for sky subtraction (Drory et al. 2015). All of the fibers feed the dual-channel Baryon Oscillation Spectroscopic Survey spectrographs (Smee et al. 2013), which cover a wavelength range of 3622–10354 Å with a median spectral resolution of ∼2000.

In this paper we use the reduced MaNGA data produced by the MaNGA Data Reduction Pipeline (Law et al. 2016) as well as derived data products produced by the MaNGA Data Analysis Pipeline (DAP; Westfall et al. 2019). These derived products include maps of various emission lines ([O ii], Hβ, [O ii], [N ii], Hα, [S ii]), and emission line and stellar velocities. We access and interact with MaNGA data using the Marvin (Cherinka et al. 2019) Python package.

We also make use of integrated galaxy properties included in the MaNGA data set that are derived from the extended version of the NSA. These include redshift, total stellar mass (M_*), elliptical effective radius (R_e ), and inclination, all derived from elliptical Petrosian aperture photometry (see Wake et al. 2017, for details).

2.3.1. Nebular Metallicity and Ionization Parameter

2.3.2. Galaxy Rotational Velocities

Beyond the ionization properties described above, we are also interested to see if there is any association between the velocity of the CGM absorption systems and galaxy rotational velocity. One might imagine the absorption systems tracing the gas dynamics at large radii.

In order to make such a connection, we fit disk rotation models to the stellar and gas velocity fields using models similar to those described in Bekiaris et al. (2016). We assume a flat thin disk in all cases linking the observed coordinates (x, y) to the projected major and minor axes coordinates of the disk (x_e, y_e) using:

$$\begin{eqnarray}&&{x}_{{\rm{e}}}=-(x-{x}_{{\rm{o}}})\sin \,\mathrm{PA}+(y-{y}_{{\rm{o}}})\cos \,\mathrm{PA},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{y}_{{\rm{e}}}=-(x-{x}_{{\rm{o}}})\cos \,\mathrm{PA}-(y-{y}_{{\rm{o}}})\sin \,\mathrm{PA},\end{eqnarray} \tag{ 2 }$$

where PA is position angle, and (x₀, y₀) are the coordinates of the center of the disk.

We define the radius of the disk r in the disk plane at the observed coordinates (x, y) as:

$$\begin{eqnarray}&&r=\sqrt{{x}_{{\rm{e}}}^{2}+{\left(\displaystyle \frac{{y}_{{\rm{e}}}}{\cos i}\right)}^{2}},\end{eqnarray} \tag{ 3 }$$

where i is the inclination of the disk to the line of sight.

The position angle relative to the major axis of the disk, θ, at (x, y) is given by

$$\begin{eqnarray}&&\cos \theta =\displaystyle \frac{{x}_{{\rm{e}}}}{r}.\end{eqnarray} \tag{ 4 }$$

To model the rotation curve, we make use of a two-parameter arctan profile (Willick et al. 1997):

$$\begin{eqnarray}&&{V}_{\mathrm{rot}}(r)=\displaystyle \frac{2}{\pi }{V}_{{\rm{t}}}\arctan \displaystyle \frac{r}{{r}_{{\rm{t}}}},\end{eqnarray} \tag{ 5 }$$

where V_rot(r) gives the rotation velocity at radius r, r_t is the turnover radius, and V_t is the asymptotic circular velocity. At large radii beyond r_t, this model represents a very slowly rising rotation curve.

Our final model for the velocity in the plane of the sky is given by

$$\begin{eqnarray}&&{v}_{\mathrm{model}}(x,y)={V}_{\mathrm{sys}}+{V}_{\mathrm{rot}}(r)\sin i\cos \theta \end{eqnarray} \tag{ 6 }$$

where V_sys represents any velocity offset from the systemic redshift used to generate the MaNGA velocity field. This model contains seven free parameters that we must fit for.

For all galaxies, we attempt to fit both the emission line and stellar velocity maps provided by the MaNGA DAP. We make use of the default MILESHC-MASTARSSP hybrid maps, which use a Voronoi binning scheme for the stellar velocities and individual spaxels for the emission-line velocities (see Westfall et al. 2019, for details). For the stellar velocity maps, we fit to all Voronoi bins that have not been masked by the DAP and have an S/N > 10. For the emission-line maps, we again exclude all masked spaxels and fit to those spaxels where any of the Hα, [O ii], or [O iii] lines have an S/N > 5. We also mask any regions of the maps not associated with the target galaxy, for instance the very close satellite galaxy of 1-44487.

We fit our model using the MCMC code emcee (Foreman-Mackey et al. 2013). We make an initial simpler fit to estimate the position angle and use that as our initial guess for that fit parameter. For the center, inclination, and r_t we make initial estimates based on the NSA photometry. For V_sys, our initial estimate is the median velocity within $0.5{R}_{e}$. Finally, we set V_t to 200 km s⁻¹ as our initial guess for all galaxies. For each fit, use 64 walkers each with 20,000 steps, discarding the first 10,000. We fit both the emission and stellar velocity maps simultaneously and each independently, potentially giving three fits for each galaxy.

Since our systems are not self-shielded from ionizing UV radiation, we need to calculate the ionization corrections to estimate the physical conditions and metallicity.

We used the photoionization code cloudy to infer the ionization structure of systems and estimate the metallicity, ionization parameter, and total hydrogen column density. We assumed a constant-density model in a plane parallel geometry illuminated by the radiation field and cosmic rays (CRs). The radiation field was modeled as consisting of two parts: the extragalactic UV background (UVB) radiation at z = 0.1 as computed by Khaire & Srianand (2019), ¹⁶ and the galaxy light component modeled by the interstellar radiation field as per the cloudy template, which is consistent with the Draine model in the UV range (Draine 1978). The interstellar radiation field was scaled by the factor I_UV to characterize the strength of the UV radiation from the nearby galaxy. This factor is especially important for our AGN sight lines (i.e., those with zero impact parameter), for which the distance of the absorbing region from the galactic center is unknown.

The UV and X-ray radiation produced by the galaxy (by stars and the AGN) is generally ignored for the CGM absorption systems because the H i ionizing photons produced within the galaxy are assumed to be absorbed by the neutral hydrogen and dust within the galaxy. Indeed, the average escape fraction of the H i ionizing photons from galaxies is assumed to be very low (<1%) at z < 1 (see, e.g., Khaire & Srianand 2019). However, the UV spectral observations of nearby galaxies (including our AGN sight lines) do not show the strong damped Lyα absorption line associated with the neutral hydrogen in those galaxies. Moreover, the spectra usually have strong Lyα emission lines. This indicates that the H i ionizing radiation can leak out of the galaxies along these sight lines and increase the UV background around the galaxies. The intrinsic spectral energy distribution (SED) of the galactic radiation is unknown for our galaxies; therefore, we chose one of the cloudy templates to model this radiation. The SED of this interstellar radiation model is similar to that for the UVB model, and about 100 times more intense in the range of 1–100 eV at I_UV = 1. Therefore, we varied this parameter in the range of $-3\leqslant \mathrm{log}{I}_{\mathrm{UV}}\leqslant 1.0$ to allow for a wide range of values of the escape fraction and the galactic SFR/AGN activity.

We also took into account the ionization of the CGM by cosmic rays (CR), given that simulations predict a strong effect of CR on the evolution of the CGM up to a distance of about several hundred kiloparsecs from the galaxy (Salem et al. 2016). The intensity of CR ionization rate was consistently scaled with the same factor I_UV. The initial value of CR ionization rate was set to the average value in the Milky Way (MW; 2 × 10⁻¹⁶ s⁻¹). The number density in the models is characterized by the parameter (n_H) and the chemical composition by the parameter of gas metallicity [X/H]. The element abundance pattern was chosen according to the model by Jenkins (2009), where the parameter F_⋆ regulates the value of dust depletion. F_⋆ is varied from 0–1, where F_⋆ = 0 and F_⋆ = 1 denote the minimum and maximum level of depletion, respectively. The depletion pattern in these cases roughly corresponds to typical values seen in the MW halo and MW ISM (Welty et al. 1999).

The size of the model cloud is calculated by cloudy in such a way that the modeled H i column density was equal to the observed value. Since the observed values of the H i column density (total and for individual components) are not very well constrained for the quasar sight lines (within ∼0.1–0.7 dex), we set the H i column density as an additional fitting parameter. Then we calculated a grid of models that uniformly covers the parameter space in the ranges of $-3.5\leqslant \mathrm{log}{n}_{{\rm{H}}}/{\mathrm{cm}}^{-3}\leqslant 1.0$ (with a 0.5 dex step), $-3\leqslant \mathrm{log}{I}_{\mathrm{UV}}\leqslant 1.0$ (with a 0.5 dex step), $-3\leqslant \mathrm{log}[{\rm{X}}/{\rm{H}}]\leqslant 2.0$ (with a 0.5 dex step), 0 < F_⋆ < 1 (with a 0.25 step), and $13\lt \mathrm{log}N({\rm{H}}\,{\rm\small{I}})\lt 20.5$ (with a 0.5 dex step). For each node of the grid, we saved the column densities of metals (Si ii, Si iii, S ii, C ii, N i, N ii, N v, Fe ii, and O i) and the ionization parameter q = Q/4π R² n_H c, and calculated interpolations of metal column densities and q on the grid.

Then we calculated the likelihood function for the fitting parameters (n_H, I_UV, [X/H], F_⋆, and N(H I)) based on a least-squares comparison of the observed and modeled column densities for the various ionic species. For this, we used the MCMC approach with implementation of the affine-invariant ensemble sampler. The parameters were varied simultaneously to derive maximum probability values, and their uncertainties corresponded to the 63.8% interval. The results are presented in Table 3 for the total column densities and Table 5 for the individual velocity components. A comparison of metal column densities predicted by cloudy with the observed one in the absorption systems is shown in Figure 36 in Appendix B.

The cloudy models allow us to describe the observed column densities relatively well. As can be seen from Figure 36, the observed column density values and their uncertainties show good consistency with the predicted ranges of values for the ions of Si ii, Si iii, and C ii (which show strong absorption lines and are detectable in our data even at relatively low S/N). For other ions whose lines are relatively weak (e.g., N i, N v, and S ii), the cloudy models predict lower column densities than the observed values. This difference may be caused by an overestimate of the measured column densities from the noisy spectra. In Table 6 we also present estimates of the metallicity and the ionization parameter in the individual velocity components. In some systems (e.g., J1237+4447 or J0950+4309), large differences are observed between the different components, which may indicate substantial differences in physical conditions between the components (e.g., in the ionization parameters, which can cause different Si iii/Si ii ratios). In such cases, the fit to the total column densities is not reliable, and we need to analyze the parameters in individual components. In some cases, we are not able to resolve individual absorption components in the H i Lyα line and therefore cannot accurately measure their H i column densities, although the total column density is well constrained (e.g., J1338+2620). In the case of J1338+2620, we analyze the physical conditions assuming equal metallicity for the components. We also note that, in some cases (e.g., J0758+4219), there is good consistency between the physical conditions inferred for the different velocity components.

Figure 7 shows the comparison of the parameters derived with cloudy (metallicity, depletion level, ionization parameter, and total hydrogen column density) and column density of H i. The metallicity spans over 3 orders of magnitude from −1.5 to 2 dex and is anticorrelated with the hydrogen column density. Low H i column density systems tend to have higher metallicities and higher ionization. Similar results were found by Muzahid et al. (2018) and Werk et al. (2014). There is good agreement, but it is probably caused by fitting with the same photoionization code. We should also reiterate that cloudy indeed contains many assumptions: perhaps most importantly, it is a 1D calculation.

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We note an interesting difference in the physical conditions between the absorbing regions in our quasar sight lines and AGN sight lines. The AGN absorbing regions are located at different ends of the distributions of the physical conditions. For J0755+0311 and J0838+2453, we detect high values of the metallicity and the q parameter, whereas J1338+2620 has a low metallicity and a low q parameter. The depletion level for J1338+2620 is also unusually high F_⋆ = 0.8 ± 0.2, while it is low for other systems (F_⋆ < 0.3). A high value of F_* is typical for the cold neutral phase of the ISM of the MW, while a lower depletion level (∼0.2) corresponds to gas in the warm phase and galaxy halo (Welty et al. 1999). We speculate that the absorption in J0755+0311 and J0838+2453 may be associated with outflowing gas driven by those AGNs, while the absorption in J1338+2620 may be associated with inflowing cold gas falling into the AGN.

Also, we note that there is no detection of low metallicity and low N(H I) gas, which could correspond to infalling metal-free gas in the outskirts of the galaxies. This may be caused by a selection effect due to the difficulty of detecting weak metal lines: for low N(H I) and low metallicity, we can set only upper limits on the metal column densities, which do not allow us to constrain physical conditions with cloudy, so the estimates for such absorbers are very uncertain.

First, we check the correlation of the total H i column density with the impact parameter. ¹⁷ We find that the quasar and galaxy sight lines in our sample show different behaviors. The quasar sight lines probe gas around galaxies with impact parameters in the range 20–130 kpc. For them we find a decrease in the H i column density with increasing impact parameter. This result is in line with other studies of quasar–galaxy pairs at low redshift, such as the COS-Halos, COS-Weak, and the Galaxies on Top of Quasars (within impact parameters ∼1–7 kpc) surveys (e.g., Tumlinson et al. 2013; Muzahid et al. 2018; Kulkarni et al. 2022), and at higher redshift (z = 0.3–1.2, e.g., the MUSE-ALMA Halos, MAH, survey; Karki et al. 2023; Weng et al. 2023). A comparison of our results with these other studies is shown in Figure 8.

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The AGN sight lines have, technically, zero impact parameter, but the absorbing gas can be separated from the galactic center at any distance along the sight line. In one case, J1338+2620, we found a high H i column density (≃10^20.2 cm⁻²), consistent with what is seen in quasar sight lines at very low impact parameters (Kulkarni et al. 2022). In other AGNs, the H i absorption lines are weak (≃10¹³ cm⁻²) or not detected. A natural explanation in these latter cases may be a high ionization of the gas in the central outflow or (less likely) highly ionized gas in the IGM. To avoid confusion, we do not show the cases of the AGN sight lines in Figure 8.

The top-left and top-right panels of Figure 8 show the H i column density plotted versus the impact parameter in physical (proper) and comoving ¹⁸ units, respectively. The physical units correspond to the distance in the rest frame of each galaxy and can be meaningfully compared to simulations in physical units. The comoving units factor out the cosmological expansion, allowing for a comparison of the properties of galaxies at different redshifts. The difference between the physical and comoving impact parameters is not significant for our MaNGA galaxies due to their low redshift (z = 0.01–0.10), but is larger for higher-redshift galaxies in the literature (z = 0.15–0.35 for the COS-Halos galaxies, z = 0–0.3 for the COS-Weak galaxies, and z = 0.3–1.2 for the MAH galaxies), and for the simulations of the higher-redshift CGM. We also plot in Figure 8 the median radial profile of the H i column density and the 1σ scatter around that from magnetohydrodynamic simulations of an isolated MW-mass galaxy at z = 0–0.3 by van de Voort et al. (2019; based on the Auriga project, Grand et al. 2017), and from the study of the distribution of cold gas in the CGM around galaxy groups ($\mathrm{log}{M}_{\mathrm{halo}}\sim 13.2\mbox{--}13.8$ and $\mathrm{log}{M}_{* }\sim 11.3\mbox{--}11.8$) at z = 0.5 by post-processing TNG50 simulations by Nelson et al. (2020).

Combining the observational data from the different studies mentioned above, we cover relatively well a wide range in b parameters of 1–150 kpc. There is agreement between most of the observations and the radial profile from the simulations within the uncertainties, although we note higher H i column densities compared to the simulations for a few MAH galaxies at high impact parameters. These outliers have z > 0.7, which is higher than for the rest of the observed galaxies. A similar increase in the N(H I) profile at high impact parameters for high-redshift galaxies was reported earlier by Kulkarni et al. (2022). In the comoving coordinates, the median N(H I) radial profiles from the Auriga and TNG50 simulations are in better agreement with each other, suggesting that the difference between them is probably due to the difference in redshift. Most of our MaNGA galaxies show weaker H i absorption than the simulated Auriga galaxy. The agreement with the simulated TNG50 galaxies is better than with the Auriga galaxy. We note, however, that our MaNGA galaxies are lower in redshift than the TNG50 galaxies, and are also lower in stellar mass than the Auriga and TNG50 galaxies.

The bottom-left and bottom-right panels of Figure 8 show the H i column density plotted versus the impact parameter normalized to the effective radius (R_e) and virial radius (R_vir). The virial radius was estimated as ${(3{M}_{\mathrm{halo}}/200{\rho }_{\mathrm{cr}}4\pi )}^{1/3}$, where M_halo was estimated from the M_⋆–M_halo relation by Girelli et al. (2020), and ρ_cr is the critical density at the redshift of the galaxy. For galaxies at low redshift, all absorbers classified as DLAs and several classified as sub-DLAs are associated with the region within ∼3 effective radii. Most LLSs appear to correspond to the region from ∼3 to ∼30 effective radii. The trend of N(H I) with b/R_e is similar to the trend with b. Comparison of N(H I) with b/R_vir shows that all of the detected H i absorbers are within the virial radius.

Figure 9 shows the relations between the H i column density of the associated absorbers, and the stellar mass, the specific star formation rate (sSFR = SFR/M_*), and the D_n (4000) index of the host galaxies, based on our sample and the literature. The stellar mass and sSFR in our sample range from 10⁷ M_⊙to 10¹² M_⊙ and from 10⁻¹² yr⁻¹ to 10⁻⁹ yr⁻¹, respectively. Most of our galaxies are star-forming (sSFR > 10⁻¹¹ yr⁻¹). The value of D_n (4000) index ranges from 1.27 to 2.14 and characterizes the star formation history in the center of the galaxy.

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Absorption systems with a high H i column density are more likely related to low-stellar-mass galaxies (Kulkarni et al. 2022), while systems with a lower H i column density are associated with the halos of more massive galaxies (e.g., Kulkarni et al. 2010; Tumlinson et al. 2013; Augustin et al. 2018).

The MaNGA galaxies from our sample also follow this trend. Three systems with the highest H i column density (N(H I) ≥ 10¹⁸ cm⁻²) are observed near galaxies with M_* ≤ 10⁹ M_⊙, while the other systems correspond to high stellar mass galaxies with M_* ≃ 10¹⁰–10¹¹ M_⊙. For the sample of low-redshift z < 0.35 systems (our data; Tumlinson et al. 2013; Kulkarni et al. 2022), we obtain a correlation coefficient r_S = − 0.34 and p-value of 5 × 10⁻³, for the entire sample, including MUSE-ALMA observations, r_S = − 0.44 and p = 2 × 10⁻⁵. We do not see a difference in the H i content for galaxies with low or high sSFRs. However, a strong negative correlation is observed between the sSFR and stellar mass for AGNs in all of the samples examined here, including our own galaxies and those from the literature (r_S = − 0.66, p = 2 × 10⁻⁹).

We also report a strong dependence of N(H I) decreasing with increasing D_n (4000) for quasar sight lines—discounting the nondetection of 1-564490 due to a large impact parameter. The Spearman rank-order correlation coefficient is r_S = − 0.94, and the p-value is 0.015. It is interesting that this correlation connects the gas content at very large radii to the star formation history in the center of the galaxy. We suspect we would see the same thing with sSFR if we had measures of sSFR for the three quasar sight-line galaxies with D_n (4000) > 1.7. For galaxy sight lines (when we get the spectrum from the central AGN), we do no see a such dependence probably due to the contamination of the observed spectra by the AGN.

Comparing the correlations between N(H I) and b, M_*, D_n (4000) we believe that a primary correlation is likely with stellar mass. Higher-mass galaxies have a higher D_n (4000) index, and their higher past star formation activity is expected to affect cool gas around them, both because cool gas is consumed in star formation and because AGN radiation and stellar winds blow out gas around these galaxies. We do not have many observations of cool gas around massive galaxies at low impact parameters to check this statement in further detail.

At the spectral resolution of COS G130M, we can obtain fairly reliable velocity profiles for the absorbing gas along the sight line through the galaxy. This can be compared with kinematics of the ionized gas from MaNGA data. With this in mind, we used the radial velocity maps of the stellar disk and H_α gas for our galaxies to reconstruct the position of the quasar sight lines relative to the gaseous disks of the galaxies and examined the correspondence between the radial velocities of the absorbers and the rotation of the galactic gaseous disks.

First, we fitted both the gas velocity map (H_α line emission) and the stellar velocity map with symmetric models of thin disk rotation. This formalism was described in Section 2.3.2. We choose the best fit, giving priority to the joint fit (stellar+H_α emission) first, followed by the H_α emission-line fit, using only the stellar fit if others did not fit. The position angle (PA), inclination angle (i), and maximal rotation velocities (${V}_{\max }$) are presented in Table 4. The fitted velocity map and rotation curve for each galaxy are shown in Figures 18–26.

Table 4. Properties of MaNGA Galaxies

MaNGA	zgal	Re	[O/H]	∇R[O/H]	$\mathrm{log}{q}_{\mathrm{ion}}$	∇R[q]	${V}_{\max }$ a	PA	Incl.	ϕstand b	ϕmodel c
ID		(kpc)		(10−3 kpc−1)		(10−3 kpc−1)	(km s−1)	(deg)	(deg)	(deg)	(deg)
1-71974	0.03316	4.9	0.31 ± 0.04	−7 ± 2	7.16 ± 0.07	−13 ± 2	151	147	33	${57}_{-4}^{+4}$	${57}_{-4}^{+4}$
1-385099	0.02866	5.4	N/A	N/A	N/A	N/A	200	21	32	${58}_{-2}^{+2}$	${58}_{-2}^{+2}$
1-585207	0.02825	2.4	N/A	N/A	N/A	N/A	155	13	47	${34}_{-2}^{+2}$	${18}_{-20}^{+20}$
12-192116	0.02615	3.3	−0.25 ± 0.08	−18 ± 2	7.05 ± 0.20	−40 ± 2	64	141	36	${54}_{-1}^{+1}$	${54}_{-2}^{+2}$
1-594755	0.03493	1.3	N/A	N/A	N/A	N/A	144	162	22	${68}_{-4}^{+4}$	${68}_{-4}^{+4}$
1-575668	0.06018	10.6	N/A	N/A	N/A	N/A	500	172	8	${10}_{-4}^{+4}$	${0}_{-24}^{+24}$
1-166736	0.01708	3.4	−0.16 ± 0.10	−18 ± 8	6.96 ± 0.18	−8 ± 1	58	156	53	${50}_{-8}^{+8}$	${28}_{-23}^{+25}$
1-180522	0.02014	4.1	0.06 ± 0.07	−26 ± 2	7.02 ± 0.12	3 ± 1	124	122	74	${4}_{-12}^{+12}$	${4}_{-15}^{+15}$
1-635629	0.01989	1.7	0.35 ± 0.05	−14 ± 4	7.04 ± 0.10	−50 ± 5	124	16	65	${28}_{-2}^{+2}$	${27}_{-15}^{+15}$
1-561034	0.09008	6.0	N/A	N/A	N/A	N/A	236	61	50	${44}_{-3}^{+3}$	${28}_{-18}^{+27}$
1-113242	0.04372	5.5	N/A	N/A	N/A	N/A	550	12	26	${17}_{-2}^{+2}$	${5}_{-23}^{+22}$
1-44487	0.03157	6.2	0.33 ± 0.05	−14 ± 1	7.06 ± 0.10	−11 ± 1	225	25	78	${6}_{-2}^{+2}$	${9}_{-8}^{+6}$
1-564490	0.02588	5.7	0.36 ± 0.05	−20 ± 2	7.10 ± 0.13	−60 ± 3	150	129	52	${56}_{-2}^{+2}$	${30}_{-22}^{+25}$

Notes.

^a The maximal rotation velocity of the galaxy derived from fitting the "arctan" model. ^b The elevation angle derived by the standard method. ^c The elevation angle using the model of gas distribution around the galaxy.

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4.3.1. Elevation Angle and the Position of Absorbers

The analysis of velocity maps gives us the orientation of the galactic disk relative to the quasar/or galaxy sight line. Here we determine the orientation of absorption system along the quasar sight line with respect to disk plane. To be consistent with Péroux et al. (2020), we adopt (ϕ) to be the elevation angle (90° − polar angle) or latitude with respect to the disk plane and (θ) to be the deprojected angle in the disk plane with respect to the major axis. ¹⁹

We estimated the elevation angle (ϕ) of absorption systems in two ways:

(a) using the standard approach as the angle between the galaxy's major axis and the line joining the galactic center to the quasar on the sky plane (Bouché et al. 2012), and

(b) by integrating the elevation angle along the quasar sight line using a model for the gas distribution around the galaxy. In this approach, we assume that the probability of detecting gas absorption along the sight line can be described as follows:

$$\begin{eqnarray}&&f(r,\phi )=C\times {f}_{{\rm{\Omega }}}{f}_{r}{f}_{\phi },\end{eqnarray} \tag{ 7 }$$

where (r, ϕ) are the radial coordinates and elevation angle of the point along the sight line, C is a normalization coefficient, f_Ω = 1/r² characterizes the decrease in the gas cross section with increasing distance from the galactic center (lower solid angles are probed at larger distances), and f_r and f_ϕ are model distributions of the gas density around the galaxy. For f(r), we adopt the Navarro–Frenk–White halo density profile (Navarro et al. 1997)

$$\begin{eqnarray}&&{f}_{r}={r}_{s}/r{\left(r+{r}_{s}\right)}^{2},\end{eqnarray} \tag{ 8 }$$

with the parameter r_s = 6R_e . For the elevation angle distribution f_ϕ , we adopt

$$\begin{eqnarray}&&{f}_{\phi }={ \mathcal N }(0,\pi /6)+{ \mathcal N }(\pi /2,\pi /6),\end{eqnarray} \tag{ 9 }$$

where ${ \mathcal N }(\mu ,\sigma )$ is a Gaussian distribution with a mean μ and a width σ. Thus, f_ϕ is a bimodal distribution with two peaks, one near the galaxy plane and the other near the polar axis, with opening angles of about 30°, consistent with the range of outflow opening angles from ${\theta }_{\max }=30^\circ$ to 45° estimated from galaxy spectra with outflow detections (e.g., Martin et al. 2012). Using the probability function of Equation (7), we calculate the mean value of the elevation angle as:

$$\begin{eqnarray}&&\overline{\phi }={\int }_{-\infty }^{\infty }\phi (x)f(r(x),\phi (x)){dx},\end{eqnarray} \tag{ 10 }$$

where x is the coordinate along the quasar sight line.

Figure 10 compares these two estimates of the elevation angle. The values agree mostly within the uncertainties. Approach (b) usually predicts lower elevation angles, because it takes into account a higher probability of detection for directions along the galactic plane, while the standard method corresponds to the direction with the smallest impact parameter. For galaxy sight lines (i.e., those with zero impact parameters), we estimated the elevation angle of absorption systems as (π/2) − i, where i is the inclination angle of the galaxy. Using approach (b), we also calculated the deprojected radial coordinate of the absorption system in the disk plane (d) and height of the absorption system above the disk plane (h) as follows:

$$\begin{eqnarray}&&d=r\cos \overline{\phi },h=r\sin \overline{\phi },\end{eqnarray} \tag{ 11 }$$

where r is the radial coordinate of the point along the sight line with the highest probability f(r, ϕ).

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4.4.1. Quasar Sight Lines

We now compare the absorber velocities in the five quasar sight lines that show absorption detections with the corresponding best-fit models of galactic disk rotation in six MaNGA galaxies. Using the fits to MaNGA emission-line velocities maps, we calculate the radial velocity of the galactic disk along the direction toward the quasar sight line. The comparison is shown in Figure 11. We show both the components seen in H i alone and the components seen in H i as well as metals. Additionally, we show each of these quasar–galaxy pairs in Figures 18, 19, 21, 22, and 23 in Appendix B.

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For three of the six galaxies (1-166736, 1-180522, and 1-575668) there is good agreement between the velocities of the strongest H i absorption components and the predicted radial velocities of the galactic disks within ±50 km s⁻¹. We note that these quasar sight lines are located within 10 effective radii from the corresponding galaxies. For two other galaxies (1-635629 and 1-113242), the absorption velocity is in the opposite direction to that expected from the galactic disk rotation. And for one galaxy (1-44487), the absorption components are spread over a wide range ∼350 km s⁻¹. However, this range is comparable with the velocity of galaxy rotation in the quasar sight line direction (∼250 km s⁻¹).

The middle panel of Figure 11 shows the velocity offset normalized by the predicted galactic disk rotation radial velocity at the appropriate distance. It is clear that this normalized velocity offset is within ∼±1 in most cases. In other words, the absorbing gas velocity is generally consistent with corotation with the galactic disk within ∼25 effective radii.

We comment now on the difference between the kinematics of the absorbing gas components seen in both H i and metal lines, and those seen in only H i lines. In all cases, only H i absorption is observed in components with a low H i column density (∼10¹³ cm⁻²), whereas absorption in both H i and metals is observed in components with N(H I) > 10¹⁵ cm⁻². Thus the absence of metal absorption in only H i components is likely to be due to a limit in the sensitivity for detecting weak lines at the S/N reached. Second, two out of the three cases of large normalized velocity offsets are for H i-only absorbers, possibly suggesting that the H i-only absorption may be related to the galaxy halo or the IGM and thus not participate in the galaxy disk's rotation. The metal-bearing H i absorbers are, however, likely to relate to the disk gas and hence corotate with it.

It is of interest to understand whether or not the H i-only absorption is bound to the galaxies. To examine this, we compare the velocity offsets of the absorbers relative to the systemic redshifts of the galaxies with the expected escape velocities at the impact parameters of the quasar sight lines. To estimate the escape velocity at a distance r from the center of galaxy with stellar mass M_* we used the methodology described in Kulkarni et al. (2022). The right panel of Figure 11 shows the velocity offsets with respect to galactic redshifts ²⁰ for the quasar sight lines in our sample. The curves show the escape velocity as a function of the distance for stellar masses of $\mathrm{log}{M}_{* }=9$, 9.5, 10, 10.5, and 11. There are two galaxies (1-166736 and 1-44487), for which the velocity offset of only H i components exceeds the escape velocity at the corresponding distance: these components may be associated with unbound outflow or be formed from the IGM. At the same time, the other two cases of only H i absorption correspond to more massive galaxies (1-575668 and 1-113242, M_* ∼ 10¹¹ M_⊙), where the gas is likely bound to the galaxies. The metal-bearing H i absorbers appear to be bound to the galaxies (only one such absorber, associated with the galaxy 1-180522, has a radial velocity very close to the escape velocity).

The most interesting case is that of the quasar−galaxy pair, J2130−0025 and 1−180522. The galaxy is observed with a high inclination angle of about 70° (nearly "edge-on"), and the quasar sight line is located very close to the galactic plane (elevation angle is ∼3° ± 7°) at ∼8.5 effective radii. In this case, we find very good consistency between the absorption velocity and the galactic disk rotation velocity. The sight line of J2130−0025 is also close to another galaxy, 1-635629, which has a similar redshift as 1-180522, but is located at a distance of about 39 effective radii. In fact, the velocity of the absorption system is opposite to the expected disk velocity for 1-635629. We therefore infer that the absorption system corresponds to only one galaxy, 1-180522, and that there is no detection for 1-635629.

In two cases, 1-166736 and 1-575668, we also detected high-velocity components with velocity offset v ≃ − 200 km s⁻¹ and +400 km s⁻¹, respectively. Since these components have low H i column densities ∼10^13.5 cm⁻², they are likely to be highly ionized clouds. In the case of 1-166736, the direction of the cloud velocity is consistent with the direction of the gas outflow, which can be detected with the targeted quasar sight line (see Figure 18). Assuming that the galaxy has two cone-shaped outflows from the center in both directions along the polar axis, the quasar sight line can probe the outflow only in the direction to the observer (with negative radial velocity) and cannot probe the outflow in the opposite direction (with positive radial velocity), because this part of the sight line is located far from the galactic center; see the "Z–Y" projection in Figure 18. In the second case, galaxy 1-575668 is observed nearly "face-on" with a small inclination ∼8° (see Figure 22). The quasar sight line can probe both outflows; however, the distance between the sight line and galactic polar axis is lower from the side of positive velocity outflow. Therefore, the probability of detecting an absorption system with a positive radial velocity is higher, which is in line with observations.

Two other galaxies, 1-44487, and 1-113242 show velocity offsets, with the velocity of the strongest H i components about −100 and +200 km s⁻¹, respectively. In both of these cases, the quasar sight lines are located at ∼23 effective radii, which is about twice the distance of the first group, where we detect a good agreement. In the case of 1-44487, we find at least four absorption components with velocities spanning a wide range of ∼300 km s⁻¹. Since the galaxy is relatively far from the quasar and the absorption has a complex structure, relatively high N(H I) ∼ 10¹⁵ cm⁻² and supersolar metallicity ([X/H] = + 0.8), we checked the area around the quasar for other galaxies with similar redshift, but found none. However, we note that this galaxy is merging with another smaller galaxy, and it is likely that the observed high metallicity is due to outflows in a region of enhanced star formation caused by the merger.

Summing up, we find consistency with gas corotation along with the galactic disk within at least 10 effective radii in most cases. The sign of the velocity of higher-velocity absorption, when detected, is consistent with the direction of the central galactic outflows, which have a higher probability of detection in these sight lines. For quasar sight lines at larger impact parameters, the situation is less clear.

4.4.2. AGN Sight Lines

Combining the cool-gas metallicity along with the warm-gas metallicity is essential to building a complete census of metals in and around galaxies. While such comparisons of cool-gas metallicity and warm-gas metallicity have been performed in IFS studies of quasar absorbers at higher redshifts (e.g., Péroux et al. 2012, 2014), such comparisons have not been performed for the z ∼ 0 galaxies that have much more detailed information. Our study of the CGM of MaNGA galaxies offers an opportunity to study differences in metallicity in the inner versus outer parts of galaxies in some of the closest venues available, and can thus provide fresh insights into processes affecting galactic evolution.

With this in mind, we study how the gradient of IZI metallicity derived from the fit to MaNGA emission-line maps within a few effective radii corresponds to the metallicity measured in the absorption systems along the targeted sight lines. Simulations predict a change in the metallicity gradient from an almost linear relation in the galactic disk (e.g., Mingozzi et al. 2020) to a flatter behavior in the CGM (Péroux et al. 2020). Our sight lines probe the transition region between these two limits. Figure 12 shows the comparison for five galaxies, where we simultaneously measured metallicity in the galaxy and the absorption system. For the absorption systems, we show the average metallicity and local metallicity in individual components derived from fits with the cloudy photoionization models (see Section 3.1). For the studied systems, the average and local values are in good agreement with each other. For absorption in quasar sight lines, we use the deprojected radial coordinate of the absorption system in the disk plane (d) calculated in Section 4.3.1. For the galaxies, we calculate the gradient of the IZI metallicity in the galactic disk in two ways: (i) by averaging over all directions and (ii) by averaging over only the spaxels within ±15° opening angle around the direction to the quasar sight line. The second way is possible only for quasar−galaxy pairs, when we have a preferred direction. The gradients are shown by gray and pink lines, respectively. In Figures 18–26 we also present the IZI metallicity maps and fits to their radial profiles. The deprojected radial coordinate of each spaxel in the MaNGA maps was derived from the best-fit model of the galactic radial velocity map (see Section 2.3.2). The model for the metallicity radial gradient in the CGM has been taken from post-processing of the TNG50 galaxy simulation presented by Péroux et al. (2020) in their Figure 5. It represents measurements of the CGM metallicity in the TNG50 simulation at four values of impact parameter: b = 25, 50, 100, and 200 kpc, and four values of azimuthal angle: 0°, 30°, 60°, and 90°. Other parameters were set to the appropriate values, which are: redshift z = 0, stellar mass M_* equal to stellar mass of the MaNGA galaxies. The metallicity is decreased by 0.4–0.7 dex between 25 and 200 kpc in outflow (at 90°) and galactic disk (at 0°) directions, respectively. It is greater than the metallicity gradient due to the elevation angle change, 0.1–0.4 dex at 25 and 200 kpc, respectively. Péroux et al. (2020) suggested that this is because fountains do not yet promote metal mixing over the full volume (i.e., range of elevation angles) at the distances b ∼ 100 kpc, as occurs closer to the galaxy. For the absorption systems in the AGN sight lines, we show the level of metallicity in the absorption system with the horizontal red line, since the distance of the absorbing region from the galactic center is not known.

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Comparing the five panels of Figure 12, we note that we confirm the increase of the galactic central metallicity with the stellar mass, previously reported by Mingozzi et al. (2020) for star-forming galaxies from the MaNGA survey. Second, we detect a consistency of metallicity in the absorption system in the quasar sight lines with the prediction from the metallicity gradient for two galaxies (1-180522 and 1-166736). These quasar sight lines (J2130−0025 and J0950+4309, respectively) more likely probe gas near the galactic plane at ∼7 and ∼8 effective radii. In these cases, the metallicity gradient measured from the fit to MaNGA maps (at 2–3 effective radii) can persist over a longer distance. The metallicities in these absorption systems are also consistent with the prediction for the CGM metallicity showing that the simulations may reproduce the CGM properties well. For the third galaxy, 1-44487, we measure about 2 orders of magnitude higher metallicity, than the predictions from the "galaxy" gradient. Since the impact parameter is high (137 kpc), this quasar sight line should probe metallicity in the CGM, which is expected to be higher than that predicted from the "galaxy" gradient. For stellar mass ∼10^10.5 M_⊙, the CGM metallicity is expected to be about [X/H] = − 0.5, which is still ∼1.5 orders of magnitude lower than the measured value. This discrepancy may result from the activity of the merged galaxy. For the absorption systems located toward the galactic centers of 1-71974 and 12-192116 galaxies, we found an excess of metallicity in the first case, which can be caused by a high-metallicity central outflow, and one order lower metallicity in the second, which may be the metallicity of the "satellite" galaxy or an HVC (see the discussion of this case in Section 4.4.2.).

Hydrodynamic simulations of galactic evolution predict an increase of CGM metallicity with the elevation angle with respect to the disk plane (see, e.g., Péroux et al. 2020). Metal-free gas is expected to fall into the galaxy along directions close to the galactic disk plane, while metal-rich gas is expected to flows out of the galactic disk in directions near the perpendicular to the plane by stellar winds and supernova explosions. Therefore, we can expect an increase of gas metallicity with the elevation angle (e.g., see Figure 5 in Péroux et al. 2020). The angular gradient of metallicity is predicted to be around +0.4 dex/90° for galaxies at z ≃ 0.

Figure 13 presents the dependence of metallicity in absorption systems on the elevation angle in our sample. For each system, we show the metallicity measured in the velocity components to test the variation of physical conditions. We also show the two estimates of the elevation angle discussed in Section 4.3.1 ((a) from the standard method, and (b) from the model of gas distribution). We find that, if we consider the metallicity only in quasar absorption systems (apart from the case of the merged galaxy, 1-44487), we have a good agreement between the observed absorption metallicities and the simulations. The main difference in the measured metallicities is due to the difference in galaxy stellar masses, whereas the gradient with the elevation angle is small. The metallicity measurements in the AGN sight lines should not follow the trend in the simulations, because they probably do not probe the CGM. The galaxy sight lines can probe gas at very low distances and in AGN central ejections, which could describe high metallicity and high ionization of these systems. However these processes were not considered in the simulations by Péroux et al. (2020), van de Voort et al. (2021), and Wendt et al. (2021), meaning no AGN at low M_⋆ in simulations. At the same time, the galaxy 12-192116 shows good consistency. In this case, we may be dealing with a galactic absorption system with an unusually large elevation angle, and we suggest that it may be caused by absorption from a "satellite" galaxy, or from metal-poor inflowing gas.

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We also compare our results with metallicity measurements in the COS-Halos survey (Werk et al. 2014). The effective radii of the COS-Halos galaxies were derived from the relation between the effective radius and the stellar mass by Mowla et al. (2019). We do not detect a significant correlation between [X/H] and b/R_e for the joint sample, with a Spearman rank-order correlation coefficient of 0.1 and a p-value of 0.46.

Figure 14 shows the ionization parameter versus impact parameter and elevation angle for our sample galaxies. We find the ionization parameter to be roughly constant for MaNGA galaxies with a mean of ∼10^−3.3 and the dispersion of ∼0.1 dex (see Table 3). On the contrary, the ionization parameter in the absorption systems spans over 2 orders of magnitude above the average galactic ionization. The difference may be primarily due to the difference of gas number density between the ISM (∼10² cm⁻³; e.g., Mingozzi et al. 2020) and the CGM (∼10⁻¹–10⁻³ cm⁻³). The ionization parameter q = n_γ /n_H is proportional to the ratio of I_UV/n_H. Assuming the ionization of the CGM is due to the extragalactic background only (whose intensity is about 10⁻² of the average UV galactic radiation), the difference in q parameter is obtained from ${({n}_{{\rm{H}}}^{\mathrm{CGM}})}^{-1}$, which gives a factor 10–10³ for the range of the CGM number densities. The factor will be lower if the galactic UV intensity is stronger than the average UV galactic radiation.

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We did not find much correlation of the ionization parameter of the absorption systems with galactic properties such as stellar mass, SFR, or sSFR. However, it correlates with the elevation angle (see the right panel of Figure 14).

As shown above, quasar sight lines probe gas around galaxies at lower elevation angles and at higher impact parameters than AGN sight lines (1-385099 and 1-71974), and for the former, we found lower ionization parameters. This is consistent with the picture that gas at small elevation angles corresponds to galactic disks (or inflowing gas) and has lower metallicity and lower ionization parameters than the gas observed in absorption at larger elevation angles (which may arise in outflows with higher ionization fractions and higher metallicity). For the quasar sight line J0950+4309, which probes the gas around the galaxy 1-166736 at a moderate elevation angle, we found a large difference in the ionization parameter between the components seen in the Si ii and Si iii absorption lines. The low-ionization gas traced by Si ii may correspond to the galactic disk, while the highly ionized gas observed only in Si iii may correspond to the CGM. The higher ionization component in 1-166736 is consistent with the trend observed between the ionization parameter and the elevation angle.

We also compare our data with measurements of the ionization parameter in the COS-Halos survey (Werk et al. 2014). Our results are consistent with their results and cover the same range of ionization parameter. However, we do not confirm the trend log q = −2.2 ± 0.3 + (0.8 ± 0.3) × log (R/R_vir) reported by Werk et al. (2014; based on the points at very low and high impact parameters). Combining our sample with the COS-Halos sample, we find that the correlation of ionization parameter with impact parameter is not statistically significant with a Spearman rank-order correlation coefficient of 0.2 and p-value 0.16. Indeed, high-ionization parameters, on average, correspond to a higher impact parameter. However, there is a large scatter of q parameters that likely reflects the inhomogeneity of physical conditions in the CGM of different galaxies.

B.1.1. J0755+3911

We measured the H i and metal species column densities of the absorption system at the redshift of the AGN 1-71974 (z_gal = 0.0336). The absorption system consists of at least four velocity components detected in H i Lyα and Si iii 1206 Å transitions. The H i absorption consists of two weak components with column densities ∼10^12.8 and 10^13.3 cm⁻², which are blueshifted by −62 and −228 km s⁻¹ with respect to the galaxy redshift. The Si iii 1206 absorption is detected in two components at −130 and −200 km s⁻¹, which are shifted with respect to H i absorption lines. We fitted the absorption system with four velocity components with the redshifts tied to the redshift of the prominent H i and Si iii absorptions. The result of the fit is given in Table 5, and line profiles are shown in Figure 32.

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Table 5. Fit Results to Absorption Systems

zabs	v	b	$\mathrm{log}N({\rm{X}})$
	(km s−1)	(km s−1)	(H i)	(Si ii)	(Si iii)	(C ii)	(S ii)	(S iv)	(N i)	(N ii)	(N v)	(O i)	(O vi)	(Fe ii)	(Fe iii)	(Ar i)
J0755+3911, zem,corr = 0.03362
0.03284	−228	${16}_{-1}^{+5}$	<12.8	${12.4}_{-1.0}^{+0.4}$	${12.7}_{-1.1}^{+0.5}$	<13.4	<14.7	N/C	<13.5	N/C	N/C	<13.8	N/C	<13.7	<13.5	N/C
0.03292	−203	${17}_{-2}^{+20}$	<13	<12.7	${12.0}_{-0.8}^{+0.3}$	<13.4	<14.0	N/C	<13.3	N/C	N/C	<13.1	N/C	<13.7	<13.5	N/C
0.03315	−136	<20	<12.2	<12.8	${12.3}_{-0.5}^{+0.3}$	<15	<13.8	N/C	<13.0	N/C	N/C	<13.8	N/C	<13.7	<13.2	N/C
0.03342	−62	${24}_{-5}^{+5}$	${13.3}_{-0.1}^{+0.1}$	<12.7	<12.6	<13.6	<14.5	N/C	<13.7	N/C	N/C	<13.5	N/C	<13.9	<13.5	N/C
Total:			${13.6}_{-0.1}^{+0.1}$	${12.7}_{-0.5}^{+0.3}$	${12.4}_{-0.5}^{+0.2}$	${13.0}_{-0.3}^{+0.2}$	<15.0	N/C	${13.1}_{-0.9}^{+0.4}$	N/C	N/C	${13.1}_{-0.6}^{+0.4}$	N/C	${13.2}_{-0.9}^{+0.3}$	<13.5	N/C
J0758+4219, zem,corr = 0.03181
0.03138	−115	${42}_{-7}^{+7}$	${14.2}_{-0.2}^{+0.3}$	${12.3}_{-0.9}^{+0.2}$	${11.9}_{-0.6}^{+1.8}$	N/C	<14.4	<14.5	<13.8	<14.3	<13.6	<14.0	N/C	<13.7	<14.0	<14.0
0.03202	52	${41}_{-6}^{+8}$	${14.9}_{-0.2}^{+0.2}$	${12.7}_{-0.2}^{+0.2}$	${13.2}_{-0.1}^{+0.1}$	N/C	${14.2}_{-0.5}^{+0.2}$	<15.0	<13.7	<14.0	<13.3	<13.9	N/C	<14.0	<14.3	<14.3
0.03226	130	${27}_{-4}^{+8}$	${14.8}_{-0.3}^{+0.5}$	${13.0}_{-0.1}^{+0.1}$	${12.8}_{-0.2}^{+0.2}$	N/C	${13.8}_{-0.7}^{+0.5}$	<15.0	<13.6	<14.1	<13.3	<13.9	N/C	<13.8	<14.4	<14.3
0.03263	230	${17}_{-2}^{+50}$	${13.1}_{-0.2}^{+0.3}$	N/A	<12.3	N/C	N/A	N/A	N/A	N/A	N/A	N/C	N/A	N/A	N/A	N/A
Total:			${15.2}_{-0.2}^{+0.3}$	${13.2}_{-0.1}^{+0.1}$	${13.4}_{-0.1}^{+0.1}$	N/C	${14.7}_{-0.2}^{+0.1}$	<15.0	${13.2}_{-2.0}^{+0.2}$	${13.5}_{-0.4}^{+0.4}$	<13.5	<14.0	N/C	<13.9	<14.4	<14.3
J0838+2453(A), zem,corr = 0.02843
0.02834	−34	${41}_{-10}^{+10}$	${13.2}_{-0.1}^{+0.1}$	<13.5	${12.5}_{-0.7}^{+0.4}$	N/C	<14.7	N/C	<14.7	N/A	N/A	<14.7	N/A	<15.5	N/A	N/A
0.02812	−93	<20	N/A	${12.3}_{-1.0}^{+0.5}$	${12.8}_{-0.3}^{+0.3}$	N/C	<15	N/C	<13.6	N/A	N/A	<14.5	<14.1	N/A	N/A	N/A
0.02774	−201	${20}_{-10}^{+10}$	N/A	${12.8}_{-0.3}^{+0.4}$	<13.5	N/C	1 < 13.5	N/A	<13.7	N/A	N/A	<14.3	N/A	N/A	N/A	N/A
Total:	−100		${13.2}_{-0.1}^{+0.1}$	${13.4}_{-0.2}^{+0.2}$	${13.8}_{-0.5}^{+0.6}$	N/C	${14.8}_{-1.0}^{+0.4}$	N/A	<14.7	N/A	N/A	<15	N/A	<15	N/A	N/A
J0838+2453(B), zem,corr = 0.02843
0.02584	−754	${55}_{-15}^{+15}$	${14.0}_{-0.1}^{+0.1}$	${12.8}_{-1.3}^{+0.5}$	${13.2}_{-1.7}^{+0.8}$	N/C	${14.2}_{-1.5}^{+0.8}$	N/A	<13.7	N/A	N/A	<13.0	N/A	<16.0	N/A	N/A
0.02556	−853	<80	N/A	${13.4}_{-0.7}^{+1.1}$	<13.3	N/C	${13.4}_{-1.4}^{+0.5}$	N/A	<14.4	N/A	N/A	<13.0	N/A	N/A	N/A	N/A
Total:	−800		${14.0}_{-0.1}^{+0.1}$	<13.6	${13.6}_{-1.1}^{+0.5}$	N/C	${14.5}_{-1.4}^{+0.5}$	N/A	<14.4	N/A	N/A	<14.5	N/A	N/A	N/A	N/A
J0950+4309, zem,corr = 0.01714
0.01713	−2	${28}_{-6}^{+6}$	${17.6}_{-0.8}^{+0.3}$	${13.0}_{-0.1}^{+0.1}$	${13.0}_{-0.3}^{+0.2}$	${14.0}_{-0.1}^{+0.1}$	<14.7	N/C	<14.3	N/A	<13.8	<14.0	N/C	<14.3	<14.0	N/C
0.01696	−52	${70}_{-10}^{+10}$	${15.1}_{-0.2}^{+0.7}$	<12.4	${13.4}_{-0.1}^{+0.1}$	<13.6	<14.6	N/C	<14.4	<16.3	<14.1	<14.0	N/C	<14.2	${14.0}_{-1.2}^{+0.3}$	N/C
0.01630	−247	<100	${13.4}_{-0.2}^{+0.2}$	<12.7	<12.7	<14.1	<14.6	N/C	<14.0	<16.0	<13.5	<14.6	N/C	<14.0	N/A	N/C
Total:			${17.6}_{-0.7}^{+0.3}$	${13.0}_{-0.1}^{+0.1}$	${13.6}_{-0.1}^{+0.1}$	${14.1}_{-0.2}^{+0.2}$	${14.2}_{-0.2}^{+0.2}$	N/C	${13.6}_{-0.8}^{+0.4}$	<16.2	${14.0}_{-0.4}^{+0.2}$	${13.6}_{-0.6}^{+0.3}$	N/C	${13.6}_{-0.6}^{+0.3}$	${14.0}_{-1.2}^{+0.3}$	N/C
J1237+4447(A), zem,corr = 0.06013
0.05960	−151	${38}_{-19}^{+7}$	${14.8}_{-0.3}^{+0.6}$	<13.0	${12.8}_{-0.1}^{+0.1}$	${13.9}_{-3.0}^{+0.3}$	${14.3}_{-1.5}^{+0.5}$	<14.3	<13.3	<13.5	${13.2}_{-2.5}^{+0.1}$	N/A	<14.3	<13.8	<13.8	<13.4
0.05993	−57	${16}_{-1}^{+4}$	${17.1}_{-0.7}^{+0.3}$	<12.5	${12.3}_{-0.3}^{+0.2}$	<14.7	<14.3	<14.1	<13.4	<13.8	<13.2	N/C	<15.3	${13.5}_{-1.5}^{+0.4}$	<14.0	<13.3
0.06119	302	${20}_{-9}^{+9}$	${13.6}_{-0.1}^{+0.1}$	N/A	<12	N/A	N/A	N/A	N/A	N/A	N/A	N/C	N/A	N/A	N/A	N/A
Total:			${17.2}_{-0.4}^{+0.3}$	<13	${12.9}_{-0.1}^{+0.1}$	<14.7	${14.3}_{-0.8}^{+0.5}$	<14.2	${12.9}_{-1.3}^{+0.5}$	<13.5	${13.2}_{-0.5}^{+0.3}$	N/C	<14.3	${13.5}_{-0.6}^{+0.5}$	<11.0	<13.5
J1237+4447(B), zem,corr = 0.06013
0.05960	−151	${38}_{-19}^{+7}$	${14.8}_{-0.3}^{+0.6}$	<13.0	${12.8}_{-0.1}^{+0.1}$	${13.9}_{-3.0}^{+0.3}$	${14.3}_{-1.5}^{+0.5}$	<14.3	<13.3	<13.5	${13.2}_{-2.5}^{+0.1}$	N/A	<14.3	<13.8	<13.8	<13.4
0.05993	−57	${28}_{-6}^{+6}$	${14.8}_{-0.2}^{+0.8}$	<12.6	${12.4}_{-0.2}^{+0.2}$	<14.8	<14.2	<14.1	<13.3	<13.6	<13.2	N/C	${14.0}_{-1.5}^{+0.2}$	${13.7}_{-1.5}^{+0.3}$	<14.2	<13.2
0.06119	302	${20}_{-9}^{+9}$	${13.6}_{-0.1}^{+0.1}$	N/A	<12	N/A	N/A	N/A	N/A	N/A	N/A	N/C	N/A	N/A	N/A	N/A
Total:			${15.2}_{-0.3}^{+0.5}$	${12.4}_{-0.8}^{+0.4}$	${12.9}_{-0.1}^{+0.1}$	${14.0}_{-1.4}^{+0.5}$	${14.3}_{-1.2}^{+0.3}$	<13.9	${12.9}_{-1.0}^{+0.3}$	<13.5	${13.2}_{-0.8}^{+0.3}$	N/C	${14.1}_{-1.5}^{+0.5}$	${13.7}_{-0.9}^{+0.3}$	<11.0	<13.2
J1338+0311, zem,corr = 0.02604
0.02543	−178	${15}_{-5}^{+13}$	N/A	${12.9}_{-1.6}^{+0.6}$	${13.0}_{-1.7}^{+1.1}$	N/C	${10.1}_{-0.1}^{+2.4}$	N/C	${14.1}_{-0.9}^{+0.4}$	${13.3}_{-2.4}^{+1.6}$	${13.2}_{-1.4}^{+0.5}$	<15.0	N/C	${13.2}_{-0.7}^{+0.7}$	${14.6}_{-1.6}^{+0.6}$	N/A
0.02566	−110	${80}_{-20}^{+30}$	N/A	${13.4}_{-0.2}^{+0.2}$	${13.6}_{-0.5}^{+0.3}$	N/C	${10.1}_{-0.1}^{+2.5}$	N/C	${13.7}_{-1.6}^{+0.6}$	${10.1}_{-0.1}^{+4.6}$	${10.3}_{-0.3}^{+1.1}$	${15.0}_{-0.3}^{+0.2}$	N/C	${10.5}_{-0.5}^{+2.0}$	N/A	N/A
0.02603	2	${77}_{-13}^{+18}$	${20.2}_{-0.1}^{+0.1}$	${13.6}_{-0.3}^{+0.2}$	${13.5}_{-0.3}^{+0.3}$	N/C	${15.2}_{-0.1}^{+0.1}$	N/C	${14.2}_{-0.6}^{+0.2}$	${14.9}_{-0.2}^{+0.2}$	${11.5}_{-1.5}^{+0.8}$	${15.0}_{-0.2}^{+0.2}$	N/C	${14.6}_{-1.0}^{+0.4}$	<14.6	N/A
0.02639	146	${50}_{-13}^{+10}$	N/A	${12.7}_{-0.3}^{+0.4}$	${12.6}_{-2.6}^{+0.3}$	N/C	${14.3}_{-2.5}^{+0.3}$	N/C	${14.2}_{-0.3}^{+0.2}$	${13.9}_{-2.8}^{+1.0}$	<12	${14.2}_{-0.8}^{+0.4}$	N/C	<14.0	<14	N/A
Total:			${20.2}_{-0.1}^{+0.1}$	${13.9}_{-0.2}^{+0.2}$	${13.9}_{-0.2}^{+0.4}$	N/C	${15.2}_{-0.2}^{+0.1}$	N/C	<14.3	<16	<13.8	${15.5}_{-0.1}^{+0.1}$	N/C	<14.6	<14.3	N/A
J2106+0909, zem,corr = 0.0437
0.04423	135	${30}_{-10}^{+10}$	${13.7}_{-0.2}^{+0.2}$	<13.0	<13.2	N/C	<14.8	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A
J2130−0025, zem,corr = 0.0200
0.01967	−146	${26}_{-4}^{+6}$	${18.8}_{-0.1}^{+0.1}$	${13.8}_{-0.2}^{+0.1}$	${14.6}_{-0.5}^{+0.9}$	${15.3}_{-0.5}^{+0.9}$	<14.6	N/C	${13.1}_{-1.1}^{+0.3}$	<14.7	<13.7	${14.6}_{-0.5}^{+0.9}$	N/C	${13.6}_{-1.9}^{+0.4}$	<11	N/A

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B.1.2. J0758+4219

B.1.3. J0838+2453

In the spectrum of the AGN J0838+2453, we detected two H i absorptions at −34 and −750 km s⁻¹ with respect to the redshift of the host galaxy. Because of the low S/N for this spectrum, the associated metal absorption lines are detected only in Si iii 1206 Å transition, which is located close to the H i Lyα quasar emission line. The Si iii absorption has five velocity components. Two velocity components correspond well with the position of the H i absorption components, whereas other three component are detected only in Si iii. Therefore, we fitted the absorption system with five velocity components. The result of the fit is given in Table 5, and line profiles are shown in Figure 33.

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B.1.4. J0950+4309

B.1.5. J1237+4447

B.1.6. J1338+0311

The absorption system associated with the host galaxy of the AGN 12-192116 has strong damped H i Lyα absorption (N = 10^20.2 cm⁻²). We described the fit to the H i Lyα line in Section 2.2.2. The associated metal absorption lines are fitted by four velocity components. The result of the fit is given in Table 5, and line profiles are shown in Figure 31.

Table 6. Fit Results to cloudy Photoionization Model of Absorption Systems

Quasar	zabs	v	$\mathrm{log}{N}_{{\rm{H}}\,{\rm\small{I}}}$	$\mathrm{log}{N}_{{{\rm{H}}}_{{tot}}}$	[X/H]	$\mathrm{log}q$	$\mathrm{log}{I}_{\mathrm{UV}}/{n}_{{\rm{H}}}$	F*
		(km s−1)	(cm−2)	(cm−2)			(Drain/cm−3)
J0755+3911	Average:		${13.5}_{-0.3}^{+0.3}$	${16.5}_{-0.3}^{+0.3}$	${1.2}_{-0.2}^{+0.2}$	$-{1.5}_{-0.3}^{+0.3}$	${2.0}_{-0.2}^{+0.3}$	${0.0}_{-0.0}^{+0.4}$
J0758+4219	0.03138	−115	${14.2}_{-0.2}^{+0.3}$	${16.9}_{-0.7}^{+1.0}$	${0.7}_{-0.8}^{+0.6}$	$-{2.4}_{-0.4}^{+1.0}$	${1.0}_{-0.5}^{+1.0}$	<1
	0.03202	52	${14.2}_{-0.1}^{+0.3}$	${17.8}_{-0.2}^{+0.2}$	${0.6}_{-0.3}^{+0.3}$	$-{2.0}_{-0.3}^{+0.3}$	${1.4}_{-0.3}^{+0.3}$	${0.0}_{-0.0}^{+0.4}$
	0.03226	130	${15.0}_{-0.3}^{+0.4}$	${17.6}_{-0.3}^{+0.3}$	${0.9}_{-0.4}^{+0.4}$	$-{2.1}_{-0.6}^{+0.6}$	${1.4}_{-0.6}^{+0.4}$	${0.2}_{-0.2}^{+0.4}$
	0.03261	230	N/A	N/A	N/A	N/A	N/A	N/A
	Average:		${15.3}_{-0.2}^{+0.3}$	${18.1}_{-0.4}^{+0.3}$	${0.8}_{-0.3}^{+0.3}$	$-{2.0}_{-0.4}^{+0.3}$	${1.4}_{-0.4}^{+0.3}$	${0.1}_{-0.1}^{+0.5}$
J0838+2453	Average(A):		${13.2}_{-0.3}^{+0.2}$	${16.7}_{-0.3}^{+0.3}$	${1.9}_{-0.3}^{+0.3}$	$-{0.8}_{-0.5}^{+0.2}$	${2.7}_{-0.5}^{+0.3}$	${0.0}_{-0.0}^{+0.1}$
	Average(B):		${13.8}_{-0.3}^{+0.2}$	${17.1}_{-0.3}^{+1.5}$	${0.5}_{-0.5}^{+1.5}$	$-{1.1}_{-0.7}^{+0.5}$	${2.4}_{-0.7}^{+0.5}$	<1
J0950+4309	0.01713	−2	${17.6}_{-0.7}^{+0.3}$	${18.9}_{-0.5}^{+0.3}$	$-{1.1}_{-0.3}^{+0.5}$	$-{3.8}_{-0.3}^{+0.3}$	$-{0.5}_{-0.2}^{+0.3}$	${0.0}_{-0.0}^{+0.2}$
	0.01696	−52	${14.9}_{-0.3}^{+0.3}$	${19.4}_{-0.5}^{+0.4}$	$-{0.5}_{-0.5}^{+0.4}$	$-{1.2}_{-0.3}^{+0.4}$	${2.3}_{-0.4}^{+0.3}$	${0.0}_{-0.0}^{+0.3}$
	0.01630	−247	N/A	N/A	N/A	N/A	N/A	N/A
	Average:		${16.8}_{-0.3}^{+0.8}$	${19.0}_{-0.2}^{+0.6}$	$-{0.6}_{-0.7}^{+0.2}$	$-{3.2}_{-0.2}^{+0.2}$	$-{0.1}_{-0.2}^{+0.4}$	${0.0}_{-0.0}^{+0.2}$
J1237+4447	0.05960	−151	${14.9}_{-0.3}^{+0.6}$	${18.2}_{-0.6}^{+1.3}$	$-{0.2}_{-1.1}^{+0.7}$	$-{2.0}_{-0.5}^{+0.9}$	${1.5}_{-0.8}^{+0.6}$	<1
	0.05993(A)	−57	${17.0}_{-0.3}^{+0.4}$	${19.3}_{-0.9}^{+0.8}$	$-{1.6}_{-1.0}^{+1.0}$	$-{3.1}_{-0.5}^{+0.6}$	${0.0}_{-0.3}^{+0.9}$	${0.0}_{-0.0}^{+0.2}$
	0.05993(B)	−57	${14.8}_{-0.3}^{+0.7}$	${18.1}_{-0.7}^{+1.4}$	$-{0.7}_{-1.4}^{+0.6}$	$-{2.6}_{-0.5}^{+1.1}$	${0.9}_{-0.5}^{+1.2}$	${0.0}_{-0.0}^{+0.2}$
	0.06119	302	N/A	N/A	N/A	N/A	N/A	N/A
	Average(A):		${17.2}_{-0.7}^{+0.2}$	${19.4}_{-0.5}^{+0.8}$	$-{1.8}_{-0.8}^{+0.8}$	$-{2.9}_{-0.6}^{+0.9}$	${0.3}_{-0.6}^{+0.9}$	${0.2}_{-0.2}^{+0.0}$
	Average(B):		${15.2}_{-0.3}^{+0.5}$	${18.1}_{-0.5}^{+0.9}$	$-{0.2}_{-1.0}^{+0.5}$	$-{2.5}_{-0.4}^{+0.6}$	${0.9}_{-0.5}^{+0.6}$	${0.0}_{-0.0}^{+0.2}$
J1338+0311	Average:		${20.2}_{-0.1}^{+0.1}$	${20.5}_{-0.2}^{+0.2}$	$-{0.4}_{-0.3}^{+0.4}$	$-{2.8}_{-0.2}^{+0.3}$		${0.5}_{-0.3}^{+0.3}$
J2106+0909	0.04423	135	N/A	N/A	N/A	N/A	N/A	N/A
J2130−0025	0.01967	−110	${18.8}_{-0.1}^{+0.1}$	${21.1}_{-0.6}^{+0.4}$	$-{1.1}_{-0.2}^{+0.2}$	$-{2.1}_{-0.5}^{+0.4}$	${1.4}_{-0.6}^{+0.4}$	${0.1}_{-0.1}^{+0.3}$

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B.1.7. J2106+0909

We detected only one weak absorption line of H i Lyα (N = 10^13.7 cm⁻²) at the redshift of galaxy 1-113242. The associated Si iii absorption line is blended with the MW S ii absorption lines; therefore, we can set only an upper limit to the Si iii column density. The result of the fit is given in Table 5, and line profiles are shown in Figure 34.

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B.1.8. J2130-0025

B.1.9. Nondetection

In three cases (J1653+3945, J1709+3421 and J1629+4007), we do not detect any absorption (in H i or any of the metal ions) within the range of $\pm 800$ km s${}^{-1}$ relative to the galaxy redshifts (1-594755, 1-561034, 1-564490). Figure 36 shows the parts of quasar spectra near the expected positions of HI, SiII, SiIII, NV lines. We set upper limits on N(HI)$\unicode{x0007E}{10}^{13}$ cm${}^{-2}$.

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