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# MUSEQuBES: The Column Density, Covering Fraction, and Mass of O VI-bearing Gas in and Around Low-redshift Galaxies

Sayak Dutta<fnref n="1" />, Sowgat Muzahid<fnref n="1" />, Joop Schaye<fnref n="2" />, Nicolas F. Bouche<fnref n="3" />, Sebastiano Cantalupo<fnref n="4" />, Hsiao-Wen Chen<fnref n="5" />, and Sean Johnson<fnref n="6" />

Received 2024 September 18; revised 2025 March 11; accepted 2025 March 15; published 2025 May 14

## Abstract

We present a study of O VI-bearing gas around 247 low-mass (median $log_{10}(M_*/M_\odot) = 8.7$) galaxies at low redshifts ($0.1 < z < 0.7$) using background quasars as part of the MUSE Quasar-fields Blind Emitters Survey (MUSEQuBES). We find that the average O VI column density, $log_{10}\langle N(O VI)/\text{cm}^{-2}\rangle = 14.14_{-0.10}^{+0.09}$, measured within the virial radius for our sample, is significantly lower than for $L_*$ galaxies. Combining 253 star-forming galaxies (mostly more massive) from the literature with 176 star-forming galaxies from MUSEQuBES, we find that both $\langle N(O VI) \rangle$ and the average covering fraction peak at $log_{10}(M_*/M_\odot) \approx 9.5$. The virial temperature corresponding to this stellar mass is ideal for O VI production via collisional ionization. However, we argue that photoionization and/or nonequilibrium processes are necessary to produce the O VI associated with low-mass, dwarf galaxies ($log_{10}(M_*/M_\odot) < 9$). The average O VI mass within the virial radius of dwarf galaxies is measured to be $10^{5.2^{+0.1}_{-0.1}} M_\odot$. The characteristic normalized impact parameter ($D/R_{\text{vir}}$) at which the O VI covering fraction drops to half of its peak value is largest ($\approx 1.1$) for galaxies with stellar mass $log_{10}(M_*/M_\odot) \approx 9.5$. We report the presence of a highly ionized metal floor with $log_{10}N(O VI)/\text{cm}^{-2} = 13.2$ outside the virial radius of dwarf galaxies inferred from median spectral stacking.

*Unified Astronomy Thesaurus concepts: Circumgalactic medium (1879); Galaxy evolution (594)*

## 1. Introduction

The gaseous halos surrounding galaxies, known as the circumgalactic medium (CGM), are thought to retain evidence of both gas accretion and galactic outflows—the two poorly understood aspects of galaxy evolution models. The CGM consists of metal-rich, kinematically complex, multiphase gas that extends at least out to the virial radius of galaxies (see J. Tumlinson et al. 2017, for a review). The total gas and metal masses across the different phases of the CGM can potentially account for the “missing baryons” and “missing metals” in galaxy halos (e.g., S. S. McGaugh et al. 2010; M. S. Peeples et al. 2014). Therefore, probing and characterizing different gas phases in the CGM is crucial. Owing to its tenuous nature, the CGM is challenging to study in emission. With the advent of state-of-the-art integral field spectrographs (IFSs), however, the situation is changing dramatically (see e.g., J. Zabl et al. 2021; Y. Guo et al. 2023; S. Dutta et al. 2024).

The atomic and ionic transitions serving as sensitive diagnostics for the physical and chemical conditions of the CGM predominantly fall within the rest-frame ultraviolet (UV) region. Absorption-line spectroscopy of bright background quasars has paved the way for CGM studies (e.g., J. Bergeron & G. Stasińska 1986; P. Petitjean & J. Bergeron 1990). With the availability of the far-UV (FUV) sensitive Cosmic Origins Spectrograph (COS) onboard the Hubble Space Telescope

(HST), multiple surveys have been conducted to investigate the connection between low-z galaxies and the gas surrounding them. The rest-frame UV transitions of the fifth ionization state of oxygen (i.e., the O VI $\lambda\lambda$1031, 1037 doublet) are among the favorite line diagnostics for studying the metal enrichment in diffuse gas across different cosmic times (see e.g., A. Aguirre et al. 2008; T. M. Tripp et al. 2008; S. Muzahid et al. 2012). This is owing to the suitable rest-frame wavelengths, the large oscillator strengths of the transitions, and the large cosmic abundance of oxygen. However, O VI is not the dominant ionization state of oxygen. The ionization fraction of O VI, $f_{\text{O VI}}$, reaches its peak ($\approx 0.2$) at ionization parameter of $10^{-1}$ under photoionization equilibrium (PIE; B. D. Oppenheimer & J. Schaye 2013) or at a gas temperature of $T \approx 10^{5.5}$ K under collisional ionization equilibrium (CIE; O. Gnat & A. Sternberg 2007; B. D. Oppenheimer & J. Schaye 2013). Since the cooling function peaks at around similar temperatures, the cooling time for collisionally ionized, O VI-bearing gas is rather short, particularly when the metallicity is relatively high. In case of nonequilibrium, when the gas can cool faster than it recombines, or if photoionization dominates, O VI can trace lower temperatures (B. D. Oppenheimer & J. Schaye 2013; S. Kumar & H.-W. Chen 2025). Therefore, a wide range of physical processes give rise to O VI (see R. J. Edgar & R. A. Chevalier 1986; M. A. Dopita & R. S. Sutherland 1996; M. C. Begelman & A. C. Fabian 1990; K. J. Borkowski & J. M. Shull 1990; T. M. Heckman et al. 2002).

The connection between bright galaxies and O VI absorption has been investigated extensively using statistically significant samples of galaxy-absorber pairs. Studies have reported a near

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Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹ Inter-University Centre for Astronomy & Astrophysics, Post Bag 04, Pune, 411007, India</footnote>

<footnote n="2">² Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 RA Leiden, The Netherlands</footnote>

<footnote n="3">³ Centre de Recherche Astrophysique de Lyon (CRAL) UMR5574, Univ Lyon1, Ens de Lyon, CNRS, 69230 Saint-Genis-Laval, France</footnote>

<footnote n="4">⁴ Department of Physics, University of Milan Bicocca, Piazza della Scienza 3, 20126, Milano, Italy</footnote>

<footnote n="5">⁵ Department of Astronomy & Astrophysics, The University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA</footnote>

<footnote n="6">⁶ Department of Astronomy, University of Michigan, 1085 S. University Avenue, Ann Arbor, MI 48109, USA</footnote>
unity covering fraction of O VI absorption extending out to ≈100 kpc around bright galaxies (e.g., J. X. Prochaska et al. 2011; J. Tumlinson et al. 2011; S. D. Johnson et al. 2015; G. G. Kacprzak et al. 2015). Moreover, the late-type, star-forming, blue galaxies in these studies exhibited a significantly higher covering fraction and higher N(O VI) compared to the early-type, passive, red galaxies. H.-W. Chen & J. S. Mulchaey (2009) observed a stronger clustering of O VI absorbers around star-forming galaxies compared to passive, absorption-line-dominated galaxies up to a projected distance of 3h⁻¹ Mpc (but see C. W. Finn et al. 2016). The reasons for this dichotomy are debated in the literature. Some theoretical studies have attributed the cause to the difference in halo mass between the observational samples of star-forming and passive galaxies (e.g., B. D. Oppenheimer et al. 2016; N. N. Sanchez et al. 2019). This conclusion is supported by the fact that halos with virial temperatures of ≈10⁵.⁵ K are conducive to O VI formation under collisional ionization. The observational study of K. Tchernyshyov et al. (2023), however, showed that such a dichotomy exists even when the halo mass is controlled for the star-forming and passive samples. They advocated that a transformation of the CGM occurs concurrently with galaxy quenching, as predicted by simulations (see B. D. Oppenheimer et al. 2016). J. Suresh et al. (2017) also argued that the dichotomy stems from the effect of AGN feedback in their simulation. Theoretical studies of Milky Way-type galaxies further suggested that O VI could arise in supernova-driven outflows (e.g., C. J. Liang et al. 2016; M. Li & S. Tonnesen 2020) and photoionized inflows (e.g., J. Stern et al. 2018). It is therefore crucial to study O VI-bearing gas around galaxies with a large dynamic range in properties such as stellar mass ($M_*$) and star formation rate (SFR) to better understand its origin.

The bulk of the circumgalactic O VI observations in the literature are for high-mass galaxies ($M_* \gtrsim 10^{9.5} M_\odot$). Consequently, almost all of the theoretical studies aiming to reproduce the O VI observables focus on Milky Way-type galaxies. A wide range of physical models can reproduce such observables for Milky Way-type galaxies, and a consensus on the origin of O VI absorbers in galaxy halos is yet to emerge. With the advent of state-of-the-art IFSs such as MUSE (R. Bacon et al. 2010) on VLT/UT4 and KCWI (P. Morrissey et al. 2018) on Keck, it is now efficient to find and identify low-mass galaxies around bright background quasars. As a consequence, the availability of O VI measurements around low-mass galaxies is gradually increasing (see e.g., Z. Qu et al. 2024).

In this study, we revisit the connection between low-z galaxies and O VI-bearing gas surrounding them using a unique, low-mass sample of galaxies drawn from the low-z part of the MUSE Quasar-fields Blind Emitters Survey (MUSE-QuBES; S. Dutta et al. 2024). Exploiting a total of ≈65 hr of GTO observations, MUSEQuBES conducted a galaxy survey around 16 UV-bright background quasars that have high-quality HST/COS spectra. Each MUSE field yields ≈90,000 spectra from each 0.′′2 × 0.′′2 spaxel, enabling the identification of low-mass galaxies without the need for any preselection. Our deep MUSE observations, with on-source exposure times ranging from 2 to 10 hr, yielded a homogeneous sample primarily composed of low-mass (median $M_* \approx 10^{8.7} M_\odot$), sub-L* galaxies. A significant fraction of these galaxies exhibited impact parameters from the background quasars, $D < R_{vir}$,

where $R_{vir}$ is the inferred virial radius of the halo hosting the intervening galaxy.

This paper is organized as follows. In Section 2, we describe the galaxy sample used in this paper. Section 3, provides the details of the absorption-line data and galaxy-absorber pairs. The results are presented in Section 4, followed by a discussion in Section 5. Our key findings are summarized in Section 6. Throughout this paper, we adopt a Λ-CDM cosmology with $\Omega_m = 0.3$, $\Omega_\Lambda = 0.7$, and a Hubble constant of $H_0 = 70 \text{ km s}^{-1} \text{ Mpc}^{-1}$. All distances are in physical units unless specified otherwise.

## 2. Data

A galaxy survey centered on UV-bright quasars is essential for our study of circumgalactic O VI absorption. In this work, we primarily used the galaxies from the MUSEQuBES at low z (S. Dutta et al. 2024). This provides a set of 247 new quasar-galaxy pairs for which O VI absorption can be studied. An overview of the survey design and analysis procedure for MUSEQuBES is given in S. Dutta et al. (2024). A brief summary is given below.

### 2.1. The MUSEQuBES Galaxy Survey

We carried out a blind spectroscopic redshift survey in the fields centered on 16 quasars using the MUSE instrument, which is mounted on the VLT/UT4, and has a 1 × 1 arcmin field-of-view (FoV). The selected 16 quasars (with emission redshift, $z_{qso}$ ranging from 0.42 to 1.44) have the best signal-to-noise ratio (S/N; 15–85 per resolution element) FUV spectra available in the HST Spectroscopic Legacy Archive (M. Peebles et al. 2017, HSLA). With on-source exposure time ranging from 2 to 10 hr per MUSE field, we detected a total of 413 galaxies foreground to the quasars (at least 2000 km s⁻¹ bluewards of the quasar redshifts). These galaxies, with secured spectroscopic redshifts, are detected in the MUSE white-light images (see S. Dutta et al. 2024, for details). The 1D spectra of these continuum-detected galaxies are extracted from MUSE cubes and examined through MARZ (S. Hinton et al. 2016) to determine the redshift based on the spectral features. The line fluxes of available emission and absorption lines are measured using PLATEFIT (C. A. Tremonti et al. 2004).

The SFR are determined by the $H\alpha$ or [O II] (when $H\alpha$ is not covered or not detected at $>3\sigma$) line fluxes returned by PLATEFIT using the R. C. Kennicutt (1998) relations (for $H\alpha$) or L. J. Kewley et al. (2004) relations (for O II), corrected to the G. Chabrier (2003) initial mass function. Further, a dust correction is applied to SFRs measured from $H\alpha$ whenever the $H\beta$ line is detected with $>3\sigma$ significance. For galaxies without S/N > 3 detection of $H\alpha$, $H\beta$ (in combination with $H\gamma$), or [O II], we could not estimate the SFR. For these galaxies, we use the PLATEFIT error on the $H\alpha$ (for $z < 0.42$) or [O II] (for $z > 0.42$) line flux to derive a $3\sigma$ upper limit on the SFR.

Stellar masses ($M_*$) for the galaxy sample are calculated using the spectral energy distribution fitting code FAST (M. Kriek et al. 2009). We created a series of 11 boxcar filters from the full available wavelength range of MUSE to perform the fit. Once the stellar mass is estimated, we use the abundance matching relation from B. P. Moster et al. (2013) to obtain the halo mass ($M_{halo}$) and virial radius ($R_{vir}$) which we define as the radius at which the mean enclosed density is 200 times the critical density of the universe.
<figure><img src="image_3.png" /><figcaption>**Figure 1.** The sSFR of all MUSEQuBES galaxies plotted against the stellar mass. The filled circles and open triangles represent the detection of and $3\sigma$ upper limits on the sSFR, respectively. The points are color-coded by the redshift of the galaxies. The points with red squares around them represent quenched galaxies, defined as galaxies with sSFR measurements (detection or $3\sigma$ upper limits) below $3\sigma$ scatter of redshift-dependent SFMS (L. A. Boogaard et al. 2018). The SFMS relation at $z=0.5$ and its $3\sigma$ scatter are shown with the black solid line and the gray-shaded region.</figcaption></figure>

The specific star formation rate (sSFR $\equiv$ SFR/$M_*$) is plotted against the $\log_{10}(M_*/M_\odot)$ for the complete MUSE-QuBES sample in Figure 1. The $3\sigma$ upper limits and detections are shown with hollow downward triangles and filled circles, color-coded by the redshift of the galaxies. The passive galaxies, defined as galaxies located $3\sigma$ below the redshift-dependent star-forming main sequence (SFMS; see L. A. Boogaard et al. 2018), are marked with red squares.<fnref n="7" /> These passive/quenched galaxies are flagged as “E.” Among the remaining galaxies, those with measured SFR and $3\sigma$ upper limits on the SFR are classified as star-forming (“SF”) and unclassified (“U”) galaxies, respectively. Note that the galaxies in our sample show a large dynamic range in stellar mass and SFR, and the vast majority of them lie along the main-sequence relation. The color gradient for the points at a given stellar mass indicates the cosmic evolution of SFR (see e.g., M. D. Lehnert et al. 2015).

The top, middle, and bottom panels of Figure 2 show the SFR, sSFR, and stellar mass plotted against galaxy redshift with gray circles. The stellar masses of these galaxies range from $10^{7.8}$ to $10^{9.8} M_\odot$ (68 percentile), with a median stellar mass of $10^{8.8} M_\odot$. Note that the galaxies for which the circumgalactic O VI absorption can be studied with the COS FUV spectra are indicated by the blue color. In the next section, we discuss the subsample of MUSEQuBES galaxies used in this study.

## 2.2. Selection of MUSEQuBES Galaxies for O VI Study

In order to study the CGM of the MUSEQuBES galaxies using the O VI $\lambda\lambda$1031, 1037 doublet, we used the following selection criteria:

1. A foreground galaxy (at least 2000 km s$^{-1}$ bluewards of the quasar redshift) is selected if the redshift

wavelength of the O VI doublet falls within the coverage of the COS spectra of the corresponding background quasar.

2. Galaxies for which the redshifted O VI absorption falls within the geocoronal Ly$\alpha$ emission or Galactic absorption (1205–1220 Å) or geocoronal O I emission (1301–1305 Å) are excluded from our analysis.

3. There are Lyman-limit systems in two of the sightlines used in this work (TEX0206-048 and Q1354+048). Galaxies in these fields for which the redshifted O VI lines fall below the respective Lyman limits are excluded from this work.

4. Additionally, the redshifted O VI lines for eight foreground galaxies toward quasar PKS0552–640 fall within the COS spectral gap. All these galaxies are excluded from this work.

A sample of 247 galaxies from our MUSEQuBES satisfies the aforementioned conditions. Among these, 176, 29, and 42 galaxies are classified as “SF,” “E,” and “U,” respectively. Applying a Friends-of-Friend algorithm, we found that 124 out of the 247 galaxies do not have a neighboring galaxy within a line-of-sight (LOS) velocity of $\pm 500$ km s$^{-1}$ and 500 kpc transverse distance. These are referred to as “isolated galaxies.” The remaining 123 galaxies have one or more neighboring galaxies within the aforementioned cuts and are categorized as “group galaxies.” The SFR, sSFR, and $M_*$ of the 247 galaxies are plotted against the redshift in Figure 2 with blue circles. The gray circles indicate the galaxies in the MUSEQuBES catalog, that are not included in this work.

In the top panel of Figure 2, a mild correlation is seen between SFR and redshift for the galaxies included in this work (generalized Kendall-$\tau=0.27, p \ll 0.1$). The presence of a lower envelope suggests that this correlation is likely driven by the flux limit of our MUSE data. The red solid line, which adequately explains the lower envelope, shows the limiting SFR for a fixed $H\alpha$ line flux of $10^{-18}$ erg cm$^{-2}$ s$^{-1}$. The relatively weak correlation seen between $\log_{10}(M_*/M_\odot)$ and $z$ ($\tau=0.14, p \ll 0.1$) in the bottom panel could be a manifestation of the underlying correlation between SFR and $z$ propagated through the SFMS. The middle panel shows that no significant trend is seen between sSFR (SFR/$M_*$) and $z$ ($\tau=0.06, p=0.13$). This is expected because the stellar-mass dependence on redshift cancels the sSFR dependence on redshift.

The MUSE FoV of $1' \times 1'$ restricts the impact parameter to $\approx 300$ kpc at $z \approx 0.6$ ($\approx 100$ kpc at $z \approx 0.1$). In the top left and bottom left panels of Figure 3, we show the impact parameter ($D$) and normalized impact parameter ($D/R_{vir}$), respectively, plotted against the redshift of MUSEQuBES galaxies ($z_{gal}$) included in this work with solid circles. The data points are color-coded by the stellar mass. The red line in the top left panel represents the maximum impact parameter probed by the MUSE FoV. The moderate correlation between $D$ and $z_{gal}$ ($\tau=0.37, p \ll 0.1$) most likely arises due to this envelope restricting high-impact parameter galaxies from being detected at lower redshifts. The crosses in the two panels of Figure 3 are the galaxies selected from literature for this work (see Section 2.3 for more details). Many of these galaxies are observed in non-IFU surveys with a larger FoV. Consequently, their impact parameters go beyond our MUSEQuBES galaxies. The right panel of Figure 3 shows the $z$, $\log_{10}(M_*/M_\odot)$, and $D/R_{vir}$ distribution of the combined sample of literature and

<footnote n="7">⁷ The handful of cases with red squares within the $3\sigma$ of SFMS arise from redshift differences between the galaxies and $z=0.5$, for which the SFMS is plotted.</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** The SFR (top), sSFR (middle), and stellar mass (bottom) of all MUSEQuBES galaxies plotted against redshift. The subsample of galaxies used in this work is shown in blue. The upper limits are indicated by the downward arrows in the top and middle panels. The red solid line in the top panel represents the limiting SFR for a fiducial Hα line flux of $10^{-18}$ erg cm$^{-2}$ s$^{-1}$. The results of generalized Kendall's-$\tau$ rank correlation tests for the subsample used in this work (including the upper limits) are indicated in each panel.</figcaption></figure>

MUSEQuBES plotted against each other. The corresponding histograms are plotted along the diagonal. The MUSEQuBES sample is shown with filled blue circles and solid blue lines, while the literature sample is shown with hollow red circles and dashed red lines.

## 2.3. Galaxies from the Literature for O VI Study

Although our analysis primarily uses galaxies from MUSEQuBES, the relatively smaller number of galaxies with

high masses prompted us to combine our MUSEQuBES sample with galaxy samples from the literature. Recently, K. Tchernyshyov et al. (2022) compiled N(O VI) measurements for a sample of 249 galaxies from several surveys in the literature alongside their own galaxy survey using Gemini-GMOS (M. C. Wilde et al. 2021). For the galaxy sample compiled by K. Tchernyshyov et al. (2022), they considered the smallest $D/R_{vir}$ galaxies when the LOS velocity search window of ±300 km s$^{-1}$ of one galaxy coincides with another.

K. Tchernyshyov et al. (2022) used either public photometry, when available, to measure the galaxies' $M_*$ and sSFR—e.g., the galaxies in J. Tumlinson et al. (2011), COS-Halos; S. D. Johnson et al. (2015), eCGM; H.-W. Chen et al. (2018), B. A. Keeney et al. (2018), and F. S. Zahedy et al. (2019), COS-LRG; and M. A. Berg et al. (2019), RDR—or the measurements reported in the original papers—e.g., S. D. Johnson et al. (2017), B. A. Keeney et al. (2017), and R. M. Bielby et al. (2019), QSAGE. K. Tchernyshyov et al. (2022) provided the $M_*$, $R_{vir}$, and star formation flags (“SF” for star-forming and “E” for quenched) for all 249 galaxies. Among these, 197 galaxies are classified as “SF” and 52 as “E.” K. Tchernyshyov et al. (2022) used a fixed sSFR cut of $10^{-10}$ yr$^{-1}$ to define the “SF” and “E” galaxy populations. We note that the galaxy sample from K. Tchernyshyov et al. (2022) was not reclassified by their sSFR based on the redshift-dependent SFMS because galaxies above this sSFR are always consistent with being star-forming according to the redshift-dependent SFMS for the entire redshift range of our interest. Hence, it does not significantly affect our results.

Additionally, we included N(O VI) measurements (detection and upper limits) for 98 out of 103 unique galaxies from the CUBS survey (Y. Chen et al. 2020; Z. Qu et al. 2024) for which SFR measurements are available.<fnref n="8" /> Using the SFR and $M_*$ from their catalog, we classified the galaxies with “SF,” “E,” or “U” based on their position relative to the SFMS, following the conditions adopted for the MUSEQuBES galaxies in Section 2.1. In the CUBS data set, there are 56 galaxies classified as “SF,” 39 galaxies as “E,” and three galaxies as “U.”

These 347 (249+98) galaxies from the literature are combined with the 247 MUSEQuBES galaxies to investigate the stellar-mass dependence of the column density (N(O VI)) and covering fraction ($\kappa$) profiles. In total, we compiled a sample of 594 galaxies for which circumgalactic O VI measurements are available. Among these, 429 galaxies are categorized as “SF,” 120 as “E,” and 45 are classified as “U.” The median galaxy properties ($z$, $D$, $D/R_{vir}$ and $\log_{10}(M_*/M_\odot)$) for the MUSEQuBES and literature samples are summarized in Table 1.

## 3. Absorption Data Analysis

We study the circumgalactic O VI absorption for the galaxies observed with MUSE using the spectra of UV-bright background quasars with $z_{qso} = 0.42-1.44$. The G130M+G160M grating spectra of COS covering 1150–1800 Å provide O VI coverage in the redshift range of ≈0.13–0.73. All of the 16 quasars in this work have G130M (1150–1450 Å) and G160M (1450–1800 Å) grating spectra available in the HSLA archive

<footnote n="8">⁸ We note here that the CUBS catalog associates the galaxy and N(O VI) absorption based on the smallest $D/R_{vir}$ when multiple galaxies reside in a group environment.</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Left: The impact parameter (top left) and normalized impact parameter (bottom left) are plotted against the redshift of galaxies used in this work. The points are color-coded by the stellar mass of the galaxies. The filled circles and crosses represent galaxies from MUSEQuBES and literature, respectively. The red solid line in the top left panel shows the maximum physical distance corresponding to the MUSE FoV as a function of redshift. The impact parameters (both physical and normalized) of the MUSEQuBES galaxies used in this work show a moderate correlation with redshift, as indicated by Kendall's τ coefficients. The correlation is relatively weak in the combined sample of galaxies from MUSEQuBES and literature. Right: The *z*, log₁₀(M*/M☉), and D/Rvir distribution of the combined sample of literature and MUSEQuBES plotted against each other, with histograms plotted along the diagonal. The MUSEQuBES sample is shown with filled blue circles and solid blue lines, while the literature sample is shown with hollow red circles and dashed red lines.</figcaption></figure>

<table><caption>**Table 1**
Galaxy Properties from MUSEQuBES and Literature</caption><thead><tr><th rowspan="2">Property</th><th colspan="2">MUSEQuBES<br>(N<sub>gal</sub> = 247)</th><th colspan="2">Literature (N<sub>gal</sub> = 347)</th></tr><tr><th>Median</th><th>68% Range</th><th>Median</th><th>68% Range</th></tr></thead><tbody><tr><td>D (kpc)</td><td>140</td><td>77–196</td><td>199</td><td>78–345</td></tr><tr><td>log<sub>10</sub>(M*/M☉)</td><td>8.7</td><td>7.5–9.6</td><td>9.7</td><td>8.8–10.8</td></tr><tr><td>D/R<sub>vir</sub></td><td>1.6</td><td>0.8–2.7</td><td>1.5</td><td>0.6–2.7</td></tr><tr><td>z</td><td>0.4</td><td>0.3–0.6</td><td>0.3</td><td>0.2–0.6</td></tr></tbody></table>

(M. Peeples et al. 2017). They are spliced together at a wavelength where the S/N becomes approximately equal for the two grating spectra. The median S/N and other information regarding the 16 quasar spectra are given in Table 1 of S. Dutta et al. (2024).

## 3.1. Blind O VI Absorber Catalog

A blind catalog of O VI absorbers in the 16 QSO spectra is created through visual inspection of the spectra using the doublet matching technique. “Blind” catalog, in this context, refers to the search for O VI absorbers without prior information regarding galaxy locations. The candidate absorbers are then decomposed into individual Voigt profile

components using VPFIT (R. F. Carswell & J. K. Webb 2014) using the wavelength-dependent line spread function of COS. Each identified O VI component is assigned a quality flag (*Q*), where *Q*=3 indicates the high-confidence O VI components with both the doublet components detected without contamination and the corresponding H I absorption also being detected. The components for which one of the doublet members is mildly blended or weak/noisy are classified as *Q*=2. H I or other metal lines may be present but are not required for classification. Finally, *Q*=1 are tentative components for which both the doublet members are blended, or very weak or noisy. Only O VI absorption components with *Q*=2 and 3 are used in this work.

There are a total of 118 O VI components detected in the spectra of 16 quasars in the redshift range of 0.13 < *z*<sub>abs</sub> < 0.71 (74 are flagged as *Q*=3 and 44 as *Q*=2). These 118 components are shared by 67 systems of O VI absorbers, with 35 systems containing more than one component. The best-fit component column densities (*N*<sub>OVI</sub><sup>comp</sup>) and *b*-parameters returned by VPFIT are shown in the left panel of Figure 4. The median *N*<sub>OVI</sub><sup>comp</sup> and *b* values are ≈10<sup>13.9</sup> cm<sup>-2</sup> and ≈25 km s<sup>-1</sup>, respectively. A moderate correlation (Kendall-τ = 0.38, *p* < 0.001) between *N*<sub>OVI</sub><sup>comp</sup> and *b* is observed. However, this correlation does not persist when the components with *N*<sub>OVI</sub><sup>comp</sup> ≳ 10<sup>14</sup> cm<sup>-2</sup> are considered, below which our survey suffers from incompleteness.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** The column densities of the O VI components obtained in the blind search across 16 background quasar spectra used in the MUSEQuBES plotted against b-parameter (left) and redshift (right). The histograms on the top represent b and redshift distribution in the left and right panels, respectively. The histograms on the right represent the column-density distribution in both panels. The vertical lines in the histograms represent the median values of the distributions.</figcaption></figure>

The right panel of Figure 4 shows no significant correlation between $z_{abs}$ and $N_{OVI}^{comp}$ (Kendall-$\tau$ = 0.1). However, we noticed a dearth of data points with $N_{OVI}^{comp} < 10^{13.7}$ cm$^{-2}$ and $z > 0.4$. This can be attributed to the lower S/N of the G160M grating spectra used in this work.

### 3.2. Associating Galaxies with Absorbers

For galaxy-absorber association, we cross match our galaxy catalog with the blind O VI absorber catalog with a linking velocity of $\pm 300$ km s$^{-1}$ centered on each galaxy redshift in a given field. The column densities of all absorption components within the velocity windows are summed to obtain the total column density associated with a galaxy. The O VI measurements for the 247 galaxies are tabulated in Appendix Table 6.

Out of the 247 galaxies, 60 exhibit associated O VI absorption with a median of two components per system.<fnref n="9" /> For the remaining 187 galaxies, we estimated the $3\sigma$ upper limits on O VI column density over a velocity window of $\pm 60$ km s$^{-1}$ using the standard deviation of flux from regions devoid of any absorption. The velocity window used here is twice the typical b-parameter of O VI absorbers (see e.g., J. K. Werk et al. 2013; S. D. Johnson et al. 2015). The kinematics of the O VI-bearing gas phase around the 60 galaxies with detected O VI absorption are presented in a separate paper (S. Dutta et al. 2025). Among the 60 galaxies with detected O VI absorption, 25 and 35 galaxies are classified as “isolated” and “group” galaxies, respectively. Note that, in our study, multiple “group” galaxies can share the absorption system. A detailed investigation of the role of environment on the O VI absorption is beyond the scope of this work. However, in Appendix C, we have shown that a unique absorption-halo connection for these nonisolated galaxies does not change the results presented in this work.

### 4. Results

In this section, we investigate the spatial distribution of O VI-bearing gas around galaxies through the column-density profile and covering fraction profiles.

#### 4.1. O VI Column Density Profile

Probing the variation of total O VI column density with impact parameter is the first step to mapping the O VI distribution in and around galaxies. In the left panel of Figure 5, the total column density of O VI is plotted against the normalized impact parameter ($D/R_{vir}$) of the MUSEQuBES galaxies. Since our galaxies show a large dynamic range in stellar mass, it is essential to scale the impact parameter by $R_{vir}$ to minimize scatter due to varying halo sizes. The different symbols with different colors indicate the different galaxy types, as indicated in the legend (see Section 2.1 for details). The solid and open symbols denote the detection and $3\sigma$ upper limits on column densities, respectively.

To explore potential correlations between $N(OVI)$ and $D/R_{vir}$, we conduct a Kendall-$\tau$ survival analysis using the NADA package in R, including the upper limits. The Kendall-$\tau$ test reveals a weak anticorrelation between $N(OVI)$ and $D/R_{vir}$ for the star-forming (“SF”) galaxies ($\tau = -0.14, p = 0.005$). We note that several galaxies closely separated in redshift (residing in a “group”) sharing a common O VI absorption system increases the scatter in this relation. Consistent with Z. Qu et al. (2024), we find a tighter anticorrelation for the star-forming galaxies when the smallest $D/R_{vir}$ galaxy of a group is associated with the measured column density ($\tau = -0.24, p < 0.001$). No significant correlation is seen for the quenched (“E”) galaxies ($p = 0.453$).

Prompted by the weak anticorrelation seen for the “SF” galaxies, we proceed to model the corresponding $N(OVI)$-profile, adopting an empirical $N(OVI)$ profile given by a modified exponential function:

$$N_{OVI}(D/R_{vir}) = N_0 \exp\left[-\left(\frac{D/R_{vir}}{L_s}\right)^\gamma\right], \quad (1)$$

where $N_0$, $L_s$, and $\gamma$ are the free parameters of the model, signifying the maximum $N(OVI)$, the length scale of exponential decline, and the slope of the profile, respectively.

Here, we used all the “SF” galaxies, but we verified that our results do not change appreciably when only the smallest $D/R_{vir}$ galaxies are considered for groups.

<footnote n="9">⁹ Note that a single system can be shared by multiple galaxies.</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Left: $N(O \text{VI})$ plotted against $D/R_{\text{vir}}$ for the galaxies in MUSEQuBES. The hollow points represent the $3\sigma$ upper limits on $N(O \text{VI})$ for nondetections. The blue squares, red circles, and green triangles indicate star-forming (SF), quenched (E), and unclassified (U) galaxies, respectively. The results of the Kendall-$\tau$ correlation test, including the upper limits, between $N(O \text{VI})$ and $D/R_{\text{vir}}$ for the “SF” and “E” galaxies are indicated inside the panel. A weak anticorrelation between $N(O \text{VI})$ and $D/R_{\text{vir}}$ is observed for the “SF” galaxies. Right: $N(O \text{VI})$ plotted against $D/R_{\text{vir}}$ only for the “SF” galaxies in MUSEQuBES. The solid line represents the best-fit model median (see text). The blue-shaded region represents the 68% confidence intervals on the best-fit model median. The cyan-shaded region indicates the intrinsic scatter.</figcaption></figure>

<figure><img src="image_8.png" /></figure>

The likelihood function for producing the observed data set with *m* detections, and *n* nondetections with the model parameters $N_0$, $L_s$, $\gamma$ is given by,

$$ \mathcal{L} \propto \prod_{i=1}^{m} \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(N_i - N_{O\,\text{VI}})^2}{2\sigma^2}\right) \times \prod_{i=1}^{n} \left[ \frac{1}{\sqrt{2\pi\sigma_p^2}} \int_0^{N_i^{\text{uplim}}} \exp\left(-\frac{(y - N_{O\,\text{VI}})^2}{2\sigma_p^2}\right) dy \right] \quad (2) $$

where $\sigma^2 = \sigma_i^2 + \sigma_p^2$, with $\sigma_p = N_{O\,\text{VI}} \sigma_{\text{intr}}$ denoting the intrinsic scatter, assuming a constant intrinsic scatter $\sigma_{\text{intr}}$ in the logarithmic space and $\sigma_i$ denoting the uncertainty in individual measurements.

We use uniform priors to construct the posteriors of individual model parameters using the Markov Chain Monte Carlo (MCMC) method, which is implemented using the EMCEE package. The model median, alongside the 68% confidence interval, is shown with the blue solid line and shaded region in the right panel of Figure 5.

We have also adopted a couple of other empirical models used in the literature to quantify the $N(O \text{VI})$-profile. A comparison between the different models is discussed in Appendix A. However, our main conclusions do not change appreciably when different models are adopted to fit the $N(O \text{VI})$-profile.

This empirical fit to the $N(O \text{VI})$ measurements allows us to determine the average O VI column density ($\langle N(O \text{VI}) \rangle$) within the virial radius:

$$ \langle N_{O\,\text{VI}} \rangle = \int_{0}^{1} N_{O\,\text{VI}}(x') 2x' dx'. \quad (3) $$

Here, the variable $x'$ is $D/R_{\text{vir}}$. We use the $N(O \text{VI})$-profile given by Equation (1) with the best-fit parameters obtained with MCMC sampling to calculate $\langle N(O \text{VI}) \rangle$.

The $\log_{10}\langle N(O \text{VI})/\text{cm}^{-2}\rangle$ for the full MUSEQuBES measurement is $14.14^{+0.09}_{-0.10}$. This is significantly lower than the reported average $N(O \text{VI})$ of $10^{14.6} \text{ cm}^{-2}$ for $\approx L_*$ galaxies in J. Tumlinson et al. (2011). However, their measurements are limited to sightlines within $\approx 0.6 R_{\text{vir}}$. The best-fit $N(O \text{VI})$-profile for the MUSEQuBES sample yields $\log_{10}\langle N(O \text{VI})/\text{cm}^{-2}\rangle = 14.2$ within $0.6 R_{\text{vir}}$, which is three times lower than for the $\approx L_*$ galaxies.

It is worth mentioning that although the median $\log_{10}(M_*/M_\odot)$ is 8.7 for our sample, galaxies with a large dynamic range of stellar mass contribute (68% range of $\log_{10}(M_*/M_\odot)$ is 7.9–9.4), which can introduce additional scatter in the $N(O \text{VI})$-profile. Disentangling the role of stellar mass on the $N(O \text{VI})$-profile is thus necessary.

### 4.1.1. The Effect of Stellar Mass on the $N(O \text{VI})$-profile for the Star-forming Galaxies

Expressing the O VI column-density profile in terms of $D/R_{\text{vir}}$ does not entirely eliminate the effects of varying stellar masses (halo sizes). The $N(O \text{VI})$ at a given $D/R_{\text{vir}}$ may depend on the stellar mass due to other physical factors. Since the 176 “SF” galaxies in MUSEQuBES are predominantly low-mass (median [68% range] $\log_{10}(M_*/M_\odot) = 8.7[7.9–9.4]$), we combine MUSEQuBES with additional 253 “SF” galaxies from the literature (median [68% range] $\log_{10}(M_*/M_\odot) = 9.5[8.6–10.3]$); see Section. 2.3) to robustly probe the $M_*$ dependence of the $N(O \text{VI})$-profile.

We generate the model $N(O \text{VI})$ profile for different mass bins to quantify the role of stellar mass on the $N(O \text{VI})$-profiles. We divide the 429 (253+176) galaxies into six mass bins. The lowest stellar-mass bin comprises galaxies with $\log_{10}(M_*/M_\odot) < 8$. The galaxies with $\log_{10}(M_*/M_\odot) = 8–10.4$ are divided into four bins of 0.6 dex. The highest stellar-mass bin consists of galaxies with $\log_{10}(M_*/M_\odot) > 10.4$. The median $\log_{10}(M_*/M_\odot)$ of the six stellar-mass bins are 7.6, 8.3, 8.8, 9.5, 10.0, and 10.5. The numbers of galaxies in each bin are 40, 76, 104, 111, 58, and 40, respectively. The best-fit posterior values of the model parameters along with their
<table><caption>**Table 2**
Best-fit Model Parameters of N(O VI)-profiles for Star-forming Galaxies</caption><thead><tr><th rowspan="2">Parameter</th><th colspan="6">Best-fit Value of the Parameter for Bins with log<sub>10</sub>(M<sub>*</sub>/M<sub>☉</sub>)</th><th rowspan="2">MUSEQuBES<sup>a</sup></th></tr><tr><th>6.0–8.0</th><th>8.0–8.6</th><th>8.6–9.2</th><th>9.2–9.8</th><th>9.8–10.4</th><th>10.4–11.2</th></tr></thead><tbody><tr><td>log<sub>10</sub>N<sub>0</sub></td><td>14.0<sup>+0.2</sup><sub>-0.2</sub></td><td>13.9<sup>+0.2</sup><sub>-0.1</sub></td><td>13.9<sup>+0.1</sup><sub>-0.1</sub></td><td>14.6<sup>+0.3</sup><sub>-0.2</sub></td><td>14.6<sup>+0.3</sup><sub>-0.2</sub></td><td>14.3<sup>+0.2</sup><sub>-0.2</sub></td><td>14.3<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>γ</td><td>1.0<sup>+1.2</sup><sub>-0.5</sub></td><td>1.4<sup>+1.6</sup><sub>-0.9</sub></td><td>3.1<sup>+0.6</sup><sub>-0.8</sub></td><td>1.2<sup>+0.5</sup><sub>-0.4</sub></td><td>1.1<sup>+0.8</sup><sub>-0.4</sub></td><td>0.8<sup>+0.8</sup><sub>-0.3</sub></td><td>1.0<sup>+0.5</sup><sub>-0.3</sub></td></tr><tr><td>L<sub>s</sub></td><td>3.0<sup>+0.7</sup><sub>-1.3</sub></td><td>3.2<sup>+0.6</sup><sub>-1.3</sub></td><td>2.6<sup>+0.2</sup><sub>-0.3</sub></td><td>1.2<sup>+0.4</sup><sub>-0.6</sub></td><td>0.9<sup>+0.5</sup><sub>-0.5</sub></td><td>1.6<sup>+1.2</sup><sub>-0.8</sub></td><td>1.5<sup>+0.7</sup><sub>-0.8</sub></td></tr><tr><td>σ<sub>intr</sub></td><td>1.3<sup>+0.4</sup><sub>-0.3</sub></td><td>1.3<sup>+0.4</sup><sub>-0.3</sub></td><td>1.2<sup>+0.3</sup><sub>-0.2</sub></td><td>1.2<sup>+0.3</sup><sub>-0.2</sub></td><td>0.9<sup>+0.3</sup><sub>-0.2</sub></td><td>1.4<sup>+0.4</sup><sub>-0.4</sub></td><td>1.4<sup>+0.3</sup><sub>-0.2</sub></td></tr><tr><td>N<sub>gal</sub><sup>b</sup></td><td>40</td><td>76</td><td>104</td><td>111</td><td>58</td><td>40</td><td>176</td></tr></tbody></table>

**Notes.** For each parameter, the best-fit estimate represents the median value of the corresponding posterior distributions. The quoted uncertainties are 68% confidence intervals of the posterior probability distributions.

<sup>a</sup> The best-fit parameters are for the full star-forming galaxy sample from MUSEQuBES only.

<sup>b</sup> The number of galaxies in different mass bins.

confidence intervals for different mass bins are summarized in Table 2.

For each bin, we calculated the $\langle N(\text{O VI}) \rangle$ within the virial radius as discussed earlier.<fnref n="10" /> The $\langle N(\text{O VI}) \rangle$ are plotted against the stellar mass in Figure 6 with red triangles. The x-error bar represents the 68 percentile range of $M_*$ in each bin. The y-error bar represents the 68% confidence interval of $\langle N(\text{O VI}) \rangle$, which is derived by propagating the 68% confidence intervals of the posterior distributions. The $\langle N(\text{O VI}) \rangle$ shows a peak at $log_{10}(M_*/M_{\odot}) \approx 9.5$ and declines at both higher and lower mass ends (see also Table 3). Nonetheless, the halos of low-mass ($log_{10}(M_*/M_{\odot}) < 9$) galaxies exhibit an appreciable amount of O VI with $N(\text{O VI}) > 10^{13.5} \text{ cm}^{-2}$. Note that this is the first time the $\langle N(\text{O VI}) \rangle$ is measured for galaxies with $log_{10}(M_*/M_{\odot}) \lesssim 8$ with a statistically meaningful sample. A similar trend of $\langle N(\text{O VI}) \rangle$ with stellar mass is also shown in F. S. Zahedy et al. (2019). However, while for their sample passive luminous red galaxies dominate the high-mass bin, we observe the suppression of $\langle N(\text{O VI}) \rangle$, even for the high-mass, star-forming galaxies.

The filled and hollow circles in Figure 6 represent individual O VI detection and $3\sigma$ upper limits, respectively, within the $R_{vir}$ for all the galaxies we compiled here. The median values of these measurements are shown by the gray squares. The median and 68% confidence intervals are obtained with the Lifelines package of PYTHON, including the upper limits.<fnref n="11" /> These directly measured median values are consistent with our model-averaged N(O VI). The model-averaged and median N(O VI) along with the results of the generalized Kendall-$\tau$ correlation test between N(O VI) and $D/R_{vir}$ in each stellar-mass bin are summarized in Table 3. The strongest anticorrelation is observed for the bins with $log_{10}(M_*/M_{\odot}) = 9.2-9.8$ and $log_{10}(M_*/M_{\odot}) = 9.8-10.4$, where the $\langle N(\text{O VI}) \rangle$ peaks.

Finally, we modeled the N(O VI) measurements for 120 passive galaxies from the literature and MUSEQuBES using the procedure described above, despite the lack of anticorrelation of N(O VI) with $D/R_{vir}$ for these galaxies (see Appendix B). The model-averaged and median N(O VI) within $R_{vir}$ for the passive galaxy sample is significantly lower than

that of the star-forming galaxies when the stellar mass is controlled (Figure 19).

## 4.2. O VI Covering Fraction ($\kappa$) Profile

The covering fraction ($\kappa$) is the fraction of the sightlines passing through the CGM with measured column density above a certain threshold. This is a measure of the patchiness of the absorbing medium in the projected 2D plane perpendicular to the LOS. In our analysis of the covering fraction, we do not consider the galaxy-absorption pairs for which the $3\sigma$ limiting column density is higher than the threshold column density. As a result, 0% and 13% of the data points are excluded for the threshold N(O VI) = $10^{14} \text{ cm}^{-2}$ and $10^{13.75} \text{ cm}^{-2}$, respectively.

The $\kappa$ of “SF” and “E” galaxy populations of the MUSEQuBES sample are plotted against $D/R_{vir}$ in Figure 7 with blue squares and red circles, respectively. The left and right panels show the $\kappa$-profile for a threshold $log_{10}(N(\text{O VI})/\text{cm}^{-2})$ of 14.0 and 13.75, respectively. The “SF” galaxies are split into four $D/R_{vir}$ bins, with the bin boundaries being 0.5, 1.0, and 3.0. There are 7, 31, 126, and 12 star-forming galaxies in the four $D/R_{vir}$ bins, respectively. The quenched galaxies are split into two $D/R_{vir}$ bins separated by $D/R_{vir} = 1$, with 16 (13) galaxies with $D<R_{vir}$ ($D>R_{vir}$). The x- and y-error bars represent the 68% interval of the $D/R_{vir}$ distribution and the 68% Wilson-score interval on $\kappa$ in each bin, respectively.

As an alternate method to obtain the $\kappa$-profile, we used the novel approach introduced by I. Schroetter et al. (2021) that does not require binning of the data points in the impact parameter. Briefly, we assume that the detection probability of a circumgalactic O VI absorber above a threshold column density follows a logistic function. The conventional definition of the logistic function requires a smooth transition from 0 to 1. We slightly modified the logistic function such that it produces a smooth transition between $\kappa_1$ and $\kappa_0 + \kappa_1$, where $\kappa_1$ and $\kappa_0$ are free parameters. We used

$$p[Y=1] = \frac{\kappa_0}{1 + e^{-t}} + \kappa_1, \quad (4)$$

where $p[Y=1]$ represents the probability of a detection (implied by $Y=1$) above the threshold N(O VI), essentially the $\kappa$. Following I. Schroetter et al. (2021), the parameter $t$ is taken to be a function of the independent variable $D/R_{vir}$. We adopted

$$t = \alpha(\log_{10}(D/R_{\text{vir}}) - \beta), \quad (5)$$

<footnote n="10">¹⁰ K. Tchernyshyov et al. (2022) did not report the error in N(O VI) (i.e., $\sigma_i$) for the 197 “SF” galaxies. We used a uniform $\sigma_i$ of 0.1 dex for these galaxies. We verified that changing the $\sigma_i$ from 0.1 to 0.3 dex does not alter our conclusions.</footnote>

<footnote n="11">¹¹ For two bins, the package failed to return a nonzero median value due to the excessive upper limits. We only showed the 68 percentile range for the two bins.</footnote>
<figure><img src="image_9.png" /><figcaption>**Figure 6.** N(O VI) measured within the virial radius of the star-forming galaxies plotted against the stellar mass. The circles represent the combined galaxy sample (filled and open represent measurements and $3\sigma$ upper limits, respectively), and the color-coding indicates the survey. The average N(O VI) values (using Equation (3)) for six stellar-mass bins are shown with the red triangles. The gray squares indicate the median N(O VI) for these stellar-mass bins using survival analysis. The x-error bars represent the 68% confidence intervals of $\log_{10}(M_*/M_\odot)$ in each bin. The y-error bars represent the 68% confidence intervals of average $\log_{10}(N_{O VI}/\text{cm}^{-2})$ propagated from the 68% confidence intervals of the best-fit parameters for the red triangles, and 68% confidence intervals for the gray squares. Only upper limits on the median can be obtained for the second and last stellar-mass bins since in these bins the number of nondetections is greater than the number of detections.</figcaption></figure>

<table><caption>**Table 3**
Summary of N(O VI) Measurements (Figure 6) and Kendall-$\tau$ Test Results for Star-forming Galaxies</caption><thead><tr><th>log<sub>10</sub>(M<sub>*</sub>/M<sub>☉</sub>)<br>(1)</th><th>log<sub>10</sub> &lang;N(O VI)&rang;/cm<sup>-2</sup><br>(2)</th><th>log<sub>10</sub> N&#773;(O VI)/cm<sup>-2</sup><br>(3)</th><th>&tau;<br>(4)</th><th>p<br>(5)</th></tr></thead><tbody><tr><td>6.0–8.0</td><td>13.86<sup>+0.11</sup><sub>-0.14</sub></td><td>13.7<sup>+0.3</sup><sub>-13.7</sub></td><td>-0.18</td><td>0.084</td></tr><tr><td>8.0–8.6</td><td>13.79<sup>+0.11</sup><sub>-0.10</sub></td><td>&lt;13.6</td><td>-0.14</td><td>0.069</td></tr><tr><td>8.6–9.2</td><td>13.91<sup>+0.10</sup><sub>-0.10</sub></td><td>14.0<sup>+0.1</sup><sub>-0.4</sub></td><td>-0.20</td><td>0.002</td></tr><tr><td>9.2–9.8</td><td>14.38<sup>+0.10</sup><sub>-0.10</sub></td><td>14.5<sup>+0.1</sup><sub>-0.1</sub></td><td>-0.32</td><td>&lt;0.001</td></tr><tr><td>9.8–10.4</td><td>14.27<sup>+0.09</sup><sub>-0.10</sub></td><td>14.4<sup>+0.1</sup><sub>-0.1</sub></td><td>-0.50</td><td>&lt;0.001</td></tr><tr><td>10.4–11.2</td><td>14.07<sup>+0.11</sup><sub>-0.11</sub></td><td>&lt;13.9</td><td>-0.23</td><td>0.027</td></tr></tbody></table>

**Note.** (1) The stellar mass range of the bin. (2) The profile-averaged N(O VI) calculated within $R_{vir}$. (3) The median N(O VI) directly calculated using Lifelines. (4) The Kendall-$\tau$ parameter for the trend of N(O VI) with $D/R_{vir}$. (5) The corresponding probability.

where $\alpha$ and $\beta$ are two free parameters. $\alpha$ describes the slope of the covering fraction profiles, and $\beta$ represents $\log_{10}(D/R_{vir})$, where $\kappa$ (or $p[Y=1]$) = $\kappa_0/2 + \kappa_1(\equiv \kappa_{50})$, analogous to the zero-point at 50% covering fraction.

The parameter space is sampled to generate the dichotomous observable (1 if detected and 0 otherwise) based on the Bernoulli distribution. We use the PYMC3 for the MCMC sampling in order to obtain the best-fit parameters. The best-fit modeled $\kappa$ on the unbinned data for the star-forming sample is shown with the blue solid line in the left and right panel of Figure 7 for $\log_{10}(N(O VI)/\text{cm}^{-2})$ threshold of 14 and 13.75, respectively. The best-fit parameters are given in Table 4. The blue-shaded region represents the 68% confidence interval on the best-fit model. It is evident that the logistic model

reproduces the binned $\kappa$ profile reliably. A similar analysis could not be done for the “E” galaxies owing to the small numbers.

The best-fit model in the left panel of Figure 7 reveals a smooth transition of $\kappa$ from ≈70% at ≈0.1D/R$_{vir}$ for star-forming galaxies to a modest value of ≈30% at the virial radius. Similar to the N(O VI)-profile, the modeled $\kappa$-profile enables us to measure the average covering fraction ($\langle\kappa\rangle$) within the virial radius as:

$$ \langle\kappa\rangle = \int_{0}^{1} \kappa(x')2x'dx'. \qquad (6) $$

We obtain $\langle\kappa\rangle = 0.46_{-0.08}^{+0.08}$ for a threshold N(O VI) = $10^{14}\text{cm}^{-2}$ and $0.50_{-0.08}^{+0.07}$ for a threshold N(O VI) = $10^{13.75}\text{cm}^{-2}$. Similar to
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Left: O VI covering fraction ($\kappa$) plotted against $D/R_{vir}$ for the MUSEQuBES galaxies for a threshold $\log_{10}(N_{O VI}/\text{cm}^{-2}) = 14.0$. The blue squares and red circles indicate $\kappa$ for star-forming and quenched galaxies, respectively. The $D/R_{vir}$ is split into four bins with 0.5, 1.0, and 3.0 as the separating value to compute the covering fraction for the star-forming galaxies. The quenched galaxies are split into two bins with $D/R_{vir} = 1$ as the bin boundary. The y-error bar represents the 68% Wilson-score confidence interval. The solid blue line indicates the best-fit model to the unbinned data for star-forming galaxies (see text). The blue-shaded regions represent the 68% confidence interval on the best-fit model. The numbers next to the data points represent the median $\log_{10}(M_*/M_\odot)$ of the galaxies in each bin. Right: Same as left but for a threshold $\log_{10}(N_{O VI}/\text{cm}^{-2}) = 13.75$.</figcaption></figure>

<table><caption>**Table 4**

Best-fit Model Parameters for the $\kappa$-profiles for Star-forming Galaxies Shown in Figure 7</caption><thead><tr><th rowspan="2">Threshold<br>log<sub>10</sub>(N<sub>O VI</sub>/cm<sup>-2</sup>)</th><th colspan="4">Best-fit Value of the Parameter</th></tr><tr><th>α</th><th>β</th><th>κ<sub>0</sub></th><th>κ<sub>1</sub></th></tr></thead><tbody><tr><td>13.75</td><td>-3.1<sup>+1.4</sup><sub>-2.3</sub></td><td>-0.08<sup>+0.2</sup><sub>-0.3</sub></td><td>0.66<sup>+0.2</sup><sub>-0.2</sub></td><td>0.1<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>14.0</td><td>-7.9<sup>+2.3</sup><sub>-4.0</sub></td><td>-0.1<sup>+0.1</sup><sub>-0.1</sub></td><td>0.58<sup>+0.1</sup><sub>-0.1</sub></td><td>0.1<sup>+0.02</sup><sub>-0.02</sub></td></tr></tbody></table>

**Note.** For each parameter, the best-fit estimate represents the median value of the corresponding posterior distributions. The quoted uncertainties are 68% confidence intervals of the posterior probability distributions.

⟨N(O VI)⟩, these numbers are substantially lower compared to $\kappa = 0.8-1$ for O VI absorption around ≈0.6$R_{vir}$ of ≈$L_*$ galaxies observed in the COS-Halos survey.

Figure 7 shows that the star-forming galaxies exhibit a significantly enhanced $\kappa$ for both the column-density thresholds within $R_{vir}$. However, no significant difference in $\kappa$ between the “SF” and “E” galaxies is seen beyond the virial radius. Similar to our findings, a bimodality in the O VI covering fraction was also observed in the COS-Halos survey between star-forming and passive galaxies. However, we point out that the median stellar mass of the “SF” galaxies is more than an order of magnitude lower than that of the “E” galaxies. The median $M_*$ for each $D/R_{vir}$ bin is indicated next to the data points in Figure 7. It is therefore important to control the $M_*$ for the “SF” and “E” to disentangle the role of star formation in the O VI covering fraction.

Recently, K. Tchernyshyov et al. (2023) showed that the bimodality of O VI absorption persists inside the virial radius, even when controlled for stellar mass and halo mass. The lack of high-mass, star-forming galaxies in MUSEQuBES prevents us from carrying out a similar analysis robustly. The majority of the passive galaxies in our sample have $\log_{10}(M_*/M_\odot) > 10$. None of the passive galaxies with $\log_{10}(M_*/M_\odot) > 10$ show any detectable O VI absorption within $R_{vir}$. However, out of five star-forming galaxies with $\log_{10}(M_*/M_\odot) > 10$,

only one (20%) shows O VI absorption within $R_{vir}$ and it has $\log_{10}(N(O VI)/\text{cm}^{-2}) = 14.4$.

### 4.2.1. The Effect of Stellar Mass on the $\kappa$-profile for the Star-forming Galaxies

In order to investigate the role of stellar mass on the covering fraction of star-forming galaxies, we used the logistic regression method introduced earlier to obtain the $\kappa$-profile for multiple stellar-mass bins. For this exercise, we included galaxies from the literature as well (see Section 2.3). The $M_*$ range of the star-forming galaxies from the combined data set is split into three bins with $\log_{10}(M_*/M_\odot) < 9$, $9 \le \log_{10}(M_*/M_\odot) < 10$, and $\log_{10}(M_*/M_\odot) \ge 10$. There are 197, 155, and 77 galaxies in the three bins. We use the logistic model described in Section 4.2, allowing the parameters $\kappa_0$, $\kappa_1$, $\alpha$, and $\beta$ to vary across the $M_*$ bins. The best-fit parameters for the three mass bins are tabulated in Table 5.

In Figure 8, we show the median modeled $\kappa$-profile for the unbinned data (for a threshold $N(O VI) = 10^{14} \text{cm}^{-2}$) for the three mass bins with solid blue lines in the three panels. The cyan narrow lines indicate 500 randomly drawn models within 68% confidence intervals of the posterior distributions. We also show the binned covering fractions and 68% Wilson-score intervals with solid blue squares and error bars.

The $\kappa$-profiles across different $M_*$ bins show the steepest slope for the intermediate mass bin, while the slopes are significantly shallower for both the higher and lower mass bins (see Table 5). Additionally, similar to the N(O VI), a significant enhancement in the $\kappa$ within the $R_{vir}$ is observed for the intermediate mass bin. The median stellar mass of this bin ($\log_{10}(M_*/M_\odot) \approx 9.5$) is consistent with halos with the virial temperature of ≈$10^{5.5}$ K at which the ion fraction of O VI peaks in the CIE.

The $\langle\kappa\rangle$ within $R_{vir}$ for galaxies in the three mass bins are obtained using two methods. First, $\langle\kappa\rangle$ is obtained by averaging over the best-fit logistic models in each stellar-mass bin. These are shown by the purple squares in Figure 9. The 68%
<figure><img src="image_11.png" /><figcaption>**Figure 8.** The covering fraction profile for a threshold $log_{10}(N_{OVI}/cm^{-2}) = 14$ plotted against the $D/R_{vir}$ for three mass bins with $log_{10}(M_{*}/M_{\odot}) < 9$ (left), $\le 9log_{10}(M_{*}/M_{\odot}) < 10$ (middle), and $log_{10}(M_{*}/M_{\odot}) \ge 10$ (right) for the combined “SF” galaxy sample (MUSEQuBES+literature). The median $log_{10}(M_{*}/M_{\odot})$ for the bins are 8.4, 9.5, and 10.4. The blue squares and y-error bars represent the binned $\kappa$ and 68% confidence intervals. The blue solid line and the shaded region in cyan represent the model $\kappa$ along with the 68% confidence intervals.</figcaption></figure>

<table><caption>**Table 5**
Best-fit Model Parameters for the $\kappa$-profiles for a Threshold $log_{10}(N_{OVI}/cm^{-2}) = 14$ for Different $M_{*}$ Bins for Star-forming Galaxies Shown in Figure 8</caption><thead><tr><th rowspan="2">log<sub>10</sub>(M<sub>*</sub>/M<sub>☉</sub>)</th><th colspan="4">Best-fit Value of the Parameter</th></tr><tr><th>α</th><th>β</th><th>κ<sub>0</sub></th><th>κ<sub>1</sub></th></tr></thead><tbody><tr><td>&lt;9</td><td>-8.6<sup>+1.9</sup><sub>-2.8</sub></td><td>-0.23<sup>+0.05</sup><sub>-0.06</sub></td><td>0.71<sup>+0.10</sup><sub>-0.09</sub></td><td>0.09<sup>+0.01</sup><sub>-0.01</sub></td></tr><tr><td>9-10</td><td>-15.0<sup>+3.0</sup><sub>-3.3</sub></td><td>0.04<sup>+0.02</sup><sub>-0.02</sub></td><td>0.72<sup>+0.04</sup><sub>-0.04</sub></td><td>0.09<sup>+0.01</sup><sub>-0.01</sub></td></tr><tr><td>≥10</td><td>-6.4<sup>+1.8</sup><sub>-2.1</sub></td><td>-0.13<sup>+0.09</sup><sub>-0.07</sub></td><td>0.68<sup>+0.08</sup><sub>-0.07</sub></td><td>0.10<sup>+0.01</sup><sub>-0.01</sub></td></tr></tbody></table>

**Note.** For each parameter, the best-fit estimate represents the median value of the corresponding posterior distributions. The quoted uncertainties are 68% confidence intervals of the posterior probability distributions.

confidence interval of $\langle \kappa \rangle$ is derived from the 68% confidence intervals of the posterior distributions and shown as the y-error bars. We also show the nonparametric $\kappa$ determined directly using the N(O VI) measurements for each stellar-mass bin for galaxies with $D/R_{vir} < 1$. These measurements are shown by the blue circles in Figure 9. The corresponding y-error bars represent 68% Wilson-score intervals. The mean and median $\kappa$ within $R_{vir}$ are consistent within $1\sigma$ uncertainty.

Note that the parameter $\beta$ represents $log_{10}(D/R_{vir})$ where $\kappa = \kappa_{0}/2 + \kappa_{1}(\equiv\kappa_{50})$. This is analogous to the zero-point at 50% covering fraction. Interestingly, the best-fit $\beta \approx 0.04$ for the intermediate mass bin suggests a length scale of $\approx 1.1 R_{vir}$, which is significantly larger compared to the values of $\approx 0.6 R_{vir}$ and $\approx 0.7 R_{vir}$ for the lower and higher $log_{10}(M_{*}/M_{\odot})$ bins, respectively (see Table 5). Equation (5) can be modified to include the variation of $\beta$ with $log_{10}(M_{*}/M_{\odot})$. Guided by the peak of $\beta$ in the intermediate mass bin, we used a simple Gaussian function to modify Equation (5) as follows:

$$t = \alpha \left[ \log_{10}(D/R_{\text{vir}}) - \left( \tilde{\beta} \ e^{-\frac{(m-m_0)^2}{2\sigma_m^2}} - \epsilon \right) \right], \quad (7)$$

where $m$ represents $log_{10}(M_{*}/M_{\odot})$, and $m_0$, $\tilde{\beta}$, and $\epsilon$ are three additional free parameters in the fit to account for the variation with $log_{10}(M_{*}/M_{\odot})$. We do not impose an explicit mass dependence on $\kappa_0$, $\kappa_1$ or $\alpha$.

In the left panel of Figure 10, the stellar mass-dependent-$\beta$, denoted by $\mathcal{R}_{50}$, is shown as a function of stellar mass with the

<figure><img src="image_12.png" /><figcaption>**Figure 9.** The covering fraction ($\kappa$) measured within $R_{vir}$ for a threshold $log_{10}(N_{OVI}/cm^{-2}) = 14$ plotted against the median $M_{*}$ for the combined “SF” galaxy sample. The purple squares represent the mean $\kappa$ obtained using the best-fit logistic models for each stellar-mass bin (Equation (5)). The blue circles represent directly measured $\kappa$ values for galaxies with $D/R_{vir} < 1$. The x- and y-error bars are similar to Figure 6. The slight offset between the purple and blue points along the x-axis is for clarity.</figcaption></figure>

blue solid line. $\mathcal{R}_{50}$ is expressed in units of $log_{10} D/R_{vir}$ and is given by

$$\mathcal{R}_{50} = \left( \tilde{\beta} \ e^{-\frac{(m-m_0)^2}{2\sigma_m^2}} - \epsilon \right). \quad (8)$$

The gray-shaded region represents the 68% confidence interval on the best-fit model. The red squares represent the $\mathcal{R}_{50}$ (identical to $\beta$) measured for three individual $log_{10}(M_{*}/M_{\odot})$ bins (see Table 5). The best-fit $\mathcal{R}_{50}$ peaks at $log_{10}(M_{*}/M_{\odot}) \approx 9.5$, consistent with the peak observed in $\langle \kappa \rangle$. In the right panel of Figure 10, the modeled $\kappa$ following Equation (7) for a threshold N(O VI) of $10^{14} cm^{-2}$ is color-coded as a function of $D/R_{vir}$ along the x-axis and $log_{10}(M_{*}/M_{\odot})$ along the y-axis. The individual star symbols, squares, and triangles represent the binned $\kappa$ with the same
<figure><img src="image_13.png" /><figcaption>**Figure 10.** Left: The best-fit $R_{50}$ (see Equation (8)) plotted against the stellar mass with blue solid line. The gray-shaded region represents the 68% confidence interval on the best-fit model. The red squares represent the $R_{50}$ (identical to $\beta$) measured for three individual $\log_{10}(M_*/M_\odot)$ bins. Right: The best-fit $\kappa$ color-map as a function of $D/R_{vir}$ along the x-axis and $\log_{10}(M_*/M_\odot)$ along the y-axis. The star symbols, squares, and triangles are binned $\kappa$ in four $D/R_{vir}$ and three $\log_{10}(M_*/M_\odot)$ bins. The model reproduces the binned measurements except for the lowest $D/R_{vir}$, where the difference is within $1\sigma$.</figcaption></figure>

threshold for three stellar-mass bins and four $D/R_{vir}$ bins, adopting the same color convention. Our model adequately reproduces the binned $\kappa$ within the $1\sigma$ uncertainty.

We have verified that the $\kappa$-profiles do not change appreciably with redshift, at least within the redshift range of our interest.

## 5. Discussion

We have studied the properties of O VI-bearing gas in the CGM of low-redshift (0.1–0.7) galaxies. In particular, we investigated the connection between host galaxy properties and the strength and incidence rate of O VI absorption. In this section, we discuss the main findings from Section 4.

### 5.1. O VI Mass in the CGM as a Function of Stellar Mass

The moderate anticorrelation seen between the $N(O VI)$ and $D/R_{vir}$ for the “SF” galaxies in our sample indicates the galactic origin of the O VI absorption. Following K. Tchernyshyov et al. (2022), we determined the average O VI column density ($\langle N(O VI) \rangle$) within the virial radius of “SF” galaxies with a range of stellar masses (Figure 6). The addition of 176 predominantly low-mass galaxies from MUSEQuBES improved the $\langle N(O VI) \rangle$ measurements significantly, particularly at $\log_{10}(M_*/M_\odot) < 9$. In fact, $\langle N(O VI) \rangle$ is for the first time well-measured at $\log_{10}(M_*/M_\odot) < 8.5$.

The average O VI mass in the CGM ($<R_{vir}$) of galaxies can be obtained using:

$$M(\text{O VI}) = \langle N(\text{O VI}) \rangle \times m_{\text{O}} \times \pi R_{\text{vir}}^2, \quad (9)$$

where $m_{\text{O}}$ is the mass of an oxygen atom. In Figure 11, the derived $M(O VI)$ is plotted against $M_*$ with black solid circles. Overall, $M(O VI)$ increases with the stellar mass by an order of magnitude from $\log_{10}(M_*/M_\odot) \approx 7.5–9.5$. At higher stellar masses probed by our sample, the $M(O VI)$ remains flat at $\approx 10^{6.3} M_\odot$.

As expected, our $M(O VI)$ measurements are broadly consistent with K. Tchernyshyov et al. (2022), since their data is a subset of our combined sample. However, with the

increased sample size, we offer significantly improved measurements, especially for low-mass galaxies. For example, by increasing the number of $N(O VI)$ measurements within the virial radius by a factor of 2, we are able to constrain the $\log_{10}(M(O VI)/M_\odot)$ to $\approx 5.0_{-0.1}^{+0.1}$ for galaxies with $\log_{10}(M_*/M_\odot) < 8.0$.

The red stripe in the left panel of Figure 11 shows the expected variation of $M(O VI)$ with stellar mass, if the O VI originates from the ambient hot halo gas. We predicted $M(O VI)$ using:

$$M(\text{O VI}) = f_{\text{O VI}}(T) \times 10^{-3.31+\log[\text{H}]} \times A_{\text{O}} \times f_{\text{CGM}} \\ \times f_{\text{b}} \times M_{\text{halo}}, \quad (10)$$

where $[\text{H}]$ is the oxygen abundance in solar units, $f_{\text{CGM}}$ is the fraction of total galactic baryons in the CGM, $f_{\text{b}}(\equiv \Omega_{\text{b}}/\Omega_{\text{M}})$ is the cosmic baryon fraction, and $A_{\text{O}}$ is the atomic mass of oxygen. The O VI ion fraction, $f_{\text{O VI}}(T)$, is obtained from the CIE tables of B. D. Oppenheimer & J. Schaye (2013), determined at the virial temperature of the halo.<fnref n="12" /> Note that the abundance of the O VI-bearing gas phase and the $f_{\text{CGM}}$ for different stellar masses are largely unknown. If we assume that the $[\text{H}]$ is similar to that of the cool, photoionized gas phase, i.e., $[\text{X/H}] \approx -0.5$ (see J. X. Prochaska et al. 2017; Sameer et al. 2024), then $f_{\text{CGM}} \approx 0.15$ can explain the estimated $M(O VI)$ for galaxies at $\log_{10}(M_*/M_\odot) \approx 9.5$.

The pure CIE model under-produces $M(O VI)$ for the mass bin of $\log_{10}(M_*/M_\odot) \ge 10.4$. Note that, in the presence of nonthermal pressure support (e.g., turbulence, cosmic rays), the virial temperature for a given halo mass can be overestimated (see e.g., C. Lochhaas et al. 2021; K. Tchernyshyov et al. 2023). Another explanation for this discrepancy could be the projection effect along the LoS. Some of the detected O VI likely originate from regions outside the virial radius, even if the transverse distance is smaller than $R_{vir}$ (see S. H. Ho et al. 2021). These regions outside the virial radius are conducive to O VI production for such massive halos (e.g.,

<footnote n="12">¹² Using the $T_{vir}-M_{halo}$ relation from B. D. Oppenheimer et al. (2016)</footnote>
<figure><img src="image_14.png" /><figcaption>**Figure 11.** Left: Measured average O VI mass within the virial radius of star-forming galaxies, plotted against the stellar mass with black solid circles. The top x-axis indicates the virial temperature of the corresponding halo assuming $z=0.4$. The binning is described in Section 4.1. The x-error bars are 68% confidence intervals in a given mass bin. The y-error bars are 68% confidence interval on $M(\text{O VI})$ propagated from the posterior 68% confidence interval of the parameter space. The red stripe shows the predicted $M(\text{O VI})$ for collisionally ionized ambient hot halo with $f_{\text{CGM}} = 0.15$ and metallicity $0.3Z_{\odot}$ in CIE. The purple dashed stripe shows $M(\text{O VI})$ predicted from the same ambient hot halo in the presence of a photoionizing UVB assuming $n_{\text{H}} = 10^{-4.5} \text{ cm}^{-3}$. Right: The data points and the red stripe are the same as the left panel. The blue dashed stripe shows the predicted $M(\text{O VI})$ from the nonequilibrium cooling of hot outflows with $0.3Z_{\odot}$, and $f_{\text{CGM}} = 0.15$ in the presence of a photoionizing UVB assuming $n_{\text{H}} = 10^{-4.5} \text{ cm}^{-3}$. The orange dotted stripe shows the same but without the presence of the UVB.</figcaption></figure>

B. D. Oppenheimer et al. 2016). Alternatively, a higher $f_{\text{CGM}}$ and/or [O/H] for the highest mass bin can also account for the data. Additionally, the pure CIE model overproduces $M(\text{O VI})$ for the mass bin of $\log_{10}(M_{\star}/M_{\odot}) = 9.8–10.4$. A lower $f_{\text{CGM}}$ and/or [O/H] could resolve the discrepancy.

The pure CIE model fails to reproduce the estimated $M(\text{O VI})$ for $\log_{10}(M_{\star}/M_{\odot}) < 9.0$. A higher $f_{\text{CGM}}$ can increase $M(\text{O VI})$ for galaxies with $\log_{10}(M_{\star}/M_{\odot}) < 9$. Even at solar metallicity, the required $f_{\text{CGM}}$ exceeds 1, which is unphysical. Note that the CGM of dwarf galaxies is expected to have subsolar metallicity (e.g., J. Suresh et al. 2017). Evidently, the observed $M(\text{O VI})$ in the CGM of dwarf galaxies requires origin(s) other than the virialized gas in pure CIE since the virial temperatures are too low for collisional ionization.

O VI in the CGM of dwarf galaxies can alternatively be produced via photoionization. Note that the pure CIE model shown in Figure 11 (red stripe) does not consider any external radiation field. The extragalactic UV background (UVB) radiation field can increase the degree of ionization and reduce cooling efficiencies, favoring the production of O VI at lower temperatures. The purple dashed stripe in the left panel of Figure 11 shows the inferred $M(\text{O VI})$ for a “hybrid” model that considers both photoionization and collisional ionization, while keeping all other parameters the same as the pure CIE model. The ion fractions are obtained at $n = 10^{-4.5} \text{ cm}^{-3}$, $z = 0.4$ from an interpolated density-redshift-temperature grid from B. D. Oppenheimer & J. Schaye (2013), which are computed in the presence of the UVB HM01. The purple dashed line is highlighted at $\log_{10}(M_{\star}/M_{\odot}) < 9$, where the UVB strongly boosts the $M(\text{O VI})$ estimates as compared to the pure CIE model. Evidently, photoionization equilibrium with the UVB can account for the estimated O VI mass.

Another way to explain the estimated $M(\text{O VI})$ for dwarf galaxies is through nonequilibrium processes. Nonequilibrium effects become important when gas that was initially heated to very high temperatures ($>10^6$ K) cools faster than it

recombines (i.e., the ratio of cooling time to recombination time, $t_{\text{cool}}/t_{\text{rec}} < 1$). Consequently, the gas remains overionized for its temperature. In the right panel of Figure 11, the blue dashed stripe shows the $M(\text{O VI})$ predicted for such nonequilibrium cooling gas at the virial temperature, with a metallicity of [X/H] = -0.5 and a density of $n_{\text{H}} = 10^{-4.5} \text{ cm}^{-3}$ subject to the HM01 UVB at $z \approx 0.4$. The ion fractions are taken from an interpolated density-redshift-temperature grid from B. D. Oppenheimer & J. Schaye (2013). The $M(\text{O VI})$ predicted by this model is in good agreement with the observations for $\log_{10}(M_{\star}/M_{\odot}) < 9$. The orange dotted stripe shows the same but without the UVB radiation field. It is apparent that nonequilibrium cooling gas with a subsolar metallicity cannot produce the observed $M(\text{O VI})$ for dwarf galaxies in the absence of the UVB. While a higher metallicity (e.g., [X/H] $\gtrsim$ 0) could account for the observed $M(\text{O VI})$ without invoking the UVB, such elevated metallicities are not typically observed, even in the ISM of dwarf galaxies (L. van Zee & M. P. Haynes 2006). Thus, the presence of the UVB is crucial in both equilibrium and nonequilibrium scenarios to explain the observed $M(\text{O VI})$.

In the case of nonequilibrium cooling, it is important to understand the physical processes that can heat the gas to a very high temperature. Such high temperatures can be achieved via shocks, presumably due to star formation feedback. At higher redshift, there is strong evidence that some circumgalactic O VI traces hot, metal-rich outflows (see M. L. Turner et al. 2015). For example, an outflow velocity of $\approx 200 \text{ km s}^{-1}$ can give rise to a temperature of $>10^6$ K in the postshock medium. Note that the assumed $f_{\text{CGM}}$ of 0.15 would in this case correspond to the fraction of baryons that are shock-heated but not yet cooled. For a galaxy of $\log_{10}(M_{\star}/M_{\odot}) = 7$ ($\log_{10}M_{\text{halo}}/M_{\odot} \approx 10$), the estimated cold gas in ISM is $\approx 10^8 M_{\odot}$ (see M. S. Peeples et al. 2014). Therefore, the baryon fraction for the stellar and ISM components is only 6% (i.e., $10^{8.04}/(0.16 \times 10^{10})$). It is thus possible that 15% of the
<figure><img src="image_15.png" /><figcaption>**Figure 12.** Left: O VI column densities and $3\sigma$ upper limits for low-mass galaxies ($\log_{10}(M_*/M_{\odot}) < 9$) with $D/R_{vir} < 0.8$ plotted against the SFR by the filled circles and downward triangles, respectively. The data points are color-coded by the stellar mass. Only isolated, star-forming galaxies from MUSEQuBES are shown. The Kendall-$\tau$ correlation reveals a strong correlation ($\tau = 0.58$) with $> 2\sigma$ significance. Right: Same as left, but for the high-mass ($\log_{10}(M_*/M_{\odot}) \ge 9$) galaxies. Here, we included measurements from star-forming COS-Halos galaxies, marked with black squares. No significant correlation is observed for the high-mass sample.</figcaption></figure>

remaining 94% baryons are in hot outflows. However, we note that only a fraction of the available baryons may be out of equilibrium.

## 5.2. Importance of Local Ionization Sources

In the previous section, we emphasized the importance of photoionization in contributing significantly to the total M (O VI) for low-mass halos. The HM01 UVB model at $z \approx 0.4$ requires a low-density region with $n_H \approx 10^{-4.5} \text{ cm}^{-3}$, corresponding to an ionization parameter of $\approx 10^{-1}$, to efficiently produce O VI. Such a density corresponds to an overdensity, $\delta$ of $\approx 70$,<fnref n="13" /> which is typical of the bulk of the CGM.

This density contrast demands a cloud size of $\approx 22$ kpc to produce the observed $\langle N(\text{O VI}) \rangle \approx 10^{13.8} \text{ cm}^{-2}$ for low-mass galaxies, assuming $[X/H] \approx -0.5$ and $f_{\text{O VI}} \approx 0.2$. A lower metallicity of $[X/H] \approx -1$ results in a larger cloud size of $\approx 66$ kpc, which is consistent with the halo size of low-mass galaxies. The densities inside the virialized halo, however, can be higher than this, resulting in a smaller cloud size.

Additional photoionization from the local sources is required to maintain the ionization parameter at higher densities. Previously, J. K. Werk et al. (2016) showed that soft X-ray emission in the form of the local ionizing source alongside the UVB could result in a match to the observed line-ratios without resorting to very low-density and unusually large cloud sizes. They argued that such high-energy photons can be produced by the super-soft X-ray sources (SSSs) and/or hot ISM resulting from supernovae heating. Such high-energy photons from the local ionizing sources may play a key role in galaxy evolution (S. Cantalupo 2010). A relatively weak anticorrelation of N (O VI) and $D/R_{vir}$ for the galaxies with $\log_{10}(M_*/M_{\odot}) < 9$ ($\tau \gtrsim -0.2$, see Table 3) could be a manifestation of both the local ionizing flux and density falling as $\propto 1/D^2$, keeping a roughly flat ionization parameter.

Alternatively, a higher $f_{\text{CGM}}$ can produce the observed M (O VI) in low-mass galaxies for higher densities without requiring local ionization sources. In such a case, the required $f_{\text{CGM}}$ exceeds 50% for the dwarf galaxies.

## 5.3. The Trend Between N(O VI) and SFR for “SF” Galaxies

The COS-Halos survey reported a strong bimodality of N (O VI) with sSFR, with massive ($L_*$) star-forming galaxies showing significantly higher O VI column densities than passive galaxies which show O VI absorption in only a small fraction of the sample (J. Tumlinson et al. 2011). We confirmed this trend in Figure 7 inside $R_{vir}$, but found that quenched galaxies follow the same relation as star-forming galaxies for $D/R_{vir} = 1-2$. Subsequently, we focused on the covering fraction of “SF” galaxies only. No significant trend between N(O VI) and SFR is reported for the massive ($\approx L_*$), star-forming galaxies in the COS-Halos sample. In this section, we will investigate whether there is any trend between the N(O VI) and SFR for the low-mass, “SF” galaxies in our sample.

In the left panel of Figure 12, we show the individual N (O VI) measurements for the “SF” galaxies with $D < 0.8 R_{vir}$ ($< 70$ kpc) and $\log_{10}(M_*/M_{\odot}) < 9$ against the SFR. The $3\sigma$ upper limits in cases of nondetection are shown by the downward triangles. The N(O VI) of low-mass galaxies shows a strong correlation with SFR (Kendall-$\tau = 0.58, p = 0.014$) with $> 2\sigma$ significance. Such a correlation is expected if star formation-driven outflows give rise to the O VI in the CGM, as seems to be the case for at least part of the O VI around $z \approx 2$ SF galaxies (see M. L. Turner et al. 2015). In fact, for a given mass loading factor ($\eta \equiv \dot{M}_{\text{out}}/\text{SFR}$) and a fixed star formation timescale, a linear relation is expected between the O VI mass and the SFR with a slope of unity when plotted on a log-scale. The observed correlation between N(O VI) and SFR suggests that star formation-driven outflows can contribute to the O VI budget in the CGM of low-mass galaxies.

The right panel of Figure 12 shows the N(O VI) versus SFR for the “SF” galaxies with $\log_{10}(M_*/M_{\odot}) \ge 9$. Here, we included measurements from J. Tumlinson et al. (2011) besides MUSEQuBES to increase the sample size. Unlike for the low-mass galaxies in the left panel, no significant correlation is observed here (Kendall-$\tau = 0.07, p = 0.57$). We have seen in the previous section that the estimated M(O VI) for the high-mass galaxies can be explained if O VI arises from the ambient hot halo at the virial temperature.

<footnote n="13">¹³ Assuming the relation of mean baryon density $\bar{n}_H$ with redshift from J. Schaye (2001).</footnote>
## 5.4. Do O VI Absorbers Trace Transient Structures in the CGM of Dwarf Galaxies?

In Section 5.1, we have observed that collisional ionization at the virial temperature of subsolar metallicity gas, under both equilibrium and nonequilibrium conditions, cannot produce sufficient $M(O VI)$ to account for the observations of dwarf galaxies ($\log_{10}(M_*/M_\odot) < 9$). Indeed, photoionization by the UVB or local sources seems to be necessary since the virial temperatures of the halos are too low for O VI production. In the previous section, we reported a correlation between $N(O VI)$ and SFR for the dwarf galaxies within $\approx R_{vir}$. If such a correlation is driven by metal-rich outflows from these dwarf galaxies, then it is possible to shock-heat the CGM to super-virial temperatures ($\ge 10^6$ K) depending on the shock speed. Such shock-heated gas can give rise to O VI when cooling down.

A correlation between the $N(O VI)$ and line width ($\Delta v_{lw}$) is predicted theoretically for such radiatively cooling gas (e.g., T. M. Heckman et al. 2002; R. Bordoloi et al. 2017). Briefly, the O VI column density is given by:

$$N(O VI) = \frac{3k_B T}{\Lambda(T, Z)} v_{\text{cool}} \left(\frac{O}{H}\right) Z f_{O VI}, \quad (11)$$

where $v_{\text{cool}}$ is the velocity of the cooling flow, $\Lambda(T, Z)$ is the cooling function in the units of erg cm$^3$ s$^{-1}$, T indicates the column-density-weighted mean temperature of the cooling gas, and all other symbols have their usual meanings. The line width $\Delta v_{lw}$ in this context can be written as:

$$\Delta v_{lw}^2 = 2k_B T/m_O + v_{\text{cool}}^2. \quad (12)$$

We used the cooling function $\Lambda(T, Z)$ and the $f_{O VI}$ from B. D. Oppenheimer & J. Schaye (2013) assuming CIE to obtain the relation between $N(O VI)$ and $\Delta v_{lw}$. Note that the relation in Equation (11) is insensitive to the metallicity provided $[O/H] \gtrsim -2$.

The kinematics of the O VI bearing gas are presented in S. Dutta et al. (2025). However, in Figure 13, we show the observed component column density, $N_{O VI}^{\text{comp}}$, against the $\Delta v_{lw}$, defined as $3b/\sqrt{2}$ following the definition of R. Bordoloi et al. (2017), for the O VI components associated with isolated, low-mass ($\log_{10}(M_*/M_\odot) < 9$), MUSEQuBES galaxies. The dashed, dotted, and solid black lines represent the predicted component column density from the cooling flow models (Equation (11)) for $T = 10^6$, $10^{5.4}$ and $10^{5.5}$ K, respectively. The observed O VI component column densities in the CGM of dwarf galaxies are broadly consistent with the cooling flow model at column-density-weighted mean temperature of $T \approx 10^{5.4}$ K. We found that 12 out of 14 (7 out of 10) O VI components detected at $D < R_{vir}$ ($D \ge R_{vir}$) show b-parameters broad enough to be consistent with such a temperature. This suggests that a fraction of these O VI components may be tracing transient structures in the CGM cooling down to $\approx 10^{5.4}$ K from an initial hot phase, presumably triggered by star formation-driven shocks. However, it is worthwhile to note that the observed $N_{O VI}^{\text{comp}} - b$ correlation may partly result from the inability to detect broad, low column-density components.

## 5.5. The Robustness of M(O VI) in the CGM of Dwarf Galaxies

The $M(O VI)$ in Section 5.1 was estimated from the $N(O VI)$ measurements in the CGM within $R_{vir}$. Therefore, the robustness of $M(O VI)$ depends on the way we associate an absorber with a galaxy. Recall that we used a velocity window of $\pm 300$ km s$^{-1}$ centered on the galaxy redshift to determine the total $N(O VI)$. The $M(O VI)$ for low-mass ($\log_{10}(M_*/M_\odot) < 9$) MUSEQuBES galaxies within $R_{vir}$ with this fiducial velocity window is $\log_{10}(M(O VI)/M_\odot) = 5.2^{+0.1}_{-0.1}$. Using a smaller velocity window of $\pm 100$ km s$^{-1}$ provides consistent results.

Our $M(O VI)$ estimates are marginally lower than the mass measured for a sample of “isolated” dwarf ($\log_{10}(M_*/M_\odot) < 9$) galaxies in the CUBS survey, i.e., $\log_{10}(M(O VI)/M_\odot) \approx 5.6^{+0.1}_{-0.3}$ within $R_{vir}$ (N. Mishra et al. 2024). Note that N Mishra et al. (2024) selected only the isolated galaxies for the $M(O VI)$ measurements. Additionally, they obtained the mean $M(O VI)$ with a nonparametric measure (Equation (4) in their paper). Following the same method, we obtain $\log_{10}(M(O VI)/M_\odot) = 5.45$ and $\log_{10}(M(O VI)/M_\odot) = 5.37$ for a velocity window of $\pm 300$ km s$^{-1}$ and $\pm 100$ km s$^{-1}$, respectively. These values are consistent with their measurement within the $1\sigma$ uncertainty.

With such a fixed LOS velocity window, it is possible that a fraction of the detected absorbers may reside outside the virial radius because the exact location along the LOS is largely uncertain. This could lead to an overestimation of the measured column density within the CGM. Owing to their relatively smaller virial radii, this effect becomes more serious for dwarf galaxies (see S. H. Ho et al. 2021).

Additionally, the contributions from neighboring massive galaxies outside the MUSE FOV can also lead to an overestimation of the $M(O VI)$ for the dwarf galaxies. In order to test the robustness of the $M(O VI)$ estimates, we select a subsample of galaxies from our MUSEQuBES sample that has no neighbor detected within $\pm 500$ km s$^{-1}$ LOS separation within the MUSE FoV. The $\langle N(O VI) \rangle$ and $M(O VI)$ estimates remain unaffected even with this sample. Next, we used data from a wide-field ($\approx 20^\circ$) galaxy survey with the Magellan telescope (Johnson et al., in prep) for 6/16 quasar fields in our sample. Magellan observations show that three of the nine low-mass galaxies showing detectable O VI absorption in these six fields have a massive neighbor outside the MUSE FOV with lower $D/R_{vir}$. Thus, while the effects of massive galaxies outside the MUSE FOV are not severe, it is likely not negligible. To be conservative, the $\langle N(O VI) \rangle$ and $M(O VI)$ for galaxies with $\log_{10}(M_*/M_\odot) < 9$ could be treated as conservative upper limits.

## 5.6. O VI-floor in the Outskirts of Dwarf Galaxies

A lower covering fraction of O VI around low-mass galaxies ($\log_{10}(M_*/M_\odot) < 9$) for a threshold $N(O VI) = 10^{14}$ cm$^{-2}$ does not necessarily rule out the presence of O VI absorbers below this threshold, which are undetected because of the limited S/N of the COS spectra. In fact, most O VI upper limits are above $\log_{10}(N(O VI)/cm^{-2}) = 13.2$.

Spectral stacking is extensively used in the literature to detect weak signals that are otherwise hidden in noise (see e.g., J. Schaye et al. 2000; C. C. Steidel et al. 2010; M. L. Turner et al. 2014; Y. Chen et al. 2020). With the same motivation, we produced an O VI stack using the $\log_{10}(M_*/M_\odot) < 9$ galaxies in our sample that do not exhibit any detectable O VI absorption in their CGM (124 out of 247 cases). To obtain the median
<figure><img src="image_16.png" /><figcaption>**Figure 13.** The observed component column density, $N_{\text{O VI}}^{\text{comp}}$, plotted against the line width ($\Delta v_{\text{lw}} \equiv 3b/\sqrt{2}$) for the O VI components associated with isolated, low-mass ($\log_{10}(M_*/M_{\odot}) < 9$), MUSEQuBES galaxies. The dashed, dotted, and solid lines represent the predicted $N_{\text{O VI}}^{\text{comp}}$ from the cooling flow models of T. M. Heckman et al. (2002) for $T = 10^{10}$, $10^{5.4}$, and $10^{5.5}$ K, respectively. The points with black triangle envelopes indicate O VI components detected at $D > R_{\text{vir}}$.</figcaption></figure>

stack, we adopted a method similar to S. Dutta et al. (2024). Briefly, (a) for each galaxy, we select a region of $\pm 1500$ km s$^{-1}$ around its redshifted O VI wavelength in the normalized spectrum of the corresponding background quasar. (b) We calculate the median normalized flux in 40 km s$^{-1}$ wide velocity bins for all such quasar-galaxy pairs. This is referred to as the observed median-stacked flux spectrum. (c) Next, a local pseudo-continuum is estimated and subtracted from the observed median-stacked flux spectrum. We use the median flux far away from the galaxy redshifts ($\pm 5000-10,000$ km s$^{-1}$) as the pseudo-continuum. Finally, (d) the O VI rest-frame equivalent widths are measured by direct integration of the pseudo-continuum-subtracted median-stacked spectra for LOS velocity windows of $\pm 300$ km s$^{-1}$ ($W_{r,300}$) from the line center.

The median-stacked flux profile, along with the standard deviation, is shown in Figure 14. O VI is detected in the median stack with $>90\%$ confidence, with a rest-frame equivalent width of $0.02 \pm 0.01$ Å. The detection significance and the error on the $W_{r,300}$ measurement (68% confidence interval) are obtained from the $W_{r,300}$ distribution obtained from 1000 bootstrap resampled median spectra. For such a weak line,<fnref n="14" /> it is appropriate to convert the $W_{r,300}$ to column density, assuming the linear part of the curve of growth. This yields $\log_{10}(N(\text{O VI})/\text{cm}^{-2}) = 13.2_{-0.3}^{+0.2}$. We point out here that the majority of the galaxies (113/124) contributing to the stack have $D > R_{\text{vir}}$ with a median $D/R_{\text{vir}} \approx 2$. Thus, the detection of O VI absorption in the stacked spectrum may suggests that there may be an O VI-floor far outside the virial radius of low-mass galaxies with an average column density of $\approx 10^{13.2}$ cm$^{-2}$.

J. X. Prochaska et al. (2011) found that the virialized halos of sub-$L_*$ galaxies can account for almost all of the strong O VI absorption ($W_{r,1031} > 100$ mÅ) seen in the quasar spectra. A similar conclusion was reached by

<figure><img src="image_17.png" /><figcaption>**Figure 14.** The median-stacked O VI absorption profile for the low-mass ($\log_{10}(M_*/M_{\odot}) < 9$) MUSEQuBES galaxies without any individually detected O VI is shown with the black histogram. The black horizontal line represents the pseudo-continuum used to obtain the rest-frame equivalent width. The gray-shaded region represents the standard deviation of flux obtained from 1000 bootstrap realizations.</figcaption></figure>

K. Tchernyshyov et al. (2022) who showed that O VI absorbers with $N(\text{O VI}) > 10^{14.5}$ cm$^{-2}$ are mostly contributed by the halos of star-forming galaxies with $M_*$ ranging from $10^{8.8}$ to $10^{10.4} M_{\odot}$. However, both J. X. Prochaska et al. (2011) and K. Tchernyshyov et al. (2022) argued that the halos of star-forming galaxies cannot account for the low column density O VI absorbers ($N(\text{O VI}) < 10^{13.5}$ cm$^{-2}$). K. Tchernyshyov et al. (2022) speculated the existence of an extended CGM out to 300 kpc around galaxies where these low column-density absorbers might reside. The detected O VI with $N(\text{O VI}) \approx 10^{13.2}$ cm$^{-2}$ in the stacked spectrum is in line with their speculations.

To understand the physical and chemical properties of the O VI-bearing gas detected in the stack, we estimated the median H I column density using two approaches. First, we measured H I column densities (47 cases) and upper limits (77 cases) for all the galaxies. Second, we produced a stack of Ly$\beta$ absorption for galaxies without individually detected Ly$\beta$ absorption. In both cases, we obtained a consistent $N(\text{H I})$ of $10^{13.6}$ cm$^{-2}$, indicating a mild overdensity ($\delta \sim 10$) of the absorbing medium, under the assumption that hydrogen is photoionized (e.g., J. Schaye 2001). Under CIE at $T \approx 10^{5.5}$ K, the O VI and H I column densities suggest an oxygen abundance of [O/H] $\approx -2.3$ and total hydrogen column density of $\sim 10^{19}$ cm$^{-2}$. Note that, the average metallicity of the cool enriched gas phase is observed to be [X/H] $\approx -0.5$ to $-1.0$ within $\approx 0.5-1 R_{\text{vir}}$ of massive galaxies (see J. X. Prochaska et al. 2017; S. K. Pointon et al. 2019; Sameer et al. 2024). Therefore, it is unlikely that the gas temperature is $< 10^{5.3}$ K, since it yields an unreasonably high oxygen abundance (i.e., [O/H] $> -1$) at impact parameters of $\approx 2 R_{\text{vir}}$ from dwarf galaxies ($\log_{10}(M_*/M_{\odot}) < 9$). The expected low metallicity suggest that the detected O VI absorption may be tracing the relatively cooler phase of the canonical warm-hot intergalactic medium (WHIM; e.g., R. Cen et al. 2001; R. Davé et al. 2001). Indeed, R. Davé et al. (2001) argued that WHIM gas is heated to $T > 10^5$ K primarily by shock heating of gas accreting onto large-scale filamentary structures that are not yet virialized or in dynamical equilibrium. This is consistent with the large impact parameters ($\approx 2 R_{\text{vir}}$) of the dwarf galaxies contributing to the stack, which may be embedded in such filaments.

<footnote n="14">¹⁴ Recall that absorption is not detected in individual spectra.</footnote>
On the contrary, if the gas detected in the stack is in photoionization equilibrium with the extragalactic UVB radiation, the inferred oxygen abundance would be [O/H] ≳ −1.0 for all plausible densities. Such a high metallicity is unlikely to be present at ≈2R<sub>vir</sub> from dwarf galaxies (J. Suresh et al. 2017). However, the metallicity of the oxygen-bearing phase can be much higher than the rest of the CGM because the metal can be poorly mixed (see J. Schaye et al. 2007; T. Tepper-García et al. 2011).

## 6. Summary

In this paper, we present a study of the O VI-bearing gas around 247 low-redshift (0.1 ≲ z ≲ 0.7) galaxies with a median log<sub>10</sub>(M<sub>*</sub>/M<sub>☉</sub>) = 8.7 observed in 16 quasar fields in MUSEQuBES. The 60 detected O VI absorption systems, along with the stringent 3σ upper limits for the nondetections, enabled us to investigate the connections between galaxy properties on the O VI column density (N(O VI)) and covering fraction (κ) profiles. Our key findings are:

1. The O VI column-density shows a weak anticorrelation with D/R<sub>vir</sub> (τ = −0.15, p = 0.003) for the star-forming galaxies, which is not present for the quenched galaxies (τ = 0.10, p = 0.453) in our sample (Figure 5).

2. The O VI covering fraction profiles for MUSEQuBES galaxies show a significantly higher covering fraction within the virial radius of star-forming galaxies compared to quenched galaxies. No significant difference in covering fraction is observed at D/R<sub>vir</sub> = 1–2 for these two galaxy populations (Figure 7).

3. Including the O VI measurements around 253 star-forming galaxies from the literature, we provide fitting formulae and best-fit parameters for (i) the O VI column-density profile for different mass bins (Table 2) and (ii) the O VI covering fraction profiles at threshold N (O VI) = 10<sup>14</sup> cm<sup>−2</sup> for different mass bins (Table 5). The impact parameter averaged O VI column density log<sub>10</sub>⟨N(O VI)/cm<sup>−2</sup>⟩ ≈ 14.1 within R<sub>vir</sub> for our MUSE-QuBES sample is significantly lower than for ≈L<sub>*</sub> galaxies.

4. Using the combined sample of star-forming galaxies, we show that both ⟨N(O VI)⟩ and ⟨κ(O VI)⟩ peak for galaxies with log<sub>10</sub>(M<sub>*</sub>/M<sub>☉</sub>) ≈ 9.5 (Figures 6 and 9). The virial temperature for these galaxies is optimal for O VI under collisional ionization. Moreover, these galaxies show the strongest anticorrelation of N(O VI) with D/R<sub>vir</sub> compared to their lower- and higher-mass counterparts (Table 3).

5. The average O VI mass estimated within R<sub>vir</sub> shows a peak at log<sub>10</sub>(M<sub>*</sub>/M<sub>☉</sub>) ≳ 9.5 and is almost an order of magnitude lower at log<sub>10</sub>(M<sub>*</sub>/M<sub>☉</sub>) ≲ 8.5. CIE at the virial temperature can explain the estimated M(O VI) for the high-mass galaxies but not for the dwarf galaxies. Photoionization and/or collisionally ionized cooling gas transitioning through ≈10<sup>5.4</sup> K can account for the N(O VI) and M(O VI) measurements for the dwarf galaxies (Figure 11).

6. The N(O VI) of low-mass (log<sub>10</sub>(M<sub>*</sub>/M<sub>☉</sub>) < 9), star-forming galaxies within 0.8R<sub>vir</sub> shows a strong correlation with the SFR of the host galaxies (τ = 0.58, p = 0.014),

which is not present for the high-mass, star-forming counterparts (Figure 12).

7. Using spectral stacking, we report the presence of a highly ionized metal floor outside the virial radius of dwarf galaxies with log<sub>10</sub>(N(O VI)/cm<sup>−2</sup>) = 13.2 (Figure 14). We argued that the detected O VI signal may be tracing the relatively cooler phase of the canonical WHIM gas in the cosmic filaments in which the dwarf galaxies are embedded.

## Acknowledgments

This work is based on observations collected at the European Southern Observatory under ESO programmes 094.A-0131(B), 095.A-0200(A), 096.A-0222(A). We express our sincere gratitude to the anonymous referee for their valuable feedback. We extend our thanks to Marijke Segers, Lorrie Straka, and Monica Turner for their early contributions to the MUSE-QuBES project. S.C., S.D., and S.M. gratefully acknowledge the support of the Indo-Italian Executive Programme of Scientific and Technological Cooperation 2022-2024 (TPN: 63673). S.D. and S.M. thank R. Srianand and Aseem Paranjape for insightful discussions. S.D. acknowledges Alankar Dutta and Prateek Sharma for meaningful suggestions.

## Appendix A
Model Comparison

In Section 4.1, we have computed the model-averaged ⟨N(O VI)⟩ following a modified exponential profile. The best-fit N(O VI) profiles for the 6 stellar mass bins are presented in the Figure 15. In the literature, several other functional forms are adopted to determine the N(O VI)-profiles. Here, we present a brief overview of two such models and compare the results.

### A.1. Z. Qu et al. (2024)

Z. Qu et al. (2024) adopted a simple power law (i.e., N ∝ (D/R<sub>vir</sub>)<sup>−α</sup>) to model the N(O VI)-profile, but added an intrinsic covering fraction to account for the nondetections at smaller impact parameters. The two-component model, similar to the one used by Y.-H. Huang et al. (2021) has a modified exponential covering fraction given by

$$ \epsilon(D/R_{\text{vir}}) = \text{Min} \left[ 1, \epsilon_0 \exp \left( - \left( \frac{D/R_{\text{vir}}}{x_0} \right)^{\beta} \right) \right]. \quad (A1) $$

The best-fit N(O VI)-profiles for this model are shown in Figure 16.

### A.2. K. Tchernyshyov et al. (2022)

K. Tchernyshyov et al. (2022) adopted a modified exponential profile similar to our work with a baseline column density. Their N(O VI)-profile is given by:

$$ \log_{10} N_{\text{O VI}}(D/R_{\text{vir}}) = \log_{10} \left( 10^{N_0 e^{-\left(\frac{D}{L_s R_{\text{vir}}}\right)^{\gamma}}} + 10^{N_b} \right). \quad (A2) $$

Following their methodology, we have generated the N(O VI)-profiles keeping the baseline N<sub>b</sub>, slope γ and length-scale L<sub>s</sub> tied in the six mass bins, only allowing the normalization N<sub>0</sub> to vary in different log<sub>10</sub>(M<sub>*</sub>/M<sub>☉</sub>) bins. The best-fit profiles are shown in Figure 17. The ⟨N(O VI)⟩ and M(O VI) are
<figure><img src="image_18.png" /><figcaption>**Figure 15.** Same as the right panel of Figure 5, but for different mass bins, as indicated in the panels. We adopted a modified exponential function given in Equation (1) to model the profiles.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 16.** Model N(O VI)-profiles for different mass bins following the procedure of Z. Qu et al. (2024). The smaller upper panels show the variation of the parameter $\epsilon$ (see Equation (A1)) with normalized impact parameter. The square symbols represent binned covering fraction with a threshold column density of $log_{10}(N_{O VI}/\text{cm}^{-2}) = 14$.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Figure 17.** Model $N(O\,VI)$-profiles for different mass bins following the procedure of K. Tchernyshyov et al. (2022) briefly outlined in Appendix A.2.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 18.** Left: Same as Figure 6 but with added measurements following the prescriptions of K. Tchernyshyov et al. (2022, green star symbols) and Z. Qu et al. (2024, black pentagons). Our measurements (red triangles) are in good agreement with the measurements obtained from their prescriptions. Right: $M(O\,VI)$ within $R_{vir}$ for the star-forming galaxies obtained from the model-averaged $N(O\,VI)$ shown on the right panel plotted against the $\log_{10}(M_*/M_\odot)$ of host galaxies.</figcaption></figure>

shown with green stars in the left and right panels of Figure 18, respectively. The $\langle N(O\,VI) \rangle$ and $M(O\,VI)$ obtained with the Z. Qu et al. (2024) model are shown with black pentagons in the left and right panels of Figure 18, respectively.

## Appendix B

### $\langle N(O\,VI) \rangle$ Comparison for Star-forming and Passive Galaxies

The $O\,VI$ column densities for passive galaxies in the MUSEQuBES sample do not show any significant anticorrelation with $D/R_{vir}$ (see Figure 5). This is also true for the combined

sample of passive galaxies from MUSEQuBES and the literature ($\tau = -0.1, p = 0.08$). In order to quantify the difference of $\langle N(O\,VI) \rangle$ inside $R_{vir}$ for the star-forming and passive galaxies, we adopted the modified exponential function used in this work to model the $N(O\,VI)$-profile of passive galaxies. The model-averaged $\langle N(O\,VI) \rangle$ for passive galaxies is $\approx 10^{14} \text{ cm}^{-2}$ within $R_{vir}$. Star-forming galaxies with $\log_{10}(M_*/M_\odot) > 9.8$ are only considered here to control the stellar mass, while there is no such constraint on the passive galaxies since all but four have $\log_{10}(M_*/M_\odot) > 9.8$. The $\langle N(O\,VI) \rangle \approx 10^{14.3} \text{ cm}^{-2}$ within $R_{vir}$ of star-forming galaxies is significantly enhanced compared to the passive galaxies (see Figure 19).
<figure><img src="image_22.png" /><figcaption>**Figure 19.** O VI column density against stellar mass for the combined sample of MUSEQuBES and the literature. The blue star symbol and red triangle indicate the model-averaged N(O VI) within $R_{vir}$ for the star-forming and passive galaxies, respectively. The blue pentagon and red plus with a downward arrow represent the nonparametric median N(O VI) within $R_{vir}$ for star-forming galaxies and the 95% upper limit on the median for the passive galaxies, respectively, obtained with the LIFELINES package of PYTHON. The blue and red small circles represent individual measurements for star-forming and passive galaxies within $R_{vir}$. The open circles represent 3$\sigma$ upper limits. Star-forming galaxies with $\log_{10}(M_*/M_\odot) > 9.8$ are only considered here to control the stellar mass, while there is no such constraint on the passive galaxies since all but four have $\log_{10}(M_*/M_\odot) > 9.8$.</figcaption></figure>

# Appendix C

## Halo-absorption Connection for Nonisolated Galaxies

In Section 3.2, we described the construction of galaxy-absorption pairs. Our approach allows for multiple nonisolated (“group”) galaxies to be associated with a single absorption system. In this section, we investigate how our results are affected when only one galaxy within a group is associated with an absorption system.

In case of a group, we calculate the “total” stellar mass by summing the stellar masses of the member galaxies. The corresponding total halo mass of the “group” is obtained from the stellar-to-halo-mass relation of B. P. Moster et al. (2013). The halo mass of the group is subsequently used to obtain the $R_{vir}$. S. D. Johnson et al. (2015) argued that using mass-weighted projected distance as the group-centric impact parameter can introduce biases. This happens because it may artificially inflate the extent of the O VI-bearing gas for nonisolated galaxies, particularly when the absorption is stemming from the nearest galaxy. In order to circumvent this, we have selected the impact parameter of the galaxy closest to the sightline and assigned it as the *D* for the group (see also Z. Qu et al. 2023). Consistent with Section 3.2, the halo-absorption pairs are then constructed with a linking velocity of

$\pm 300 \text{ km s}^{-1}$. In the top left panel of Figure 20, we show the N(O VI)-profile for the MUSEQuBES sample where only the smallest *D* galaxy of a group is plotted. The $\langle N(\text{O VI}) \rangle$ within the virial radius (indicated inside the panel) remains consistent with the reported value in Section 4.1 within $1\sigma$.

For galaxy-halo connections, we have used a fixed linking velocity of $\pm 300 \text{ km s}^{-1}$. However, massive halos will have a larger circular velocity compared to low-mass halos. In order to test the robustness of our measurements against this fixed LOS linking velocity, we have used the circular velocity ($v_{circ} = \sqrt{2GM_{halo}/R_{vir}}$) as the linking velocities for individual halos. The resulting N(O VI)-profile for the full MUSEQuBES star-forming galaxies is shown in the right panel of Figure 20. The $\langle N(\text{O VI}) \rangle$ within the virial radius (indicated inside the panel) remains consistent with the reported value in Section 4.1 within $1\sigma$.

Additionally, in order to probe the effect of the halo mass of nonisolated galaxies, we divide the halo-absorber pairs (constructed with $\pm 300 \text{ km s}^{-1}$ linking velocity) of the MUSEQuBES sample into two stellar-mass bins (with $\log_{10}(M_*/M_\odot) < 9$ and $\log_{10}(M_*/M_\odot) \ge 9$). The resulting $\langle N(\text{O VI}) \rangle$ (green squares) do not differ appreciably from the $\langle N(\text{O VI}) \rangle$ obtained from the MUSEQuBES sample following our adopted method of galaxy-absorption construction of Section 3.2 (blue star symbols).
<figure><img src="image_23.png" /><figcaption>**Figure 20.** The top panels show the measured *N(O VI)* plotted against the *D/R<sub>vir</sub>* for the star-forming galaxies, where the minimum *D* galaxy from the group's galaxies is selected, with the *R<sub>vir</sub>* measured with the inferred halo mass from the total stellar mass of the group galaxies. The left and right panels show the halo-absorber connection with the fiducial ±300 km s<sup>-1</sup> and *v<sub>circ</sub>* as the linking velocity, respectively. The ⟨*N(O VI)*⟩ within *R<sub>vir</sub>* for both cases (indicated inside the respective panels) is consistent with the reported value in Section 4.1 within 1σ. The bottom panel shows the ⟨*N(O VI)*⟩ within *R<sub>vir</sub>* for two mass bins with the unique halo-absorber pairs constructed from the MUSEQuBES galaxies with green squares, obtained with a linking velocity of ±300 km s<sup>-1</sup>. The blue star symbols show ⟨*N(O VI)*⟩ within *R<sub>vir</sub>* obtained from the MUSEQuBES galaxies with multiple nonisolated galaxies sharing a single absorption system (the fiducial galaxy-absorber pair construction used in Section 3.2). These measurements are consistent with the measurements reported in Figure 5 (light-shaded red triangles).</figcaption></figure>
## Appendix D
Online Only Table

The O VI measurements for the 247 MUSEQuBES galaxies are tabulated in Table 6.

<table><caption>**Table 6**
The O VI Absorption Measurements and the Associated Galaxy Properties for the MUSEQuBES Sample</caption><thead><tr><th>ID<br>(1)</th><th>ζ<sub>gal</sub><br>(2)</th><th>ζ<sub>abs</sub><br>(3)</th><th>log<sub>10</sub>(N/cm<sup>-2</sup>)<br>(4)</th><th>σ[log<sub>10</sub>(N/cm<sup>-2</sup>)]<br>(5)</th><th>D in kpc<br>(6)</th><th>log<sub>10</sub>(M<sub>x</sub>/M<sub>☉</sub>)<br>(7)</th><th>log<sub>10</sub>(SFR/M<sub>☉</sub>yr<sup>-1</sup>)<br>(8)</th></tr></thead><tbody><tr><td>1</td><td>0.5101</td><td>-999</td><td>13.47</td><td>-999</td><td>174.1</td><td>8.2</td><td>-1.41</td></tr><tr><td>2</td><td>0.3333</td><td>0.3333</td><td>13.60</td><td>0.05</td><td>36.8</td><td>8.4</td><td>-1.46</td></tr><tr><td>3</td><td>0.3249</td><td>0.3245</td><td>14.23</td><td>0.27</td><td>44.2</td><td>8.7</td><td>-0.84</td></tr><tr><td>4</td><td>0.3284</td><td>0.3282</td><td>14.53</td><td>0.10</td><td>88.9</td><td>9.8</td><td>-0.43</td></tr><tr><td>5</td><td>0.3835</td><td>0.3835</td><td>14.10</td><td>0.03</td><td>50.2</td><td>8.4</td><td>-1.1</td></tr><tr><td>6</td><td>0.2496</td><td>0.2502</td><td>13.61</td><td>0.05</td><td>70.9</td><td>8.7</td><td>-1.33</td></tr><tr><td>7</td><td>0.5322</td><td>0.5333</td><td>13.87</td><td>0.05</td><td>178.4</td><td>8.3</td><td>-1.35</td></tr><tr><td>8</td><td>0.4021</td><td>-999</td><td>13.48</td><td>-999</td><td>77.6</td><td>8.2</td><td>-1.71</td></tr><tr><td>9</td><td>0.2111</td><td>-999</td><td>13.47</td><td>-999</td><td>68.8</td><td>8.2</td><td>-1.25</td></tr><tr><td>10</td><td>0.3994</td><td>-999</td><td>13.48</td><td>-999</td><td>155.3</td><td>8.1</td><td>-1.01</td></tr><tr><td>11</td><td>0.5941</td><td>-999</td><td>13.56</td><td>-999</td><td>216.3</td><td>9.2</td><td>0.5</td></tr><tr><td>12</td><td>0.2656</td><td>-999</td><td>13.98</td><td>-999</td><td>155.9</td><td>7.9</td><td>-2.27</td></tr><tr><td>13</td><td>0.4318</td><td>0.4317</td><td>13.98</td><td>0.10</td><td>176.5</td><td>10.1</td><td>0.38</td></tr><tr><td>14</td><td>0.3227</td><td>0.3231</td><td>13.38</td><td>0.07</td><td>149.8</td><td>8.8</td><td>-1.39</td></tr><tr><td>15</td><td>0.4789</td><td>-999</td><td>13.75</td><td>-999</td><td>183.2</td><td>8.2</td><td>-0.76</td></tr><tr><td>16</td><td>0.4224</td><td>-999</td><td>13.50</td><td>-999</td><td>207.0</td><td>8.3</td><td>-1.55</td></tr><tr><td>17</td><td>0.1321</td><td>-999</td><td>13.39</td><td>-999</td><td>13.8</td><td>7.1</td><td>-2.3</td></tr><tr><td>18</td><td>0.2256</td><td>0.226</td><td>14.20</td><td>0.01</td><td>103.3</td><td>7.6</td><td>-2.29</td></tr><tr><td>19</td><td>0.2909</td><td>0.2911</td><td>14.11</td><td>0.04</td><td>72.9</td><td>7.9</td><td>-1.46</td></tr><tr><td>20</td><td>0.4002</td><td>0.4003</td><td>14.32</td><td>0.02</td><td>67.1</td><td>8.7</td><td>-0.67</td></tr><tr><td>21</td><td>0.2222</td><td>-999</td><td>13.83</td><td>-999</td><td>96.2</td><td>7.2</td><td>-1.16</td></tr><tr><td>22</td><td>0.3721</td><td>-999</td><td>13.29</td><td>-999</td><td>183.6</td><td>8.4</td><td>-1.06</td></tr><tr><td>23</td><td>0.5317</td><td>-999</td><td>13.43</td><td>-999</td><td>170.4</td><td>7.6</td><td>-1.82</td></tr><tr><td>24</td><td>0.6019</td><td>-999</td><td>13.59</td><td>-999</td><td>213.7</td><td>9.5</td><td>-1.76</td></tr><tr><td>25</td><td>0.3139</td><td>-999</td><td>13.27</td><td>-999</td><td>79.3</td><td>7.3</td><td>-2.02</td></tr><tr><td>26</td><td>0.4243</td><td>0.4241</td><td>14.57</td><td>0.01</td><td>130.2</td><td>9.4</td><td>-0.45</td></tr><tr><td>27</td><td>0.3124</td><td>-999</td><td>13.34</td><td>-999</td><td>85.9</td><td>8.3</td><td>-2.09</td></tr><tr><td>28</td><td>0.2717</td><td>-999</td><td>13.61</td><td>-999</td><td>35.4</td><td>7.1</td><td>-2.13</td></tr><tr><td>29</td><td>0.5308</td><td>-999</td><td>13.92</td><td>-999</td><td>227.0</td><td>10.6</td><td>0.07</td></tr><tr><td>30</td><td>0.6811</td><td>-999</td><td>13.75</td><td>-999</td><td>227.8</td><td>7.0</td><td>-1.06</td></tr><tr><td>31</td><td>0.3085</td><td>0.3083</td><td>14.27</td><td>0.02</td><td>153.4</td><td>7.2</td><td>-0.78</td></tr><tr><td>32</td><td>0.7023</td><td>-999</td><td>13.72</td><td>-999</td><td>226.6</td><td>10.4</td><td>-1.0</td></tr><tr><td>33</td><td>0.5723</td><td>0.5726</td><td>14.31</td><td>0.03</td><td>27.9</td><td>7.6</td><td>-1.36</td></tr><tr><td>34</td><td>0.6028</td><td>-999</td><td>13.88</td><td>-999</td><td>141.5</td><td>8.8</td><td>-0.99</td></tr><tr><td>35</td><td>0.3004</td><td>-999</td><td>13.61</td><td>-999</td><td>140.9</td><td>7.8</td><td>-2.07</td></tr><tr><td>36</td><td>0.3089</td><td>0.3083</td><td>14.27</td><td>0.02</td><td>125.3</td><td>8.3</td><td>-0.73</td></tr><tr><td>37</td><td>0.4455</td><td>-999</td><td>13.69</td><td>-999</td><td>79.7</td><td>10.0</td><td>-1.68</td></tr><tr><td>38</td><td>0.4454</td><td>-999</td><td>13.69</td><td>-999</td><td>115.4</td><td>9.6</td><td>-1.75</td></tr><tr><td>39</td><td>0.6158</td><td>0.6151</td><td>15.03</td><td>0.04</td><td>127.5</td><td>9.7</td><td>-1.14</td></tr><tr><td>40</td><td>0.3681</td><td>-999</td><td>13.55</td><td>-999</td><td>103.2</td><td>8.9</td><td>-0.73</td></tr><tr><td>41</td><td>0.6027</td><td>-999</td><td>13.87</td><td>-999</td><td>196.6</td><td>10.5</td><td>-1.11</td></tr><tr><td>42</td><td>0.6151</td><td>0.6151</td><td>15.03</td><td>0.04</td><td>102.4</td><td>9.6</td><td>-0.12</td></tr><tr><td>43</td><td>0.6153</td><td>0.6151</td><td>15.03</td><td>0.04</td><td>47.9</td><td>9.4</td><td>1.03</td></tr><tr><td>44</td><td>0.7024</td><td>-999</td><td>13.72</td><td>-999</td><td>206.1</td><td>9.1</td><td>-1.28</td></tr><tr><td>45</td><td>0.4399</td><td>-999</td><td>13.68</td><td>-999</td><td>54.9</td><td>9.0</td><td>-0.74</td></tr><tr><td>46</td><td>0.5159</td><td>-999</td><td>13.65</td><td>-999</td><td>75.2</td><td>8.9</td><td>0.78</td></tr><tr><td>47</td><td>0.4408</td><td>-999</td><td>13.67</td><td>-999</td><td>73.2</td><td>9.6</td><td>0.22</td></tr><tr><td>48</td><td>0.6489</td><td>-999</td><td>13.68</td><td>-999</td><td>164.9</td><td>9.2</td><td>0.52</td></tr><tr><td>49</td><td>0.4435</td><td>-999</td><td>13.73</td><td>-999</td><td>82.2</td><td>6.9</td><td>-1.79</td></tr><tr><td>50</td><td>0.6017</td><td>-999</td><td>13.83</td><td>-999</td><td>126.0</td><td>9.3</td><td>-0.22</td></tr><tr><td>51</td><td>0.4419</td><td>-999</td><td>13.66</td><td>-999</td><td>139.3</td><td>8.9</td><td>-1.6</td></tr><tr><td>52</td><td>0.4477</td><td>-999</td><td>13.71</td><td>-999</td><td>168.3</td><td>8.8</td><td>-1.49</td></tr><tr><td>53</td><td>0.4419</td><td>-999</td><td>13.66</td><td>-999</td><td>176.2</td><td>8.8</td><td>-0.96</td></tr><tr><td>54</td><td>0.5827</td><td>-999</td><td>13.68</td><td>-999</td><td>254.6</td><td>7.4</td><td>-0.32</td></tr><tr><td>55</td><td>0.4384</td><td>-999</td><td>13.68</td><td>-999</td><td>193.9</td><td>9.9</td><td>0.51</td></tr><tr><td>56</td><td>0.4446</td><td>-999</td><td>13.70</td><td>-999</td><td>169.0</td><td>9.4</td><td>-0.92</td></tr><tr><td>57</td><td>0.4428</td><td>-999</td><td>13.72</td><td>-999</td><td>149.3</td><td>9.2</td><td>-0.97</td></tr><tr><td>58</td><td>0.5080</td><td>-999</td><td>13.66</td><td>-999</td><td>225.4</td><td>7.5</td><td>-1.9</td></tr><tr><td>59</td><td>0.5308</td><td>-999</td><td>13.92</td><td>-999</td><td>185.6</td><td>8.1</td><td>-1.36</td></tr></tbody></table>
<table><caption>**Table 6**
(Continued)</caption><thead><tr><th>ID<br>(1)</th><th>z<sub>gal</sub><br>(2)</th><th>z<sub>abs</sub><br>(3)</th><th>log<sub>10</sub>(N/cm<sup>-2</sup>)<br>(4)</th><th>σ[log<sub>10</sub>(N/cm<sup>-2</sup>)]<br>(5)</th><th>D in kpc<br>(6)</th><th>log<sub>10</sub>(M<sub>☉</sub>/M<sub>☉</sub>)<br>(7)</th><th>log<sub>10</sub>(SFR/M<sub>☉</sub>yr<sup>-1</sup>)<br>(8)</th></tr></thead><tbody><tr><td>60</td><td>0.3081</td><td>0.3083</td><td>14.27</td><td>0.02</td><td>157.2</td><td>8.8</td><td>-1.12</td></tr><tr><td>61</td><td>0.5101</td><td>-999</td><td>13.54</td><td>-999</td><td>211.6</td><td>9.5</td><td>-0.56</td></tr><tr><td>62</td><td>0.4758</td><td>-999</td><td>13.57</td><td>-999</td><td>158.2</td><td>10.6</td><td>&lt;-0.54</td></tr><tr><td>63</td><td>0.3720</td><td>-999</td><td>13.57</td><td>-999</td><td>120.2</td><td>9.7</td><td>0.02</td></tr><tr><td>64</td><td>0.4166</td><td>-999</td><td>13.45</td><td>-999</td><td>127.8</td><td>8.8</td><td>-1.59</td></tr><tr><td>65</td><td>0.4179</td><td>0.4185</td><td>13.49</td><td>0.08</td><td>122.3</td><td>8.3</td><td>-1.13</td></tr><tr><td>66</td><td>0.4394</td><td>-999</td><td>13.67</td><td>-999</td><td>133.1</td><td>8.1</td><td>&lt;-1.17</td></tr><tr><td>67</td><td>0.4192</td><td>0.4185</td><td>13.49</td><td>0.08</td><td>122.0</td><td>8.3</td><td>-0.7</td></tr><tr><td>68</td><td>0.7378</td><td>-999</td><td>13.96</td><td>-999</td><td>66.2</td><td>8.5</td><td>-1.12</td></tr><tr><td>69</td><td>0.7104</td><td>-999</td><td>13.62</td><td>-999</td><td>161.6</td><td>8.1</td><td>-0.46</td></tr><tr><td>70</td><td>0.6607</td><td>-999</td><td>13.72</td><td>-999</td><td>138.8</td><td>8.0</td><td>&lt;-1.39</td></tr><tr><td>71</td><td>0.6606</td><td>-999</td><td>13.72</td><td>-999</td><td>142.1</td><td>9.4</td><td>-0.12</td></tr><tr><td>72</td><td>0.7257</td><td>-999</td><td>13.79</td><td>-999</td><td>202.4</td><td>8.2</td><td>-1.18</td></tr><tr><td>73</td><td>0.7254</td><td>-999</td><td>13.79</td><td>-999</td><td>214.7</td><td>9.5</td><td>0.3</td></tr><tr><td>74</td><td>0.2021</td><td>0.2031</td><td>14.00</td><td>0.05</td><td>100.0</td><td>8.6</td><td>-1.61</td></tr><tr><td>75</td><td>0.4490</td><td>-999</td><td>13.73</td><td>-999</td><td>182.5</td><td>10.6</td><td>0.87</td></tr><tr><td>76</td><td>0.4353</td><td>-999</td><td>13.66</td><td>-999</td><td>218.8</td><td>7.9</td><td>&lt;-0.92</td></tr><tr><td>77</td><td>0.3992</td><td>0.3992</td><td>14.39</td><td>0.02</td><td>199.3</td><td>10.1</td><td>&lt;-1.46</td></tr><tr><td>78</td><td>0.7177</td><td>0.7179</td><td>14.57</td><td>0.05</td><td>227.6</td><td>9.8</td><td>0.0</td></tr><tr><td>79</td><td>0.7178</td><td>0.7179</td><td>14.57</td><td>0.05</td><td>154.6</td><td>8.9</td><td>-0.47</td></tr><tr><td>80</td><td>0.5355</td><td>-999</td><td>13.76</td><td>-999</td><td>111.0</td><td>8.4</td><td>-1.43</td></tr><tr><td>81</td><td>0.5172</td><td>0.5171</td><td>14.47</td><td>0.05</td><td>93.0</td><td>9.6</td><td>0.24</td></tr><tr><td>82</td><td>0.4490</td><td>-999</td><td>13.72</td><td>-999</td><td>188.1</td><td>10.7</td><td>0.78</td></tr><tr><td>83</td><td>0.7175</td><td>0.7179</td><td>14.57</td><td>0.05</td><td>71.4</td><td>9.4</td><td>-1.06</td></tr><tr><td>84</td><td>0.7181</td><td>0.7179</td><td>14.57</td><td>0.05</td><td>182.6</td><td>9.3</td><td>0.04</td></tr><tr><td>85</td><td>0.7369</td><td>-999</td><td>14.01</td><td>-999</td><td>255.4</td><td>10.1</td><td>&lt;-0.46</td></tr><tr><td>86</td><td>0.4784</td><td>-999</td><td>13.67</td><td>-999</td><td>197.3</td><td>8.9</td><td>-0.65</td></tr><tr><td>87</td><td>0.5256</td><td>-999</td><td>13.52</td><td>-999</td><td>227.4</td><td>6.6</td><td>&lt;-1.61</td></tr><tr><td>88</td><td>0.6476</td><td>-999</td><td>13.53</td><td>-999</td><td>155.3</td><td>8.7</td><td>&lt;-1.05</td></tr><tr><td>89</td><td>0.5355</td><td>-999</td><td>13.62</td><td>-999</td><td>204.8</td><td>10.3</td><td>-0.06</td></tr><tr><td>90</td><td>0.4581</td><td>-999</td><td>13.46</td><td>-999</td><td>171.1</td><td>9.0</td><td>1.01</td></tr><tr><td>91</td><td>0.1392</td><td>-999</td><td>13.61</td><td>-999</td><td>83.9</td><td>7.9</td><td>-2.25</td></tr><tr><td>92</td><td>0.6469</td><td>-999</td><td>13.47</td><td>-999</td><td>156.3</td><td>8.3</td><td>-1.11</td></tr><tr><td>93</td><td>0.1203</td><td>-999</td><td>13.76</td><td>-999</td><td>20.2</td><td>9.3</td><td>-1.61</td></tr><tr><td>94</td><td>0.1201</td><td>-999</td><td>13.75</td><td>-999</td><td>11.3</td><td>10.4</td><td>&lt;-2.37</td></tr><tr><td>95</td><td>0.6531</td><td>-999</td><td>13.56</td><td>-999</td><td>124.9</td><td>8.7</td><td>-0.59</td></tr><tr><td>96</td><td>0.5717</td><td>-999</td><td>13.76</td><td>-999</td><td>106.1</td><td>10.2</td><td>&lt;-1.08</td></tr><tr><td>97</td><td>0.7293</td><td>-999</td><td>13.64</td><td>-999</td><td>175.9</td><td>9.5</td><td>0.93</td></tr><tr><td>98</td><td>0.3760</td><td>-999</td><td>13.48</td><td>-999</td><td>71.5</td><td>7.9</td><td>&lt;-1.66</td></tr><tr><td>99</td><td>0.3198</td><td>-999</td><td>13.66</td><td>-999</td><td>49.4</td><td>8.5</td><td>-1.25</td></tr><tr><td>100</td><td>0.3291</td><td>-999</td><td>13.62</td><td>-999</td><td>75.4</td><td>10.6</td><td>&lt;-1.48</td></tr><tr><td>101</td><td>0.5205</td><td>-999</td><td>13.58</td><td>-999</td><td>171.3</td><td>9.6</td><td>0.09</td></tr><tr><td>102</td><td>0.2790</td><td>-999</td><td>13.77</td><td>-999</td><td>105.2</td><td>7.3</td><td>&lt;-2.18</td></tr><tr><td>103</td><td>0.6173</td><td>-999</td><td>13.68</td><td>-999</td><td>116.3</td><td>8.1</td><td>-1.14</td></tr><tr><td>104</td><td>0.3751</td><td>-999</td><td>13.48</td><td>-999</td><td>110.7</td><td>7.6</td><td>-1.81</td></tr><tr><td>105</td><td>0.6178</td><td>-999</td><td>13.69</td><td>-999</td><td>161.5</td><td>8.9</td><td>-0.39</td></tr><tr><td>106</td><td>0.6183</td><td>-999</td><td>13.68</td><td>-999</td><td>189.6</td><td>8.1</td><td>0.24</td></tr><tr><td>107</td><td>0.4395</td><td>-999</td><td>13.60</td><td>-999</td><td>212.2</td><td>8.9</td><td>-1.33</td></tr><tr><td>108</td><td>0.3282</td><td>-999</td><td>13.61</td><td>-999</td><td>143.6</td><td>8.3</td><td>&lt;-1.86</td></tr><tr><td>109</td><td>0.4339</td><td>-999</td><td>13.91</td><td>-999</td><td>182.3</td><td>8.3</td><td>-1.03</td></tr><tr><td>110</td><td>0.6929</td><td>-999</td><td>13.58</td><td>-999</td><td>161.6</td><td>9.3</td><td>-0.4</td></tr><tr><td>111</td><td>0.5112</td><td>-999</td><td>13.58</td><td>-999</td><td>164.5</td><td>8.4</td><td>-1.59</td></tr><tr><td>112</td><td>0.6926</td><td>-999</td><td>13.58</td><td>-999</td><td>150.0</td><td>8.8</td><td>-0.65</td></tr><tr><td>113</td><td>0.7318</td><td>-999</td><td>13.80</td><td>-999</td><td>125.7</td><td>9.3</td><td>-1.17</td></tr><tr><td>114</td><td>0.6153</td><td>-999</td><td>13.60</td><td>-999</td><td>193.0</td><td>8.1</td><td>-1.32</td></tr><tr><td>115</td><td>0.5553</td><td>-999</td><td>13.89</td><td>-999</td><td>167.1</td><td>8.6</td><td>0.35</td></tr><tr><td>116</td><td>0.2961</td><td>-999</td><td>13.53</td><td>-999</td><td>48.7</td><td>8.5</td><td>-1.68</td></tr><tr><td>117</td><td>0.6928</td><td>-999</td><td>13.57</td><td>-999</td><td>154.1</td><td>8.3</td><td>-1.08</td></tr><tr><td>118</td><td>0.5394</td><td>-999</td><td>13.30</td><td>-999</td><td>234.9</td><td>7.7</td><td>&lt;-1.87</td></tr><tr><td>119</td><td>0.5385</td><td>-999</td><td>13.32</td><td>-999</td><td>245.4</td><td>8.0</td><td>-1.61</td></tr><tr><td>120</td><td>0.3612</td><td>0.3615</td><td>13.87</td><td>0.01</td><td>193.5</td><td>7.8</td><td>-1.3</td></tr><tr><td>121</td><td>0.4949</td><td>0.4951</td><td>14.45</td><td>0.01</td><td>109.8</td><td>9.5</td><td>0.22</td></tr><tr><td>122</td><td>0.4950</td><td>0.4951</td><td>14.45</td><td>0.01</td><td>83.7</td><td>8.1</td><td>-1.0</td></tr><tr><td>123</td><td>0.2453</td><td>-999</td><td>12.96</td><td>-999</td><td>77.4</td><td>7.1</td><td>-2.84</td></tr><tr><td>124</td><td>0.4506</td><td>-999</td><td>13.12</td><td>-999</td><td>98.7</td><td>7.0</td><td>&lt;-1.78</td></tr></tbody></table>
<table><caption>**Table 6**
(Continued)</caption><thead><tr><th>ID<br>(1)</th><th>z<sub>gal</sub><br>(2)</th><th>z<sub>abs</sub><br>(3)</th><th>log<sub>10</sub>(N/cm<sup>-2</sup>)<br>(4)</th><th>σ[log<sub>10</sub>(N/cm<sup>-2</sup>)]<br>(5)</th><th>D in kpc<br>(6)</th><th>log<sub>10</sub>(M<sub>☉</sub>/M<sub>☉</sub>)<br>(7)</th><th>log<sub>10</sub>(SFR/M<sub>☉</sub>yr<sup>-1</sup>)<br>(8)</th></tr></thead><tbody><tr><td>125</td><td>0.3452</td><td>-999</td><td>13.15</td><td>-999</td><td>56.3</td><td>6.0</td><td>&lt;-1.93</td></tr><tr><td>126</td><td>0.4832</td><td>-999</td><td>13.35</td><td>-999</td><td>154.3</td><td>8.1</td><td>-1.53</td></tr><tr><td>127</td><td>0.1825</td><td>0.1828</td><td>14.03</td><td>0.06</td><td>50.7</td><td>7.9</td><td>-1.97</td></tr><tr><td>128</td><td>0.5623</td><td>-999</td><td>13.40</td><td>-999</td><td>183.8</td><td>6.5</td><td>&lt;-1.72</td></tr><tr><td>129</td><td>0.5394</td><td>-999</td><td>13.31</td><td>-999</td><td>189.7</td><td>8.4</td><td>-0.99</td></tr><tr><td>130</td><td>0.6330</td><td>0.6318</td><td>14.10</td><td>0.03</td><td>247.9</td><td>10.6</td><td>&lt;-0.8</td></tr><tr><td>131</td><td>0.6335</td><td>0.6319</td><td>13.89</td><td>0.04</td><td>220.2</td><td>8.9</td><td>-1.09</td></tr><tr><td>132</td><td>0.1487</td><td>-999</td><td>13.51</td><td>-999</td><td>41.1</td><td>7.5</td><td>-2.34</td></tr><tr><td>133</td><td>0.4252</td><td>-999</td><td>13.42</td><td>-999</td><td>169.1</td><td>9.4</td><td>-0.72</td></tr><tr><td>134</td><td>0.5099</td><td>-999</td><td>13.43</td><td>-999</td><td>140.5</td><td>11.4</td><td>&lt;-1.12</td></tr><tr><td>135</td><td>0.3444</td><td>-999</td><td>13.40</td><td>-999</td><td>135.4</td><td>10.2</td><td>-1.23</td></tr><tr><td>136</td><td>0.1109</td><td>-999</td><td>13.73</td><td>-999</td><td>72.9</td><td>8.4</td><td>-1.24</td></tr><tr><td>137</td><td>0.3799</td><td>-999</td><td>13.33</td><td>-999</td><td>183.4</td><td>8.4</td><td>-1.36</td></tr><tr><td>138</td><td>0.3768</td><td>-999</td><td>13.38</td><td>-999</td><td>96.0</td><td>8.7</td><td>-0.75</td></tr><tr><td>139</td><td>0.6326</td><td>0.6318</td><td>14.10</td><td>0.03</td><td>216.4</td><td>9.8</td><td>&lt;-1.68</td></tr><tr><td>140</td><td>0.3794</td><td>-999</td><td>13.33</td><td>-999</td><td>163.5</td><td>8.8</td><td>-0.64</td></tr><tr><td>141</td><td>0.3801</td><td>-999</td><td>13.33</td><td>-999</td><td>134.2</td><td>10.4</td><td>-1.03</td></tr><tr><td>142</td><td>0.3437</td><td>-999</td><td>13.41</td><td>-999</td><td>138.5</td><td>9.6</td><td>-0.46</td></tr><tr><td>143</td><td>0.6314</td><td>0.6318</td><td>14.10</td><td>0.03</td><td>202.6</td><td>9.0</td><td>-1.05</td></tr><tr><td>144</td><td>0.1953</td><td>-999</td><td>13.78</td><td>-999</td><td>75.0</td><td>7.7</td><td>-2.26</td></tr><tr><td>145</td><td>0.6306</td><td>0.6318</td><td>14.10</td><td>0.03</td><td>204.6</td><td>8.3</td><td>-0.87</td></tr><tr><td>146</td><td>0.5102</td><td>-999</td><td>13.43</td><td>-999</td><td>171.6</td><td>10.2</td><td>-1.17</td></tr><tr><td>147</td><td>0.3439</td><td>-999</td><td>13.41</td><td>-999</td><td>82.3</td><td>9.5</td><td>&lt;-1.82</td></tr><tr><td>148</td><td>0.4468</td><td>0.4461</td><td>13.77</td><td>0.06</td><td>65.5</td><td>6.9</td><td>&lt;-1.78</td></tr><tr><td>149</td><td>0.3453</td><td>-999</td><td>13.40</td><td>-999</td><td>77.2</td><td>9.3</td><td>-1.59</td></tr><tr><td>150</td><td>0.5582</td><td>0.5576</td><td>14.31</td><td>0.10</td><td>196.4</td><td>8.5</td><td>-1.05</td></tr><tr><td>151</td><td>0.5578</td><td>0.5576</td><td>14.31</td><td>0.10</td><td>174.7</td><td>8.0</td><td>-0.8</td></tr><tr><td>152</td><td>0.3993</td><td>0.3994</td><td>14.38</td><td>0.05</td><td>176.9</td><td>9.2</td><td>-0.09</td></tr><tr><td>153</td><td>0.5572</td><td>0.5576</td><td>14.31</td><td>0.10</td><td>141.6</td><td>8.8</td><td>-0.68</td></tr><tr><td>154</td><td>0.4879</td><td>-999</td><td>13.76</td><td>-999</td><td>137.9</td><td>9.1</td><td>-0.76</td></tr><tr><td>155</td><td>0.7186</td><td>-999</td><td>13.78</td><td>-999</td><td>101.7</td><td>10.7</td><td>&lt;-0.93</td></tr><tr><td>156</td><td>0.3845</td><td>0.3848</td><td>14.37</td><td>0.08</td><td>36.0</td><td>9.3</td><td>-1.62</td></tr><tr><td>157</td><td>0.5358</td><td>0.5360</td><td>14.42</td><td>0.09</td><td>116.9</td><td>9.6</td><td>-1.09</td></tr><tr><td>158</td><td>0.5361</td><td>0.5360</td><td>14.42</td><td>0.09</td><td>110.4</td><td>10.1</td><td>0.08</td></tr><tr><td>159</td><td>0.6589</td><td>-999</td><td>13.65</td><td>-999</td><td>113.1</td><td>7.4</td><td>&lt;-1.11</td></tr><tr><td>160</td><td>0.4297</td><td>0.43</td><td>14.12</td><td>0.03</td><td>77.2</td><td>9.1</td><td>-0.86</td></tr><tr><td>161</td><td>0.7183</td><td>-999</td><td>13.79</td><td>-999</td><td>135.7</td><td>6.9</td><td>-1.28</td></tr><tr><td>162</td><td>0.4950</td><td>-999</td><td>13.65</td><td>-999</td><td>236.7</td><td>8.4</td><td>&lt;1.45</td></tr><tr><td>163</td><td>0.4779</td><td>-999</td><td>13.73</td><td>-999</td><td>255.4</td><td>9.7</td><td>-0.79</td></tr><tr><td>164</td><td>0.3293</td><td>-999</td><td>13.67</td><td>-999</td><td>101.9</td><td>8.7</td><td>-1.55</td></tr><tr><td>165</td><td>0.2161</td><td>-999</td><td>13.57</td><td>-999</td><td>109.9</td><td>8.6</td><td>-1.01</td></tr><tr><td>166</td><td>0.3299</td><td>-999</td><td>13.64</td><td>-999</td><td>126.1</td><td>11.0</td><td>&lt;-1.41</td></tr><tr><td>167</td><td>0.3304</td><td>-999</td><td>13.64</td><td>-999</td><td>130.2</td><td>9.5</td><td>&lt;-2.12</td></tr><tr><td>168</td><td>0.6407</td><td>0.6405</td><td>14.16</td><td>0.05</td><td>190.8</td><td>9.7</td><td>-0.18</td></tr><tr><td>169</td><td>0.3292</td><td>-999</td><td>13.67</td><td>-999</td><td>107.8</td><td>9.9</td><td>-1.41</td></tr><tr><td>170</td><td>0.3568</td><td>-999</td><td>13.72</td><td>-999</td><td>115.1</td><td>8.9</td><td>-0.22</td></tr><tr><td>171</td><td>0.3989</td><td>-999</td><td>13.49</td><td>-999</td><td>107.5</td><td>8.0</td><td>-1.14</td></tr><tr><td>172</td><td>0.3626</td><td>-999</td><td>13.85</td><td>-999</td><td>92.3</td><td>7.2</td><td>&lt;-1.62</td></tr><tr><td>173</td><td>0.6513</td><td>-999</td><td>13.80</td><td>-999</td><td>201.5</td><td>10.5</td><td>-0.06</td></tr><tr><td>174</td><td>0.6504</td><td>-999</td><td>13.77</td><td>-999</td><td>129.7</td><td>8.9</td><td>-1.18</td></tr><tr><td>175</td><td>0.6103</td><td>0.6101</td><td>14.78</td><td>0.04</td><td>113.5</td><td>9.4</td><td>0.72</td></tr><tr><td>176</td><td>0.4434</td><td>-999</td><td>13.60</td><td>-999</td><td>63.9</td><td>7.4</td><td>&lt;-1.71</td></tr><tr><td>177</td><td>0.3286</td><td>-999</td><td>13.64</td><td>-999</td><td>99.8</td><td>8.1</td><td>-1.02</td></tr><tr><td>178</td><td>0.5102</td><td>-999</td><td>13.66</td><td>-999</td><td>84.0</td><td>6.1</td><td>-1.38</td></tr><tr><td>179</td><td>0.6314</td><td>-999</td><td>13.88</td><td>-999</td><td>167.8</td><td>8.7</td><td>-1.44</td></tr><tr><td>180</td><td>0.5097</td><td>-999</td><td>13.65</td><td>-999</td><td>99.2</td><td>8.3</td><td>-0.84</td></tr><tr><td>181</td><td>0.5010</td><td>-999</td><td>13.73</td><td>-999</td><td>196.0</td><td>7.4</td><td>&lt;-1.65</td></tr><tr><td>182</td><td>0.4151</td><td>-999</td><td>13.58</td><td>-999</td><td>142.3</td><td>6.2</td><td>-0.83</td></tr><tr><td>183</td><td>0.6401</td><td>0.6405</td><td>14.16</td><td>0.05</td><td>210.5</td><td>9.2</td><td>0.19</td></tr><tr><td>184</td><td>0.3296</td><td>-999</td><td>13.66</td><td>-999</td><td>151.6</td><td>9.6</td><td>&lt;-2.0</td></tr><tr><td>185</td><td>0.3870</td><td>-999</td><td>13.70</td><td>-999</td><td>163.8</td><td>6.8</td><td>-1.57</td></tr><tr><td>186</td><td>0.5399</td><td>-999</td><td>13.39</td><td>-999</td><td>287.0</td><td>6.8</td><td>-0.8</td></tr><tr><td>187</td><td>0.6597</td><td>-999</td><td>13.39</td><td>-999</td><td>238.9</td><td>9.4</td><td>&lt;-0.73</td></tr><tr><td>188</td><td>0.3217</td><td>0.3217</td><td>13.86</td><td>0.07</td><td>142.6</td><td>8.6</td><td>-0.43</td></tr><tr><td>189</td><td>0.2502</td><td>0.2512</td><td>13.91</td><td>0.06</td><td>108.0</td><td>6.6</td><td>-2.13</td></tr></tbody></table>
<table><caption>**Table 6**
(Continued)</caption><thead><tr><th>ID<br>(1)</th><th>z<sub>gal</sub><br>(2)</th><th>z<sub>abs</sub><br>(3)</th><th>log<sub>10</sub>(N/cm<sup>-2</sup>)<br>(4)</th><th>σ[log<sub>10</sub>(N/cm<sup>-2</sup>)]<br>(5)</th><th>D in kpc<br>(6)</th><th>log<sub>10</sub>(M<sub>☉</sub>/M<sub>☉</sub>)<br>(7)</th><th>log<sub>10</sub>(SFR/M<sub>☉</sub>yr<sup>-1</sup>)<br>(8)</th></tr></thead><tbody><tr><td>190</td><td>0.6120</td><td>-999</td><td>13.40</td><td>-999</td><td>141.3</td><td>10.9</td><td>-0.03</td></tr><tr><td>191</td><td>0.7150</td><td>-999</td><td>13.39</td><td>-999</td><td>250.3</td><td>8.8</td><td>-0.51</td></tr><tr><td>192</td><td>0.3073</td><td>-999</td><td>13.26</td><td>-999</td><td>153.0</td><td>7.2</td><td>&lt;-1.95</td></tr><tr><td>193</td><td>0.6130</td><td>-999</td><td>13.40</td><td>-999</td><td>152.5</td><td>9.2</td><td>-1.01</td></tr><tr><td>194</td><td>0.3215</td><td>0.3217</td><td>13.86</td><td>0.07</td><td>127.3</td><td>9.4</td><td>-0.2</td></tr><tr><td>195</td><td>0.3214</td><td>0.3217</td><td>13.86</td><td>0.07</td><td>140.6</td><td>9.3</td><td>-0.11</td></tr><tr><td>196</td><td>0.5450</td><td>-999</td><td>13.64</td><td>-999</td><td>200.3</td><td>10.0</td><td>&lt;-1.1</td></tr><tr><td>197</td><td>0.1840</td><td>0.1838</td><td>14.05</td><td>0.03</td><td>63.1</td><td>8.8</td><td>-0.86</td></tr><tr><td>198</td><td>0.4129</td><td>0.4128</td><td>13.76</td><td>0.02</td><td>101.3</td><td>8.8</td><td>-1.11</td></tr><tr><td>199</td><td>0.3005</td><td>-999</td><td>13.41</td><td>-999</td><td>139.8</td><td>9.3</td><td>-0.83</td></tr><tr><td>200</td><td>0.5469</td><td>-999</td><td>13.65</td><td>-999</td><td>181.2</td><td>8.1</td><td>&lt;-1.15</td></tr><tr><td>201</td><td>0.6100</td><td>-999</td><td>13.55</td><td>-999</td><td>165.5</td><td>6.0</td><td>&lt;-1.41</td></tr><tr><td>202</td><td>0.5091</td><td>-999</td><td>13.33</td><td>-999</td><td>159.1</td><td>7.7</td><td>-0.61</td></tr><tr><td>203</td><td>0.5307</td><td>-999</td><td>13.80</td><td>-999</td><td>141.6</td><td>9.4</td><td>&lt;-1.25</td></tr><tr><td>204</td><td>0.2514</td><td>0.2514</td><td>14.41</td><td>0.03</td><td>74.9</td><td>8.5</td><td>-0.8</td></tr><tr><td>205</td><td>0.7398</td><td>-999</td><td>13.74</td><td>-999</td><td>163.9</td><td>9.0</td><td>&lt;-1.27</td></tr><tr><td>206</td><td>0.6119</td><td>-999</td><td>13.40</td><td>-999</td><td>127.4</td><td>9.7</td><td>-0.34</td></tr><tr><td>207</td><td>0.3625</td><td>-999</td><td>13.29</td><td>-999</td><td>130.1</td><td>6.8</td><td>&lt;-1.67</td></tr><tr><td>208</td><td>0.6119</td><td>-999</td><td>13.39</td><td>-999</td><td>255.1</td><td>10.9</td><td>&lt;-1.04</td></tr><tr><td>209</td><td>0.2682</td><td>-999</td><td>13.30</td><td>-999</td><td>151.6</td><td>8.7</td><td>-0.96</td></tr><tr><td>210</td><td>0.2066</td><td>0.2070</td><td>14.39</td><td>0.03</td><td>108.3</td><td>9.1</td><td>-0.35</td></tr><tr><td>211</td><td>0.2451</td><td>-999</td><td>13.31</td><td>-999</td><td>125.5</td><td>8.1</td><td>-1.45</td></tr><tr><td>212</td><td>0.3159</td><td>-999</td><td>13.30</td><td>-999</td><td>128.2</td><td>7.6</td><td>&lt;-2.35</td></tr><tr><td>213</td><td>0.2451</td><td>-999</td><td>13.31</td><td>-999</td><td>123.3</td><td>7.9</td><td>-1.43</td></tr><tr><td>214</td><td>0.2654</td><td>-999</td><td>13.67</td><td>-999</td><td>58.9</td><td>7.8</td><td>-2.3</td></tr><tr><td>215</td><td>0.2066</td><td>0.2070</td><td>14.39</td><td>0.03</td><td>38.2</td><td>8.5</td><td>-1.03</td></tr><tr><td>216</td><td>0.4242</td><td>-999</td><td>13.82</td><td>-999</td><td>147.5</td><td>6.4</td><td>&lt;-2.32</td></tr><tr><td>217</td><td>0.3847</td><td>-999</td><td>13.29</td><td>-999</td><td>166.1</td><td>7.9</td><td>-1.45</td></tr><tr><td>218</td><td>0.2674</td><td>-999</td><td>13.41</td><td>-999</td><td>70.5</td><td>10.2</td><td>-0.7</td></tr><tr><td>219</td><td>0.4056</td><td>-999</td><td>13.46</td><td>-999</td><td>98.0</td><td>7.1</td><td>&lt;-1.94</td></tr><tr><td>220</td><td>0.4196</td><td>-999</td><td>13.68</td><td>-999</td><td>158.3</td><td>8.7</td><td>-0.73</td></tr><tr><td>221</td><td>0.3093</td><td>-999</td><td>13.16</td><td>-999</td><td>114.5</td><td>8.4</td><td>-0.32</td></tr><tr><td>222</td><td>0.4155</td><td>-999</td><td>13.53</td><td>-999</td><td>149.5</td><td>7.3</td><td>-2.04</td></tr><tr><td>223</td><td>0.6385</td><td>-999</td><td>13.88</td><td>-999</td><td>151.8</td><td>10.0</td><td>&lt;-1.15</td></tr><tr><td>224</td><td>0.3376</td><td>-999</td><td>13.77</td><td>-999</td><td>79.8</td><td>7.6</td><td>-1.41</td></tr><tr><td>225</td><td>0.5232</td><td>-999</td><td>13.78</td><td>-999</td><td>112.3</td><td>9.3</td><td>-0.51</td></tr><tr><td>226</td><td>0.3904</td><td>0.3902</td><td>14.57</td><td>0.05</td><td>9.5</td><td>6.0</td><td>-1.86</td></tr><tr><td>227</td><td>0.7241</td><td>-999</td><td>13.83</td><td>-999</td><td>218.4</td><td>6.8</td><td>&lt;-1.68</td></tr><tr><td>228</td><td>0.5227</td><td>-999</td><td>13.78</td><td>-999</td><td>158.4</td><td>9.1</td><td>-0.26</td></tr><tr><td>229</td><td>0.4164</td><td>-999</td><td>13.42</td><td>-999</td><td>131.9</td><td>8.3</td><td>-1.73</td></tr><tr><td>230</td><td>0.5230</td><td>-999</td><td>13.78</td><td>-999</td><td>129.1</td><td>8.2</td><td>-0.39</td></tr><tr><td>231</td><td>0.3449</td><td>-999</td><td>13.72</td><td>-999</td><td>123.8</td><td>6.2</td><td>&lt;-1.69</td></tr><tr><td>232</td><td>0.4231</td><td>-999</td><td>13.49</td><td>-999</td><td>119.5</td><td>6.8</td><td>-1.88</td></tr><tr><td>233</td><td>0.3451</td><td>-999</td><td>13.72</td><td>-999</td><td>98.2</td><td>6.2</td><td>-1.38</td></tr><tr><td>234</td><td>0.6390</td><td>-999</td><td>13.90</td><td>-999</td><td>97.4</td><td>7.2</td><td>&lt;-2.45</td></tr><tr><td>235</td><td>0.5593</td><td>-999</td><td>13.76</td><td>-999</td><td>139.3</td><td>9.5</td><td>-1.59</td></tr><tr><td>236</td><td>0.3898</td><td>0.3902</td><td>14.57</td><td>0.05</td><td>104.4</td><td>10.0</td><td>0.25</td></tr><tr><td>237</td><td>0.7016</td><td>-999</td><td>13.61</td><td>-999</td><td>89.2</td><td>8.3</td><td>-1.67</td></tr><tr><td>238</td><td>0.7275</td><td>-999</td><td>13.79</td><td>-999</td><td>243.4</td><td>10.1</td><td>-0.61</td></tr><tr><td>239</td><td>0.2851</td><td>-999</td><td>13.51</td><td>-999</td><td>76.9</td><td>7.9</td><td>-1.87</td></tr><tr><td>240</td><td>0.5741</td><td>-999</td><td>13.73</td><td>-999</td><td>191.4</td><td>8.4</td><td>-0.69</td></tr><tr><td>241</td><td>0.3381</td><td>-999</td><td>13.78</td><td>-999</td><td>77.7</td><td>9.5</td><td>0.12</td></tr><tr><td>242</td><td>0.6273</td><td>-999</td><td>13.94</td><td>-999</td><td>161.0</td><td>7.1</td><td>&lt;-1.63</td></tr><tr><td>243</td><td>0.3951</td><td>-999</td><td>13.85</td><td>-999</td><td>148.7</td><td>7.3</td><td>-1.67</td></tr><tr><td>244</td><td>0.6630</td><td>-999</td><td>13.64</td><td>-999</td><td>216.2</td><td>8.8</td><td>-0.34</td></tr><tr><td>245</td><td>0.7155</td><td>-999</td><td>13.67</td><td>-999</td><td>160.7</td><td>8.0</td><td>&lt;-1.26</td></tr><tr><td>246</td><td>0.6831</td><td>-999</td><td>13.67</td><td>-999</td><td>187.1</td><td>7.9</td><td>&lt;-1.73</td></tr><tr><td>247</td><td>0.6628</td><td>-999</td><td>13.64</td><td>-999</td><td>194.3</td><td>8.2</td><td>-1.18</td></tr></tbody></table>

Note. (1) Running ID of the galaxy. (2) Galaxy redshift. (3) Corresponding O VI column density-weighted absorption redshift. (4) Total O VI column density. (5) Error in the total O VI column density. (6) Impact parameter. (7) Stellar mass of the galaxy. (8) SFR of the galaxy (" < " indicates 3σ upper limit on SFR). The flag value of -999 in columns for $z_{abs}$ and $\sigma[\log_{10}(N/cm^{-2})]$ represents nondetections of O VI absorption. In these cases, the $\log_{10}(N/cm^{-2})$ column corresponds to the 3σ upper limit.
ORCID iDs

Sayak Dutta https://orcid.org/0009-0000-0797-7365

Sowgat Muzahid https://orcid.org/0000-0003-3938-8762

Joop Schaye https://orcid.org/0000-0002-0668-5560

Nicolas F. Bouché https://orcid.org/0000-0003-0068-9920

Sebastiano Cantalupo https://orcid.org/0000-0001-5804-1428

Hsiao-Wen Chen https://orcid.org/0000-0001-8813-4182

Sean Johnson https://orcid.org/0000-0001-9487-8583

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