The Nature of Ionized Gas in the Milky Way Galactic Fountain

FUV spectra were obtained with COS (Froning & Green 2009; Green et al. 2012) on the Hubble Space Telescope (Program ID: 14140). We observed our BHB targets with the COS G160M grating with a central wavelength of 1577 Å with exposure times adjusted to achieve a signal-to-noise ratio (S/N) ≈ 15 per resolution element over λ_obs ≈ 1385–1760 Å. Table 2 contains a summary of the COS observations.

Our COS data probe absorption due to the following metal ions: Si ii (λ1526), Fe ii (λ1608), Al ii (λ1670), Si iv (λλ1393, 1402), and C iv (λλ1548, 1550). We refer to singly ionized species as low ions. These low ions have ionization potential energies ranging from ≈16 to 18 eV and are most likely arising in cool gas photoionized by stellar radiation from the MW, with some contribution from the extragalactic UV background (EUVB). We refer to Si iv and C iv as intermediate ions. The ionization potential energies of Si iv and C iv are 45 and 64 eV, respectively. The intermediate ions may trace warm photoionized material and/or may be produced in part by collisional ionization.

We combine the CALCOS-generated x1D files using v3.1.1 of the COADD_X1D routine provided by the COS-GTO team (Danforth et al. 2016), which properly treats the error arrays of the input files using Poisson statistics. The code aligns the different exposures by determining a constant offset determined by cross-correlating strong ISM lines in a 10 Å wide region of the spectrum. With COS spectra, misalignments with magnitudes up to ±30 km s⁻¹ between spectral lines in the same target have been described, which leads to smearing and unphysical velocity offsets between different absorption lines. We discuss these wavelength calibration issues in detail in Section 2.3.

The COS line-spread function (LSF) is well described by a Gaussian convolved with a power law that extends to many tens of pixels beyond the line center (Ghavamian et al. 2009). These broad wings both affect the precision of our equivalent width measurements and complicate assessments of line saturation. We mediate these effects when we fit absorption lines (described in Section 3) by convolving with the real LSF. Each COS resolution element at R ∼ 18,000 covers 16 km s⁻¹ and is sampled by six raw pixels. We performed our analysis on the data binned by three native spectral pixels to a dispersion of Δλ ≈ 0.0367 Å. The resulting science-grade spectra are characterized by an FWHM ≈ 18 km s⁻¹.

As a complement to our HST/COS data, in 2015A we began obtaining Keck HIRES spectra covering Ca ii H + K (λλ3934, 3969) and Na i (λλ5892, 5897) along the BHB lines of sight through several programs. The Keck HIRES data are fully described in Bish et al. (2019) and are summarized here. Exposure times varied with the magnitude of the star and are given in Table 2. Generally, we aimed to achieve an S/N of ≳20 over the range of 3900–5900 Å. Our final wavelength ranges varied slightly with different cross-disperser and echelle angles for the BHB stars on different nights, depending on the program for which it was observed. We obtained HIRESr spectra with the C5 decker with the image rotator in vertical-angle mode, and the kv370 order blocking filter with 2 × 1 binning. The C5 decker with a 1148 slit provides spectroscopic resolution of 1.3 km s⁻¹ pixel⁻¹ and R = 36,000, which corresponds to a velocity FWHM of 8.3 km s⁻¹. The C1 decker with a 0861 slit provides spectroscopic resolution of 1.0 km s⁻¹ pixel⁻¹ and R = 48,000, which corresponds to a velocity FWHM of 6.2 km s⁻¹. Our final velocity resolution of 5–10 km s⁻¹ allows us to distinguish material from the disk of the MW and the star and resolve different absorption components from each other.

The ionization potential energies of Ca ii and Na i are 11.9 and 5.1 eV, respectively. Because they lie below 1 ryd, these ions are likely associated with cool, predominantly neutral material. However, Na i is known to show up sporadically along MW ISM lines of sight and exhibit little correlation with gas-phase metallicity or H i column density (Jenkins 2009). Thus, the interpretation of the Na i line is complex, whereas Ca ii is a typical ion tracing neutral and low ionization state gas.

Here we describe our analysis to ensure that the COS wavelength solution of the co-added, aligned spectra produced by the Danforth routine (Danforth et al. 2016) is accurate. Our strategy is to check our solution against Ca ii stellar absorption lines detected in Keck HIRES spectra and SDSS SEGUE stellar radial velocities of the same targets. We fit unsaturated, unblended stellar absorption lines of Ca ii in the Keck spectra and C i, Si ii, and Fe ii in the COS spectra to check for potential systematic errors in the COS wavelength calibration that have been reported and discussed in detail by Wakker et al. (2015). We fit stellar absorption profiles along with gas absorption profiles as described in Section 3. We compare our fitted stellar radial velocities from HIRES and COS spectra with the SDSS DR8 radial velocities for the BHB stars in the v_LSR rest frame.

Existing methods to test and correct for systematic errors in the COS wavelength calibration assume alignment in MW interstellar absorption lines of various species, sometimes with a range of ionization potential energies (e.g., Wakker et al. 2015; Danforth et al. 2016). The primary benefit of these methods is that they are broadly applicable to a variety of data sets, including QSO spectra. Instead, our method assumes that stellar absorption lines of different ionic species observed with different instruments should give a consistent value for the stellar radial velocity of each BHB star. Notably, our method will allow for velocity offsets between different ionic species owing to foreground gas absorption at z ≈ 0 along each BHB line of sight. Thus, any differences between gas kinematics of different ionic species at the disk–halo interface of the MW may correspond to physical velocity offsets between different gas phases.

Figure 2 shows velocity offsets of stellar absorption lines between those measured in SDSS spectra (Xue et al. 2011) and those measured in our Keck or COS spectra. We show the offsets (Δv_SDSS) for the different ionic species that consistently exhibit stellar absorption: Ca ii λ3934 (Keck), C i λ1656, Fe ii λ1608, and Si ii λ1526 (COS). We use a rest wavelength for C i λ1656 of 1656.9283, which is the wavelength of the ³P₀ ground-state transition of C i, and do not include any contribution from weaker excited fine-structure levels of the C i multiplet that span ±335 km s⁻¹ since they do not appear to be present in our data. We note that Al ii λ1670 often shows absorption from the BHB star; however, we exclude it here because it is invariably saturated and often blended with the MW interstellar absorption, which makes its fitted velocity centroid more uncertain.

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Figure 2 shows that for most BHB stars the stellar radial velocities measured in Keck and COS spectra are consistent with SDSS radial velocities within approximately ±10 km s⁻¹. The velocity centroids of Ca ii λ3934 as measured in the Keck data (small, red squares) are generally in better agreement with the SDSS radial velocities, with a median $| {\rm{\Delta }}{v}_{\mathrm{SDSS}}|$ of 5.5 km s⁻¹. Next, we note that there are no apparent trends between ${\rm{\Delta }}{v}_{\mathrm{SDSS}}$ and wavelength for the stellar absorption lines detected in the COS G160M spectra. The gray shaded regions indicate the approximate mean rms of the dispersion solutions for our Keck HIRES (dark gray; ∼2 km s⁻¹) and COS G160M (light gray; ∼7.5 km s⁻¹) spectra. Reported errors in the SDSS heliocentric radial velocities for each BHB range between 1 and 3 km s⁻¹.

In general, we find that SDSS radial velocities are in agreement with those measured from the Keck and COS spectra. One exception is the stellar absorption we detect along the line of sight to BHB6 (J1341+2823). The fits to the stellar velocities in both Keck HIRES and COS G160M spectra show >10 km s⁻¹ offset from the SDSS-reported heliocentric radial velocity (HRV). Despite this lack of agreement with SDSS, the HIRES and COS spectra give self-consistent results for BHB6. The remainder of our analysis does not use SDSS spectra, so if there is an error in the SDSS spectra, it has no effect on our analysis. Overall, Figure 2 indicates that stellar radial velocities inferred from our HIRES and COS spectra are largely consistent within typical wavelength calibration errors for each instrument. Hidden systematic errors in the COS G160M wavelength solution that have been reported elsewhere (e.g., Wakker et al. 2012) do not appear to significantly impact our BHB star COS spectra.

H i 21 cm emission can provide constraints on the distribution of neutral hydrogen in the general vicinity of our BHB sight lines. However, direct comparisons of measured column densities in absorption and emission data are ill-advised for two reasons. First, the spatial resolution of the H i data is 108, orders of magnitude larger than the much narrower ∼1'' HIRES slit or the 25 circular COS aperture. This disparity implies that emission and absorption measurements do not trace material on the same spatial scales. Second, there are only radial velocity and no distance constraints for material detected in 21 cm emission. Nonetheless, these H i data are useful because of their all-sky coverage and their excellent constraints on the large-scale structure of the IV material we wish to examine.

We use data from the Effelsberg-Bonn H i Survey (EBHIS; Winkel et al. 2016), which images the full sky with a bandwidth of 100 MHz. The effective beam FWHM is 108, and the effective velocity resolution is 1.44 km s⁻¹. We show in Figure 3 integrated H i 21 cm column density maps from EBHIS over two velocity ranges (left: a broad velocity range $-150\,\mathrm{km}\,{{\rm{s}}}^{-1}\lt {v}_{\mathrm{LSR}}\lt 50\,\mathrm{km}\,{{\rm{s}}}^{-1}$ ; right: the velocity range over which we detect the bulk of our IV absorption, $-45\,\mathrm{km}\,{{\rm{s}}}^{-1}\lt {v}_{\mathrm{LSR}}\lt -25\,\mathrm{km}\,{{\rm{s}}}^{-1}$) in the approximate location of our sample of BHB stars. Figure 3 shows that none of our BHB lines of sight intersect the dense neutral clumps visible in this image, and instead seem to trace the wispy structures that extend across tens of degrees.

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At the position of each BHB, we download the H i spectra that are generated using a weighted interpolation with a Gaussian kernel from the H i Survey server of the Argelander-Institut für Astronomie.¹¹ We show these EBHIS H i 21 cm brightness temperature profiles as a function of ${v}_{\mathrm{LSR}}$ on the right column of Figure 4. IV neutral gas with ${v}_{\mathrm{LSR}}\,\lt -25\,\mathrm{km}\,{{\rm{s}}}^{-1}$ is apparent along each of our seven lines of sight. In order to determine the H i column density in the IV gas along each line of sight, we perform simple, dual Gaussian fits to these double-peaked, asymmetric profiles seen in Figure 4. In the optically thin limit, the H i column density is directly proportional to the integrated 21 cm emission line brightness (T_b), which we calculate using the standard relation (Draine 2011):

$$\begin{eqnarray}&&\displaystyle \frac{{N}_{{\rm{H}}{\rm{I}}}}{{\mathrm{cm}}^{-2}}\approx 1.82\times {10}^{18}{\int }_{}^{}\left[\displaystyle \frac{{T}_{b}(v)}{{\rm{K}}}\right]d\left(\displaystyle \frac{v}{\mathrm{km}\,{{\rm{s}}}^{-1}}\right).\end{eqnarray} \tag{ 1 }$$

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We use the FWHM, velocity centroid, and peak T_b from the simple Gaussian fits to the IV components to determine their column densities within the 108 beam. The relatively large beam size gives the average ${N}_{{\rm{H}}{\rm{I}}}$ on scales of 9.4 pc at a distance of z = 3 kpc [or ℓ ≈ (3.1 pc) × (z/1 kpc)]. Smaller-scale structures will be averaged out, including any unresolved structures probed by the absorption-line data along the BHB sight lines. Thus, values of N_{H i} determined from EBHIS data cannot be used as either upper or lower limits to the neutral gas column density associated with the absorption we see in Keck/HIRES or HST/COS spectra. However, the variation in N_{H i} over the area traced by our sight lines will prove useful for our analysis.

The FWHM of a single resolution element in our COS G160M spectra is more than two times broader than that of our HIRES spectra (18 km s⁻¹ vs. 7 km s⁻¹). As a result, the MW ISM is blended with absorption owing to the IV extraplanar features we aim to examine in the COS data. The HIRES data allow a cleaner separation of MW local ISM and additional absorption features, seen in Figure 4. The Ca ii K absorption at v_LSR ≈ 0 km s⁻¹ lines up with the narrow, strong emission at v_LSR ≈ 0 km s⁻¹ visible in the EBHIS H i 21 cm data. Consistent with previous studies of Na i that report its patchy detection in the MW, the v_LSR ≈ 0 km s⁻¹ component of Na i absorption appears in only four of seven cases (e.g., Meyer & Lauroesch 1999). In addition, absorption consistent with the BHB stellar radial velocity is visible in Ca ii K, C i, Si ii, Al ii, and Fe ii (Ca ii H is catastrophically blended with broad stellar H absorption). We do not see stellar absorption in Na i, Si iv, and C iv in our HIRES or COS data for the targeted BHB stars.

For all BHB stellar sight lines, a simple visual inspection of the line profiles for the "intermediate ions," Si iv and C iv, compared to those of the "low ions," i.e., the neutral and singly ionized species, can instruct our profile fitting. In the COS spectra, the blended intermediate ions consistently exhibit broader line widths and more highly blueshifted velocity centroids (≳25 km s⁻¹) than the blended low ions. This apparent velocity offset most likely arises because the contribution of the predominantly neutral, higher-density, v_LSR ≈ 0 km s⁻¹, MW ISM to the line profile is much greater in low ions than it is for intermediate ions. Adopting this assumption leads directly to the inference that extraplanar IV gas must exhibit a higher ionization parameter than the MW ISM. The precise quantitative difference in ionization parameter (and density, by extension) between the MW and IV gas depends strongly on the total H i column of each component, the gas-phase metallicity of each component, and the background ionizing spectrum affecting each component. We note that with our current data set we cannot independently constrain any of these quantities.

Our iterative fitting program for absorption lines detected with both Keck/HIRES and COS uses the MPFIT software¹² (Markwardt 2009). The line profiles we derive from Voigt profile fitting of the COS data are convolved with the COS LSF at LP3 as given at the nearest observed wavelength grid point in the compilation by Ghavamian et al. (2009). Different transitions of the same ionic species (e.g., Si iv λ1393 and Si iv λ1402) are required to have the same component structure and are therefore fit simultaneously to give a single solution. Each fit gives a value of the component column density N, Doppler b, and velocity centroid v in the LSR frame. The best fits emerge after a χ² minimization process implemented in our code and depend strongly on the number of components assumed to be present. Reported errors in fitted parameters and overall goodness of fit via reduced χ² are not independent of the assumptions in the analysis or the limitations of the data (e.g., due to saturation).

For the Keck/HIRES line profile analysis, we adopt a minimum number of components that results in profile fits to the data such that the reduced ${\chi }_{\nu }$² < 1.1. Not including stellar absorption, we fit an average of two to three Ca ii components per sight line in the Keck data. Stellar absorption is seen in Ca ii (yellow fits shown in Figure 4) and is generally well separated from the MW and IV gas. Each sight line has a distinctly separable MW component visible in Ca ii, sometimes detected in Na i. When Na i is detected in either IV or MW gas, its components' velocity alignment with the Ca ii components is excellent.

In our analysis of the COS spectra, we proceed under the assumption that both MW ISM and IV components are present with varying contributions in the low and intermediate ions. The main reason for "forcing" a two-component fit is to be able to compare low and intermediate ionic column densities directly without worrying about different levels of contamination from an MW component. This assumption is physically motivated and supported by the Keck/HIRES spectra, which show a distinct MW component in Ca ii and H i along all sight lines. To ensure that two components are present in the COS data, our fitting procedure imposes lower limits on the column density of the MW components (details below). If these limits are not imposed, the iterative Voigt profile fits sometimes converge on a solution such that a single component dominates the result (i.e., the minimized second component contributes a column <10⁹ cm⁻²). In general, the precise values of our imposed lower limits, as long as they are not unreasonably large so as to be completely inconsistent with the data, have very little impact on the final fit parameters. Finally, we note that our results, which focus primarily on IV Si iv and C iv, depend very little on the fitting assumptions described in this section.

We present the component fits for each line of sight for select transitions in both Keck and COS spectra in Figures 4 and 5. We tabulate our component fitting results for the column density N, Doppler parameter b, and velocity offset v from ${v}_{\mathrm{LSR}}$, along with associated errors, in Tables 3 and 4 for the MW and IV components, respectively. We also show the results from the dual Gaussian fits to the H i 21 cm ${T}_{{\rm{b}}}$ profiles; in this case the b column is in fact a Gaussian σ and not a Doppler b parameter. The Voigt profile fits give typical values of χ² ranging from 200 to 400, corresponding to values of reduced χ_ν² < 1.4. Our best constraints on the MW low-ion column densities in the COS data are from Fe ii, which is the least saturated low ion. Fits for MW C iv and Si iv are poorly constrained by the data, and thus their best-fit parameters are often given as limits. Below, we describe our COS absorption-line fitting procedure and all associated assumptions in detail.

• 1.  
  Identifying the stellar absorption by SEGUE radial velocity. As described in Section 2.3, the low-ion transitions in COS show absorption roughly consistent with SEGUE-reported stellar radial velocities. When present, we fit this stellar component allowing N, b, and v_cen to vary freely, and the results are consistent with expectations from HIRES spectra in which stellar absorption in Ca ii is cleanly separated from the MW and IV components. In Figures 4 and 5, the stellar component is colored in gold. In one case, BHB3, absorption centered on the expected stellar velocity in Ca ii demands two components, one very broad and one weak, narrow component. Physically, both may not be associated with the star, but we proceed by simply noting that the IV column density for Ca ii along this sight line may be an underestimate.
• 2.  
  Defining the MW component in velocity space. For every BHB line of sight observed with COS, we fit one MW ISM component within ±10 km s⁻¹ of the LSR velocity for the Ca ii K MW line fit as defined by the HIRES spectra (v${}_{\mathrm{cen},\mathrm{Ca}{\rm{II}}}$). We force this MW component to have a minimum column density as defined below. In this analysis, we do not use the Na i line directly, since an MW component is not consistently detected in Na i owing to its rather dramatic patchiness in the ISM (e.g., Münch & Zirin 1961). However, we note that when Na i is detected in the HIRES spectra at v_LSR ≈ 0 km s⁻¹, its velocity centroid is consistent with Ca ii MW absorption within a few kilometers per second. In Figures 4 and 5, the MW component is colored green. Table 3 shows that in approximately 50% of the cases our MW Voigt profile fits do not fully converge because they they are constrained not to venture outside of the ±10 km s⁻¹ band. In these cases, the values for the velocity centroid of the MW component are reported as limits: e.g., v_cen < ${v}_{\mathrm{cen},\mathrm{Ca}{\rm{II}}}$ —10 km s⁻¹.
• 3.  
  Lower limit on the Low-ion MW component column densities. The combined IV and MW components of the strong low-ion transitions detected in the COS spectra (Si ii, Al ii, Fe ii) show signs of saturation along every line of sight. Due to its non-Gaussian LSF, COS is known to saturate at normalized fluxes of ∼0.2. In our fitting procedure, we assume that the MW ISM dominates the column density contribution to the observed saturated absorption features near v_LSR ≈ 0 km s⁻¹. This assumption corresponds to a minimum column density contribution from each transition, which we can compute using its oscillator strength and rest wavelength, and assuming that the lines are unresolved, with b ≈ 20 km s⁻¹. To compute this lower limit on the MW column density, we use the XIDL routine "ism_pltlin.pro."¹³ Lower-limit log N [cm⁻²] values for Si ii, Fe ii, and Al ii, respectively, are determined to be 14.5, 14.8, and 13.3. In practice, this limit serves to demand a dominant MW component for the neutral, low ionization state ISM. Our minimization procedure converges to this MW column density lower limit for the low ions in only three cases seen in Table 3. Because the Voigt profile fits would prefer a lower column density than we allow, we report log N_ion in these three cases as conservative upper limits.
• 4.  
  Setting limits on the intermediate-ion MW component column densities. Our primary assumption is that there are two detected components along the BHB lines of sight corresponding to MW ISM and IV gas in the halo. For the intermediate ions that do not have a dominant MW component visible in the data, we use the XIDL routine "ism_pltlin.pro" to determine the column density floors for Si iv and C iv. The median equivalent width 2σ detection limits computed on each COS spectrum are 36 and 51 mÅ for Si iv and C iv, respectively. Corresponding log N [cm⁻²] values for Si iv and C iv are determined to be 12.8 and 13.2. We artificially impose the requirement that the column densities not go below these upper limits when we fit for two velocity components. In practice, this limit serves to demand a detected but weak MW component for the ISM in intermediate ionization states. The fits for the majority of the sight lines hit this lower column density limit in the intermediate-ionization species because there are simply not easily separable MW components visible in the data. Indeed, most of the Si iv and C iv prefers a single component fit that is very similar to the reported IV fits in Table 4, with a slightly higher column density. Nonetheless, to present a consistent analysis, we demand an MW component in Si iv and C iv with the above minimum columns. Thus, in the tables, the reported fits are given as upper limits, since the Voigt profiles would prefer to converge on an arbitrarily low column density for the MW intermediate ions.

The above steps define the primary assumptions that set our best two-component IV + MW fits in the COS spectra. In addition, we assume that each component in the COS spectra cannot have a Doppler b parameter <10 km s⁻¹ or >50 km s⁻¹. These limits ensure that the iterative fitting procedure does not simply minimize a second component by giving it a very small or large line width. We define a lower limit of 10 km s⁻¹ to be the narrowest resolvable line given the COS line FWHM of 18 km s⁻¹. For reference, the relation between the two quantities is given by FWHM ≈ 1.665b. The precise values of the imposed Doppler b parameter limits make very little difference to the IV and MW column density values, and the cases in which our profile fits hit these limits are mostly for the poorly constrained MW components. In the following sections, we primarily focus on the properties of the IV component. In general, this procedure produces well-constrained column densities and velocities for the IV components tabulated in Table 4, which are the focus of this study.

The estimated distance and position of each BHB in our sample allow us to place an upper limit on the distance and height to the observed IV gas along the line of sight. Examining how the measured absorption properties (N, v, Doppler b) vary with both distance upper limits and height upper limits may provide insight into the 3D distribution of the gas. For example, an increase in column density with z would signify gas located at the full range of scale heights probed by our BHB stars (3 kpc < z < 14 kpc). However, we find no significant correlation between any of these quantities and either distance or height. We note, however, that our data are not sensitive to variations in column density below 3.4 kpc. Below, we limit our discussion to the Galactic-latitude-corrected "vertical" projections (e.g., log N sin b, v sin b) and height.

The top panels of Figure 6 show that the vertical component of the IV gas column density in every ionization state, from Ca ii to C iv, remains roughly constant over the range of heights probed by our observations. Each panel shows a median of the value for log N sin b or v sin b for each ion in the IV component only. For the low ions, we show only Ca ii and Fe ii IV absorption properties since these two ions have the best-constrained IV Voigt profile fits. There is only small scatter of ±0.2 dex for the intermediate ions (top left) and a more moderate scatter of ±0.3–0.4 dex for the low ions (top right). This narrow span of low- and intermediate-ion column densities indicates that the majority of the gas traced by absorption lies at heights ≲3.4 kpc.

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The lack of any discernible increase in column density with z above 3.4 kpc is in agreement with the analysis of Savage & Wakker (2009). In their study of numerous halo star and QSO sight lines, they determined an exponential scale height of a given ion by comparing column densities projected along the z-axis to a simple "plane-parallel" model of column densities with an exponential decline in the z-direction. In this plane-parallel framework, they find that Si iv and C iv have similar exponential scale heights of 3.2 and 3.6 kpc, with typical errors on the order of ±1 kpc. Low ions tend to exhibit much smaller exponential scale heights <1 kpc.

The median values of log N sin b of both Si iv and C iv along our BHB sight lines agree with the median log N sin b reported by Savage & Wakker (2009) for extragalactic lines of sight with b > 45°. Their median values of log N sin b are 13.63 ± 0.21 and 14.12 ± 0.25 for Si iv and C iv, respectively, while our corresponding values of log N sin b are 13.35 ± 0.17 and 14.04 ± 0.18. We note that the apparent optical depth method column densities they report include any contribution from the MW itself, which is consistent with our median values of log N sin b being slightly lower than theirs. Adding back in the MW contribution to our values for log N sin b, we get medians of 13.48 ± 0.22 and 14.10 ± 0.24 for Si iv and C iv, respectively. This additional contribution brings our median vertical column densities into even better agreement with those of Savage & Wakker (2009).

There is minor tension, at the ∼1σ level, between the best-fit vertical velocity values for the intermediate (Si iv) and low ions (Ca ii) seen in the bottom two panels of Figure 6. This tension increases when we consider IV H i 21 cm emission radial velocities (in the range of −40 < v_LSR [km s⁻¹] < −15). The IV gas traced by intermediate-ion absorption appears to be moving toward the disk of the MW approximately 10 km s⁻¹ faster than the material traced by the low-ion absorption. This offset could be due to systematic uncertainty introduced by our Voigt profile fitting assumptions not accounted for by the errors propagated during the iterative fitting procedure. It may also arise if we have underestimated the wavelength calibration uncertainty (but see Figure 2). While there may be physical implications of a velocity offset between different gas phases, we do not comment on it further given its low significance in our data.

Having established that our data show no significant trends with z, here we focus on a comparison between column densities of the fitted IV components as a function of their transverse separation from one another. Column densities of Si iv and C iv, with ionization potential energies of 45.1 and 64.5 eV, respectively, exhibit the strongest correlation with each other from sight line to sight line. For log N_{Si iv} versus log N_{C iv}, the Spearman's rho rank correlation coefficient (a value of 1 = perfectly increasing monotonic correlation) is 0.86 and the linear Pearson correlation coefficient (a value of 1 = perfectly increasing linear correlation) is 0.97. Figure 7 clearly shows that the seven IV column density measurements of Si iv and C iv are strongly correlated with each other. The low ions (e.g., Ca ii, Fe ii) with ionization potential energies <20 eV exhibit weak to moderate correlations with each other (Spearman's rho = 0.2–0.3; Pearson's coefficient = 0.3–0.5), the larger scatter likely due to the large uncertainties in the fitted column densities of the weak IV component.

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Next, we examine whether the column densities of low ionization state gas traced by Si ii, Fe ii, and Ca ii correlate with the columns of intermediate ionization state gas traced by Si iv and C iv. The Spearman's rho rank correlation coefficient between log N_lowion and log N_highion ranges between −0.1 and 0.1 for the various species, strongly indicating no monotonic correlation of any kind between the species of different ionization states. As we will explore in Section 6, this result is consistent with pictures put forth by many previous studies of the MW halo and Magellanic Stream (Putman et al. 2003; Fox et al. 2004; Richter et al. 2017), in which larger envelopes of ionized gas contain patchy clumps of cooler, more neutral gas.

Finally, we search for trends between ionic column densities and the IV log N_{H i} in order to assess whether the gas seen in absorption toward the BHB stars is tracing the same material as that seen in emission in Figure 3. First, it is important to recall that the H i column densities based on the EBHIS 21 cm emission data are averaged over a much larger angular scale than the absorption-line column densities. Furthermore, the precise value of N_{H i} associated with N_ion is impossible to determine using the 21 cm data alone. Any dense clumps or "cloudlets" along each line of sight with angular sizes <108 would be washed out by the larger EBHIS beam (Wakker et al. 2001; Lockman et al. 2002; Saul et al. 2012). Any differential depletion would add additional scatter. For these reasons, it is not surprising that gas column densities of the low ions traced by Ca ii, Fe ii, and Si ii in Keck and COS data do not correlate at all with N_{H i}. We show this lack of correlation in the right panel of Figure 8 for Ca ii, which offers the best constraints on the absorption properties of the low ions.

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There is, however, a moderate to strong correlation between both Si iv and C iv and H i, seen in the left panel of Figure 8. For both intermediate ions, the linear least-squares fit is shown as a gray line, indicating positive slopes of 0.59 ± 0.076 (Si iv) and 0.75 ± 0.096 (C iv). The Spearman's rho rank coefficient (such that a value of 1 = a perfectly monotonic positive correlation) in each case indicates a moderately strong correlation, with values of 0.78 and 0.75 for Si iv and C iv, respectively. What this likely means is that the H i column densities in the 108 beam on average are tracing the larger-scale, diffuse structures rather than the smaller-scale, dense "cloudlets" probed by the low ions.

Directly addressing the angular scale of the absorbing and emitting structures, Figure 9 shows the difference in column density between each unique IV component "pair" for the seven lines of sight (21 pairs total) versus the pair angular separation. The C iv and Si iv are tracing a coherent, large-scale structure, as evidenced by the strong correlation between Δlog N and the separation over 40°. Both intermediate-ion correlations give a Spearman's rho coefficient of 0.82, with a two-sided significance of its deviation from 0 of <0.000004. The scatter in this correlation is only ∼0.15 dex, and within 10° the median Δlog N is only 0.05 dex, indicating a relatively smooth structure. Furthermore, the IV H i 21 cm column densities (shown for reference as gray diamonds) seem to follow a similar trend, but with a slightly larger scatter. At a distance of 3 kpc, roughly the upper limit we can set with our data, 10° ≈ 0.5 kpc. At the lower distance limit to the IV arch of 0.9 kpc (Wakker 2001), the structure of which the BHB sight lines skirt the edge, 10° ≈ 0.15 kpc.

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In the right panel of Figure 9, we show the same pairwise Δlog N versus angular separation for two low ionization state transitions, Ca ii (gold) and Fe ii (green). While the Ca ii IV component column densities are well determined from the Keck HIRES data, the log N_{Fe ii} of the IV component has a much larger error owing to the many assumptions and limits imposed on the lower-resolution COS spectrum. Nonetheless, we can rule out any correlation between ΔlogN_lowion and angular separation with high confidence. Furthermore, the scatter of the data over the 40° angular scales is >0.4 dex. This large scatter and lack of a correlation are consistent with patchy, small-scale clumps of material. Considering the monotonic increase with small scatter to 40° of the intermediate ions and the large scatter and lack of trend seen in the low ions (right panel of Figure 9), our data directly support the physical picture of large ionized envelopes or streams containing cooler condensations or clumps.

In principle, additional archival UV absorption-line data could support this picture of ∼kiloparsec-scale ionized structures with even larger area coverage. As an initial step, we harvested Si iv column densities from the COS-GAL QSO sight-line database (Zheng et al. 2019) to explore Δlog N variations over a similar area in the northern Galactic sky to that of our BHB stars. In total, we selected 11 COS-GAL sight lines against which to compare our BHB Si iv IV component column densities. The results can be seen in Figure 10, where the gray points track the pairwise Si iv column density differences for the extragalactic COS-GAL sight lines. This archival sample shows only a weak to moderate increasing correlation between pair column density difference and angular separation, with a Spearman's rho correlation coefficient of 0.35 and a two-sided significance of its deviation from 0 of ≈0.04.

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The most likely reason for the weaker correlation in Figure 10 is that there is a contribution to the absorption along the QSO sight lines from the more extended, ionized CGM up to much larger heights, ∼200 kpc (Zheng et al. 2019). Each QSO sight line probes the full MW halo virial radius and likely pierces multiple kiloparsec-scale structures in Si iv. The effect would be to wash out the individual structure coherence seen for our stellar sight lines. Furthermore, the apparent optical depth method column densities reported by COS-GAL include an MW component, whereas we explicitly do not. The MW component's contribution to the total column density is minimal for Si iv and C iv but still exists at the 20% level and likely adds additional scatter to the relation. Thus, we consider Figure 10 to offer tentative support for our physical picture (explored in detail in the discussion). Further support would come from analyzing all stellar sight lines with distance constraints probed by COS and STIS, including a full Voigt profile analysis similar to that which we present in this work. Such an analysis over large angular area, while beyond the scope of our study, would potentially be sensitive to the maximum size scale of these large, ionized structures.

Photoionization models, such as those constructed with the spectral synthesis code CLOUDY (Ferland et al. 2017), perform detailed radiative transfer through a parcel of gas characterized by some neutral column density, N_{H i}, metallicity, [M/H], and ionization parameter, U (U ≡ (n_H × c)/Φ_tot, where Φ_tot is the integrated ionizing photon flux generated by the assumed photoionizing spectrum). One must make several assumptions to run such a CLOUDY model: (1) thermal and ionization equilibrium, (2) an ionizing background radiation field, and (3) a density structure for the parcel of gas, often approximated as a uniform density slab (but see Stern et al. 2016). Another common assumption of these models is relative solar abundances of the elements, although these element ratios can be allowed to vary to account for depletion onto dust (Jenkins 2009). Comparing the outputs of a grid of ionization models with the data (e.g., systematically varying N_{H i}, [M/H], and/or U) ultimately allows one to find the model or set of models that are consistent with the constraints set by the ionic column densities determined from the observations.

We construct such a grid of CLOUDY models to constrain the physical state of the IV gas probed by our observations of Si iv and C iv only, assuming that they are predominantly photoionized (we address collisional ionization in and out of equilibrium in Section 5.2). We assume solar ratios of the elements and exclude the low ions from this analysis. We are justified in doing so, as our previous analysis has shown that they are almost certainly not cospatial with the intermediate ionization state material. We note that if both the low ions and the intermediate ions are part of the photoionized WIM, then the WIM material itself cannot be characterized by a single density "slab." However, our CLOUDY models of the single-phase intermediate-ionization IV gas assume a uniform density layer irradiated by the extragalactic UV background and escaping radiation from the MW disk, as presented by Fox et al. (2005). These models represent a simplified picture that nonetheless may prove informative.

Φ_tot (the number of ionizing photons emitted per second by the assumed radiation field) at the MW disk–halo interface is highly uncertain and depends strongly on (1) the absorbing feature's distance from the MW and (2) an assumed escape fraction of the ionizing photons from the disk. In practice, adjusting Φ_tot affects primarily the calculated hydrogen number densities, n_H = Φ_tot/(U × c). To address this uncertainty, we ran several CLOUDY models, assuming the Fox et al. (2005) ionizing spectrum at different heights above the disk. For reference, we find that at 10, 2, and 0 kpc above the MW disk, Φ_tot = 340,000, 5,500,000, and 37,000,000 s⁻¹, respectively. We note that the ionization parameters and ionized fractions of hydrogen and metals are consistent among these models owing to identical spectral shapes. However, it is apparent that such a range in disk heights produces ionizing photon fluxes, and thus gas volume densities, that vary over two orders of magnitude. Specifically, the assumed hydrogen number densities shift upward by two orders of magnitude with a corresponding increase in Φ_tot. Thus, constraining the volume density of this IV material is not possible without additional constraints on key parameters (namely, N_H and [M/H], aka metallicity). In the following analysis, we report metallicities relative to solar abundances, X[M/H]/[M/H]_⊙, using the compact notation [M/H] = X, where X is some fraction of solar.

Under the above assumptions, the column density ratio log N_{Si iv}/N_{C iv} is a sensitive probe of the fraction of total carbon seen as C iv ≡ f_{C iv}. This dependence is shown in Figure 11. The median log N_{Si iv}/N_{C iv} = −0.69 ± 0.04 and shows little variation from sight line to sight line. The precise value of f_{C iv} inferred by the measured range of −0.76 < log N_{Si iv}/N_{C iv} < −0.68 depends strongly on the assumed metallicity of the gas. This metallicity dependence is a result of the shape of the cooling curve and the strong dependence of the high and intermediate ionic fractions on the metal line cooling. The left panel shows that these models are very sensitive to the gas-phase metallicity. We chose an N_{H i} = 17.5 at which to plot these CLOUDY models on the left, and we note that the models are only sensitive to the choice of N_{H i} at [M/H] ≳ 1.0 (at metallicities ≲ solar, there is no sharp turnover for optically thick models, and the spread in f_{C iv} looks similar to the blue curves in the left panel). In the right panel, we see that these curves shift slightly with variations in assumed N_{H i} over a range of 16.0 < log N_{H i} < 19.0, with greater differences between optically thin and thick gas at high metallicity. The fraction of carbon in C iv does not depend at all on the assumed Φ_tot (although it does depend on the slope of the assumed ionizing spectrum). For the range of log N_{Si iv}/N_{C iv} in the observed IV gas along our BHB sight lines, these models indicate that anywhere between 7% and 32% of the carbon is in C iv. Thus, for our median log N_{C iv} sin b of 14.04, this implies 14.5 < log N_C,total sin b < 15.2. In principle, if we had some way of independently constraining either the metallicity of the material or the total hydrogen column density along the line of sight, N_H, we would fully constrain the metal content of the IV gas along our sight lines.

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5.1.1. Independent Constraints on [M/H] and N_H

5.1.2. A Self-consistent Photoionization Solution Requires an Si-depleted Ionized Medium

Can we resolve this tension in the models, or must we reject photoionization of Si iv and C iv altogether? There is a solution we have not yet considered. That is, the photoionization models are perfectly self-consistent if we assume that there is a substantial fraction of silicon depleted onto dust in the warm ionized disk–halo interface of the MW. Turning again to Figure 11, we see that the orange and brownish-red curves (metallicities of 0.5–1.0 solar) are brought into consistency with the pulsar dispersion constraints (light-blue shaded region) when we allow for silicon depletion relative to carbon between −0.25 and −0.35 dex. That is, the undepleted ratio of log N_{Si iv}/N_{C iv} should be closer to ≈−0.4 if the gas is metal enriched at a level of 0.5−1.0 solar.

Addressing the photoionization model's self-consistency, we note that the length scale implied by this fiducial model (${\ell }\,=$ N_H/n_H) is

$$\begin{eqnarray}&&{\ell }\approx 3.2\,\mathrm{kpc}\left(\displaystyle \frac{{N}_{{\rm{H}}}}{{10}^{19.7}\,{\mathrm{cm}}^{-2}}\right)\left(\displaystyle \frac{{10}^{-2.3}\,{\mathrm{cm}}^{-3}}{{n}_{{\rm{H}}}}\right).\end{eqnarray} \tag{ 2 }$$

This value of n_H = 0.0055 cm⁻³ occurs at Φ_tot = 5,500,000 s⁻¹ (the value from a Fox et al. 2005 spectrum 2 kpc from the disk) precisely at an f_{C iv} of 11%. While there is a slight mismatch (2 kpc vs. 3.2 kpc), the length scales are consistent enough within the uncertainty of Φ_tot not to raise any red flags. Additionally, a ≈3 kpc length scale is consistent with the scale heights of Si iv and C iv given by Savage & Wakker (2009). Finally, we do note that this gas density is more than an order of magnitude lower than the volume density of the WIM of the MW disk inferred from measurements of singly and doubly ionized species (Reynolds 1993; Sembach et al. 2000). If IV Si iv and C iv are an extension of the MW's photoionized WIM, they would represent a lower-density extension (e.g., Stern et al. 2016).

Collisional ionization is the dominant process in low-density plasma in the absence of a significant ionizing radiation field. In collisional ionization equilibrium (CIE), the ion fractions produced by this process are a function of only gas temperature and are determined by detailed balance between electron impact collisional ionization, electron–ion recombination, and charge transfer reactions (Gnat & Sternberg 2007). Outside of equilibrium, the ionization state of the plasma depends on whether the gas is cooling at a constant density (isochoric) or at a constant pressure (isobaric) and also on the gas-phase metallicity (e.g., Gnat & Sternberg 2009; Wiersma et al. 2009). Furthermore, complex nonequilibrium collisional ionization processes have been calculated for a number of physical processes, including supersonic shocks, conductive interfaces, and turbulent mixing layers between cool clouds and a hot ambient medium (Allen et al. 2008; Gnat et al. 2010; Kwak & Shelton 2010; Wakker et al. 2012). Here we explore a physical scenario in which Si iv and C iv trace so-called "transitional temperature" 10⁵ K gas and are produced predominantly via collisionally driven cooling from a hot, ionized coronal plasma (e.g., Savage & Wakker 2009).

The physical conditions that would give rise to a scenario in which, e.g., Si ii, Si iii, C ii, and C iii are photoionized, but Si iv and C iv are collisionally ionized, would involve an ionizing spectrum that does not produce sufficient photons with energies >45 eV. In their study of HVCs exposed to a radiation field owing to Galactic ionizing photons and the extragalactic background, Fox et al. (2005) find that it is difficult to put both C iv and O vi into the same photoionized phase as the low ions. While this may result from C iv and O vi simply arising in lower-density material that is nonetheless still photoionized, it may instead be indicative of collisional processes at work. Figure 8 of Fox et al. (2005) shows several ionization "edges" in their assumed spectrum and a particularly steep drop at 54 eV caused by the He ii edge in hot stars. There are still photons with energies >54 eV, but the uncertainty in their overall flux is large enough to make the collisional ionization scenario for Si iv and C iv plausible. In our analysis that follows, we ignore photoionization and require the majority of the Si iv and C iv to be collisionally ionized in a ∼10⁵ K medium.

Figure 12 shows predictions of gas column densities and ionization fractions from collisional ionization models both in and out of equilibrium (Gnat & Sternberg 2007; Gnat et al. 2010). In CIE, as shown with the black curve in Figure 12, the fraction of C in C iv at these temperatures is ∼15% for the observed range of log N_{Si iv}/N_{C iv}. This fraction implies a total vertical carbon column density of log ${N}_{{\rm{C}},\mathrm{total}}$ sin b ≈ 14.9. Nonequilibrium models, seen in brownish-red and green in Figure 12, suggest an even higher total carbon column density.

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We now turn to the implied total hydrogen column in the supposed tenuous gas phase in CIE for a range of gas-phase metallicities. If the gas is metal enriched at the solar level, this implies log N_H sin b = 18.4, or ∼5% of the total N_H sin b implied by pulsar DM estimates described in the previous section. If this gas is instead at [M/H] = 0.3, the amount of hydrogen would increase to log N_H sin b = 18.9, or ∼16% of the total N_H sin b measurement in the MW thick disk. Given well-reasoned estimates by Howk et al. (2006) that the log ${N}_{{\rm{H}},\mathrm{HIM}}$ sin b ≈ 19.0, the CIE model strongly implies an [M/H] > 0.3 for the warm and hot components of the MW halo. We further note that the lower f_{C iv} values implied by nonequilibrium models with [M/H] ranging from 0.1 to 1.0 (brownish-red and green curves in Figure 12) would require N_H sin b > 19.4, or that >50% of the ionized hydrogen column in the halo be in this collisionally ionized 10⁵ K phase. This picture is not physical and would directly contradict the observational evidence that the WIM and the HIM are likely dominant contributors to the line-of-sight N_e (Reynolds 1993; Howk et al. 2006; Gaensler et al. 2008).

Previous considerations of collisionally ionized 10⁵ K gas in the MW halo have envisioned layers and/or interfaces (e.g., Fox et al. 2009; Wakker et al. 2012). In these structures, either conductive interfaces or turbulent mixing layers, predictions of log ${N}_{\mathrm{Si}{\rm{}}\mathrm{iv}}$/N_{C iv} lie in our observed range, but the total C iv column densities of each layer are closer to ∼10¹² cm⁻², two orders of magnitude lower than we observe (Kwak & Shelton 2010). This inconsistency is alleviated if we demand that our line of sight intersect hundreds of such overlapping layers. However, in this scenario, hundreds of layers cooling out of equilibrium would tend to imply values of log N_H sin b > 19.4 in this 10⁵ K "tenuous" gas phase, just as we described in the previous paragraph. Furthermore, hundreds of interfaces or layers between small cool clouds and the HIM are difficult to reconcile with the roughly kiloparsec-scale spatial correlations of the Si iv and C iv in the x-y plane.

Gas cooling behind supersonic shocks has also been invoked to explain the presence of highly ionized species such as Si iv and C iv in the CGM (Dopita & Sutherland 1996; Werk et al. 2016; McQuinn & Werk 2018). Under the assumption of a steady, 1D flow and a given metallicity, several models predict column densities of high and intermediate ions in the post-shock cooling layers. Here we use the results of Allen et al. (2008), who produce tables for gas at solar metallicity, shock speeds that range from 100 to 1000 km s⁻¹, and pressure exerted by the transverse magnetic field (Bn${}^{-\tfrac{1}{2}}$) ranging from 10⁻⁴ to 10 μG cm^−3/2. The magnetic pressure is important because it limits the compression through the shock, and thus higher magnetic parameters produce higher gas column densities. These shock models predict values of log N_{Si iv}/N_{C iv} to range widely from −1.0 to 0, mostly dependent on the shock speed. However, when we consider the predicted values of the gas column densities at the observed ratio of −0.7, they are closer to a few times 10¹² cm⁻² and 10¹³ cm⁻² for Si iv and C iv, respectively, or more than an order of magnitude lower than we observe.

We conclude that the collisional ionization case is most plausible if the intermediate-ionization gas is in CIE, presumably cooling from the hot coronal medium. In this picture, the 10⁶ K gas and the 10⁵ K gas would have the same metallicity, and the majority of the cooling would be taking place within 3 kpc of the MW disk. The contribution of the HIM to the value of N_e is uncertain, but if we return to the discussion in Section 5.1, we may use log ${N}_{{\rm{H}},\mathrm{HIM}}$ sin b ≈ 19.0 (Howk et al. 2006). Using the corresponding constraint on log ${N}_{{\rm{C}},\mathrm{total}}$ sin b ≈ 14.9 (Figure 12) in the collisionally ionized medium (CIM) and requiring that ${N}_{{\rm{H}},\mathrm{CIM}}$ < ${N}_{{\rm{H}},\mathrm{HIM}}$, we find that the hot corona of the MW must have [M/H] > 0.3 in this physical scenario.

Given the above constraints on the physical conditions of the C iv-bearing gas, we may estimate areal gas accretion rate for the observed region of sky containing our BHB lines of sight, parameterized as

$$\begin{eqnarray}&&\displaystyle \frac{{{dM}}_{\mathrm{gas}}}{{dtdA}}\equiv \displaystyle \frac{{M}_{\mathrm{gas}}{v}_{\mathrm{infall}}}{{d}_{\mathrm{gas}}\pi {R}_{\mathrm{cloud}}^{2}}\left[{M}_{\odot }\,{\mathrm{kpc}}^{-2}\,{\mathrm{yr}}^{-1}\right].\end{eqnarray} \tag{ 3 }$$

We determine the total gas mass from column density measurements, using an effective surface area calculation:

$$\begin{eqnarray}&&{M}_{\mathrm{gas}}=310\left(\displaystyle \frac{{Z}_{\odot }}{Z}\right)\pi {R}_{\mathrm{cloud}}^{2}\left\langle {N}_{{\rm{C}}{\rm{IV}}}\sin {\text{}}{\rm{b}}\right\rangle {\text{}}{m}_{{\rm{C}}}\left(\displaystyle \frac{1}{{f}_{{\rm{C}}{\rm{IV}}}}\right)\left[{M}_{\odot }\right].\end{eqnarray} \tag{ 4 }$$

Equation (4) assumes the solar abundance of carbon, 12 + log (C/H), to be 8.43 (Asplund et al. 2009). Among the quantities relevant to this calculation, we allow for the following values and ranges of values: (1) the vertical component of the mean C iv column density of the IV gas, $\left\langle {N}_{{\rm{C}}{\rm{IV}}}\sin {\text{}}b\right\rangle$ = 10^14.04 cm⁻²; (2) the fraction of carbon in C iv, 0.09 < f_{C iv} < 0.17; (3) the gas-phase metallicity, 0.3 < Z/Z_⊙ < 1.0; (4) the physical size scale of the absorbing structure R_cloud ≈ 1 kpc; (5) the vertical infall velocity of the IV component of C iv absorption, v_infall ≡ −v sin b ≈ 45 km s⁻¹; and (6) the distance to the absorbing structure, 1.0 kpc < d_gas < 3 kpc. We note that this areal mass infall rate considers only the material in this intermediate ionization state gas containing C iv and Si iv but captures constraints from both photo- and collisional ionization within the range of allowed f_{C iv} values and metallicities.

Following Equations (3) and (4), the resulting bounds on the areal mass accretion rate in warm, ionized gas at high Galactic latitudes are

$$\begin{eqnarray}&&0.0003\lt \displaystyle \frac{{{dM}}_{\mathrm{gas}}}{{dtdA}}\lt 0.006\left[{M}_{\odot }\,{\mathrm{kpc}}^{-2}\,{\mathrm{yr}}^{-1}\right].\end{eqnarray} \tag{ 5 }$$

This range of areal mass accretion rate encompasses the mean star formation rate surface density of the MW disk, $\left\langle {{\rm{\Sigma }}}_{\mathrm{SFR},\mathrm{MW}}\right\rangle$ = 0.0033 M_⊙ yr⁻¹ kpc⁻² (Kennicutt & Evans 2012). Our implied total mass infall rate of high-latitude WIM, dM_gas/dt, is 0.02 M_⊙ yr⁻¹ at most and at least 0.001 M_⊙ yr⁻¹. This range is lower than estimates from all-sky studies of the mass infall rates from the ionized components of HVCs and IVCs, excluding the Magellanic Stream, which find ranges of dM_gas/dt to be 0.45–1.40 M_⊙ yr⁻¹ at d < 15 kpc (Lehner & Howk 2011; Fox et al. 2019). It is also considerably lower than the mass infall rate for the entire MW halo, ≳5 M_⊙ yr⁻¹ (Fox et al. 2014; Richter et al. 2017). It is unlikely that the small neutral clumps we have observed in this region provide a substantive boost to this mass infall rate (e.g., Putman et al. 2012). However, it is possible that material from elsewhere in the halo makes it to the disk via other routes followed by radially mixing within the disk (e.g., Sellwood & Binney 2002). In contrast, our observations may instead imply that much of the more distant ionized halo material that is moving toward the MW disk never in fact makes it through the disk–halo interface to eventually form new stars (Joung et al. 2012).

Our data provide novel, independent constraints on the coherence scales of IV gas in low and intermediate ionization states at the disk–halo interface. We find that C iv and Si iv are strongly correlated over the full range of transverse separations probed by our sight lines (∼40° or 2 kpc at z = 3 kpc) and with N_{H i} from 21 cm emission. In contrast, the low ionization state material traced by Ca ii and Fe ii exhibits neither a correlation with N_{H i} nor a transverse separation (Figures 8 and 9). This readily apparent difference in ionic behavior indicates the existence of large, coherent ionized structures ≳1 kpc in size, containing cool, neutral cloudlets or clumps with spatial scales ≲10 pc (108 at z = 3 kpc). We explore the implications of this result in Section 6.2. Finally, we find that the implied areal mass infall rate of the high-latitude WIM encompasses the present-day mean star formation rate surface density of the MW disk, although it is slightly lower than previous estimates from all-sky data.

The Si iv/C iv ratio of the IV gas along our sight lines, −0.69 ± 0.04, shows remarkably little variation over ∼40°. We argue that this column density ratio places two mutually exclusive constraints on the physical conditions of the extraplanar gas under two distinct sets of assumptions: photoionization and collisional ionization. In the photoionization case:

• 1.  
  We assume that Si iv and C iv are produced by photoionization from a combination of starlight from the MW disk and the extragalactic UV background at z = 0 (Fox et al. 2005).
• 2.  
  We adopt constraints from in-depth work that constrains the cool, low ionization state IV gas to have a metallicity of approximately solar value, requiring that cool and warm gas are well mixed in terms of their metal content (Wakker et al. 2008).
• 3.  
  Finally, we assume that the total hydrogen column associated with the Si iv and C iv is given by the total electron column measured from pulsar DM experiments at high Galactic latitude, with appropriate corrections for He, the HIM, and the neutral gas fraction.

Proceeding in this framework of a photoionized WIM, we find that log N_{Si iv}/N_{C iv} ≈ −0.7 requires that Si be depleted relative to C by 0.25–0.35 dex compared to the solar value of Si/C. Under these assumptions, this paper would present observational evidence for a dusty WIM at the MW disk–halo interface. We explore the implications of this result in Section 6.3.

The other constraint on the physical state of the material relies only on the production of Si iv and C iv by collisional ionization in a ${10}^{5.2}$ K gas-phase cooling out of a hotter, 10⁶ K ambient medium with a density <8 × 10⁻⁴ cm⁻³ (e.g., Bregman & Lloyd-Davies 2007). When we consider the implied total hydrogen content of this transient, cooling phase, we find that there is significant tension if we allow halo [M/H] < 0.3. Thus, in the collisional ionization framework, our constraint on the total carbon content implies an MW corona that is enriched at a level of greater than one-third solar. This constraint would represent the first observational constraint on the metallicity of the hot corona of the MW.

Additional observations are required to determine which of these two models of the physical state of the IV gas is accurate. For example, access to doubly ionized species such as Si iii, S iii, Al iii, and Fe iii would better constrain the photoionization models and possibly provide further evidence of dust depletion in the ionized extraplanar material (e.g., Howk & Savage 1999). The detection of more highly ionized species such as O vi, O vii, or O viii in the IV gas would be crucial for a complete understanding of the nature of collisionally ionized material in the halo (Faerman et al. 2017). Finally, our results underscore the importance of ionization modeling that considers multiple gas phases under different ionization conditions, with the additional complicating consideration of significant depletion onto dust in ionized extraplanar material. Thus, to convincingly model the physical state of diffuse gas requires observers to study as many ionic species as possible along any given sight line.

We find that IV absorption from C iv and Si iv likely traces a coherent ionized structure at the disk–halo interface spanning at least ∼1 kpc across. The much larger scatter in the low ions (e.g., Ca ii) on the same spatial scales is consistent with a picture in which cool clumps of gas are considerably more compact (<10 pc in length scale). All of this gas most likely lies within 3.4 kpc of the MW disk and may contain enough total mass to maintain the current star formation rate of the MW.

6.2.1. Comparison with Complimentary Observational Analyses

6.2.2. Comparison with Simulations

Our photoionization modeling of extraplanar Si iv and C iv column densities suggests the presence of Si-bearing dust in the high-latitude WIM. Silicon depletions on the order of a few tenths of a dex are consistent with levels of depletion in DLAs of δ_Si = −0.27 ± 0.16 dex (measured with Si/Zn) assuming that carbon is not depleted itself (Vladilo et al. 2011). Si/C ratios of ∼−0.7 appear to occur in the neutral MW ISM at a value of F* of 0.3–0.5, where F* is the line-of-sight depletion strength factor (Jenkins 2009) that increases with increasing depletion. Notably, the 1σ sight-line-to-sight-line variation in Si/C we observe is only ±0.04 dex. Under the assumption of photoionization, this constant ratio would indicate remarkably uniform dust coverage over the kiloparsec-sized spatial scales of the material traced by Si iv and C iv.

We note that depletion onto dust from ionized material is not entirely unexpected. Howk & Savage (1999) discovered the first evidence for dust in the diffuse ionized gas of the Galactic ISM from modeling the observed ratio of Al iii/S iii, which traces the ratio of a depleted element (aluminum) to a nondepleted element (sulfur) in the ISM. Their result, like this one, is contingent on S iii and Al iii not having significant contributions from collisional ionization. Further confirmation of dust in an ionized phase came from Lagache et al. (1999, 2000), who first detected far-IR emission from high-latitude dust using COBE and H i data and refined this measurement with data from the Wisconsin Hα Mapper (WHAM). Additionally, Dobler et al. (2009) find evidence for a spinning dust component of the MW WIM by analyzing the Hα-correlated emission spectrum of the 5 yr WMAP data. Finally, a study by Gringel et al. (2000) found an absorption component of molecular hydrogen in an ORFEUS-Echelle spectrum at −62 km s⁻¹, which they associated with the MW halo, a sign that there are grains present on which H₂ can form. Both absorption and emission studies support a picture in which dust temperature and emissivity are similar between neutral and ionized gas, and that the processing of dust grains in the WIM is similar to that in the H i gas.

Dust may persist up to several megaparsecs from the disks of galaxies, as traced by a reddening coefficient similar to that of interstellar dust (Ménard et al. 2010; Peek et al. 2015). Furthermore, a substantial fraction of the metals generated within the galaxy may be lurking in a circumgalactic dust phase (Peeples et al. 2014). The coexistence of dust and highly ionized gas in galactic coronae has far-reaching implications for self-shielding, magnetic fields, molecule formation, gas cooling, and grain destruction in rarefied environments. Future studies of gas physics in the disk–halo interface and the CGM should incorporate the physics of dust and allow for nonsolar ratios of the elements to accurately interpret observations with hydrodynamical simulations.