Discovery of a Very Hot Phase of the Milky Way Circumgalactic Medium with Non-solar Abundance Ratios

To detect and characterize the absorption lines, we need to determine the source continuum first, which we model as a power law plus blackbody spectrum, absorbed by the cold and warm ISM of the Milky Way (model ISMabs∗(powerlaw+bbody)in XSPEC). ISMabs accounts for the neutral, singly, and doubly ionized metal lines and takes care of the oxygen and neon edges (Gatuzz et al. 2016). We allowed the column densities of H, O (${\rm{O}}\,{\rm{I}}$, ${\rm{O}}\,{\rm{II}}$, ${\rm{O}}\,{\rm{III}}$), Ne ($\mathrm{Ne}\,{\rm{I}}$, $\mathrm{Ne}\,{\rm{II}}$, $\mathrm{Ne}\,{\rm{III}}$), and Fe to vary; other elements do not affect the spectra significantly, so we fix their column densities at the relative solar abundances. This resulted in good fit of the continuum, but absorption lines from highly ionized elements were clearly seen in the residuals. We modeled these lines with Gaussian profiles with central wavelengths fixed at the known z = 0 values of respective ions. We detect the ${\rm{N}}\,{\rm{VI}}$ Heα and Heβ, ${\rm{N}}\,{\rm{VII}}$ Lyα, ${\rm{O}}\,{\rm{VII}}$ Heα, and Heβ, ${\rm{O}}\,{\rm{VIII}}$ Lyα, $\mathrm{Ne}\,{\rm{IX}}$ Heα, and $\mathrm{Ne}\,{\rm{X}}$ Lyα lines at 3.4σ, 2.6σ, 2.3σ, 3.9σ, 1.5σ, 2.4σ, 2.4σ, and 3.4σ significance, respectively.⁸ We calculate the column density of these lines from their respective equivalent widths assuming that they are in the linear regime of the curve of growth (Table 1). Also, we repeat the analysis by removing the channels at and around the wavelengths of expected transitions to obtain the continuum, and add the channels back to calculate the equivalent widths. The equivalent width values are similar to those obtained earlier. This confirms that the continuum is not incorrectly estimated due to the presence of absorption lines, and the equivalent widths are not over/underestimated.

Our detected absorption line strengths suggest several interesting aspects of the observed system. In collisional ionization equilibrium (CIE),⁹ the fractional ionization of ${\rm{O}}\,{\rm{VII}}$ peaks (${f}_{{\rm{O}}{\rm{VII}}}\geqslant 0.9$) in the temperature range 10^5.6−6.2 K, and that of ${\rm{O}}\,{\rm{VIII}}$ peaks at ≈10^6.4 K. Similarly, the fractional ionization of ${\rm{N}}\,{\rm{VI}}$ peaks (${f}_{{\rm{N}}{\rm{VI}}}\geqslant 0.9$) at 10^5.4−6.0 K and of ${\rm{N}}\,{\rm{VII}}$ at ≈10^6.2 K, the fractional ionization of $\mathrm{Ne}\,{\rm{IX}}$ peaks (${f}_{\mathrm{Ne}{\rm{IX}}}\geqslant 0.9$) at 10^6.1−6.3 K and of $\mathrm{Ne}\,{\rm{X}}$ at ≈10^6.6 K. The column density ratio of the same element's two ions can uniquely determine the temperature. The ${\rm{N}}\,{\rm{VI}}$ to ${\rm{N}}\,{\rm{VII}}$ ratio implies T = 10^5.98−6.09 K, ${\rm{O}}\,{\rm{VII}}$ to ${\rm{O}}\,{\rm{VIII}}$ ratio implies T = 10^6.14−6.26 K, while the $\mathrm{Ne}\,{\rm{IX}}$ to $\mathrm{Ne}\,{\rm{X}}$ ratio implies T = 10^6.50−6.71 K. Clearly, the temperature windows do not overlap with each other. This already suggests that a single-temperature model may be inadequate to characterize the observed spectra. Second, the column density of neon and nitrogen are as large as that of oxygen: $\tfrac{N({\rm{N}}\,{\rm{VI}})+N({\rm{N}}\,{\rm{VII}})}{N({\rm{O}}\,{\rm{VII}})+N({\rm{O}}\,{\rm{VIII}})}$ = $0.8\pm 0.4,\tfrac{N(\mathrm{Ne}\,{\rm{IX}})+N(\mathrm{Ne}\,{\rm{X}})}{N({\rm{O}}\,{\rm{VII}})+N({\rm{O}}\,{\rm{VIII}})}=1.4\pm 0.6$, even though oxygen is far more abundant than neon and nitrogen in solar composition (A_O,⊙ = (4.9 ± 0.6) × 10⁻⁴, A_Ne,⊙ = (0.8 ± 0.2) × 10⁻⁴, A_N,⊙ = (0.7 ± 0.1) × 10⁻⁴; Asplund et al. 2009). This suggests that the neon and nitrogen are super-solar relative to oxygen in the observed phase. $\mathrm{Fe}\,{\rm{XVII}}$–Fe xxiv lines and the Fe unresolved transition array (UTA) of $\mathrm{Fe}\,{\rm{XVI}}$–$\mathrm{Fe}\,{\rm{XVIII}}$ are not detected at better than 1σ significance. This suggests α-enhancement relative to iron.

To confirm and quantitatively determine the suggestive results obtained in Section 2.1, we now model the data in detail. We use the hybrid-ionization model (models of collisionally ionized gas perturbed by photoionization by the meta-galactic radiation field, at a given redshift) PHASE (Nicastro et al. 2018) to fit the data and calculate the temperature, equivalent H column density, and the relative abundance of the metals in the Galactic warm-hot/hot absorbers. The model assumes relative abundances and absolute metallicities to be solar by default, but allows them to vary between 0.01 and 100 times solar, independently for each elements from He to Ni (He, C, N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe, and Ni).

As N, O, and Ne have prominent absorption features (Figure 1), and Fe lines (primarily, $\mathrm{Fe}\,{\rm{XVII}}$ at 12.123 Å, and $\mathrm{Fe}\,{\rm{XXI}}$ at 12.165 Å) can contaminate the Ne lines through blending, we vary the abundance of N, O, Ne, and Fe only. The spectrum is insensitive to the abundance of other elements, so we fix their abundance with respect to oxygen at solar. As noted above, the CGM is assumed to be in CIE; therefore, we fix the photoionization parameter¹⁰ to the lowest possible value allowed by PHASE, at U = 10⁻⁴. This ensures that photoionization is negligible and that the gas is collisionally ionized. To begin with, we fit the spectra with a single-temperature PHASE model with solar composition: ISMabs*(powerlaw+bbody)*PHASE. The fit is not very good (χ²/dof = 2563.54/2479), showing that the abundance ratios are likely non-solar. Therefore, we fit the spectra with a single-temperature model, but with non-solar composition; this improves the fit (χ²/dof = 2548.07/2476), but it cannot reproduce all the detected lines in the spectra; in particular, it does not account for the $\mathrm{Ne}\,{\rm{X}}$ line and it underestimates the ${\rm{O}}\,{\rm{VIII}}$ absorption. Therefore, we fit the spectra with two PHASE models: ISMabs∗(powerlaw+bbody)∗PHASE1∗PHASE2. We allow the H column density and the temperatures in two phases to be different, but do not force them to be different. However, we force the relative abundances (N/O, Ne/O, O/Fe) to be same in both phases, which implies similar chemical composition, and hence similar sources of metal enrichment. The best-fitted model (${\chi }_{\nu }^{2}=1.02714;$ dof:2471, P(χ², dof) = 0.622 × P_max) reproduces the lines found in the previous section well (Figure 1, Table 1).¹¹ The best-fitted values of the parameters in PHASE models are quoted in Table 2; the errors are quoted at 3σ intervals, i.e., at 99.73% confidence.

Table 2.  Parameters of the Best-fitted PHASE Model (Uncertainties are Represented as 99.73% Confidence Intervals, and Abundances are in log₁₀ with Respect to Solar Composition, According to the Prescription of Asplund et al. 2009)

Parameters	Values
log T1(K)	${6.11}_{-0.49}^{+0.19}$
log T2(K)	${7.06}_{-0.72}^{+0.80}$
[Ne/O]	${0.72}_{-0.25}^{+1.57}$
[N/O]	${0.75}_{-0.25}^{+1.57}$
[O/Fe]	${0.86}_{-0.33}^{+0.67}$
[Ne/Fe]	${1.59}_{-0.38}^{+1.16}$
[N/Fe]	${1.62}_{-0.30}^{+0.56}$

Download table as:  ASCIITypeset image

The column densities of the detected ions from the two-temperature PHASE model are presented in Table 1 (fifth and sixth columns). The sum of these column densities is given in the seventh column. Comparing these with the column densities estimated from the curve-of-growth analysis (last column), we find that the two are in excellent agreement for ${\rm{O}}\,{\rm{VII}}$ and the H-like ions. ${\rm{N}}\,{\rm{VI}}$ and $\mathrm{Ne}\,{\rm{IX}}$ columns are consistent within 2σ. It should be clarified that we do not use the results of Gaussian line-fitting as a prior in the PHASE modeling. Therefore, fitting the data using PHASE is completely independent from the curve-of-growth analysis in the previous section. Because PHASE takes into account line saturation by Voigt profile fitting, the agreement between the two shows that the effect of saturation in the absorption lines, if any, is negligible.

The presence of a warm-hot phase of the Milky Way CGM with log T(K) ≈ 6 has been known from X-ray absorption line studies (Gupta et al. 2012; Nicastro et al. 2016a, 2016b; Gupta et al. 2017; Nevalainen et al. 2017; Gatuzz & Churazov 2018). Focusing on the sightline toward 1ES 1553+113, our measurement of the temperature (and hydrogen column density) of the warm-hot phase is consistent with that of Gatuzz & Churazov (2018), who assumed a solar metallicity and solar chemical composition. Their three-temperature model is equivalent with ISMabs and PHASE1 in our model, containing the cold/warm ISM and the warm-hot CGM.

The strong $\mathrm{Ne}\,{\rm{X}}$ line detected in our high S/N spectra allowed us to discover the hotter (T₂) component. Our observations by themselves cannot determine if it resides in the Galactic ISM, CGM, or in the Local Group medium. From the knowledge of the different ISM phases studied so far, we know that the Galactic ISM is dominated by neutral and mildly ionized gas, and the distribution of the warm-hot phase indicates a significant contribution from the CGM (Nicastro et al. 2016a, 2016b; Gatuzz & Churazov 2018). Extrapolating this idea to the higher temperature, the hot gas likely resides in the extended region. Nonetheless, we investigated whether dense structures such as supernovae remnants (SNRs) or superbubbles made by expanding and merging SNRs are responsible for the observed hot gas phase.

(a) There is no evidence of an individual SNR along our sightline, but the local hot bubble (LHB) is present. With a density of ≈(3.9 ± 0.4) × 10⁻³ cm⁻³ and path length of ≈100 pc (Snowden et al. 2014), the LHB column density is 1.4 × 10¹⁸ cm⁻², smaller than the column density of the hot gas by order(s) of magnitude. Thus, the LHB contribution to the observed column density is negligible.

(b) The sightline to 1ES 1553+113 (l = 2191, b = 4396) passes close to the Fermi Bubble (FB; $| l| \leqslant 20^\circ ,| b| \lt 50^\circ$), therefore we investigated the possibility that our observed hot gas is from the structures in or around the FB (Su et al. 2010; Kataoka et al. 2018). The temperature inside the FB is believed to be hot (≥10⁷K, Su et al. 2010); however, our sightline does not pass through the FB. The sightline to 1ES 1553+113 passes through the North Polar Spur (NPS). The temperature of NPS is 0.25–0.29 keV (Kataoka et al. 2018), which is significantly lower than the temperature of the hot phase. Second, using the emission measure (0.02–0.07 cm⁻⁶ pc) and the line-of-sight width (≈5 kpc) of the NPS (Kataoka et al. 2018), the column density is (3–5.6) × 10¹⁹ cm⁻², which is lower than the column density of the hot gas by a factor of ∼5–10. Assuming the density of the X-ray shell around FB to be n_FB ≈ 10⁻³cm⁻³ as derived by Miller & Bregman (2016), the implied path length for the hot component is $L={N}_{{\rm{H}},2}^{Z}/{n}_{\mathrm{FB}}={100}_{-67}^{+80}$ kpc. This is much larger than the spatial extent of the X-ray shell around the FB. While the NPS and the X-ray shell must contribute to the observed column density, they are unlikely to be a primary contributor unless the hot gas is much denser than that obtained by Miller & Bregman (2016).

Next, we investigated whether the hot gas is from the Local Group. Using the T_X–M relation for galaxy clusters: T_X ∝ M^2/3, the temperature of the Local Group is ≈10^6.69−6.91 K, assuming the Local Group mass = 6.4 × 10¹² M_⊙ (Peebles 1990). This is consistent with T₂. However, our sightline (2191, 4396) is away from M31 and the center of the Local Group. Therefore, the contribution of the Local Group to the hot phase, if any, might not be significant. Oppenheimer (2018) found that the thermal feedback can buoyantly rise to the outer CGM of Milky-Way–like halos of M₂₀₀ ≤ 10¹² M_⊙, moving baryons beyond the virial radius (R₂₀₀) and extending the CGM out to at least 2 × R₂₀₀. Therefore, if the observed hot gas is extended beyond R₂₀₀, it is just a matter of nomenclature whether it should be called the CGM or the Local Group gas.

With the above considerations, we argue that the newly detected hot phase is primarily from the CGM of the Galaxy. Hydrodynamic simulations that take into account multistage stellar feedback from the bulges of Milky-Way–type galaxies predict that the temperature in the CGM can be as hot as T₂ (Tang et al. 2009). Analytic models predict that the CGM can significantly deviate from thermal equilibrium due to mechanical feedback (ejection of low angular momentum material) or thermal feedback (heating of the central regions), resulting in super-virial temperature as high as T₂ in the inner 50 kpc of the halo (Pezzulli et al. 2017). The absence of a strong $\mathrm{Ne}\,{\rm{X}}$ line in a deep ∼3 Ms absorption study toward PKS 2155-304 (Nevalainen et al. 2017) indicates that this hot phase might not be ubiquitous, and is likely anisotropic. On the other hand, there have been hints of such hot gas in the halo of Milky Way in emission (Henley & Shelton 2013; Nakashima et al. 2018) away from the Galactic center, showing that the hot gas may not necessarily be related to the nuclear activity. However, emission is dominated by denser regions, so the hot gas detected in emission is perhaps located closer to the disk of the Galaxy. The presence of the hot gas in absorption with a high H column density of ≈10²⁰ cm⁻² indicates that the hot gas can in fact be present in a low-density extended medium. Based on combined emission and absorption measurements toward the Galactic bulge, Hagihara et al. (2011) found that a two-T hot ISM was necessary to reproduce the observed spectra. However, the two temperatures that they obtain (T₁ = (1.7 ± 0.2) × 10⁶ K and ${T}_{2}={3.9}_{-0.3}^{+0.4}\times {10}^{6}$ K) differ by only a factor of 2, and their hotter component is significantly cooler than the hot gas that we find. Thus, the ≈10⁷ K hot gas that we have discovered was not observed before either from the ISM or from the CGM of the Milky Way.

We have measured two sets of abundance ratios: (1) oxygen, neon, and nitrogen relative to iron; and (2) neon and nitrogen relative to oxygen (with three out of five of these being independent measurements). We find super-solar [Ne/Fe] and [O/Fe]; this shows that the CGM is α-enhanced, indicating core-collapse supernovae enrichment (Nomoto et al. 2006). We also find super-solar [Ne/O] and similar [N/O]. The super-solar [Ne/O] is, at least partially, a result of the core-collapse supernovae enrichment (Nomoto et al. 2006). The large amount of nitrogen relative to neon suggests that there is an additional contribution to nitrogen, such as from dying asymptotic giant branch (AGB) stars (Herwig 2005). However, it is highly unlikely that the two different sources of enrichment have contributed N and Ne to yield similar abundance ratios relative to oxygen. It is more likely that oxygen is sub-solar with respect to N and Ne. The lower oxygen abundance can be a result of different processes. Dust of silicates and other forms containing oxygen can be formed 300–600 days after core-collapse supernovae explosions (Todini & Ferrara 2001). Thus, oxygen can be depleted onto dust in the ISM (as found by Pinto et al. 2013 in the high-resolution X-ray absorption spectra of Galactic low-mass X-ray binaries) before the outflows from the stellar feedback/supernovae reach the halo and enrich it with metals. Alternatively, if the CGM is inhomogeneously mixed as suggested by simulations (Ford et al. 2013, 2014) and observed in cooler phases of the CGM (Schaye et al. 2007), oxygen can cool to lower temperatures without affecting the temperature of the gas at which other elements are abundant. This is reasonable to expect because the emissivity of oxygen at the CGM temperatures (>10⁶ K) is ∼3–10 times higher than the emissivity of nitrogen and neon (Bertone et al. 2013). Thus, it is possible that nitrogen and neon remain in the hot/warm-hot phases while oxygen "prefers" to transit to the warm or cooler phases. A similar transition of oxygen has already been found in cosmological simulations (Ford et al. 2013) and observations (Nevalainen et al. 2017). If cooled sufficiently, oxygen may eventually get depleted onto circumgalactic dust. It requires more than 10⁷ yr to evaporate in a low-density environment with n ≈10⁻³ cm⁻³, so a significant amount of metals may be held in circumgalactic dust (Tielens et al. 1994). This is consistent with observations that a larger fraction of CGM metals (42%) are in solid phase compared to that in the ISM (∼30%) (Peeples et al. 2014). While the deficit of oxygen with respect to neon and nitrogen are qualitatively consistent with the chemical enrichment by core-collapse supernovae and AGB stars, oxygen's depletion onto dust is likely to be necessary to explain the abundance ratios quantitatively. Determining the relative importance of all sources affecting the abundance ratios is beyond the scope of this Letter. An alternative explanation might be as follows. Inhomogeneous mixing causes the density distribution of all ions (i.e., different ionization states of same/different elements) to be not necessarily the same (Ford et al. 2013, 2014). In that case, local abundance ratios, which we measure along our line of sight, would differ from the global average.

The hot gas (T₂) that we discover in the Milky Way CGM along this sightline, as well as the non-solar abundance ratios, have not been detected in the CGM of any Milky Way-type external galaxies (Strickland et al. 2004; Yamasaki et al. 2009) or in most of the absorption studies of the Galactic ISM (Yao & Wang 2006; Yao et al. 2006, 2009a). Mildly super-solar Ne/O has been observed in absorption in the warm-hot ISM (Yao et al. 2009b), and α-enhancement has been observed in the CGM in a couple of emission studies (Strickland et al. 2004; Yamasaki et al. 2009; Nakashima et al. 2018), though with poor constraints. In external galaxies, the α-enhancement has been observed along the minor axes and in extra-planar regions within 10 kpc of the galactic disks (Strickland et al. 2004; Yamasaki et al. 2009); therefore it is associated with outflow/galactic fountain. As discussed in Section 4.1, the hot gas that we discover is spatially extended, and is primarily from the Milky Way CGM. Therefore, the α-enhancement in the hot gas (Figure 3) shows that the feedback from the core-collapse supernovae has extended to a large length scale.

We have detected the hot component and non-solar abundance ratios in the Milky Way CGM along one sightline. Depending on the path length, density, and covering factor, it would affect the calculation of the baryonic mass and the metal mass of the CGM.

The previous X-ray absorption-line studies were not sensitive to the non-solar abundance patterns, and the mass of metals in the warm-hot CGM was derived from the oxygen measurements:

$$\begin{eqnarray}&&M({\rm{Z}})=\displaystyle \frac{M({\rm{O}})}{{f}_{O}}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&M({\rm{O}})\propto N({\rm{O}})=\displaystyle \frac{N({\rm{O}}\,{\rm{VII}})}{{f}_{{\rm{O}}{\rm{VII}}(T)}}\mathrm{or},\,\displaystyle \frac{N({\rm{O}}\,{\rm{VIII}})}{{f}_{{\rm{O}}{\rm{VIII}}(T)}}\end{eqnarray} \tag{ 2 }$$

here M(Z) and M(O) are, respectively, the total mass of metals and oxygen in the X-ray traced CGM and f_O is oxygen-to-metal ratio. The temperature in the warm-hot (T ≈ 10⁶ K) phase was determined using the ${\rm{O}}\,{\rm{VIII}}$/${\rm{O}}\,{\rm{VII}}$ ratio. If a good fraction of ${\rm{O}}\,{\rm{VIII}}$ arises in the hot (T ≈ 10⁷ K) phase, in a single-temperature model the ${\rm{O}}\,{\rm{VIII}}$ ionization fraction would be overestimated, and hence the warm-hot phase temperature (T₁) would be overestimated. Depending on whether ${\rm{O}}\,{\rm{VII}}$ or ${\rm{O}}\,{\rm{VIII}}$ is used to calculate the total mass of oxygen, the overestimation of temperature will lead to an over-/underestimation of oxygen mass in the warm-hot phase, because f_{O vii} decreases and f_{O viii} increases with temperature above 10⁶ K. Inclusion of the hot component not only resolves this issue, it also traces an extra component of metals. Second, sub-solar gas-phase oxygen, with the f_O range of ≈9% to 28%, compared to f_O ≈ 44% for solar oxygen, may affect M(Z) by a factor of ≈2–5. This shows how the census of other metals, along with oxygen, in the X-ray traced CGM is so vital.

The calculation of total baryonic mass

$$\begin{eqnarray}&&{M}_{b}=\displaystyle \frac{M({\rm{Z}})}{0.02}{\left(\displaystyle \frac{Z}{{Z}_{\odot }}\right)}^{-1}\end{eqnarray} \tag{ 3 }$$

follows directly from the total metallic mass. For an assumed metallicity, if the oxygen is sub-solar as we find here, the total baryonic mass of the warm-hot CGM would be underestimated by the same factor (2–5 in our case) as the total metallic mass. Additionally, the hot CGM was not included in the previous works, so the mass in the X-ray traced CGM was underestimated. Once again, the contribution of the hot component to the baryonic budget would depend on its path length, density, covering factor, and volume-filling factor.

We calculated relative abundances of metals using the solar model of Asplund et al. (2009). If we use other values of relative solar abundances, the results remain the same: $[{\rm{O}}/\mathrm{Fe}]\,={0.8}_{-0.3}^{+0.7},[\mathrm{Ne}/{\rm{O}}]=[{\rm{N}}/{\rm{O}}]={0.7}_{-0.2}^{+1.6}$ for Wilms et al. (2000) abundances, $[{\rm{O}}/\mathrm{Fe}]={0.8}_{-0.3}^{+0.7},[\mathrm{Ne}/{\rm{O}}]={0.8}_{-0.2}^{+1.6}$ and $[{\rm{N}}/{\rm{O}}]\,={0.7}_{-0.2}^{+1.6}$ for Lodders (2003) abundances. This shows that our abundance measurement is not affected by the composition prescription.

Our temperature estimates are subject to the assumption that the gas is in CIE. However, the gas at T₂ is not at the virial temperature of the Milky Way, so it might not be in equilibrium. If the hot gas is stretched across a large length scale (∼a few 100 kpc), the average density will be low enough to have the post-shock electron-ion relaxation timescale comparable with or longer than the Hubble time (Yoshida et al. 2005). In that case, the electron temperature will be overestimated and the abundance of metals will be over-/underestimated. Similarly, if the gas in our sightline is photoionized (for reasons unknown) instead of being in CIE, then the abundance ratios would be over-/underestimated.

As the cooling efficiency and dust depletion rate of N, O, and Ne are different, the chemical composition in two temperature phases are not necessarily the same. However, we do not have any diagnostics of nitrogen lines or ${\rm{O}}\,{\rm{VII}}$ lines in the hotter phase, thus we cannot determine the abundance ratios in the two temperature phases independently, and we have assumed the ratios to be the same. The strongest constraints on iron abundance are for the hot phase, so in the least, our observed super-solar [Ne/Fe] and [O/Fe] are for the hot component. Similarly, the observed super-solar [N/O] and [Ne/O] are, in the least, for the warm-hot component. The same abundance ratios are implicitly assumed in the derivation of the total column density of the hot phase ${N}_{{\rm{H}},2}^{Z}$, which may be under-/overestimated. Also, the calculation of ${N}_{{\rm{H}},2}^{Z}$ involves the ionization fraction of individual lines. If the hot component is not at ionization equilibrium, the ionization fractions of H-like ions can be different from those at CIE (Oppenheimer & Schaye 2013). This will affect the derivation of ${N}_{{\rm{H}},2}^{Z}$.

In the Discussions section, we have commented on how sub-solar oxygen may affect the calculations of metals and baryons in the CGM. A more complete calculation will have to involve the non-solar abundance ratios with respect to iron, and the abundance ratio of other α-elements (C, Mg, Si) as well.