The Cosmic Ultraviolet Baryon Survey (CUBS). VII. On the Warm-hot Circumgalactic Medium Probed by O vi and Ne viii at 0.4 ≲ z ≲ 0.7

This paper presents a newly established sample of 103 unique galaxies or galaxy groups at 0.4 ≲ z ≲ 0.7 from the Cosmic Ultraviolet Baryon Survey (CUBS) for studying the warm-hot circumgalactic medium (CGM) probed by both O vi and Ne viii absorption. The galaxies and associated neighbors are identified at <1 physical Mpc from the sightlines toward 15 CUBS QSOs at z QSO ≳ 0.8. A total of 30 galaxies or galaxy groups exhibit associated O vi λ λ 1031, 1037 doublet absorption within a line-of-sight velocity interval of ±250 km s−1, while the rest show no trace of O vi to a detection limit of logNOVI/cm−2≈13.7 . Meanwhile, only five galaxies or galaxy groups exhibit the Ne viii λ λ 770, 780 doublet absorption, down to a limiting column density of logNNeVIII/cm−2≈14.0 . These O vi- and Ne viii-bearing halos reside in different galaxy environments with stellar masses ranging from logMstar/M⊙≈8 to ≈11.5. The warm-hot CGM around galaxies of different stellar masses and star formation rates exhibits different spatial profiles and kinematics. In particular, star-forming galaxies with logMstar/M⊙≈9–11 show a significant concentration of metal-enriched warm-hot CGM within the virial radius, while massive quiescent galaxies exhibit flatter radial profiles of both column densities and covering fractions. In addition, the velocity dispersion of O vi absorption is broad with σ υ > 40 km s−1 for galaxies of logMstar/M⊙>9 within the virial radius, suggesting a more dynamic warm-hot halo around these galaxies. Finally, the warm-hot CGM probed by O vi and Ne viii is suggested to be the dominant phase in sub-L* galaxies with logMstar/M⊙≈9–10 based on their high ionization fractions in the CGM.


INTRODUCTION
Corresponding author: Zhĳie Qu quzhĳie@uchicago.edu The circumgalactic medium (CGM) is a multiphase gaseous reservoir surrounding galaxies.It spans a range in temperature and ionization conditions from the cool photoionized gas (log /K ≈ 4) to the collisionally ionized hot gas (log /K ≈ 6; see Donahue & Voit 2022;Faucher-Giguère & Oh 2023 for recent reviews).In this multiphase gas, the warm-hot phase at log /K ∼ 5 − 6 is of particular importance in understanding the transformation of the CGM and its connection with galaxy evolution (e.g., Tepper-García et al. 2013;Oppenheimer et al. 2016;Rahmati et al. 2016;Nelson et al. 2018;McQuinn & Werk 2018;Stern et al. 2019;Faerman et al. 2020;Wĳers et al. 2020;Ho et al. 2021;Appleby et al. 2023;Wĳers et al. 2024).The warm-hot gas may be short-lived in the CGM, compared to the cool and hot phases because of its high radiative emissivity (e.g., Oppenheimer & Schaye 2013;Gnat 2017).At the same time, it may be crucial for the survival or growth of cool clouds as an interface mixed in the hot gas (e.g., Gronke et al. 2022), making the warm-hot CGM potential fuel for future star formation in galaxies.
In principle, O VI and Ne VIII may also be photoionized by the ultraviolet background (UVB; e.g., Haardt & Madau 2001;Hussain et al. 2017;Khaire & Srianand 2019;Faucher-Giguère 2020) in the density range of log  H /cm −3 ≈ −6 to −4.In practice, the low density of log  H /cm −3 ≲ −5 is rarely seen in the CGM in simulations (e.g.Rahmati et al. 2016).The expected low gas density implies a temperature of log /K > 4.5 under photoionization equilibrium (PIE).Furthermore, careful comparison of line profiles of O VI and Ne VIII with low ions (e.g., O II and C II; tracing cool photoionized CGM of log /K ≲ 4.5) suggests that they are not in the same phase (e.g., Zahedy et al. 2019;Rudie et al. 2019;Cooper et al. 2021;Sameer et al. 2021).Therefore, the O VI and Ne VIII absorption transitions trace the warm-hot gas at log /K > 4.5 in the CGM, irrespective of the exact ionization mechanism.
In practice, O VI and Ne VIII are detected as strong doublet transitions at 1031, 1037 Å and 770, 780 Å , respectively, in the far-ultraviolet (FUV) band, which enable robust identifications of these highly ionized species based on the anticipated wavelength separation and doublet ratio.In addition, both oxygen and neon are -elements with roughly constant relative abundance [Ne/O] and high abundances.Combining empirical constraints of these two ions, therefore, provides a sensitive probe of the physical conditions of the warm-hot CGM.
In the past few years, deep galaxy surveys have been performed in fields of distant UV bright QSOs with high-quality FUV spectra available for investigating the connection between galaxies and the CGM up to  ≈ 0.5 − 1.0 (e.g., Fossati et al. 2019;Chen et al. 2020;Dutta et al. 2020;Lofthouse et al. 2020;Muzahid et al. 2021;Wilde et al. 2021), with the warm-hot gas being a significant component in these efforts (e.g., Chen & Mulchaey 2009;Johnson et al. 2015;Burchett et al. 2019;Tchernyshyov et al. 2022Tchernyshyov et al. , 2023)).As part of the Cosmic Ultraviolet Baryon Survey (CUBS) program (Chen et al. 2020), we are constructing a sample of galaxies from dwarfs with stellar mass log  star /M ⊙ < 9 to massive quiescent galaxies of log  star /M ⊙ > 11 in the redshift range of  ≈ 0.4−0.7.All galaxies are selected based on their proximity to the QSO line of sight without any prior information on absorption features, leading to an unbiased sample for absorption property analysis.The redshift range of  ≈ 0.4 − 0.7 is chosen to cover both the O VI and Ne VIII doublets in the high signal-to-noise (S/N) FUV spectra obtained by the Hubble Space Telescope/Cosmic Origins Spectrograph (HST/COS; Green et al. 2012).
In this study, we investigate the properties of the warmhot CGM traced by O VI and Ne VIII in galaxies spanning a broad range in environments.Section 2 summarizes the available data for both absorption spectroscopy and galaxy surveys, and presents the methodology to extract galaxy and absorption properties.In Section 3, we investigate the association between absorption systems and galaxies, and the spatial distribution and kinematic properties of the warm-hot CGM.Further investigations of the dependence on galaxy properties are detailed in Section 4. In particular, we divide the entire galaxy sample into sub-samples based on the stellar mass ( star ) and star formation rate (SFR), and report different trends of absorption properties for different galaxies (Sections 4.2 and 4.3).In Section 5, we compare the results with previous studies and discuss the implication for the origin of the warm-hot CGM.The key findings are summarized in Section 6.Throughout the paper, we adopt a Λ cosmology to calculate physical distances, assuming Ω m = 0.3, Ω Λ = 0.7, and a Hubble constant of  0 = 70 km s −1 Mpc −1 .

DATA AND ANALYSIS
The CUBS program is designed to track the CGM evolution over a broad redshift range from  ≈ 0 to  ≈ 1 by combining high-quality QSO absorption spectra and deep galaxy survey data in the QSO fields (see Chen et al. 2020, for a complete description).Leveraging the CUBS data, we have established a new sample of 103 unique galaxies or galaxy groups at 0.4 ≲  ≲ 0.7, for which sensitive constraints can be obtained for both O VI and Ne VIII absorption properties in their CGM.The three-tier CUBS galaxy redshift survey provides ultradeep, deep-narrow, and shallow-wide coverage of the field around 15 NUV-bright QSOs at  QSO > 0.8 (see Chen et al. 2020 for definitions).This enables a detailed characterization of intervening galaxies and their surrounding environments along the QSO sightlines (e.g., Cooper et al. 2021).The CUBS intervening galaxy sample, spanning a wide range in mass from log  star /M ⊙ ≈ 8 to log  star /M ⊙ ≈ 11.5 and a wide range in environments from isolated field galaxies to rich galaxy groups, provide a unique opportunity to study the O VI and Ne VIII-bearing CGM in various galaxies.

QSO absorption spectra and galaxy survey data
For each CUBS QSO, high-S/N HST/COS spectra were obtained using the medium-resolution (FWHM ≈ 20 km s −1 ) G130M and G160M gratings and multiple central wavelengths to yield contiguous spectral coverage from 1100 Å to 1800 Å (PID=15163; PI: Chen).The spectra are processed and coadded using custom software and the final combined spectra have typical S/N of 12 − 31 per resolution element (see details in Chen et al. 2018Chen et al. , 2020)).The wavelength range of the final combined COS spectra provides simultaneous coverage of the O VI and Ne VIII doublets over the redshift range 0.43 ≲  ≲ 0.72.
To establish a blind sample of intervening galaxies in this redshift range, we identify galaxies at projected distances  ≲ 1 Mpc from the CUBS deep-narrow survey component that was carried out using a combination of the Multi Unit Spectroscopic Explorer (MUSE; Bacon et al. 2010), an integral field spectrograph on the Very Large Telescope (VLT) and Low Dispersion Survey Spectrograph 3 (LDSS3C), a high-efficiency optical multi-object spectrograph and imager on the Magellan Telescopes (see Chen et al. 2020;Cooper et al. 2021).While the LDSS3C component reaches a limiting magnitude of   ,AB ≈ 24 out to ≈ 1 Mpc at  ≈ 0.5, the MUSE observations provide the deepest view in the inner 200 kpc around the QSO with a limiting pseudo- magnitude of   ,AB ≈ 26.0.These spectroscopic data enable secure galaxy redshift measurements based on clearly detected spectral features (see Qu et al. 2023 for details; hereafter CUBS VI).We also include additional spectroscopic redshift survey data from the shallow-wide component, which reaches a limiting magnitude of   ,AB ≈ 22.5 out to ≈ 4 Mpc at  ≈ 0.5 using IMACS multislit observations.These are useful for characterizing the large-scale environment of those galaxies found closer to the QSO sightlines.
In addition to the spectroscopic survey data, deep optical have been obtained using LDSS3C and Inamori-Magellan Areal Camera & Spectrograph (IMACS), a wide-field imager and spectrograph; Dressler et al. 2011), and near-infrared images using FourStar (a wide field near-infrared imaging camera; (Persson et al. 2013) on the Magellan telescopes.These images reach 5- limiting magnitudes of ≈ 26.0, 25.5, 25.5, 25.5, and 24.5 in the -, -, -, -, and -band, respectively.They provide additional constraints on the broad-band spectral energy distributions (SEDs) of individual galaxies.In particular, we estimate the stellar mass for all galaxies with secure redshifts and five-band optical and near-infrared photometry available (DePalma et al. in prep.), using Bayesian Analysis of Galaxies for Physical Inference and Parameter EStimation package (BAGPIPES; Carnall et al. 2018).We adopt the Kroupa (2001) initial mass function for this exercise (see CUBS VI for detail).This exercise leads to a sample of 1657 galaxies with log  star /M ⊙ ≈ 8 − 11.5 at  ≈ 0.4 − 0.7 in the CUBS galaxy survey.
The faintest galaxies in the CUBS galaxy sample are spectroscopically identified in the MUSE observations, the deepest spectroscopic survey component in the CUBS program.As a result, the majority of these faint galaxies are not detected in the Magellan imaging survey, and only pseudo-, , and  photometric measurements are available from MUSE (e.g., Chen et al. 2020).Constraints for  star of these galaxies, therefore, rely on a color-magnitude analysis described in the following two paragraphs.
To ensure that  star is determined consistently for both bright and faint galaxies, we define a calibration galaxy sample that has both pseudo-, ,  photometry from MUSE and , , , , and  photometric measurements from Magellan.While using -, -, and -band photometry alone does not provide as strong a constraint on  star as using a combination of optical and near-infrared photometry, the three optical bands together can still place robust constraints on the restframe -band absolute magnitudes (  ) and  −  colors for galaxies at  ≈ 0.4 − 0.7.The utility of this calibration sample is therefore to explore the possibility of constraining  star using a combination of   and  −  for all galaxies in our sample (e.g., Huang et al. 2016).
We first calculate the rest-frame   and − by incorporating only available observed -, -, and -band photometry for each galaxy using the kcorrect software (Blanton & Roweis 2007).Next, we derive an empirical relation that best characterizes the correlation between BAGPIPES-inferred  star and the rest-frame   and  −  color.To account for the blue and red sequences in the galaxy population as a result of differences in star formation history (e.g., Chen et al. 2010;Johnson et al. 2015), we consider two different branches in the  star and color-magnitude correlation.We find that for blue galaxies with  −  < 0.9 log  star /M ⊙ = −(0.36±0.02)and for red galaxies with  −  ≥ 0.9 log  star /M ⊙ = −(0.36±0.02)  +(0.72±0.05)(−)+(2.4±0.3).
(2) The best-fit coefficients are determined using a Bayesian framework described in Qu et al. (2022).To determine the intrinsic scatter of this empirical relation, we select 910 galaxies at  ≈ 0.4 − 0.7 with well-measured magnitudes by filtering out galaxies with  star uncertainties larger than 0.1 dex.Using this high-quality galaxy sample, the residuals between the mean relation and the data exhibit a scatter of ≈ 0.2 dex over the covered stellar mass range of log  star /M ⊙ ≈ 8 − 11.5 (Figure 1).The best-fit empirical relation is applied to all foreground galaxies for estimating  star from the observed , , and  magnitudes.
In total, the CUBS galaxy sample consists of 11593 spectroscopically-identified foreground galaxies with available , , and  magnitudes at  gal > 0.01 and line-of-sight velocity of > 5000 km s −1 away from the QSO emission redshift.These galaxies are projected within ≈ 5 Mpc around QSO sight lines.For these galaxies, the derived  star spans the range log  star /M ⊙ ≈ 8 to 11.5.We also compute an inferred dark matter halo mass using a stellar mass-halo mass (SMHM) relation at  ≲ 1.We adopt the relation from Behroozi et al. (2019) and account for missing light described in Kravtsov et al. (2018) for all redshifts.The halo radius ( vir ) is approximated using  200 , within which the mean dark matter density is 200 times the cosmic critical density.
In addition to the stellar and halo mass estimation, we also extract SFRs using the detected nebular lines in galaxy spectra.Specifically, we adopt the equivalent widths (EWs) of two nebular lines, the [O II] doublet and H, as tracers of SFR.For these two features, we adopt the spectral windows defined in Yan et al. (2006) to calculate the EWs.For H, we infer EW(H) using the anticipated line ratio of EW(H)/EW(H) ≈ 2.8.Then, the line luminosities of [O II] and H are calculated by combining EW and restframe magnitudes ( and ), and are converted into SFRs using the empirical conversion described in Kewley et al. (2004) and Fumagalli et al. (2012, originated from Kennicutt 1998) for [O II] and H, respectively.The [O II]-based SFR is adopted for a galaxy when both [O II] and H are available.Among all 11593 galaxies in the CUBS program, 9130 and 2358 have SFRs determined based on [O II] and H, respectively.For the remaining 105 galaxies, neither spectral feature is available due to gaps in the optical spectra.

CUBS-midz: A new galaxy sample for probing the
warm-hot CGM at 0.4 ≲  ≲ 0.7 Here, we introduce a new sample of intermediate-redshift galaxies assembled from the entire CUBS galaxy sample for investigating the warm-hot CGM at 0.4 ≲  ≲ 0.7 (hereafter designated as the CUBS-midz sample).The redshift range is dictated by a simultaneous spectral coverage of the O VI and Ne VIII doublets in the COS/FUV spectra.A two-step procedure is adopted to select galaxies based on their proximity to the QSO sightlines.First, we select all galaxies at projected distances ( proj ) less than 3  vir from the QSO sightlines, leading to a sample of 212 individual galaxies.For these 212 galaxies, we then define overdense regions based on the number of galaxies with line-of-sight velocity separations of |Δ| < 500 km s −1 and projected separations of  proj ≲ 1 Mpc from the QSO sightlines.We identify 60 isolated galaxies with no neighbors found in the immediate vicinity and 43 unique overdense regions with more than one galaxy identified in the search volume, leading to a total of 103 unique galaxies or galaxy groups in this new sample.
To further characterize the galaxy environment, we expand the search of associated galaxies beyond the initial  proj < 3  vir from the QSO sightlines.Specifically, we search for all nearby galaxies with projected separations of  proj ≲ 3  vir and velocity difference of ≲ 2  vir from the galaxies in the initial CUBS-midz sample.This second iteration has led to the identification of additional neighbors, reducing the number of isolated galaxies to 50 and increasing the number of sight lines probing overdense environments to 53.Hereafter, we use galaxy groups referring to overdense environments with multiple nearby galaxies, although some systems are ambiguous to be identified as galaxy groups or not.In summary, this exercise establishes the final sample of 304 galaxies that form 103 unique galaxies or galaxy groups (summarized in Appendix Table B.1).The number of galaxies in the galaxy groups ranges from 2 to 21 with half of the groups containing more than four members.Figure 2 summarizes the ranges of  proj / vir to the QSO sightlines,  star , and SFR of the full CUBS-midz sample.In particular, these galaxies span a range in log  star /M ⊙ ≈ 7 to 11.5 and SFR from ≲ 10 −2 to 10 M ⊙ yr −1 .For each system, the galaxy with the smallest  proj / vir to the QSO sightlines is highlighted with an open red circle.
In this CUBS-midz sample, several galaxies and galaxy groups have been studied in previous CUBS papers, but none have published constraints on the properties of Ne VIII.Specifically, the new sample includes the galaxy group hosting an H 2 -bearing damped Ly absorber (DLA) at  DLA = 0.57 presented in CUBS II (Boettcher et al. 2021), three galaxies or galaxy groups hosting a Lyman Limit System (LLS) at  LLS = 0.4 − 0.6 presented in CUBS III (Zahedy et al. 2021), and two galaxy groups each hosting a partial LLS (pLLS) at  pLLS = 0.47 − 0.54 reported in CUBS IV (Cooper et al. 2021).

Absorption measurements
Having established a new CUBS-midz galaxy sample at  ≈ 0.4 − 0.7, we proceed with searches for O VI and Ne VIII absorption features within line of sight velocity of 1000 km s −1 for each galaxy or member galaxies in each galaxy group.The velocity window corresponds to roughly twice the escape velocity of the most massive galaxies in the sample.For our study, we search not only for O VI and Ne VIII absorption features, but also for low-ionization transitions, such as H I, O IV, and O V, to guide the identifications of O VI and Ne VIII based on matching kinematic absorption profiles.While these low ions may not share similar component ratios with O VI or Ne VIII, all detected O VI and Ne VIII features in the new sample have detectable H I or other low ionization transitions.We require that the detected O VI or Ne VIII absorption features exhibit matched doublet line ratios without significant contaminations, and that both lines are detected at ≳ 2.If one of the doublet members is significantly contaminated, then we consider this absorption as an upper limit.If both members are contaminated, then no constraints are available for the absorption.
Next, we measure the absorption properties for O VI and Ne VIII doublets using the Voigt profile fitting method described in Qu et al. (2022, also see Zahedy et al. 2016).The observed features of O VI and Ne VIII are decomposed into a minimum number of absorption components as required by the line profiles.Then each component is modeled based on a Voigt function, characterized by the ion column density, Doppler  parameter, and line centroid.A canonical 2:1 ratio is adopted to fit both doublet members simultaneously.For non-detections, we obtain a 2- upper limit for the column density with the line centroid fixed to either the systemic redshift of the galaxy or the redshift at the associated low ionization transitions.For galaxy groups with non-detected absorption, the line centroid is fixed to the redshift of the galaxy with the smallest  proj / vir .The  parameters of non-detections are fixed to 30 km s −1 , typical of known O VI and Ne VIII absorbers from previous studies (e.g., Werk et al. 2013;Savage et al. 2014;Johnson et al. 2015;Zahedy et al. 2019).
We compute the line-of-sight properties of the warm-hot CGM based on the integrated absorption properties of O VI and Ne VIII.Specifically, we extract the total column density () as the summation of all individual absorption components.Furthermore, we calculate the velocity centroid ( c ), and the line-of-sight velocity dispersion (  ) for each ion following where  () is the column density of the modeled Vogit profile in each velocity bin, and the zero velocity is selected to be the redshift of the galaxy with the smallest  proj / vir (see discussion in Section 3.1).Note that the velocity dispersion calculated from the second moment has different physical implications in different absorption systems.When it is a single-component system, the calculated velocity dispersion is related to  of that component according to   = / √ 2. In this case, the measured velocity dispersion represents the combined thermal and nonthermal motions within an absorbing cloud.If multiple components are detected, the velocity dispersion is dominated by the projected velocity difference between different components, which measures the large-scale relative motion between clumps.In the following analysis, we designate absorption with   ≥ 40 km s −1 as broad features, which mainly trace the inter-cloud kinematics, because the observed maximum  value is ≈ 60 km s −1 for individual O VI components (e.g., Werk et al. 2013;Savage et al. 2014;Zahedy et al. 2019).

THE WARM-HOT CGM AROUND GALAXIES
The analysis described in Section 2 returns detections of O VI in 30 galaxies or galaxy groups, while only five display associated Ne VIII absorption features.For the remaining sample, we place a 2- upper limit assuming  = 30 km s −1 to the underlying ionic column densities at the locations of individual galaxies/galaxy groups.Figure 3 shows that the detected absorbers have ionic column densities spanning from log /cm −2 = 13.5 to 15.0 for both O VI and Ne VIII, and the corresponding velocity dispersions vary from   ≈ 5 to 120 km s −1 .
Here, we also consider previously published galaxy samples for characterizing the O VI-bearing gas, including an IMACS survey from Johnson et al. (2017, hereafter the J17 sample), the COS-Halos survey (Werk et al. 2013), the COS-LRG survey (Zahedy et al. 2019) (Tchernyshyov et al. 2022) for O VI.The CASBaH sample is not included for comparisons in Figure 3 because neither the best-fit  values or velocity dispersions of Ne VIII were reported (Burchett et al. 2019).However, it will be included in comparisons of the column density profiles.We find that broad absorption features with   > 40 km s −1 occur primarily in strong absorbers with log /cm −2 > 14.5, indicating complicated kinematics in these systems.
In this section, we first explore whether and how any galaxy properties are correlated with the observed strength of the O VI and Ne VIII absorbers.Specifically, we examine the significance of the correlation between absorption properties and a combination of different host galaxy assignments, including the galaxy at the smallest  proj , the galaxy at the smallest  vir -normalized  proj , and the most massive member in a galaxy group.Next, we examine the covering fraction and gas kinematics of the warm-hot CGM probed by O VI and Ne VIII.

Connecting absorbers to galaxies in the presence of neighbors
As summarized in Section 2.2, 53 unique galaxy groups containing between 2 and 21 members are identified in the CUBS-midz sample.This sub-sample of galaxy groups provides an exciting opportunity to study the warm-hot CGM in based on different assignments of associated galaxies and projected absorber-galaxy distances. OVI is most strongly correlated with galaxies with the smallest  proj / vir , where  vir is calculated for individual galaxies (see Table 1 for statistics).We present the dependence of column density on the projected distance and the  virnormalized distance in the left and right panels, respectively.Error bars represent 68% confidence intervals of the column density measurements, and downward arrows represent the 95% upper limits for non-detections.In one case, the O VI absorber appears to be saturated, which is indicated by an upward arrow.In overdense galaxy environments, three different galaxy associations are explored, including the galaxy at the smallest  proj , the galaxy at the smallest  proj / vir , and the galaxy with the highest  star from top to bottom in the first three rows.The isolated galaxy sample is plotted in the lowest row for comparison.In the first two rows, the physically closest galaxy is also the one with the smallest  proj / vir in 31 galaxy groups.For the remaining 22 groups, we highlight the difference in the associated galaxies using red plus symbols.Overall, the combination of adopting the galaxies at the smallest  proj / vir and  vir -normalized distance yields the tightest correlation (right panel in the second row).overdense galaxy environments based on observations of O VI and Ne VIII absorption.In an overdense environment, however, the association of absorption features with individual members of the group becomes more ambiguous.By comparing mean properties of the galaxy groups such as the center of mass, previous studies have shown that the O VI-bearing gas is more likely to be associated with individual galaxies rather than the intra-group medium (e.g., Stocke et al. 2014Stocke et al. , 2017)).However, other studies also suggest that the galactic environments could regulate the properties of absorbing gas (e.g., Johnson et al. 2015;Pointon et al. 2017;Dutta et al. 2021).We will discuss the general impact of the galactic environment in future studies.Here we apply the new CUBSmidz sample, including isolated and non-isolated galaxies to explore galaxy-absorber connections in the presence of neighbors.
In particular, we test the correlation between the light-ofsight absorption characterization and galaxy properties of different nearby galaxies.In Figures 4, we show respectively the spatial profiles of O VI absorption column densities for different host galaxy assignments.Because few galaxies/galaxy groups display detectable Ne VIII absorption, no clear trend can be established for any of the host galaxy assignments (see Figure A.1 in the Appendix).From the top to bottom panels, we consider the closest galaxy at the smallest  proj in each galaxy group, the galaxy with the closest  vir -normalized projected distance (minimum  proj / vir ), and the most massive member of the group (maximum  star ).Here, virial radii are calculated for individual galaxies in each galaxy group.As a comparison, we also show the isolated galaxy sample in the rightmost panels.In the left and right panels, the radial profiles are plotted as functions of  proj and  proj / vir , respectively.In each galaxy panel, we calculate the correlation coefficient  using a generalized Kendall's rank order test including both measurements and limits, and quantify the significance of the correlation between the absorbing column density and the projected distance.The results are summarized in Table 1.
Among the three different galaxy assignments, linking the O VI absorption to the most massive member of the group exhibits the weakest correlation with either  proj or  proj / vir .A generalized Kendall's test returns a rank coefficient of || < 0.25 (< 2).This weak correlation is similar to what was found for the cool CGM in (CUBS VI).Furthermore, we examine whether galaxies at the smallest  proj or  proj / vir exhibit a tighter correlation with the observed absorption properties.In general, we find that adopting the galaxies at the smallest  proj / vir slightly improves the significance of the anti-correlation, in comparison to adopting the galaxies at the smallest  proj .In addition,  OVI correlates more strongly with  vir -normalized distance than with  proj .
The finding of a strong correlation between the observed O VI absorbers and the galaxies at the smallest  proj / vir is also supported by the bulk velocity distribution of the absorbers relative to the associated galaxies.Figure 5 shows the velocity dispersions (left panels) and escape velocity ( esc ) normalized velocity dispersion (right) between the observed O VI and Ne VIII absorbers and the designated galaxies.We calculate  esc based on the inferred dark halo mass for each galaxy in galaxy groups (see Section 2), assuming the Navarro-Frenk-White (NFW) profile (Navarro et al. 1996).While no significant difference is seen in the velocity dispersions between O VI and galaxies at either the smallest  proj or smallest  proj / vir , the  esc -normalized velocity dispersions are notably narrower for galaxies at the smallest  proj / vir (second panel in the right; showing a standard deviation of 0.40 ± 0.06) than those at the smallest  proj (top-right panel; showing 0.56 ± 0.08).The difference is qualitatively consistent with the expectation that the observed absorbing gas is more closely connected to the galaxies at the smallest  proj / vir .In the subsequent analysis, we adopt the galaxy at the smallest  vir -normalized  proj as the counterpart of the absorber to explore the connection between galaxies and absorption properties.Here, we ignore the potential impact on O VI or Ne VIII due to nearby environments (e.g., Dutta et al. 2021), which will be investigated in future CUBS works.

Spatial properties of the warm-hot CGM probed by O VI and Ne VIII
By designating the galaxies at the smallest  proj / vir as the primary driver of the observed line-of-sight absorption properties in a group environment, we proceed with a joint study of the spatial properties of the warm-hot CGM using the full sample of isolated galaxies and galaxy groups.Using this full sample, we show the spatial profiles of  OVI and  NeVIII versus  proj / vir in Figure 6.On average, both  OVI and  NeVIII exhibit a general decline with increasing distance.Specifically, the detected O VI systems exhibit high column densities of log /cm −2 ≳ 14.5 at < 0.5  vir , together with two non-detections among six sightlines showing 2 upper limits of log /cm −2 ≲ 13.5 within  vir (Figure 6).In the outskirts at ≳ 2 vir , the overall strengths of detected O VI with column densities of log /cm −2 ≈ 13.5−14.0are sufficiently weak in comparison to the sensitivity of the data that a large fraction of sightlines show non-detections with a limiting column density of log /cm −2 ≲ 13.7.We determine the covering fractions of O VI and Ne VIII absorbing gas above a column density threshold,  0 , versus projected distance.These are presented at the top of each panel in Figure 6, which shows that the gas covering fraction also decreases with increasing distance.For O VI, the adopted threshold for calculating the covering fraction is log  0 /cm −2 = 13.7, which is larger than 95% of the upper limits reported for the sample.It allows us to include the majority of the sample for the covering fraction calculation.The covering fraction is calculated assuming a binomial distribution applied to small samples (see e.g., Gehrels 1986).Within  vir , the covering fraction of O VI absorbers with log  OVI /cm −2 ≥ 13.7 is   = 67 ± 10% (median and 1 uncertainty), and declines to 25 ± 7% and 19 ± 6% at 2  vir and 3  vir , respectively.
For Ne VIII, the column density profile resembles that of O VI, exhibiting higher column densities within  vir .However, significantly fewer detections are found and the data are not sufficiently sensitive for detecting Ne VIII with log /cm −2 ≲ 14.Adopting a threshold of log  0 /cm −2 = 14.0, we estimate a covering fraction of   = 20 +12 −9 % for Ne VIII-bearing gas within  vir , which declines to 4 +3 −2 % at 1-3  vir .While the detected Ne VIII sample is small, the decline in the covering fraction is significant.To obtain a better constraint of the covering fraction, we combine the CUBS sample with literature samples, which will be presented in Section 5.2.
As described in Section 2.3, the line-of-sight velocity dispersion   can serve as a tracer of the intra-halo kinematics, when the feature is broad ≥ 40 km s −1 .Figure 6 shows that there is a general decline of   from inner halos to the outskirts for both O VI and Ne VIII.In particular, broad Ne VIII features are all associated with broad O VI features.All six broad O VI and two Ne VIII absorbers are projected within  vir , leading to a covering fraction of   = 46 ± 13% for these broad absorbers and   > 29% at the 2- level of significance for O VI and Ne VIII, respectively.Beyond  vir , we can only place a 2 upper limit of 16% and 58% for broad O VI and Ne VIII, respectively.The difference in the covering fraction of broad O VI absorbers between within and beyond  vir is statistically significant (at the level of ≈ 2 ), suggesting that the gas kinematics is more complicated at  proj <  vir .

DEPENDENCE OF THE WARM-HOT CGM ON GALAXY PROPERTIES
The new CUBS-midz sample includes isolated galaxies and galaxy groups containing 2 to 21 member galaxies.The analysis presented in Section 3 shows that in the presence of neighbors, the galaxy at the smallest  proj / vir is physically most connected to the absorbers identified along the QSO sightlines (see Section 3).In this section, we explore how the warm-hot CGM probed by O VI and Ne VIII correlates with galaxy properties.In particular, we focus on its relation to  star and SFR, which characterize a galaxy's star formation history.
For literature samples, we adopt the reported total ion column densities when these measurements are available.When the best-fit Voigt profile parameters are reported for individual components, we compute a total column density by summing all components based on the Voigt profile fitting results.For non-detections, we compute the corresponding 2- limits based on the reported upper limits for all samples.Finally, we calculate a velocity dispersion for each absorber in the literature samples based on the reported Voigt profile results, including the J17, COS-Halos, and COS-LRG samples.For the literature samples, the adopted column densities and calculated velocity dispersions are also included in Figure 3 for comparisons.
Combining the CUBS-midz and literature samples leads to a joint sample of galaxies that span a range in  star from log  star /M ⊙ ≈ 8 to 11.5 over a redshift range from  ≈ 0.1  to 1.0.To ensure a consistent treatment of the absorber and galaxy association, we examine the public samples in search of possible neighbors and identify the galaxies at smallest  proj / vir as the designated galaxies associated with the reported O VI or Ne VIII absorbers.Virial radii are adopted from each sample directly for J17 and COS-LRG samples (Johnson et al. 2017;Zahedy et al. 2019), because the calculation methods are the same.We recalculate the virial radius for the COS-Halos sample (Werk et al. 2013).However, because of inhomogeneous survey limits between the literature samples, discrepancies remain in characterizing the galaxy environments between the CUBS and these literature samples.The impact due to variations in survey depth will be discussed when combining these samples for further studies.

Dependence of O VI and Ne VIII-bearing gas on the stellar mass
In Figure 7, we examine the dependence of  OVI and  NeVIII on the stellar mass.High  OVI absorbers with log /cm −2 ≳ 14.5 are found surrounding galaxies of log  star /M ⊙ ≈ 9.5 − 10.5, which is consistent with previous studies (e.g., Werk et al. 2014;Zahedy et al. 2019;Tchernyshyov et al. 2022).For a given  star , the observed  OVI ranges from 2 upper limits of log /cm −2 ≲ 13.0 for non-detections to log /cm −2 ≳ 14.0 for measurements, which is driven by the radial decline shown in Figure 6.For comparison, we plot the predicted  OVI from semi-analytical CGM models for star-forming galaxies at  = 0.2 and at 0.2 vir and 1.0 vir from Qu & Bregman (2018, hereafter, QB18; also see Section 5.4).The predicted  OVI for galaxies of different  star differs by a factor of 5 − 10 between projected distances of 0.2  vir and 1.0  vir .The large scatter implies that the O VI-bearing gas may exhibit different radial distributions on different mass scales.We will explore this further in the following section.
For Ne VIII, we include the CASBaH sample in the analysis.However, we have to first construct a uniform sample by adopting the same identification criteria stated in Section 2.3.For absorption features with significant contamination from interlopers, we consider the reported  NeVIII as upper limits.This leaves four of the nine Ne VIII absorbers reported by Burchett et al. (2019) as detections and the remaining five as non-detections (red squares in Figure 7).The four confirmed systems are PHL1377: 221_15, PG1206+459: 178_9, and PG1407+265: 245_62, and FBQS0751+0919: 124_25 (see Figure 2 of Burchett et al. 2019).In addition, we re-calculate the halo size for the CASBaH galaxies using their reported  star and the method described in Section 2.1.This is necessary, because of the significant difference in the adopted SMHM relations (see details in Wĳers et al. 2024).
As shown in Figure 7, Ne VIII features are primarily detected around galaxies with log  star /M ⊙ ≈ 9.5 − 11.0.We find that the strongest Ne VIII features occur near galaxies of log  star /M ⊙ ≈ 10, similar to O VI.One outlying system with log  NeVIII /cm −2 = 14.98 ± 0.09 in the CASBaH sample is likely associated with outflows from a massive post-starburst galaxy of log  star /M ⊙ = 11.2 at  = 0.93.This galaxy exhibits spectral features that are indicative of the presence of an AGN (Tripp et al. 2011).It is different from typical galaxies in the combined sample, but it is still included in the following analyses.
Next, we examine how the line-of-sight velocity dispersion,   , depends on  star , which may shed light on the ionization mechanisms of the warm-hot CGM.In PIE models, the typical density of O VI is ≈ 10 −4 cm −3 (e.g., Oppenheimer & Schaye 2013;Stern et al. 2018), with an equilibrium temperature of log /K ≈ 4.5 and a velocity dispersion of   ≈ 4 km s −1 due to thermal motions.In contrast, under a CIE assumption, the ionization fraction of O VI peaks at a temperature of log /K ≈ 5.5 with an anticipated thermal broadening of   ≈ 12.8 km s −1 .
In Figure 8, the velocity dispersion of O VI absorbers spans a wide range from ≈ 5 to 120 km s −1 , while Ne VIII absorbers exhibit a minimum   ≈ 20 − 30 km s −1 .We first note that the narrow O VI features with   ≈ 5 − 10 km s −1 are likely photoionized or out of equilibrium (e.g., Oppenheimer & Schaye 2013).On the other hand, the broad components with   ≥ 40 km s −1 are preferentially seen surrounding galaxies of log  star /M ⊙ > 9 for both O VI and Ne VIII, and the majority of broad features are detected around galaxies of log  star /M ⊙ ≈ 10 − 11.For these massive galaxies, the observed gas velocity dispersion exhibits a large scatter similar to what is seen in the column density.We attribute the observed large scatter to the complex gas kinematics at small  proj / vir (Figure 6).

Dependence of O VI-bearing gas on galaxy star formation history
Next, we examine whether the radial profiles of O VI column density and kinematics depend on a galaxy's starformation history by dividing the CUBS galaxy sample into sub-samples in the  star versus SFR parameter space (Figure 2).These include (i) a low-mass dwarf galaxy sample of 29 galaxies with 7.5 ≲ log  star /M ⊙ ≤ 9.0 and a me-dian mass of ⟨log  star /M ⊙ ⟩ = 8.6; (ii) a sub- * sample of 34 galaxies with 9.0 < log  star /M ⊙ ≤ 10.3 and a median of ⟨log  star /M ⊙ ⟩ = 9.6; (iii) a massive, star-forming sample of 12 galaxies with log  star /M ⊙ > 10.3 and a median of ⟨log  star /M ⊙ ⟩ = 10.7 ± 0.3; and (iv) a massive quiescent sample of 29 galaxies with log  star /M ⊙ > 10.3 and a median of ⟨log  star /M ⊙ ⟩ = 10.9 ± 0.3.Both the low-mass dwarf and the sub- * sub-samples are predominantly star-forming galaxies with log sSFR/yr −1 > −10.3, while massive galaxies with SFR > 0.2 M ⊙ yr −1 are considered star-forming and quiescent otherwise.This SFR threshold splits massive galaxies to have roughly equal numbers in each subsample together with literature samples.
Figure 9 shows the radial profiles of column density and velocity dispersion for these sub-samples, i.e., dwarf, sub- * , massive star-forming, and massive quiescent galaxies from left to right respectively.Here we also include the COS-Halos (Werk et al. 2013), J17 (Johnson et al. 2017), and COS-LRG samples (Zahedy et al. 2019) for improved statistics but leave out CGM 2 because the SFRs their galaxies and velocity dispersions of absorbers are not available (Tchernyshyov et al. 2022).
The differences in the O VI column density profiles are significant between these four sub-samples.Strong O VI absorbers with log /cm −2 ≳ 14.5 preferentially occur in the inner halo of sub- * and massive star-forming galaxies, and the decline of  OVI with increasing  proj / vir is correspondingly significant in these two sub-samples.This behavior explains that the on average higher O VI column density observed in the COS-Halos sample relative to the others may be understood as due to the QSO sightlines probing primarily the inner halo of galaxies with log  star /M ⊙ ≈ 10.
We adopt the generalized Kendall correlation coefficient (; Figure 9) to quantify the significance of the anti-correlation in the presence of upper limits and find a significance level   Zahedy et al. 2019).We calculate Kendall's rank-order coefficient  to quantify the significance of the correlation, which is listed in each panel.We fit the column density radial profile using a two-component model, including both the radial profiles of the column density (the middle row) and rate of incidence (the top row) to account for the clumpiness of the O VI gas (see the text for details).The solid line in each panel shows the best-fit model, while the dotted lines represent the 1- uncertainties.Circles in the top panels represent the empirical covering fraction measurements obtained based on a threshold of log /cm −2 ≥ 13.7.The sub- * and massive star-forming galaxy samples exhibit steeper declines with power law slopes of ≈ 0.9, while the massive quiescent galaxy sample shows a flatter profile, consistent with a zero slope.
of > 4 for the sub- * and massive star-forming samples.In contrast, the dwarf and massive quiescent sub-samples exhibit weaker correlations between  OVI and  proj / vir .
To investigate this difference quantitatively, we perform an analysis under a Bayesian framework to obtain a best-fit radial profile of both ion column density and covering fraction for each sub-sample.This two-component model is developed to account for the possible clumpy nature of the O VI-bearing gas (also see Huang et al. 2021), and motivated by the observation that a single continuous probability distribution of  OVI cannot simultaneously reproduce the observed high- OVI systems and non-detections within  vir (Section 3.2 and Figure 6).Instead, the difference between detections and non-detections can be explained by a non-unity covering fraction, .We note that  is a theoretical parameter that depicts the presence or absence of O VI gas, while  is an empirical number that is affected by the sensitivity of the data and therefore is only meaningful with an associated column density threshold.In practice, the modeling of  may be affected by the detection limits, when QSO spectra have low S/N ratios.Here, we note the spectral S/N is sufficient to characterize  for O VI in the CUBS program.
The two-component model is implemented by combining the spatial variations of  and  OVI as a function of  proj / vir .We adopt a power-law radial profile for the expected O VI column density N where  =  proj / vir , N0 is the expected O VI column density at  vir and  is the slope.The power law is selected because detected column densities do not exhibit a sharp decline, and it is also typically adopted in such modeling (e.g., Chen et al. 1998;Huang et al. 2021).Here, we only fit data with  in the range of 0.1 to 3, so we can ignore the singularity at  = 0 for the power law.
For the covering fraction, we assume a modified exponential decline of where  0 is the  vir -normalized scale radius of the exponential model,  is the free index regulating the speed of decline, and  0 is the covering fraction at the galaxy center.Because the mathematical form as given allows  0 to be larger than unity, we impose a ceiling at  = 1.This modified exponential function is motivated by the sharp decline in the covering fraction (Figure 6), which has also been seen for Mg IIbearing gas (Huang et al. 2021;Schroetter et al. 2021).In our model, if  > 1, then  would decline faster than an exponential function.Therefore, this modified exponential function provides the flexibility to capture different degrees of declining rate.The likelihood of producing an observed data set  that contains  measurements,  non-detections, and  saturated lines under the two-population model  consisting of parameters N0 , ,  0 ,  0 , and  is the joint product of (i) the probability of measuring   for an expected N and (ii) the probability of the model values occurring within the range of allowed upper or lower limits by the data.We construct a likelihood function following this joint probability, where  = log /cm −2 ,  2 =  2  +  2 p with   representing the measurement uncertainty and  p representing the intrinsic scatter.The symbols   ,    , and    represent measurements, 95% upper limits in case of non-detections, and 95% lower limits in case of saturated lines, respectively.The term (1 − ) associated with upper limits accounts for the probability that the non-detection is from the region without O VI-bearing gas.
We assume a uniform prior and construct the posteriors of individual model parameters log N0 , ,  0 ,  0 , , and  p based on Markov chain Monte Carlo (MCMC), which is implemented using the emcee package (Foreman-Mackey et al. 2013).The best-fit parameters are summarized in Table 2.The median and 68% interval of the best-fit model are presented as solid and dashed lines in Figure 9.
Figure 9 and Table 2 show that while the sub- * and massive star-forming sub-samples share a similar power law slope for the O VI-bearing gas (0.86 ± 0.19 versus 0.75 +0.19  −0.18 ), the massive quiescent sub-sample exhibit a flatter slope of 0.10 +0.24 −0.22 , respectively.The dwarf galaxy sample shows a flatter slope of 0.39 +0.44  −0.39 , but its difference from sub- * and massive starforming galaxies is limited by the small sample size.Within a similar mass range, star-forming galaxies exhibit a steeper slope than the quiescent ones at a significance level of ≈ 1.6 .
This implies a fundamental difference in the spatial distribution of O VI between star-forming and quiescent galaxies.
We also compare the observed covering fraction at a threshold of log  OVI /cm −2 = 13.7,, with the model-predicted covering fraction, , in Figure 9. Similar to the column density profile, sub- * and massive star-forming galaxies exhibit covering fractions consistent with unity at ≲ 0.5  vir and declining to ≲ 20% beyond 2  vir .At the same time, dwarf galaxies exhibit a maximum covering fraction of ≈ 60% at 0.5 − 1.0 vir .The decline of covering fractions is significant for the three star-forming galaxy samples, with  ≈ 2. The scale radius ( 0 ) is about 1.5  vir , suggesting an enhancement of the O VI-bearing gas within ≈  vir due to the nearby star-forming galaxies.
In contrast, the massive quiescent galaxy sample exhibits a roughly constant covering fraction of ≈ 30% within 3  vir .The best-fit  = 0.7 +1.2 −0.4 is smaller than the three star-forming samples ≈ 2.0, suggesting a shallower decline.In this case, the scale radius  0 is unconstrained, because of the roughly constant covering fraction.
The difference between star-forming and quiescent galaxy CGM has also been seen in low ions.For example, the restframe absorption equivalent width (EW) of Mg II shows a power-law slope of 1.03 ± 0.22 for the star-forming sample, while the passive galaxy sample exhibits a slope of 0.12 ± 0.24 (Huang et al. 2021).The cool and warm-hot gas in the CGM both exhibit concentrations in the inner halo of starforming galaxies, compared to passive galaxies.However, the covering fraction of ≈ 50% for high column density absorbers occurs at 1 − 1.5 vir for O VI, while this radius is 0.5 vir for Mg II, indicating changing ionization states of the gas toward halo outskirts.
Figure 9 also shows a larger velocity dispersion within  vir than in the outskirts for all four sub-samples.Here, we adopt the generalized Kendall's  test to quantify the degree of anti-correlations for these samples.The sub- * sample exhibits a significant decline (4.3) from the maximum of 120 km s −1 within 0.2  vir to ≈ 20 km s −1 at 1 − 2  vir , with all broad features (≥ 40 km s −1 ) projected within the virial radius.Anti-correlations are observed for the other three sub-samples, but less significant ≲ 2.In addition, we notice almost all O VI features are broad within 0.5 vir for sub- * and massive star-forming galaxies, while there are also narrow features within 0.5  vir for massive quiescent galaxies.The joint observations of enhanced  OVI and broader   at ≲ 0.5  vir around star-forming galaxies support that these high- OVI at small  proj / vir absorbers do indeed originate in the galaxy halo, rather than appearing by projection (cf.Ho et al. 2021). For sub- * galaxies, the data do not provide distinguishing power a  0 > 1, because of a high covering fraction of O VI-bearing gas in the inner halo.The upper bound of 2.0 is the fixed boundary for  0 .

Dependence of Ne VIII-bearing gas on galaxy properties
For massive quiescent galaxies, a roughly flat covering fraction cannot distinguish  0 within the allowed range of [0.1, 3.0]. In the massive quiescent sample,  p > 0.3 dex cannot be distinguished by the data, so we fixed  p = 0.3 dex, similar to other sub-samples.Similar to O VI, we consider the dependence of Ne VIII profiles on galaxy properties.For Ne VIII, limited by the small number of detections, we only divided the uniform combined sample (Section 4.1) into three sub-samples based on  star , separated at log  star /M ⊙ = 9.0 and 10.3.In Figure 10, we present radial profiles of  NeVIII as a function of  proj / vir for these three sub-samples.
Although the nine detected Ne VIII absorption systems exhibit a declining trend with increasing distance, the radial profile of  NeVIII cannot be quantitatively modeled using the two-component model because of the small number of detections.Here, we calculate the covering fractions for the high column density Ne VIII systems of log /cm −2 ≥ 14.0 for different galaxies.There is no robust detection of Ne VIII in halos around dwarf galaxies, leading to 2 upper limits in covering fractions of 36% and 15% within and beyond  vir , respectively.For sub- * galaxies, the covering fraction exhibits a significant decline from 50 ± 17% within  vir to 6 ± 3% at 1 − 3 vir .In massive halos, the covering fraction is 23 +17 −12 % within  vir .However, the only high column density Ne VIII is associated with a post-starburst AGN-host galaxy.Ignoring this outlier, the covering fraction is < 41% within  vir .Beyond  vir , only two systems are detected with log /cm −2 ≈ 14.0, which leads to a low covering fraction of 4 +4 −2 %.The difference in Ne VIII covering fractions between sub- * and massive galaxy halos suggests that sub- * halos contain more concentrated Ne VIII-absorbing gas, similar to O VI.

DISCUSSION
Combining the CUBS-midz sample with previously published literature samples, we have demonstrated that galaxies with different star-formation histories, determined according to  star and SFR, exhibit different radial profiles of O VI and Ne VIII absorption properties ( and   ).In this section, we first examine the galaxy environments of the five new Ne VIII absorbers discovered in our survey and then discuss the implications of our findings for the warm-hot CGM, including its spatial distribution, total mass, and possible origins in halos of different masses.

Notes on individual Ne VIII absorbers
As described in Section 2.3, the detected Ne VIII absorbers are identified based on a matched doublet ratio without significant contamination and with both doublet components detected at ≳ 2.All five detected Ne VIII absorbers also exhibit low ionization species over a similar velocity range (e.g., H I and C III), as shown in Figure 11.Four of five systems have detectable O VI features, while one system shows a 2 upper limit of log /cm −2 < 13.9.
These newly discovered Ne VIII absorbers are found in a range of galactic environments (Figure 12).In particular, the strongest Ne VIII of log /cm −2 = 14.67 ± 0.05 is detected in the inner halo ( proj ≈ 30 kpc) of an isolated star-forming disk galaxy with log  star /M ⊙ = 10.0 ± 0.1 (i.e., system s37) that produces an LLS system (Chen et al. 2020;Zahedy et al. 2021).The remaining Ne VIII absorbers are detected in galaxy groups with the number of members ranging between 5 and 21 and the total stellar mass summed over all group members ranging from log  star /M ⊙ ≈ 10.2 to 11.4.All of these galaxy groups have star-forming galaxies projected close to the QSO sight lines.
A comparison of the gas kinematics between Ne VIII and O VI shows that Ne VIII typically exhibits a line width that is either comparable or broader than O VI, indicating that at least some Ne VIII absorbers do not share the same origin as O VI.This may be due to blending in Ne VIII components if these components exhibit broader  values.It is worth noting that O VI in system s18 at  = 0.4801 is exceptionally strong, with a 2 lower limit of log /cm −2 > 14.9.The doublet features cannot be explained by either an interloper Ly or Ly line, because of a lack of corresponding higherorder Lyman series lines at shorter wavelengths.The aligned Finally, the lack of O VI makes system s72 a special case, which is rare in all previous Ne VIII systems (e.g., Savage et al. 2005;Narayanan et al. 2011;Meiring et al. 2013;Burchett et al. 2019).In this system, we are able to place a 2 upper limit of log /cm −2 < 13.9 for the possible presence of O VI, while the Ne VIII lines are detected at a significance of ≈ 4 and ≈ 2 for the strong and weak members, leading to a total significance of ≈ 5.Although individual components of low ions (e.g., H I and C III) are detected with a similar line centroid to the potential Ne VIII component, the dramatically different ionization potentials make it unlikely for these low ions to share the same ionization phase with Ne VIII.We include this system as a Ne VIII detection in all analyses, but it is still possible that the matched Ne VIII doublet may be due to contaminating absorption features at different redshifts.

Covering fraction of Ne VIII
As a tracer of the warm-hot CGM, Ne VIII absorption has been detected in FUV spectra of background QSOs (e.g., Savage et al. 2005;Mulchaey & Chen 2009;Narayanan et al. 2011Narayanan et al. , 2012;;Meiring et al. 2013;Qu & Bregman 2016), although the first Ne VIII search in a blind galaxy sample established without prior knowledge of existing features was carried out by the CASBaH survey (Burchett et al. 2019).A high covering fraction of  ≈ 44 ± 20% was found at  < 200 kpc for Ne VIII of log /cm −2 > 14.0.Taken at the face value, we would expect to detect ∼ 10 new strong Ne VIII absorbers with log /cm −2 > 14.0 for 23 galaxies with log  star /M ⊙ > 9 and meaningful constraints on Ne VIII projected within 200 kpc from QSO sightlines in the CUBS-midz sample, but only five were found.Here we examine possible factors that may have contributed to this discrepancy.
The CASBaH galaxies span a range in  star from log  star /M ⊙ ≈ 9.0 to 11.3 with a median of 10.1 and a standard deviation of 0.6 dex.The lowest-mass galaxies presented by the CASBaH are still more than an order of magnitude more massive than the low-mass galaxies in the CUBS-midz sample (see e.g., Figure 2).Therefore, the first step toward a systematic comparison is to establish a comparable galaxy sample.To this end, we select all galaxies with log  star /M ⊙ > 9.0 in the CUBS-midz sample, which has a median of 10.3 and a standard deviation of 0.7 dex.
Given the challenge of robustly identifying a Ne VIII absorber in the presence of numerous interlopers, we also adopt a conservative column density threshold of log  0 /cm −2 = 14.0 for computing the covering fraction.To obtain accurate constraints for the gas covering fraction, particularly in the event of a small sample, it is critical to first establish a uniform sample of absorption spectra that offers a consistent sensitivity limit for detecting both strong and weak absorbers.While strong absorbers can be detected in both low-and high-/ data, weak absorbers can only be detected in high-/ spectra.Including low-/ sightlines based on the presence of a strong absorber, instead of matching sensitivities, would lead to an overestimate of the gas covering fraction.For this reason, we estimate a limiting column density in continuum regions around all detections to identify and exclude those low-/ sight lines even when a strong absorber is reported.This exercise leads to 57 and 26 galaxies/galaxy groups with sufficient sensitivities in the background QSO spectrum to detect Ne VIII absorbers of log  NeVIII /cm −2 > 14 in the CUBS and CASBaH surveys, respectively, projected within 3 vir .
In Figure 13, covering fractions are shown as functions of both  proj and  proj / vir .We adopt all reported Ne VIII and their log  NeVIII /cm −2 from Burchett et al. (2019) for the panel on  vir , but compute the covering fraction versus  proj / vir ourselves, because these are not reported in Burchett et al. (2019).All covering fractions obtained from the CUBS

Figure 13.
Covering fractions of Ne VIII absorption features with log /cm −2 ≥ 14.0 as functions  proj (the left panel) and  proj / vir (middle and right panels).Here, we filter the stellar mass log  star /M ⊙ > 9.0 of galaxies in the CUBS program to match with the CASBaH sample (see text for details).In the left two panels, the CUBS sample (black circles) and the CASBaH sample (gray diamonds) are presented separately.
Although the results from the two samples are consistent within the 1- uncertainties, the covering fractions estimated using the CUBS sample are consistently lower than the CASBaH measurements.In the right panel, we show the covering fractions at log /cm −2 ≥ 14.0, combining both samples.We report two sets of combined covering fraction measurements.The first is calculated including all Ne VIII reported by the CASBaH team (light blue pentagons), while the second includes only absorbers that satisfy the same set of criteria as those from CUBS (red squares; see Section 4.1).This uniform, combined sample results in conservative measurements of the Ne VIII gas covering fraction, due to uncertainties in Ne VIII identifications.
and CASBaH samples are consistent with each other within 1 at all radii, showing significant declines beyond 200 kpc or  vir .However, the CUBS sample prefers lower covering fractions than the CASBaH survey.Specifically, the CUBS sample exhibits a covering fraction of 18 +9 −7 % for Ne VIII absorbers with log /cm −2 > 14.0, while the CASBaH sample prefers 44 +22 −20 % within 200 kpc.Within  vir , the CUBS and CASBaH samples show 36 +18 −16 % and 50 ± 17%, respectively.Here, the covering fractions are higher than the values in Figure 6, because non-detections associated with low-mass galaxies are omitted from this comparison.
For an optimal statistical analysis, we combine the CUBS and CASBaH samples to assess how the gas covering fraction depends on  proj / vir .This is presented in the right panel of Figure 13.We report two sets of measurements resulted from applying different treatments for the CASBaH sample.First, we calculate the combined covering fraction using all nine reported Ne VIII absorbers from Burchett et al. (2019).The results are shown as pentagons in the right panel of Figure 13.The measured covering fractions are summarized in Table 3 Second, we apply a uniform set of selection criteria of Ne VIII absorbers described in Section 4.1 for both samples and compute the gas covering fractions based on this uniform sample.This second set of measurements represents a conservative estimate of the gas covering fraction due to the difficulties in robustly identifying Ne VIII in the presence of interlopers.
In summary, our analysis shows that the covering fraction Ne VIII declines with increasing distance out to ≈ 1.5  vir , and it may not be as high as previously thought around galaxies of log  star /M ⊙ ≈ 9.0 − 11.5.To evaluate the mass budget of the warm-hot CGM, we first calculate the average column density within  vir using the best-fit column density profiles and covering fractions for galaxies in different sub-samples presented in Section 4.2. Figure 14 shows the dependence of the area-weighted mean O VI column density with  vir on the stellar mass.The mean column density exhibits an increase of 0.8 dex from dwarfs to sub- * galaxies, followed by a decrease of 0.2 dex to massive star-forming galaxies.At log  star /M ⊙ > 10.3, massive quiescent galaxies on average exhibit a lower O VI column density in the CGM than star-forming galaxies (see also Zahedy et al. 2019).
We calculate the total enclosed O VI mass at  proj <  vir and within the maximum radius,  proj = 3  vir , surveyed in this study (Figure 14).The total O VI mass increases from  proj <  vir to  proj < 3  vir by ≈ 0.2 − 0.3 dex for starforming galaxies, while the increment is ≈ 0.6 dex for the massive quiescent galaxies.This is expected because of a flatter column density profile found in these massive quiescent halos.For the massive galaxy samples (i.e., star-forming and quiescent), the large error bars shown in Figure 14 also have , we obtain  OVI ≈ 0.1 to reproduce the observed O VI content in the CGM of sub- * galaxies, suggesting that O VI-bearing gas is the dominant phase in these galaxies (see the text for details).Right panel: Ne VIII mass, similar to the middle panel.The Ne VIII mass is calculated empirically, which may be driven by the highest column density absorbers at small  proj / vir (see the text for details).
significant contributions from the difference of halo sizes for different galaxies.
In Figure 14, we also include model predictions for the O VI mass, following a simple halo model.For each dark matter halo, we adopt a cosmic baryonic fraction of  b = 0.156 (Planck Collaboration et al. 2020), a fraction of the baryonic mass in the CGM,  CGM , and a fraction of oxygen in the O VI ionization state,  OVI .The expected total mass in O VI is then  OVI =  halo  b  CGM / ×  O (O/H)  OVI , where  = 1.4 is the atom mass per hydrogen,  O = 16 is the atomic number of oxygen, and O/H is the number ratio between oxygen and hydrogen.
In the following discussion, we use  CGM  OVI  O / O,⊙ as an integrated normalization of the model because these quantities are degenerate with one another.We adopt  O / O,⊙ to represent the oxygen abundance relative to the solar value.We find that  CGM  OVI  O / O,⊙ ≈ 0.01 is required to reproduce the observed O VI ion mass in sub- * galaxies as shown in Figure 14, which display the highest mean  OVI .A typical metallicity in the CGM is ≈ 0.3  ⊙ , and the CGM mass fraction is predicted to be 0.1 − 0.5 in recent simulations (e.g., Wĳers et al. 2020).Adopting a typical gas-phase metallicity and  CGM , we obtain an average ionization fraction ≈ 0.05 − 0.3 for O VI, which is comparable with the peak ionization fraction of 0.2 − 0.4 in CIE or PIE models (e.g., Oppenheimer & Schaye 2013;Stern et al. 2018, hereafter, S18).Therefore, we conclude that O VI-bearing gas is an important phase in these sub- * halos.We also plot the model predicted mass out to 3  vir , extrapolating a Navarro-Frank-White (NFW; Navarro et al. 1996) halo profile with a concentration of 4 for star-forming galaxies.For sub- * galaxies, the predicted O VI is consistent with observations, indicating O VI is also abundant in the outskirts of these galaxy halos.On the other hand, the observed O VI mass in the CGM of dwarf galaxies or massive quiescent galaxies is significantly lower than the model prediction, suggesting that the typical ionization state in these halos is offset from O VI assuming  CGM ≈ 0.3 (also see Zahedy et al. 2019;Zheng et al. 2024).However, the CGM mass fraction in dwarf galaxies may be as low as ≈ 0.1 (e.g., Schaller et al. 2015;Hafen et al. 2019), which also affects the O VI mass.
For Ne VIII, no best-fit model is available because of the small sample of detections.Therefore, the Ne VIII mass is calculated by summing over all available empirical constraints, including both measurements and upper limits.Specifically, we divide the radial profile into discrete bins and calculate a median Ne VIII column density in each bin.For nondetections, we estimate a median column density, ⟨  ⟩ that satisfies erf (⟨  ⟩/ 68 ) = 1 2 erf ( 95 / 68 ), where erf () is the error function and  68 and  95 represent the 68% and 95% upper limits, respectively.The empirically determined Ne VIII masses are plotted in the right panel of Figure 14.
Similar to O VI, we also plot the simple model prediction of the Ne VIII mass assuming  CGM  NeVIII  Ne / Ne,⊙ ≈ 0.01.As a lithium-like ion, Ne VIII shares a similar ionization fraction as O VI, with a peak of  NeVIII ≈ 0.2 and 0.4 in CIE and PIE, respectively (e.g. Oppenheimer & Schaye 2013).The observed Ne VIII mass is higher than the model prediction for the sub- * sample.However, we note for both the sub- * and massive galaxy samples, the mass estimates are driven by a few high column density systems at the smallest  proj / vir , which contribute 30% − 40% of the total Ne VIII mass.The total mass estimate is, therefore, subject to large stochastic uncertainties.
We note that a systematic uncertainty in the mass budget calculation may be induced by the halo model adopted for estimating  vir .Compared to the CGM 2 survey, For sub- * and massive star-forming galaxies, our mean O VI column densities are higher than the values reported in CGM 2 by 0.1 − 0.2 dex.This difference is mainly due to a different adopted stellar mass-halo mass relation for computing  vir .As stated in Section 2, we adopted the Kravtsov et al. (2018) relation that includes missing light correction in the total stellar mass of massive galaxies.This leads to a smaller inferred halo mass by ≈ 0.1 − 0.2 dex for a given  star at log  star /M ⊙ ≈ 9.5 − 10.5, compared to the Behroozi et al. (2019) model.Using the Behroozi et al. (2019) model, we would infer a higher halo mass and, as a result, a larger  vir .A larger  vir would lower the mean column density within  vir by including more non-detections at larger projected distances.

Spatial variation of the 𝑁 NeVIII /𝑁 OVI ratio
The origin of the warm-hot CGM may be explained by different scenarios, including the virialized ambient gas, the outflowing ejection from galaxy disk, and cooling gas from the hotter phase (e.g., Oppenheimer et al. 2016;McQuinn & Werk 2018, S18, QB18, Wĳers et al. 2024).The observed  NeVIII / OVI ratio provides valuable insights into the ionization mechanisms of the warm-hot CGM and its origin.In particular, we consider two different model scenarios: photoionized gas vs. radiative cooling gas in the hot halo (see S18 and QB18).These models predict distinct behaviors for  NeVIII / OVI in different scenarios.However, the current sample is still too small to establish a consistent physical understanding of the ionization mechanism of these absorbers.Here, we compare the existing sample with model predictions to shed light on future observations.S18 introduced two scenarios to generate O VI and Ne VIII in the CGM of star-forming  * galaxies.These authors considered the possibility that the warm-hot CGM is photoionized in the low-density and low-pressure halo.This low-pressure scenario shows a clear increase in  NeVIII / OVI with increasing projected distance because of a declining gas density (Figure 15).The predicted ion ratios from this lowpressure model presented in Figure 15 are for two different mass inflow rates,  in = 3 and 10 M ⊙ yr −1 ; see S18 for detail).
S18 also considered the possibility that the warm-hot gas arises in the high-pressure cooling flow from the hot phase (also see Stern et al. 2019Stern et al. , 2023)).In this high-pressure scenario, the  NeVIII / OVI ratio only depends on the maximum temperature of the cooling flow, which shows no radial dependence.
QB18 developed a hybrid model for galaxies in different mass ranges.For a gaseous halo around galaxies of  star ≈ 10 8 to 10 11 M ⊙ , these authors attributed the warm-hot gas to cooling gas from the hot halos and accounted for photoionization due to the ultra-violet background (UVB) by adopting the ionization fractions from Oppenheimer & Schaye (2013).In low-mass galaxies of  star ≈ 10 8 − 10 9 M ⊙ , the virial temperature is too low to form O VI and Ne VIII through collisional ionization.Therefore, the measured warm-hot CGM is photoionized, which shows increasing  NeVIII / OVI with radius.For massive galaxies of  star ≳ 10 10 M ⊙ , the QB18 model predicts relatively constant  NeVIII / OVI with radius because the warm-hot gas is mainly collisionally ionized at the peak temperature.
Figure 15 shows comparisons between predicted and observed  NeVIII / OVI ratios at different projected distances.The observed  NeVIII / OVI ratios are presented for absorbers with at least one ion detected (i.e., O VI or Ne VIII).In total, 23 individual systems have meaningful constraints on  NeVIII / OVI , including all five newly discovered Ne VIII absorbers (see Section 5.1).
The galaxy sample is divided into three sub-samples according to  star and SFR.For low-mass galaxies of log  star /M ⊙ < 10, the only measured  NeVIII / OVI is at ≈ 2 vir .This is consistent with the photoionization scenario, although no trend can be derived with only one detection in this mass range.For massive galaxies of log  star /M ⊙ ≥ 10, we further group them into star-forming and quiescent galaxy sub-samples with a SFR threshold of 0.2 M ⊙ yr −1 .These two sub-samples exhibit similar  NeVIII / OVI ratios.For massive star-forming galaxies, two systems with both Ne VIII and O VI detected show  NeVIII / OVI of ≈ 0.6 − 1, suggesting a temperature of log /K ≈ 5.8 in either the collisional ionization scenarios (e.g., Savage et al. 2005;Meiring et al. 2013;McQuinn & Werk 2018).
We note two special cases.For s72 with an  NeVIII / OVI ratio of ≳ 1.2, the associated galaxy at the smallest  proj / vir is the most massive with log  star /M ⊙ ≈ 10.6 among all five detected Ne VIII absorbers.This is indeed expected from the cooling flow model, in which massive galaxies should produce the highest  NeVIII / OVI ratio (QB18).For s18 with an  NeVIII / OVI ratio of ≲ 0.2, the observed O VI is exceptionally strong and narrow, suggesting a photoionized origin or a non-equilibrium condition.It is therefore likely that this system is significantly affected by local radiation due to nearby galaxies (see examples in Zahedy et al. 2021;CUBS VI).
Given the distinct predictions for  NeVIII / OVI from different model scenarios, our sample at the moment is still too small to establish a consistent physical understanding of the origin of these absorbers.In particular, existing data do not provide a sufficiently large dynamic range in the  NeVIII / OVI ratio to discriminate different models.Improving the detec-  tion limit of Ne VIII with high S/N ratio spectra is necessary to strengthen these model comparisons.

SUMMARY
In this work, we establish the CUBS-midz sample of 0.4 ≲  ≲ 0.7 galaxies with small projected distances to the 15 CUBS background QSOs (Figure 2), aiming to study the warm-hot CGM probed by the O VI and Ne VIII doublets.The new sample contains 50 individual galaxies and 53 galaxy groups with 2 to 21 member galaxies.In this sample, 30 O VI and 5 Ne VIII absorbers are detected.Combining the CUBS-midz sample with literature samples, we investigate the radial dependence of line-of-sight absorption properties (e.g., the column density and velocity dispersion) on galaxy stellar masses and SFRs.Our major results are summarized below.
• Detected O VI and Ne VIII absorption features exhibit column densities of log /cm −2 ≈ 13.5 − 15.0, while the limiting column densities are log /cm −2 ≈ 13.7 and 14.0, respectively, for a large fraction of nondetections.We calculate the velocity dispersion of detected O VI and Ne VIII features, spanning from ≈ 5 km s −1 to 120 km s −1 (Figure 3).In particular, we consider features with   ≳ 40 km s −1 as broad features, tracing the kinematics in the halo instead of the internal velocity dispersion in individual clouds.
• We examine the correlations between the O VI and Ne VIII properties and different nearby galaxies with the smallest  proj , smallest  proj / vir , and highest  star , using the 53 sight lines probing the overdense galaxy environments with multiple nearby galaxies (Figures 4 and 5).The observed O VI column density and kinematics are most correlated with the galaxy with the smallest  proj / vir , which is therefore taken as the host galaxy of absorption features in group environments.
• The detected O VI and Ne VIII absorption features exhibit bulk velocities within ≈ 200 km s −1 relative to the associated galaxies (Figure 5).Normalized by the escape velocity, the bulk velocity distribution can be modeled by a Gaussian function with a standard deviation of  ≈ 0.40.
• For both O VI and Ne VIII, particularly high column density and broad absorption features are detected around galaxies with  star /M ⊙ ≈ 10 (Figures 7 and 8).
• For O VI, we divide the CUBS-midz sample into four sub-samples based on  star and SFR: the dwarf, sub- * , massive star-forming, and massive quiescent galaxy samples.Combined with literature samples, the sub- * and massive star-forming galaxy samples show substantial radial declines of column density with a power law slope of ≈ 0.8, while the massive quiescent galaxy sample exhibits flatter radial profiles (Figure 9).
• The covering fraction of O VI is high (≈ 90 − 100%) for sub- * and massive star-forming galaxies within the virial radius, and exhibits a sharp decline at 1 − 2 vir .The massive quiescent galaxies exhibit a roughly constant covering fraction of ≈ 30% out to 3 vir (Figure 9).The joint observations of flat covering fraction and column density profiles suggest less concentrated O VIbearing gas in the CGM of quiescent galaxies.
• For Ne VIII, we divide the sample into three subsamples based only on  star considering the small sample of Ne VIII detections.Within  vir , the sub- * galaxy sample exhibits a higher covering fraction of high  NeVIII systems with log  NeVIII /cm −2 ≥ 14.0 (Figure 10).
• We compare the covering fraction of Ne VIII with the CASBaH sample for galaxies with log  star /M ⊙ ≈ 9 − 11.5, showing that the CUBS sample exhibits relatively lower covering fractions over all radii for a limiting log  NeVIII /cm −2 = 14.0 (Figure 13 and Table 3).

Figure 1 .
Figure1.Comparison between the SED-based and magnitudebased stellar masses.The intrinsic scatter of the empirical relation between  star ,   , and − color is ≈ 0.2 dex, which is determined using 910 galaxies at  ≈ 0.4 − 0.7 with high-quality observed magnitudes, leading to derived  star uncertainties of < 0.1 dex.

Figure 4 .
Figure 4. Spatial profiles of O VI column density constructed based on different assignments of associated galaxies and projected absorber-galaxy distances. OVI is most strongly correlated with galaxies with the smallest  proj / vir , where  vir is calculated for individual galaxies (see Table1for statistics).We present the dependence of column density on the projected distance and the  virnormalized distance in the left and right panels, respectively.Error bars represent 68% confidence intervals of the column density measurements, and downward arrows represent the 95% upper limits for non-detections.In one case, the O VI absorber appears to be saturated, which is indicated by an upward arrow.In overdense galaxy environments, three different galaxy associations are explored, including the galaxy at the smallest  proj , the galaxy at the smallest  proj / vir , and the galaxy with the highest  star from top to bottom in the first three rows.The isolated galaxy sample is plotted in the lowest row for comparison.In the first two rows, the physically closest galaxy is also the one with the smallest  proj / vir in 31 galaxy groups.For the remaining 22 groups, we highlight the difference in the associated galaxies using red plus symbols.Overall, the combination of adopting the galaxies at the smallest  proj / vir and  vir -normalized distance yields the tightest correlation (right panel in the second row).

Figure 5 .
Figure5.Observed line-of-sight velocity distribution of O VI and Ne VIII absorbers in the galaxy rest frame.Solid histograms represent the O VI absorbers, while dashed histograms represent the Ne VIII absorbers.Galaxies are selected following the same criteria described in Figures4 and A.1.The right panels display escape velocity ( esc ) normalized velocity dispersion.The standard deviation () of the O VI velocity distribution is marked in the top-right corner of each panel.The narrower  esc -normalized velocity dispersion in the right panel in the second row suggests a tighter kinematic connection between the O VI absorbers and the galaxies at the smallest  proj / vir in a group environment.Similar to the column density profiles displayed in Figure A.1, the small number of Ne VIII absorbers detected in our search provides little distinction for their galaxy hosts.

Figure 6 .
Figure 6.Spatial profiles of column densities and velocity dispersion for O VI and Ne VIII, together with the estimated covering fraction of high column density absorption systems with log /cm −2 ≥ 13.7 and 14.0 for O VI and Ne VIII, respectively, at the top.For velocity dispersions, the covering fractions are calculated for broad features with   ≥ 40 km s −1 .

Figure 8 .
Figure 8.The velocity dispersion dependence on the stellar mass of the galaxy with the minimal  proj / vir for O VI (left panel) and Ne VIII (right panel).Broad O VI absorption features of   ≥ 40 km s −1 are detected at log  star /M ⊙ ≳ 9.0, while narrow features are found for all stellar masses.

Figure 11 .
Figure 11.Absorption properties of all five newly discovered Ne VIII systems in the CUBS-midz sample, together with associated low-ionization transitions including Ly, C III 977, O VI 1031, 1037, and Ne VIII 770, 780.Zero velocity represents the galaxy at the smallest  proj / vir .The red lines are the best-fit models obtained from the Voigt profile fitting for each transition.The gray-shaded regions mark contaminating features or bad pixels.

Figure 12 .
Figure 12.Summary of the galactic environments of newly detected Ne VIII systems in the CUBS-midz sample.The Ne VIII column densities are labeled in the lower-left corner of each panel, and the redshift at the top-right.The QSO sightline is located at the center of each panel, marked by a green plus.The colors represent the velocity offsets, as shown in the color bar on the right, of individual galaxies relative to the redshift of the galaxy with the smallest  proj / vir .To visualize the galaxy environment, we model each associated galaxy using a 2D Gaussian, with the FWHM representing  vir and amplitude representing the inferred halo mass.With the exception of one Ne VIII associated with a single star-forming disk galaxy at  = 0.5426 (middle panel), the remaining four absorbers are all found in an overdense galaxy environment.line centroid between O VI and Ne VIII but substantially narrower O VI lines suggest that local ionizing radiation or non-equilibrium processes may be crucial for explaining the exceptional strength of O VI.Finally, the lack of O VI makes system s72 a special case, which is rare in all previous Ne VIII systems (e.g.,Savage et al. 2005;Narayanan et al. 2011;Meiring et al. 2013;Burchett et al. 2019).In this system, we are able to place a 2 upper limit of log /cm −2 < 13.9 for the possible presence of O VI, while the Ne VIII lines are detected at a significance of ≈ 4 and ≈ 2 for the strong and weak members, leading to a total significance of ≈ 5.Although individual components of low ions (e.g., H I and C III) are detected with a similar line centroid to the potential Ne VIII component, the dramatically different ionization potentials make it unlikely for these low ions to share the same ionization phase with Ne VIII.We include this system as a Ne VIII detection in all analyses, but it is still possible that the matched Ne VIII doublet may be due to contaminating absorption features at different redshifts.

Figure 14 .
Figure14.Mass content of the warm-hot CGM probed by O VI and Ne VIII versus  star .Left panel: Dependence of mean  OVI averaged within  vir on the stellar mass (black circles).The mean  OVI peaks at log  star /M ⊙ ≈ 10.For comparison, we include the mean column density of star-forming galaxies adopted fromTchernyshyov et al. (2022, gray diamonds).Middle panel: Total O VI gas mass within  vir (black circles) or 3  vir (red squares).Extending to ≈ 3  vir , the total O VI mass is a factor of ≈ 2 − 4 larger than the mass within  vir for all galaxies.As a comparison, we include the expected total O VI mass within  vir (the dashed line) and 3  vir (the dotted line) based on a model assuming a cosmic baryonic fraction,   = 0.156 and an anticipated fraction of baryonic mass in O VI,  OVI  CGM  O / O,⊙ = 0.01.Adopting typical  CGM and  O / O,⊙ , we obtain  OVI ≈ 0.1 to reproduce the observed O VI content in the CGM of sub- * galaxies, suggesting that O VI-bearing gas is the dominant phase in these galaxies (see the text for details).Right panel: Ne VIII mass, similar to the middle panel.The Ne VIII mass is calculated empirically, which may be driven by the highest column density absorbers at small  proj / vir (see the text for details).
Figure15.Comparison of dependence of  NeVIII / OVI on  proj / vir between data and models.Photoionization-dominated models predict increasing of  NeVIII / OVI at larger  proj / vir in (i.e., low-pressure models in the left panel, S18; and models for low-mass log  star /M ⊙ ≲ 9 in the right panel, QB18).The warm-hot gas in cooling gas or virialized gas suggests roughly constant  NeVIII / OVI over different radii (i.e., high-pressure models in the left panel and models for massive log  star /M ⊙ ≳ 10 in the right panel).For observations, only absorption systems with at least O VI or Ne VIII features are included to ensure meaningful constraints.The small sample size limits the ability to distinguish between models.
Figure A.1.Similar to Figure 4 but for the observed constraints on the Ne VIII column densities.Unlike O VI, few galaxies/galaxy groups display detectable Ne VIII absorption.No clear trend can be established in any panels.
Summary of the general galaxy characteristics of the CUBS sample at 0.4 ≲  ≲ 0.7, including virial-normalized projected distance ( proj / vir ), stellar mass ( star ), and star formation rate (SFR).Derived stellar masses have systematic uncertainties of 0.2 dex over the covered  star .For each galaxy group, the open red circle marks the galaxy with the smallest  proj / vir from the QSO sightline.In this sample, most galaxies are star-forming with specific SFRs of ≥ 10 −11 yr −1 .In addition, the entire sample is split into four sub-samples in the following analysis, i.e., the dwarf, sub- * , massive star-forming, and massive quiescent galaxy samples (see Section 4.2), which are classified using the dashed blue boundaries in the right panel.
, and the CGM 2 survey

Table 1 .
Summary of statistics in different galaxy associations Dependence of  OVI and  NeVIII on  proj or  proj / vir .
Generalized Kendall correlation coefficient  and corresponding significance.
Burchett et al. (2019)022density on  star for O VI (left panel) and Ne VIII (right panel).Recall that in the presence of neighbors, we associate the observed line-of-sight absorption properties with the galaxy at the smallest  proj / vir .Measurements from the literature, including COS-Halos(Werk et al. 2013), J17(Johnson et al. 2017), COS-LRG(Zahedy et al. 2019), CASBaH(Burchett et al. 2019), and CGM 2(Tchernyshyov et al. 2022) are also included.In these samples, the maximum  proj / vir are all smaller than 3. Theoretical models adopted from QB18 are plotted for comparisons (curves).Both observations and theoretical models indicate that the observed ion abundances peak at ∼ 10 10 M ⊙ for both O VI and Ne VIII.For the CASBaH Ne VIII sample, reported Ne VIII systems with significant contaminations inBurchett et al. (2019)are marked as uncertain systems in red squares (see text for details).One outlying strong Ne VIII absorber (circled in red) near a massive galaxy of log  star /M (Tripp et al. 2011;Burchett et al. 2019nucleus (AGN) is likely associated with AGN outflows(Tripp et al. 2011;Burchett et al. 2019).
Radial profiles of column density  OVI , covering fraction , and velocity dispersion  OVI of O VI-bearing gas for low-mass dwarf, sub- Johnson et al. 2017)Werk et al. 2013) quiescent galaxies from left to right columns, respectively.In this plot, we include the literature samples in the analysis, the J17 dwarf sample (diamonds;Johnson et al. 2017),COS-Halos (hexagons;Werk et al. 2013), and COS LRG (squares;

Table 2 .
The best-fit models of the radial profiles of the column density for different galaxy samples.

Table 3 .
Summary of the observed Ne VIII covering fraction (%) Comparison of dependence of  NeVIII / OVI on  proj / vir between data and models.Photoionization-dominated models predict increasing of  NeVIII / OVI at larger  proj / vir in (i.e., low-pressure models in the left panel, S18; and models for low-mass log  star /M ⊙ ≲ 9 in the right panel, QB18).The warm-hot gas in cooling gas or virialized gas suggests roughly constant  NeVIII / OVI over different radii (i.e., high-pressure models in the left panel and models for massive log  star /M ⊙ ≳ 10 in the right panel).For observations, only absorption systems with at least O VI or Ne VIII features are included to ensure meaningful constraints.The small sample size limits the ability to distinguish between models.Open symbols represent upper limits in Ne VIII, while O VI is a detection.The filled red circle with a downward arrow is s18 at  = 0.4801, for which both Ne VIII and O VI are detected but the O VI is exceptionally strong and saturated.The full sample is divided into a low-mass star-forming sample with log  star /M ⊙ ≤ 10 (blue diamonds), massive star-forming (red circles), and quiescent samples (red squares) with log  star /M ⊙ > 10.

•
The warm-hot CGM probed by O VI and Ne VIII dominates the CGM of sub- * galaxies, exhibiting the highest area-weighted mean column density within  vir (Figure14).Adopting a typical metallicity and CGM mass fraction, we show that ionization fractions of O VI and Ne VIII are comparable with the peak ionization fraction in CIE or PIE models, suggesting the warm-hot CGM probed by O VI and Ne VIII is the dominant phase in halos of sub- * galaxies.