Detection of a Multiphase Intragroup Medium: Results from the COS-IGrM Survey

We detected Lyα absorption features in 12 of our 18 galaxy groups, with four groups having accompanying Lyβ. Figure 3 presents our H i column density measurements as a function of the halo mass of the group. We found that lower mass halos exhibit a slightly narrower range of Lyα column densities compared to higher mass halos. We see no evidence of varying column densities of Lyα absorption between CGM+IGrM and IGrM sightlines. We find that there appears to be two main populations of data points: one with moderate column densities, log[N(H i)] ∼ 14.5–15, and another set clustered around log[N(H i)] ∼ 13. These groupings may indicate that the QSO sightlines are passing through patchy, nonuniform H i clouds as opposed to a continuous distribution with a decreasing density gradient.

Zoom In Zoom Out Reset image size

One sightline, J1127+2654 (Figure 2.5), was seen to have saturated Lyα and Lyβ absorption. The column density of this absorption feature should be treated as a lower limit due to the absorption line occupying the flat regime of the curve of growth. This sightline probes the IGrM as well as the CGM of the closest galaxy to the sightline, which is at ∼70 kms⁻¹ from the group’s systematic velocity and an impact parameter of ∼119 kpc. This saturated H i feature is composed of three components centered at −59, 32, and 116 kms⁻¹, respectively from the systemic velocity of the group, with the middle component being the strongest. The low impact parameter of ∼119 kpc from the closest galaxy to the sightline suggests that we are likely probing the CGM of this galaxy. The location of the QSO with respect to the group member in the full environment plot in the Appendix.

Figure 4 shows the distribution of Lyα column density as a function of impact parameter (ρ_QSO) in the left panel and as a function of normalized impact parameter in the right panel (ρ_QSO/R_vir). We overplot the Stocke et al. (2019) sample as gray squares in Figure 4. We find no statistically significant correlation between the column density of Lyα absorbers and the QSO impact parameter using the Kendall’s Tau correlation test provided in the Astronomy SURvival Analysis (ASURV) package (Feigelson & Nelson 1985; Isobe et al. 1986; Isobe & Feigelson 1990). Using the ASURV Kendall’s Tau test, we observed no correlation between the column density of Lyα absorption and IGrM or CGM+IGrM sightlines. Most of the stronger Lyα absorbers (log[N(H i)] ∼ 14.5–15) are seen in sightlines that pass through only the IGrM.

Zoom In Zoom Out Reset image size

The origins of cooler, partially neutral gas are not well understood. Possible scenarios include remnants of tidally stripped structures (Davis et al. 1997; Bekki 2009; Borthakur et al. 2010; Nestor et al. 2011; Gauthier 2013; Fossati et al. 2019; Chen et al. 2019; Péroux et al. 2019), in situ condensation (Voit 2019), outflowing material from star-forming galaxies (Veilleux et al. 2005; Tripp et al. 2011; Nielsen et al. 2018; Frye et al. 2019) and/or cold gas accretion from the IGM (Kereš et al. 2005; Vogt et al. 2015; Bielby et al. 2017; Borthakur et al. 2019). These processes are all capable of producing strong Lyα absorption. On the other hand, lower column density absorbers and nondetections are seen in sightlines irrespective of whether they probe the CGM or just the IGrM. The presence of weak Lyα absorbers (≤10¹⁴ cm²), including several nondetections, indicates that the sightlines pass through an ionized medium. In those sightlines, we do not find O vi or N v, indicating that the medium must be at temperatures greater than 10⁶ K, assuming collisional ionization equilibrium. This phenomena might be related to the inability for galaxies in groups to continue the gas accretion necessary to fuel star formation. This has been observed in galaxy clusters (Yoon & Putman 2013; Gim et al. 2021), and when scaled to the group environment, could indicate the beginning of the preprocessing and quenching processes (Zabludoff & Mulchaey 1998; McGee et al. 2009; Wetzel et al. 2013; Schawinski et al. 2014; Crossett et al. 2017; Kacprzak et al. 2021).

Apart from Lyα, we also observe other transitions like Si ii C ii and Si iii tracing gas up to the ionization potentials of 33.5 eV. C ii and Si iii are the most commonly detected low and intermediate-ionization species that are seen in five of the 18 sightlines. This is consistent with other studies of the CGM and IGM (Collins et al. 2009; Shull et al. 2009; Lehner et al. 2012, 2015; Richter et al. 2016; Borthakur et al. 2016). All of these absorbers are associated with strong, most likely saturated Lyα absorbers.

We detect O vi absorbers in eight and N v absorbers in two out of our 18 sightlines. Each N v absorption feature was also present with O vi absorption. Of the eight detections, five of the sightlines were pure IGrM sightlines, while three sightlines were CGM+IGrM. We detected both the transitions of the O vi doublet for two sightlines. Five sightlines showed the stronger of the two transition at O vi λ1031 Å, while one sightline showed absorption at O vi λ1037 Å with an intervening absorption line at the expected position of O vi λ1031 Å. As noted earlier, the redshift range places the O vi doublet at observed wavelengths lower than 1215 Å and hence we do not expect any misidentification of lower redshift Lyα absorbers as O vi. Figure 5 shows the column density of O vi absorbers from the COS-IGrM survey as well the survey by Stocke et al. (2019). Over the entire halo mass range, the O vi and N v detection rates are 44 ± 5% and 11 ± 5%, respectively.

Zoom In Zoom Out Reset image size

Figure 6 shows the O vi detections as a function of QSO impact parameter from the center of the group. We observe a flat distribution of detections from 0.1–1.5 R_vir, which suggests that the sightlines may be probing gas that is not at the virial temperature. Since X-ray studies (Helsdon & Ponman 2000b; Mulchaey 2000; Robson & Davé 2020) show temperature gradients in galaxy groups, the observed flat distribution of O vi detections provides evidence that O vi is not tracing the bulk component of the IGrM.

Zoom In Zoom Out Reset image size

Another indication that the OVI absorbers in our sample is tracing a mix of hot and cool gas is the fact that while all the systems that show O vi also show Lyα, but the kinematics can be quite different. For example, six of the eight sightlines with O vi detections show Lyα absorption with the same (or slightly offset) velocity centroid, while the remaining two sightlines have Lyα at a much larger (≳200 kms⁻¹). A single ionization process could not produce both Lyα and O vi at the levels detected in some cases. Therefore, for these two different species to be observed within a close velocity offset, multiple clouds must be present, which indicates hot and cool gas in close proximity.

In this section, we use the kinematics of the absorbers to explore further the nature and distribution of gas as traced by absorption. First, we use the velocity spread of the absorbers to ascertain if the absorbing gas is bound to the group. Figure 7 (left) shows the absorption lines detected in the COS spectra at velocity relative to the systemic velocity of the group ⁹ , which is depicted by the dashed line at v − v_sys = 0. Each species is color coded with the dominant absorption feature indicated by a larger halo around the data point. In total, there are 70 absorbers depicted in the plot. 29 and 12 of those are Lyα and O vi, respectively, while the remaining represent the other species discussed above. The solid lines show the escape velocity as a function of halo mass and virial radius. The right panel of Figure 7 includes the data from Stocke et al. (2019), which extends the dynamic range of halo masses.

Zoom In Zoom Out Reset image size

The vast majority of the absorption features are bound to the gravitational potential of the groups. There are nine out of 70 absorbers from five sightlines (J0841+1406, J1017+4702, J1020+1003, J1216+0712, and J1339+5355) that have sufficient velocities, relative to the group, to escape the gravitational potential. These are composed of five Lyα, two O vi, one C ii, and one Si iii absorbers. The same trend is observed with the data from Stocke et al. (2019) as only two absorption features (1 Lyα and 1 O vi) are observed at high enough velocity offsets to escape the group.

Among the 12 O vi absorbers detected in eight sightlines, 83% (10/12) are gravitationally bound to their group halo and only two absorbers show velocities greater than the escape velocity. One of the unbound O vi absorbers is seen in the sightline toward J0841+1406 passes through the CGM of a 4.4 L_* galaxy at 145 kpc. The velocity offset between the O vi absorber and this is ∼650 kms⁻¹. Interestingly, the O vi absorber does not have a corresponding Lyα absorber. The Lyα absorber is seen in this group is more than 600 kms⁻¹ offset from the O vi absorption feature and is offset by ∼150 kms⁻¹ to the closest member galaxy. Hence, the O vi absorber could be tracing infalling or outflowing gas. The large Doppler width of the O vi absorber of b = 81.6 kms⁻¹ suggests that this absorber is a tracing material similar to the warm, hot intergalactic medium (WHIM; Cen & Ostriker 1999; Davé et al. 2001). While this Doppler width is consistent with WHIM-like material, we cannot conclusively rule out the possibility that this absorber is not related to the overall gas phase. As stated in Oppenheimer & Davé (2009), and references therein, O vi with these Doppler widths cannot be only a result of thermal broadening, but also requires a kinematic origin. This leaves some uncertainty as to the exact gas phase due to the lack of other metal-line transitions.

The second O vi absorber with a large velocity offset relative to the group is in the sightline toward J1017+4702 (Figure 2.2). The velocity offset of this O vi absorber is sufficient to escape the gravitational potential of the group. This sightline also exhibits a saturated Lyα profile with a column density, logN(HI) > 15.2. Since Lyβ is blended with an intervening absorber, we cannot utilize it to help constrain the column density. Interestingly, in this case, the sightline does not pass within the virial radius of any spectroscopically confirmed L_* galaxy and is at 926 kpc ( ≡ 1.6 R_vir) from the group center. However, there is one galaxy with matching photometric redshift at 90 kpc from the sightline, which might be the host of this saturated absorption system. It also has a neighbor with similar photometric redshift at an impact parameter from the QSO sightline of 212 kpc. Future spectroscopic redshift measurements are needed to confirmation the association between this neighboring galaxy and the absorption features present in this sightline. If the photometric redshifts are confined, then these galaxies would most likely be part of the group.

Figure 8 (left) shows a histogram of all of the H i and O vi absorbers as a function of absolute velocity offset from the group center. This histogram quantitatively shows that the majority of both H i and O vi absorbers are gravitationally bound to the group, while ∼10% are observed to have velocities high enough to escape the group potential. These could either indicate infalling clouds or outflows. Therefore, we conclude that the large majority of the absorbers are tracing the cooler, gravitationally bound gas, which is centered well within the group’s escape velocity. A similar conclusion was made by the Stocke et al. (2019) study, which concluded that galaxy groups primarily act as closed boxes for galactic evolution at low redshifts. However, the IGrM should still experience outside-in enrichment from the IGM (Tegmark et al. 1993; Scannapieco et al. 2002; Oppenheimer et al. 2012). While the source of the initial IGM enrichment at early epochs is model dependent, each model of outside-in enrichment predicts that structures can regain metals that were expelled at earlier times.

Zoom In Zoom Out Reset image size

We also investigate the velocity of the absorbers with respect to the nearest, spectroscopically confirmed member galaxy in projection. This is illustrated in the right panel of Figure 8 where H i and O vi absorption features are shown by a histogram as a function of absolute velocity from the nearest galaxy, which could range between 0 and 1600 kms⁻¹. For both H i and O vi absorbers, we see that more than 50% are within 200 kms⁻¹ of the closest galaxy to the QSO sightline. The fraction increases to 70% within 300 kms⁻¹, which is less than the escape velocity of an L_* galaxy. This indicates that these absorption features may originate from gas in the CGM of member galaxies in the group. On the other hand, the absorbers at higher velocity offsets are most likely tracing patchy components of the IGrM, or inflows/outflows from individual group members.

In order to look at the overall ionization state of the IGrM, the ratio of O vi to H i was examined for each of the 18 sightlines in the COS-IGrM sample (Figure 9). For these ratios, only the components of H i found at the same velocity as O vi were used. If there were no O vi or H i detections, then an upper limit was used. Sightlines with no Lyα or O vi absorption were not included in this analysis. The sightlines with O vi column densities greater than the H i columns shows that there is highly ionized gas throughout the IGrM, while the lack of a correlation between the ratio of column densities and impact parameter shows that there is no significant dependence of ionization state on normalized impact parameter.

Zoom In Zoom Out Reset image size

Out of the 12 sightlines that show Lyα absorption, nine of those sightlines show evidence of multiple metal-line species detected in absorption that allows us to model the ionization state of the gas. Of these nine sightlines, seven clearly depict multiphase gas, where various metal-line species are present in varying levels suggesting that the components have very different ionization states. The presence of these multiple components in most of the sightlines indicates that the absorption is associate with pockets of gas that maybe cooler than the rest of the media (and possibly more dense if they are in pressure equilibrium). Therefore, we believe that our data is primarily tracing a complex multiphase media, which cannot be described by a single ionization process. In Table 3, we present the probable ionization process for each group, based upon the observed spectra.

For ionization modeling, the primary interest was to determine if any of the absorption lines from the COS-IGrM sample are consistent with photoionization, collisional ionization, or inconsistent with either process. For CIE modeling, the ratio of Lyα to O vi absorption at 50% solar was examined over a range of temperatures. If the observed column density ratio was consistent with CIE predictions, then it was noted that the absorption features were consistent with CIE. Since CIE predicts broad, shallow O vi without the presence of lower ionization state transitions, only those sightlines that had Lyα and O vi were examined for consistency with CIE models.

The photoionization modeling was inherently less certain due to unresolved, blended components, and a lack of multiple metal-line species in the majority of sightlines. We used CLOUDY (Ferland et al. 2013) with a Haart–Madau background and a total hydrogen density grid (log[n(h)] from [−5, −2] particles cm⁻³) in 0.5 dex increments. The total neutral column density was fixed to the observed Lyα column density. If a point in the grid existed where the column density ratio each metal species was consistent within the same density grid point, then we stated that the absorption components were consistent with photoionization.

Some sightlines show absorbers that match the ratios and strengths predicted by CIE (Gnat & Sternberg 2007) for a hot ≈10^5.5 K medium. For example, the sightline J1343+2538 (Figure 2.9) passing through a group at an impact parameter of 346 kpc ( ≡ 0.9 R_vir), shows broad Lyα (b_{Ly α} = 47 kms⁻¹) along with O vi suggestive of hot media (Richter et al. 2006). The ratio of O vi to Lyα column density of 0.65 dex is consistent with temperatures of 10^5.3−5.4 K or 10^5.9 K for 0.5−[1 Z/H]_⊙ with temperature inverse proportional to the metallicity for the same column density ratio. The choice of this metallicity range is based on measurement from X-ray studies for groups of galaxies that typically find the average metallicities of the X-ray bright IGrM to be 0.4−0.6 [Z/H]_⊙ (Helsdon & Ponman 2000b). We do not have strong metallicity constrains for non-X-ray bright groups, so we adopt the metallicities seen in X-ray studies.

Another example of collisional ionized gas are seen in the sightline toward group J1301+2819 (Figure 2.7). In addition to tracing hot gas, this sightline shows a mix of multiple ionization states at slightly different velocities possibly tracing a multiphase medium. The Lyα feature shows three components—two strong components with associated Lyβ and one weak component with log N(HI)=13.05. The strong components are seen in both N v and O vi (the components are blended in O vi), whereas the weakest component is most prominent in O vi. This indicates that the different components trace different ionization states. For the weakest component the ratios of O vi and Lyα are in agreement with collision ionization equilibrium model. The ratio of column densities, logN(OVI) − logN(HI) = 0.60, corresponds to gas at 10^5.3 or 10^5.9−6 K at 50% solar metallicity. At lower metallicities, the observed ratio of column densities between O vi and Lyα would indicate a slightly higher temperature.

On the other hand, the stronger components are quite puzzling. If photoionization was responsible for the observed ionization states, there should be other low-ionization transitions detected besides H i such as Si ii, C ii, and Si iii. Despite these transitions not being present at detectable levels in the spectra, the N v to O vi ratio is consistent with photoionization (Table 3). Therefore, we are unable to conclusively state the process behind the observed column densities, it is most likely a mixture of multiple ionization processes.

A similar case of multiphase media is seen in J1424+4214 (Figure 2.11), which shows two distinct ionization states with a velocity separation of about 45 kms⁻¹: a less ionized system at ∼ −55 kms⁻¹ and a highly ionized state at ∼ −100 kms⁻¹. One component is seen in lower ionization transitions like Lyα, C ii, and Si iii, while the second components is seen in higher ionization transitions like N v, O vi, as well as Si iii that show a weak feature suggesting Si iii is not the dominant ionization state of silicon. The ratio of these lines indicate that the two components are at very different ionization states, thus suggesting that the IGrM is multiphase and cannot be described by a single ionization state. While the ionization processes for each of the two components cannot definitively be determined based upon the data at hand, the component centered at ∼−100 kms⁻¹ is consistent with CIE at ∼10^5.2−5.3 K, while the component at ∼−55 kms⁻¹ is consistent with photoionization based upon the C ii to Si iii line ratio.

Another sightline of interest is toward the group J1127+2654 (Figure 2.5). This sightline exhibits a saturated Lyα profile with column density, logN(HI) > 18.3, which makes it a Lyman-limit system (LLS; Lanzetta et al. 1995, and references therein). The absorber complex shows multiple components commonly associated with extended disk (Lehner et al. 2009), inner CGM (Werk et al. 2014; Armillotta et al. 2017; Fielding et al. 2020), and/or tidal structures (Frye et al. 2019). This QSO passes within ∼119 kpc from a known group member; however, higher resolution spectroscopy and a rotation curve is necessary to confirm the connection between this LLS and the member galaxy. Similarly, due to the blending of O vi components in this QSO spectra, we cannot rule out photoionization as the primary ionization mechanism for these absorption lines.

Lastly, the sightline toward J1017+4702 (Figure 2.2) shows that Lyα is saturated at the same position as C ii, Si iii, and broad, shallow O vi. Photoionization alone cannot produce broad, shallow O vi and CIE does not predict the existence of saturated Lyα and broad O vi at a single temperature. Since this is an IGrM sightline, the broad O vi may be tracing a hotter component; however, the lower transitions show evidence of cooler gas at the same velocity. Photoionization modeling with CLOUDY (Ferland et al. 2013) showed that the lower velocity components of C ii and Si iii are consistent with photoionization, while the higher velocity components are inconsistent with photoionization. Overall, it is clear that the ionization states of these groups are complex and the ionization processes behind the multiphase gas cannot always be explained by either photoionization or CIE. Future studies with better modeling, higher resolution observations, and broader wavelength coverage can help shed insight into these ionization processes.

We differentiate between CGM and IGrM absorption in galaxy groups by comparing our O vi detections to those detected in the COS-Halos survey (Tumlinson et al. 2011). The COS-Halos survey discovered that a strong correlation between O vi in the CGM and the star formation rate of galaxies existed. In order to compare the our data with the COS-Halos sample, we determined the galaxy closest to the QSO sightline and then matched the galaxy to the star formation rate from the MPA-JHU DR7 ¹⁰ galaxy catalog (Brinchmann et al. 2004).

Figure 10 shows our data along with those from the COS-Halos survey. The CGM+IGrM sightlines, shown as deep blue circles, have a clear host galaxy as the sightline passes within the viral radius (assuming an isolated halo) of a member galaxy. The pure IGrM sightlines do not pass through the CGM of the nearest galaxy (shown in green circles). Therefore, they are not applicable for comparison with the COS-Halos sample; nevertheless, we show them on the plot for comparison with the CGM+IGrM subsample. It is worth noting that even the blue points that do probe the CGM pass through the outer CGM (ρ > 110 kpc) and not the inner CGM, like the COS-Halos sample.

Zoom In Zoom Out Reset image size

Overall, we do not see a trend of higher O vi levels as a function of the specific star formation rate (sSFR) or the star formation rate of the nearest galaxy. This is not surprising considering the impact parameters. However, it does suggest that the origin of our O vi absorbers are probably not related to the star formation activity of individual galaxies, and therefore, we are most likely not tracing the CGM gas physics as seen in the COS-Halos survey, but instead, a more group-related phenomena.

While we can confidently rule out the CGM of L_⋆ galaxies as the source of O vi absorbers, there could potentially be smaller galaxies that may be present closer to the sightline. A much deeper redshift survey of galaxies in the vicinity of the QSO sightlines would enable us to quantify the presence of low-mass galaxies. Nevertheless, sub-L_⋆ galaxies are not expected to have significant metal reservoirs beyond their inner CGM (ρ > 0.5 R_vir) (Bordoloi et al. 2014). Hence, it is not likely that the CGM of sub-L_⋆ galaxies could dominate the O vi detected in our sample. On the other hand, material spread out by tidal interactions can have a large cross section on the sky and may survive as faint diffuse partially neutral gas in the IGrM for hundreds of millions of years (Borthakur et al. 2010, 2015).

Our sample shows a larger fraction of green valley galaxies than typically observed in the universe. Jian et al. (2020) finds that on average, 20% of galaxies populate the green valley and the majority of those are field galaxies and not those found in more dense environments. Observing ∼33% of the closest galaxies to the QSO sightline in our sample to be in the green valley reinforces the idea that galaxy group environments may act as important sites where the process of quenching is active (Wetzel et al. 2012, 2013). The role of the IGrM or the CGM in turning these galaxies green is still unclear.

Another possibility for the origin of O vi in the IGrM could be due to active galactic nuclei (AGN) activity. In order to address this, used the emission line ratios from the MPA-JHU ¹¹ DR7 catalog to construct a Baldwin–Phillips–Terlevich (BPT) diagram (Baldwin et al. 1981) so that star-forming galaxies could be separated from AGN using the demarcation as defined by Kauffmann et al. (2003). The locations of the COS-IGrM sample compared to the SDSS DR7 sample from the MPA-JHU catalog are shown in Figure 11 as colored circles. 15 out of the 18 groups in our sample had emission line measurements for the closest galaxy to the QSO sightline and therefore, could be included in the BPT diagram. The color of the circle represents O vi detections (orange) versus nondetections (magenta). The size of the symbol represents the impact parameter of the sightline, where larger sizes indicate small impact parameter. We do not find any systematic overdensity of O vi detection or nondetection in sightlines with or without AGN. Therefore, we conclude that AGN activity is not the primarily contributor of O vi in the IGrM.

Zoom In Zoom Out Reset image size

In order to look for fainter gas associated with the IGrM, we stacked sightlines centered around the group systemic velocity for Lyα and O vi. For each species, stacks were created using all 18 sightlines as well as subsets of CGM + IGrM or IGrM only sightlines. These stacks are shown in Figure 12 along with the number of sightlines going into each subset. The equivalent widths were measured for velocities within ±400 and ±800 kms⁻¹ from the group’s systematic redshift. These values are listed as W₈₀₀ and W₁₆₀₀ respectively.

Zoom In Zoom Out Reset image size

The Lyα stacks show net absorption centered around zero velocity for the CGM +IGrM subset, and absorption corresponding to higher velocity offsets in the IGrM stack. When we stack the full COS-IGrM sample, we observe a combination of the two subsets meaning that the IGrM in our sample is traced by two distinct regions: gas at the systematic velocity of the group as well as gas that is at larger velocities than the group’s systemic velocity. This could perhaps be a result of warmer gas condensing in the outskirts and falling back toward the center of the group.

The O vi stacks show weak net absorption throughout all the sightlines. However, there is absorption in the IGrM sightlines. Both the CGM + IGrM stack and the pure IGrM stack show that the majority of the absorption is within of the central 800 kms⁻¹ of the group. The covering fraction of the IGrM stacks is more uniform than the CGM stacks as there is net absorption throughout the ±800 kms⁻¹. Nondetection of O vi in the full stack indicates that there is not a volume filling phase of the IGrM, but instead, an O vi traced IGrM is a more transient phenomena.

In order to accurately and completely characterize the IGrM, higher ionization species should be targeted in future studies. From the COS-IGrM survey, it is clear that O vi is not an ideal tracer of the IGrM. Since O vi is only observed in eight out of our 18 groups, the predominant, volume filling component of the IGrM should exist at a hotter temperature for galaxy groups at halo masses between 12. M_⊙ < log[M_halo] <14.7 M_⊙. We can rule out a pervasive media of the IGrM at cooler temperatures due to the weak low and medium ionization potential lines observed in our data. Therefore, to observe the dominant phase of the IGrM, future studies should look to O vii, O viii, Ne iii, and Mg x, which are stronger transitions at temperatures of 10^6.5–10^7.5 K.

Once the pervasive phase of the IGrM is observed, it can be combined with other studies to fully characterize the IGrM of galaxy groups. Simulations by Davé et al. (2002), Le Brun et al. (2017), and Farahi et al. (2018) have made substantial progress in determining consistent scaling relations for lower mass halos that are consistent with observational programs such as those by Sun et al. (2003), Eckmiller et al. (2011), Babyk et al. (2018), and Lovisari et al. (2020). Additionally, the thermal SZ effect is being utilized in order to determine the baryonic content of lower mass galaxy clusters and groups (Vikram et al. 2017; Henden et al. 2019; Pratt & Bregman 2020, and references therein). By the combination of these results, these hot halos can be fully characterized.