PRESENT-DAY GALACTIC EVOLUTION: LOW-METALLICITY, WARM, IONIZED GAS INFLOW ASSOCIATED WITH HIGH-VELOCITY CLOUD COMPLEX A

Low-metallicity inflows of gas influence galactic evolution by providing new material for star formation and thereby modifying the metallicity of the interstellar medium (ISM) and the stars within galaxies. Many high-velocity clouds (HVCs) show indications of interaction with the Milky Way including Complex A, the Smith Cloud (Complex GCP), and the Magellanic Stream (e.g., Brüns et al. 2000; Lockman et al. 2008; Bland-Hawthorn 2009). Other nearby galaxies, such as M31, also seem to have HVCs interacting with them (e.g., Thilker et al. 2005; Westmeier et al. 2005). These clouds exhibit velocities that are inconsistent with Galactic rotation, generally defined as a local standard of rest (LSR) velocity greater than |90 km s⁻¹|. Accreted HVCs can dilute the gas in galactic systems and modify their chemical evolution. Understanding the metallicity history of the Milky Way, partly revealed through the G dwarf problem (van den Bergh 1962; Schmidt 1963; Pagel & Patchett 1975), and its star formation rate requires an understanding of these clouds.

The origin of most of these HVCs remains a mystery. No universal mechanism exists to explain their formation, so the origin of each cloud requires investigation. Considerable work has been done to uncover these origins. Oort (1966, 1970) already proposed most of the mechanisms that are still under consideration today, but at present, it is possible to point to specific examples for three of the processes that he suggested. The Magellanic System is the nearest example of a galaxy interaction producing high-velocity gaseous structures with material strewn throughout the halos of the Milky Way and the Magellanic Clouds. Models show that tidal forces and ram pressure can partly—if not dominantly—produce this stripped material as the clouds encounter each other and the Milky Way (e.g., Lin & Lynden-Bell 1977; Murai & Fujimoto 1980; Lin & Lynden-Bell 1982; Meurer et al. 1985; Gardiner & Noguchi 1996; Moore & Davis 1994; cf. Besla et al. 2010). Other than galaxy interactions, plausible sources of HVCs include residual primordial gas from the formation of the universe and material returning as part of a galactic fountain (Bregman 1980).

Numerous 21 cm studies have provided insight into the neutral gas component of HVCs, but few studies have investigated their warm (10⁴ K), ionized gas phase. This is because the emission lines from their ionized components are usually very faint, often less than a tenth of a Rayleigh,⁶ and require a highly sensitive instrument to detect (e.g., Complex K: Haffner et al. 2001; Complex L: Haffner 2005; Smith Cloud: Bland-Hawthorn et al. 1998; Putman et al. 2003; Hill et al. 2009; Complexes M, A, C: Tufte et al. 1998). Absorption-line studies have demonstrated the existence of diffuse ionized gas in the circumgalactic medium in both our local galactic neighbors and in higher redshift galaxies (e.g., Sembach et al. 2003; Wakker et al. 2005; Fox et al. 2006; Shull et al. 2009; Wakker & Savage 2009; Lehner & Howk 2007, 2011). However, because the sampling depends on the availability of background objects, these studies cannot quantify the large-scale distribution, morphology, and total mass of the gas.

Several studies place the heliocentric distance to Complex A between 8 and 10 kpc, or 5–7 kpc above the Galactic plane (Wakker et al. 1996, 2003; Ryans et al. 1997; van Woerden et al. 1999). This distance suggests an H i mass of ∼10⁶ M_☉ (van Woerden & Wakker 2004). There are currently no estimates for the mass of the warm ionized gas. Tufte et al. (1998) identified ionized gas in Complex A toward cores AIII and AIV with Hα detections of 80 ± 10 and 90 ± 10 mR, respectively, indicating the existence of a warm ionized component. Studies have found a sub-solar composition for Complex A (Kunth et al. 1994; Schwarz et al. 1995; Wakker et al. 1996, 2001; van Woerden et al. 1999), which suggests that it is new material accreting onto the Galaxy. Quantifying how much ionized gas is in Complex A is essential to understanding how this material will affect the Milky Way and the physical conditions of the gas in the Galactic halo.

Ionizing radiation from the Milky Way and extragalactic background could ionize Complex A, but some of the ionization could also come from interactions with the Galactic halo. If photoionization is predominantly responsible for producing the Hα emission, then measuring the Hα emission will constrain the escaping Lyman continuum flux from the Milky Way. If interactions with the halo produce Hα emission, then this cloud would probe the physical conditions of the surrounding halo gas. The unique elongated morphology of Complex A enables an investigation of these processes across multiple kiloparsecs. Mapping the Hα emission along the entire length of this complex will aid in determining the source of the ionized gas.

This study quantifies the extent, the amount, and the properties of the warm gas in Complex A through faint emission lines, allowing us to understand how accretion of this ∼10⁶ M_☉ of material will impact the metallicity and star formation rate of the Milky Way. In addition, we investigate the source of ionization and where this cloud— and similar clouds—could have formed. Section 2 describes mapped Hα and pointed Hα, [S ii] λ6716, [N ii] λ6584, and [O i] λ6300 observations. In Section 3, we define the modeling parameters used to interpret the observations, including the Hα extinction correction, the distance to the cloud, and the neutral and ionized gas distribution. Section 4 investigates if photoionization modeling from the Milky Way and extragalactic background can reproduce the observed Hα emission and produce realistic cloud properties. We then use the observations and the results from the photoionization modeling to place constraints on the physical properties of the cloud. In Section 5, we use the Hα line widths to constrain the electron temperature. Then, Section 6 investigates the total mass of the cloud by addressing the distribution of neutral and ionized gas and the projection angle of the cloud. Section 7 describes how our multi-wavelength detections restrict the S/H and N/H abundances. In Sections 8 and 9, we conclude with a discussion of the implications of this study and a summary of our results.

Using the Wisconsin Hα Mapper (WHAM) at the Kitt Peak National Observatory, we observed Complex A in 2005 and 2006 at the Kitt Peak National Observatory. WHAM is optimized to detect faint optical emission from diffuse ionized sources. The spectrometer, described in detail by Haffner et al. (2003), consists of a dual-etalon Fabry-Perot that produces a 200 km s⁻¹ wide spectrum with 12 km s⁻¹ resolution integrated over its 1° beam—the emission within the 1° beam is averaged to produce one spectrum. For this study, we configured the spectrometer to detect line emission in the range of −250 km s⁻¹ ≲ v_LSR ≲ −50 km s⁻¹ in both mapped and pointed modes, described below, where v_LSR is the velocity in the LSR frame.

2.1. Mapped Observations

WHAM surveyed a large region of the Galactic halo from $(\mathit {l, b}) = (124\mbox{$^\circ $}, 18\mbox{$^\circ $})$ to (171°, 53°) and from −250 to −50 km s⁻¹ using the strategy outlined by Haffner et al. (2003) for the Northern Sky Survey. As in the survey, observations are grouped into "blocks," 30–50 spectra mapped in a raster and taken sequentially in time. Individual exposures were 60 s with some locations, primarily along the length of the cloud, observed multiple times over multiple months. Throughout the year, Earth's orbit shifts Galactic emission (fixed in the LSR velocity frame) with respect to the widespread atmospheric lines that dominate the baseline (fixed in the geocentric velocity frame). Combining observations that span many months helps extract faint emission and minimizes residuals from the removal of the atmospheric background.

Figure 1 shows a representative series of spectra taken over three nights toward two directions at a similar Galactic latitude (b = −34°). Spectra in panel (a) were obtained toward core AIII, a region of higher H i column density as mapped by 21 cm observations. Panel (b) shows spectra from a direction near, but off the neutral Complex. In the top panels, we plot unreduced data against a geocentric velocity frame where zero corresponds to the wavelength of the Hα recombination line. Atmospheric features align vertically from night to night in this frame of reference, while Galactic features may move between observations. The wide feature near v_geo = −210 km s⁻¹ is "ghost" emission from the bright Hα geocorona at v_geo = −2.3 km s⁻¹ due to incomplete suppression of a neighboring order in the high-resolution etalon (see Haffner et al. 2003, Figure 2). The rise in the spectra near the red edge is due to lower-velocity emission from the Galaxy in this direction. Remaining ripples in the baseline between these two figures arise from faint atmospheric lines (I_Hα ≲ 0.2 R) and high-velocity Galactic Hα, our target of study. Different sky conditions and zenith distances cause a slight shift in vertical displacement in the baseline continuum in these spectra.

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To extract the Galactic emission, we follow a procedure similar to Haffner et al. (2003) for the Northern Sky Survey to subtract terrestrial emission. We construct a model of the atmospheric emission with a series of Gaussians using spectra from many regions across the sky expected to contain little to no high-velocity Galactic emission. This template, consisting of the geocentric velocity centroids, widths, and relative intensities for each of the faint atmospheric lines, is scaled and combined with a best-fit, zero-order continuum level to create the background for each individual spectrum. For this work, we have extended the atmospheric template presented in Hausen et al. (2002) to more negative velocities (thin, solid line at v_LSR > −200 km s⁻¹ in Figures 1(a) and (b)). To set the scale of the template, we fit high signal-to-noise "block averages" and estimate the absolute intensity of the template by adjusting it to minimize the χ² of the fit. This value is then used to scale the template as it is applied to each individual spectrum within the block.

For this data set, an additional Gaussian for the geocoronal "ghost" (thin, solid component in Figures 1(a) and (b) near v_geo = −210 km s⁻¹) is needed in every observation. Finally, when warranted, we add any components for high-velocity Galactic emission (thick, solid component in Figure 1(a) near v_geo = −150 km s⁻¹) to fully model a spectrum. The parameters for these (typically two) Gaussian components are allowed to vary to minimize the χ² of our fit. Using these model parameters, we subtract the background continuum, atmospheric template, and "ghost" component from the raw data. Spectra from multiple nights toward the same direction are averaged in the LSR frame to produce the final spectra used in this work. Figure 1 shows a representation of this procedure for two sample directions, one toward the neutral concentration AIII and one where no 21 cm emission has been detected at the complex velocities. Panel (c) shows a distinctive component in the fully reduced spectrum from the first direction at Complex A velocities with an intensity of 65 mR.

The map shown in Figure 2 integrates this new data set over velocities that trace Complex A. We also display the corresponding 21 cm emission from the Leiden/Argentine/Bonn Galactic H i Survey (LAB; Kalberla et al. 2005) over the same velocity range for comparison. This 21 cm survey will be used throughout our work to compare the H i and Hα emission. The new Hα data set contains some of the faintest extended emission regions we have mapped with WHAM to date. Our reduction method reveals Hα emission in the mapped region from Complex A as well as from a portion of Complex C, $(\mathit {l, b}) = (124\mbox{$^\circ $}, 45\mbox{$^\circ $})$ to (150°, 53°), and an outer arm of the Galaxy $(\mathit {l, b}) = (124\mbox{$^\circ $}, 18\mbox{$^\circ $})$ to (155°, 25°). Indeed, even the faintest Hα emission components appear at a similar velocity to that seen in the 21 cm (compared later in Figure 4), giving us confidence in our methods. The Hα emission has much less contrast but a broader angular extent than the 21 cm emission. Some of this difference could be related to the different beam sizes of the H i and Hα observations, where the WHAM beam is almost two times larger in diameter than the LAB survey's, and the insensitivity of the LAB survey to highly ionized regions with low $N_{\rm H\,{\mathsc { i}}}$. The LAB survey has a 3σ $N_{\rm H\,{\mathsc { i }}}$ sensitivity of ∼2 × 10¹⁸ cm⁻² for typical HVCs with widths of 30 km s⁻¹. As a result, the diffuse ionized emission further from the cores of the complexes may represent nearly fully ionized gas in the outskirts of these halo structures. The implications of this extended plasma for Complex A are more fully discussed in Sections 3.3 and 6.

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The global velocity structures of the warm and neutral gas generally agree (see Figures 2(c) and (d)), but the Hα gas has a lower mean velocity at core A0, higher at core AII, and lower at core AVI. The Galactic foreground Hα emission toward core A0 causes confusion, which has lowered the mean velocity toward this core. Both of the H i and Hα first-moment maps of Complex A, or intensity-weighted mean velocity along the line of sight, indicate that neither the warm nor neutral velocity components behave monotonically from core A0 to core AVI.

2.2. Pointed Observations

In addition to mapping Complex A in Hα, we obtained multiple, deep, 120 s "pointed" observations in Hα, [S ii], [N ii], and [O i]. In Table 1, we list the non-extinction-corrected intensities, the integrated exposure times, and the dates observed for the pointed observations. For observations taken toward Mrk 106, PG 0822+645, PG 0832+675, PG 0836+619, and IRAS 08339+6517, weather prevented the collection of pointed Hα observations. For these sightlines, Table 1 lists intensities from the mapped observations. The atmospheric contamination in the pointed observations was removed by subtracting the spectrum of a nearby off-source direction. We remove any residual continuum in the atmospheric subtracted spectrum by fitting a constant background level.

Table 1. Pointed Intensities and Dates Observed

	Position		Hα				[S ii] λ6716				[N ii] λ6584				[O i] λ6300
		$\bar{v}_{\rm {H}\,\mathsc { i}}$	Ia	texpc	Dated		Ia	texpc	Dated		Ia	texpc	Dated		Ia	texpc	Dated
	[ℓ, b]	(km s−1)	(mR)	(min)			(mR)	(min)			(mR)	(min)			(mR)	(min)
A0	1340, 250	−174.4 ± 0.2	<10	28	2
AI	1395, 290	−183.0 ± 0.2	<22	26	2
AII	1435, 325	−142.4 ± 0.2	24 ± 3 ± 5	26	2
AIII	1480, 337	−154.6 ± 0.1	59 ± 3 ± 10	26	2
AIII†	1485, 345	−153.0 ± 0.1	67 ± 2 ± 3	36	1		<26	28	7,8		26 ± 2 ± 9	24	8,9		<40	6	10
AIV	1536, 382	−173.9 ± 0.1	37 ± 3 ± 9	26	2
AIV†	1530, 385	−175.4 ± 0.1	50 ± 2 ± 14	36	1		16 ± 6 ± 11	28	7,8		<12	24	8,9		<91	6	10
AV	1570, 396	−159.9 ± 0.2	<17	24	2
AVI	1603, 433	−157.3 ± 0.2	59 ± 2 ± 5	24	2
Mrk 106	1611, 429	−158.0 ± 0.2	39 ± 3b				<36	10	7,8		33 ± 3 ± 5	24	8,9		<120	6	10
Mrk 116	1655, 448	−163.1 ± 0.5	32 ± 6 ± 13	26			25 ± 6 ± 16	10	7,8		<22	24	8,9		<125	6	10
Mrk 25	1527, 468	⋅⋅⋅	⋅⋅⋅	24	6
PG 0822+645	1516, 346	−168.4 ± 0.2	<29b					10	7,8			24	8,9		<88	6	10
PG 0832+675	1478, 350	−149.9 ± 0.2	25 ± 3b				<31	10	7,8		<34	24	8,9		<139	6	10
PG 0836+619	1545, 366	−173.3 ± 0.3	<17b				<34	10	7,8		<28	24	8,9		<86	6	10
IRAS 08339+6517	1505, 356	−156.3 ± 0.5	<28b				<61	10	7,8		<63	24	8,9		<125	6	10
Alow	1379, 275	−180.4 ± 0.6	<17	26	3
UGC 4483	1450, 344	−136.0 ± 2.0	<21	26	3
A⊥1	1383, 310	−157.0 ± 2.0	<15	26	3
A⊥2	1397, 303	−167.8 ± 0.4	<15	28	3
A⊥3	1411, 295	−164.7 ± 0.3	<25	26	4
A⊥4	1425, 288	−171.8 ± 0.4	<27	26	4
A⊥5	1440, 280	⋅⋅⋅	<17	26	4
Knot	1593, 357	−159.7 ± 0.5	<25	24	4
UGC 4305	1443, 327	−142.9 ± 0.3	<16	24	4
A26	1363, 266	−155.6 ± 1.8	<23	24	6
A31	1490, 310	−175.4 ± 0.4	<16	26	6
A33	1470, 322	−147.5 ± 0.5	<32	26	5
A36	1500, 360	−148.8 ± 0.3	46 ± 3 ± 8	26	5
A38	1540, 385	−175.5 ± 0.1	<26	26	5
A41	1590, 410	−155.9 ± 0.2	28 ± 4 ± 8	24	6

Notes. ^aNon-extinction corrected intensities. The first set of errors represents statistical uncertainties; the second set denotes the uncertainty in measuring the intensity. These values are dominated by systematics associated with differences between the ons and offs (see Section 2.2); the mapped Hα observations presented in Figure 2 do not suffer from the same effects as they are reduced using an atmospheric template. ^bIntensity from the mapped Hα data set. ^cEach individual exposure is 120 s long; the values listed represent the integrated exposure time. ^dDates observed: (1) 2005 March 8; (2) 2005 December 5; (3) 2007 March 15; (4) 2007 March 20; (5) 2007 May 10; (6) 2007 May 11; (7) 2007 November 09; (8) 2007 December 15; (9) 2007 December 16; (10) 2008 January 29. ^†Slightly offset from the H i cores to match Tufte et al. (1998).

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Although the pointed and mapped observations have different total exposure times and underwent atmospheric subtraction through a different procedure, many of the Hα intensities agree to within the combined uncertainties in overlapping pointed and mapping observations; however, the pointed observations are prone to increased uncertainty due to systematic effects associated with minor atmospheric differences between the ons and offs. These differences can cause notable discrepancies between the intensities derived from these two methods. Two main effects increase the noise of the pointed observations. (1) Some of the offs contain trace amounts of ionized gas emission. The patchy nature of the ionized gas emission increases the probability that the offs partially overlap with regions containing ionized gas, especially with the 1° angular resolution of these observations. Furthermore, the ionized component of Complex A may extend many degrees off of the neutral component, as is typical with other HVCs (e.g., Lehner et al. 2012). (2) The atmospheric contribution varies slightly from position to position on the sky, which can significantly decrease the signal-to-noise ratio of the resultant spectra when observing extremely faint objects like Complex A. For atmospherically subtracted pointed spectra with ill-defined spectral components, we only report upper limits in Table 1. The mapped Hα observations presented in Figure 2 do not suffer from the same effects as the pointed values, as they are reduced using an atmospheric template and are therefore more reliable.

These optical emission-line spectra include emission from the Galactic warm ionized medium, especially in Hα, [S ii], and [N ii] spectra at velocities > − 120 km s⁻¹. The Hα and the [O i] suffer from an additional spectral contamination at velocities <−220 km s⁻¹ in the form of an incomplete suppression of a neighboring high-resolution etalon order of the geocoronal line. For these reasons, we avoided the v_LSR >−120 and v_LSR <−220 km s⁻¹ spectral regions when determining the background level. In addition, the [O i] spectra include faint, time-varying, atmospheric lines. As such, Table 1 only lists the upper intensity limit of the [O i] observations. The detection limit is the calculated area of a Gaussian with a width equal to that of the H i line along the same sightline and a height equal to three times the standard deviation of the scatter in the background. To account for the systematic uncertainties from the faint atmospheric lines, in addition to reporting the statistical uncertainties, Table 1 also reports systematic uncertainty—the uncertainty of the measurement. To characterize both the statistical and systematic uncertainties, we fit each spectrum multiple times. First, we calculated the value that minimizes χ² with the mean, width, and the area of the Gaussian unconstrained; this yielded the reported intensity and the statistical error. Second, we varied the base line of the fit to attain Δχ² = 1. Third, we fit the line by constraining various fitting parameters, including the mean velocity and width—measured from the average H i spectra along the same sightline—held constant; the H i spectra were smoothed to a 1° angular resolution to match the Hα resolution. Parameters describing the Hα fit with H i mean velocities and width along the same sightline were incorporated because of the asymmetrical profile of the Hα emission. The systematic uncertainties of the Hα intensity reported in Table 1 are the root mean square of the intensities derived from these fits.

The [N ii] and [S ii] emission lines from the ionized gas in Complex A are faint. In many directions, the emission is below our 3σ detection limit. The sightlines with signal above the 3σ detection limit are listed in Table 1. To visually represent this upper limit, Figure 3 includes 3σ Gaussian profiles. Figure 3 displays four sightlines with Hα detections, but only the core AIII and Mrk 106 sightlines have detectable [N ii] emission and only core AIV and Mrk 116 sightlines have detectable [S ii] emission. The construction of this "ideal" 3σ profile incorporated two assumptions for the spectra of the neutral and ionized gas along the same sightline: (1) that they have the same peak velocity and (2) that they have the same width. The height of the ideal profile is defined as three times the standard deviation of the background. Although this is an idealized profile, the center velocity of H i and the Hα lines generally agree in HVCs (see Figure 4; Bland-Hawthorn et al. 1998; Tufte et al. 1998; Putman et al. 2003; Hill et al. 2009). Since the Hα width cannot be measured directly toward sightlines with an asymmetrical distribution, the second assumption provides an estimate of the minimum width expected. Figure 5 shows that the Hα lines can be substantially wider than the H i lines. Wider Hα lines could indicate that the ionized gas is warmer, that non-thermal line-broadening effects influence the ionized gas more than the neutral gas, or that the ionized gas is present in multiple, distinct components along the line of sight. Broad Hα lines are certainly consistent with a scenario where photoionization provides an additional heating source for the gas. However, bulk dynamic effects, such as enhanced internal turbulence or expansion of an ionized region, could also account for the difference in widths. Finally, the Hα emission may be exposing regions of the complex that are highly ionized and have become kinematically distinct from its neutral core (${N}_{{\rm H}\,{\mathsc{i}}} \gtrsim 10^{17} \, \mathrm{cm}^{-2}$). In any case, the combination of the lack of correlation between the Hα and H i widths and intensities, as shown in Figure 6, suggests that the Hα-emitting gas is likely not mixed with the H i that shapes the 21 cm profiles.

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Many of the pointed Hα observations targeted dense H i cores. We obtained additional multiline spectra slightly offset from neutral cores AIII and AIV to follow up on the Hα detections in Tufte et al. (1998). The Hα intensities reported here differ from those listed in Tufte et al. (1998), 80 ± 10 mR for core AIII and 90 ± 10 mR for core AIV, as a consequence of using constant baselines instead of sloped ones. Interestingly, these sightlines show brighter Hα emission than the sightlines centered on the H i cores. Figure 3 displays the spectra for these two sightlines. Many of the combined spectra taken over the two month observing cycle toward faint directions became flattened, broadened, or an artificial multiple peaked distribution due to shifted atmospheric lines in the LSR frame.

To complement past and future absorption-line work, many of the pointed sightlines were targeted toward sightlines with known background quasars and UV-bright stars. UV absorption spectra toward background quasars constrain the metallicity of the absorbing HVCs; absorption toward foreground and background stars with known distances, such as RR Lyrae and blue horizontal branch stars, have been used to bracket the distance to the HVC (see Wakker 2001 and Wakker et al. 2008 for compilations of these studies). The noisy Mrk 116 spectra in Figure 3 suggest the presence of ionized emission, but the Hα emission is below the 3σ detection limit. A majority of the [O i] spectra also demonstrate this two-component behavior; this is likely due to contamination from small changes in the atmosphere during the observations.

These new observations of Complex A place important constraints on some of the physical properties of the HVC and its immediate environment within the halo. In Sections 4 through 7, we explore the source of ionization, electron temperature, mass, and metal abundance of Complex A. Here, we discuss several other input parameters that complement the observations which we use to model the HVC.

3.1. Hα Extinction Correction

The position of Complex A above the Galactic Plane results in minimal interstellar dust extinction. We expect that most of the extinction comes from either local interstellar dust or dust in the foreground Perseus Arm. We use the reddening given in Diplas & Savage (1994) for a warm diffuse medium with a low density:

$$\begin{equation} E(B-V)=\frac{\langle N_{\rm H\,{ \mathsc {i}}}\rangle }{4.93\times 10^{21} \, \mathrm{cm}^{-2}}\ {\rm mag}, \end{equation} \tag{ 1 }$$

where the average H i column density $\langle N_{\rm H\,{ \mathsc {i}}}\rangle$ includes only the foreground H i emission. If the extinction follows the 〈A(Hα)/A(V)〉 = 0.909 − 0.282/R_v optical curve presented in Cardelli et al. (1989) for a diffuse ISM, where R_v ≡ A(V)/E(B − V) = 3.1, then the expression for the total extinction becomes

$$\begin{equation} A(\mathrm{H} \alpha)=\frac{\langle N_{\rm H\,{ \mathsc {i}}}\rangle }{1.95\times 10^{21} \, \mathrm{cm}^{-2}} \mathrm{ mag}. \end{equation} \tag{ 2 }$$

The average H i column density of the foreground toward the dense H i cores is 3.7 × 10²⁰ cm⁻², yielding an 8% average Hα extinction correction. All subsequent sections correct for extinction using the LAB survey H i column densities, smoothed to 1° resolution to match the WHAM observations, except when comparing Hα, [N ii], and [S ii] intensity ratios as the difference in extinction is negligible over such a small wavelength range.

3.2. Distance to the Cloud

3.3. Distribution of the Neutral and Ionized Gas

The unknown morphology along the length of the cloud and the unknown distribution of the ionized gas make accurately calculating the mass of Complex A difficult. We estimate the mass using a procedure similar to that employed by Hill et al. (2009). For simplicity, these calculations assume that the neutral gas has a line-of-sight depth (L) similar to its width as listed in Column 5 of Table 2. The depth of the ionized gas depends on its distribution, which could be well mixed with the neutral gas or surrounding the neutral gas as an ionized skin. This distribution depends on the physical processes influencing the cloud. External ionizing sources, such as the Lyman continuum from the Milky Way and the extragalactic background, could create a photoionized skin around the cloud. Interactions between the cloud and Galactic halo could also ionize the outer layer of the cloud through collisional ionization or through photoionization from radiation emanating from shock heated gas (Bland-Hawthorn et al. 2007).

Table 2. Neutral and Ionized Properties

	Foreground	Neutral Properties					Ionized Skin (ne = 1/2n0)		Ionized Skin (ne = n0)		Mixed ($L_{\rm H^+}$=$L_{\rm {H}\, \mathsc { i}}$)		Assumed d
Regiona	log  〈$N_{\rm {H}\, \mathsc { i}}$〉b	log  〈$N_{\rm {H}\, \mathsc { i}}$〉b	$M_{{\rm H}^0}$c	log  $L_{\rm {H}\, \mathsc { i}}$	log  〈n0〉	〈EM〉d	$\log \ L_{\rm H^+}$d	$M_{\rm {H^+}}$d	$\log \ L_{\rm H^+}$d	$M_{\rm {H^+}}$d	log  〈ne〉d	$M_{\rm {H^+}}$d
	( cm−2)	( cm−2)	(105 M☉)	(kpc)	( cm−3)	(10−3  pc cm−6)	( kpc)	(105 M☉)	( kpc)	(105 M☉)	( cm−3)	(105 M☉)	( kpc)
Distance to each region reflects a projected angle anchored by measured distancese
A0	20.7	19.4	0.5	2.4	−1.5	136	2.6	0.7	2.0	0.3	−1.7	0.5	6.1
AI	20.6	19.6	2.2	2.7	−1.6	111	2.7	1.7	2.1	0.9	−1.8	1.5	6.9
AII	20.5	19.3	1.1	2.6	−1.8	74	3.1	2.1	2.5	1.1	−1.9	1.2	7.5
AIII	20.6	19.6	2.0	2.6	−1.6	97	2.6	1.4	2.0	0.7	−1.9	1.3	8.0e
AIV	20.6	19.6	4.5	2.8	−1.8	77	2.9	4.4	2.3	2.2	−2.0	3.6	8.6
AV	20.6	19.3	1.3	2.7	−1.8	97	3.1	3.0	2.5	1.5	−1.9	1.6	9.3e
AVI	20.3	19.4	2.4	2.8	−1.9	123	3.4	7.4	2.8	3.7	−1.9	3.4	9.9e
B	20.5	19.1	1.6	2.8	−2.1	81	3.7	9.4	3.1	4.7	−2.0	3.1	9.9
All regions assumed to have a distance of 9.0  kpc e
A0	20.7	19.4	1.1	2.6	−1.7	136	3.0	2.2	2.4	1.1	−2.9	1.3	9.0
AI	20.6	19.6	3.7	2.8	−1.7	111	2.9	3.8	2.3	1.9	−2.5	3.0	9.0
AII	20.5	19.3	1.6	2.7	−1.9	74	3.2	3.7	2.6	1.8	−2.7	1.9	9.0
AIII	20.6	19.6	2.5	2.7	−1.6	97	2.7	2.1	2.1	1.0	−2.7	1.8	9.0e
AIV	20.6	19.6	5.0	2.8	−1.8	77	3.0	5.0	2.4	2.5	−2.4	4.0	9.0
AV	20.6	19.3	1.3	2.7	−1.8	97	3.1	2.7	2.5	1.3	−2.8	1.5	9.0e
AVI	20.3	19.4	2.0	2.7	−1.8	123	3.3	5.6	2.7	2.8	−2.6	2.7	9.0e
B	20.5	19.1	1.3	2.8	−2.1	81	3.6	7.1	3.0	3.5	−2.6	2.4	9.0
All regions assumed to have a Galactic height 5.7  kpc above the disk e,f
A0	20.7	19.4	2.6	2.8	−1.8	136	3.3	7.6	2.7	3.8	−1.9	3.6	13.7
AI	20.6	19.6	6.4	2.9	−1.9	111	3.2	8.8	2.6	4.4	−2.0	6.0	11.9
AII	20.5	19.3	2.3	2.8	−2.0	74	3.4	6.3	2.8	3.2	−2.0	3.1	10.8
AIII	20.6	19.6	3.1	2.7	−1.7	97	2.8	2.8	2.2	1.4	−1.9	2.3	10.0e
AIV	20.6	19.6	5.2	2.9	−1.8	77	3.0	5.4	2.2	2.7	−1.8	4.2	9.2
AV	20.6	19.3	1.2	2.6	−1.8	97	3.1	2.5	2.4	1.3	−1.8	1.4	8.8e
AVI	20.3	19.4	1.7	2.7	−1.8	123	3.3	4.5	2.7	2.3	−1.8	2.2	8.4e
B	20.5	19.1	1.3	2.8	−2.1	81	3.7	3.8	3.1	3.8	−2.1	2.5	9.2
Distances from matching the MW and EGB ionizing flux with the ΦLC(Hα) e
A0	20.7	19.4	0.6	2.6	−1.5	136	2.7	0.8	2.1	0.4	−1.8	0.5	6.4
AI	20.6	19.6	2.2	2.8	−1.6	111	2.7	2.2	2.1	0.9	−1.9	1.5	6.9
AII	20.5	19.3	2.0	2.7	−2.0	74	3.3	5.0	2.7	2.5	−2.0	2.5	10.0
AIII	20.6	19.6	2.1	2.7	−1.6	97	2.7	1.6	2.1	0.8	−1.9	1.5	8.3 e
AIV	20.6	19.6	4.9	2.8	−1.8	77	3.0	4.9	2.4	2.4	−2.0	3.9	8.9
AV	20.6	19.3	1.1	2.7	−1.8	97	3.1	2.3	2.5	1.1	−1.9	1.3	8.5 e
AVI	20.3	19.4	1.5	2.7	−1.8	123	3.2	3.5	2.6	1.7	−1.8	1.8	7.7 e
B	20.5	19.1	1.2	2.8	−2.1	81	3.6	6.6	3.0	3.3	−2.0	2.3	8.8

Notes. ^aThese regions are defined in Table 3 and shown graphically in Figure 2. ^bThe average uncertainty for the foreground H i is 7.0 × 10¹⁶ cm⁻² and 5.8 × 10¹⁶ cm⁻² for Complex A. ^c${M}_{{\rm H}^0}=1.4$ $N_{\rm {H}\, \mathsc { i}}$ Ω d². ^dAssumes an electron temperature of 10⁴ K. ^eFrom absorption-line studies, the distance to core AIII is greater than 8.1 kpc, the distance to core AV is greater than 4.0 ± 1.0 kpc, and the distance to core AVI is less than 9.9 ± 1.0 kpc (Wakker et al. 1996, 2003; Ryans et al. 1997; van Woerden et al. 1999). ^fThe constant height above the Galactic plane at z = 5.7 kpc is defined by placing the midpoint of cores AIII and AVI at a distance of 9.0 kpc.

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If the warm gas is distributed as an ionized skin, then that skin could be either in pressure equilibrium with a small sound crossing time compared to the recombination time or in pressure imbalance with a sound crossing much larger than the recombination time. If the ionized gas is in pressure equilibrium with the neutral gas and if the gas phases are at the same temperature, then the electron density (n_e) of an ionized skin equals half the neutral hydrogen density (n₀; Hill et al. 2009). For the case of pressure imbalance, we choose to explore the properties of the cloud at a constant density with n_e = n₀. Regardless of whether the ionized skin is in pressure equilibrium with the neutral component, the emission rate of Hα is proportional to the recombination rate of hydrogen $\left(\alpha _{{\rm H}_{\alpha }}\right)$ and the average number of Hα photons produced per recombination $\left(\epsilon _{{\rm H}_{\alpha }}\right)$:

$$\begin{equation} {I_{\rm {H}\alpha }} =\left(4\pi \right)^{-1} \int \alpha _{B}(T)\ \epsilon _{{\rm H}_{\alpha }}(T)\ n_e\ n_p\ dl_{{\rm H}^+}, \end{equation} \tag{ 3 }$$

where n_p ≈ n_e, α_B = 2.584 × 10⁻¹³ (T/10⁴ K)^−0.806 cm³ s⁻¹ (Martin 1988), and $\epsilon _{{\rm H}_{\alpha }}(T)\approx 0.46\times (T/10^4\, {\rm K})^{-0.118}$. If the electron density and temperature are constant over the emitting region, then the path length of the ionized gas is given by

$$\begin{equation} L_{{\rm H}^+}=2.75\ \left(\frac{T}{10^4\, {\rm K}}\right)^{0.924} \left(\frac{{I_{\rm {H}\alpha }} }{R}\right) \left(\frac{n_e}{ \, \mathrm{cm}^{-3}}\right)^{-2} \, \mathrm{pc}. \end{equation} \tag{ 4 }$$

In deriving densities and temperatures, we assumed that the gas within each WHAM beam consists of three components: neutral gas with a density n₀ with some volume filling fraction, ionized gas with a density n_e with some volume filling fraction, and an empty void filling the rest of the sightline. This approach has long been used to describe ionized gas (e.g., Reynolds 1991) and is a reasonable approximation in the absence of detailed information about the distribution of the gas along each sightline. However, in reality, fluid interactions in the cloud likely produce a range of densities in both the neutral and ionized gas. If the gas is turbulent and the density distribution is lognormal, then this can lead to considerably lower true mean densities and higher filling fractions than suggested by the analysis used here (Hill et al. 2008).

The mass calculations of Complex A include an exploration of three possible distributions of ionized gas: an ionized skin of equal pressure to the neutral component, an ionized skin of equal density to the neutral component, and a fully mixed cloud without an ionized skin. We list the mass calculated with each of the assumptions that yield realistic cloud properties in Table 2 for each of the high H i column density core regions.

A substantial amount of the gas in Complex A is ionized, but what causes this ionization? Complex A lies within the Galactic halo at 2.6–6.8  kpc above the Galactic plane, depending on the orientation of the cloud. Photoionization from hot stars in the disk of the Milky Way and the extragalactic background could produce a significant amount of ionized gas, but hydrodynamical interactions between the cloud and the Galactic halo could also collisionally ionize the cloud. To explore whether photoionization could be responsible for the observed Hα emission, we compare the properties of a cloud bathed in enough ionizing photons to produce the observed Hα emission, constrained by the observed geometrical properties of the cloud and by the measured H i column density. We then compare these results with a cloud illuminated by the Milky Way and the extragalactic background to test if the these sources can produce the observed Hα emission.

We model the radiative processes with Cloudy (version C08.00; Ferland et al. 1998) by approximating Complex A as a plane-parallel slab with the radiation incident from one side of the cloud. Although the extragalactic background radiation is isotropic, the typical H i column density of Complex A exceeds 10¹⁸ cm⁻² and therefore is optically thick to Lyman continuum radiation. For this modeling, we use an abundance of 0.1 solar for Complex A (e.g., van Woerden & Wakker 2004; B. P. Wakker et al. 2013, in preparation) and the results from Asplund et al. (2009) for the relative abundances. With this framework, we use Cloudy to model the physical conditions in the cloud for a series of volume density values. The thickness of the cloud is constrained by requiring the total column density of neutral hydrogen to match the observed values. Cloudy then finds the column densities of all the elements for a situation where there is an equilibrium between ionization and recombination. It also yields the temperature of the gas corresponding to the heating provided by the incoming ionizing photons. For each assumed volume density, we then use the resulting thickness and electron density to calculate the Hα emission measure. We estimate the incident ionizing flux by combining the extragalactic radiation field of Haardt & Madau (2001) with the model of Bland-Hawthorn & Maloney (1999, 2001), as updated by Fox et al. (2005); this model predicts the intensity of interstellar radiation as a function of wavelength and location in the Milky Way halo. Since the H i column density is fixed for each HVC core, we only have a two-parameter fit: the assumed projection geometry of Complex A and the volume density. We show below that matching the modeled Hα emission to the observed value also fixes the volume density.

If photoionization produces the observed Hα emission, a line produced through recombination, then the rate of total hydrogen recombination must be proportional to the incident flux of the Lyman continuum:

$$\begin{eqnarray} \phi _{{\rm LC}} &= \int \alpha _B(T)\ n_e n_p dl_{{\rm H}^+} \end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray} &\simeq 4\pi \frac{{I_{\rm {H}\alpha }} (T)}{\epsilon _{{\rm H}_{\alpha }}(T)}, \end{eqnarray} \tag{ 6 }$$

Combining Equation (6) with ${\epsilon _{{\rm H}_{\alpha }}}$ (see Section 3.3) for a gas optically thick to Lyman continuum radiation, as the H i column density is greater than 10¹⁸  cm⁻², the flux reduces to

$$\begin{equation} \phi _{{\rm LC}} = 2.1\times 10^5\left(\frac{{I_{\rm {H}\alpha }} }{0.1\,{\rm R}}\right)\left(\frac{T}{10^4\, {\rm K}}\right)^{0.118}\ {\rm photons}\ {\rm cm}^{-2}\ {\rm s}^{-1}. \end{equation} \tag{ 7 }$$

For warm gas at 10⁴ K, heated only through photoionization, the observed Hα emission from Complex A corresponds to an incident ionizing flux of ∼10⁵ photons cm⁻² s⁻¹. To explore the properties of a cloud illuminated by this ionizing flux, we model the photoionization of multiple representative clouds with Cloudy. We investigate the properties of clouds with different total hydrogen densities, −4.0 < log (n_H/ cm⁻³) < 1.0, guided by the observed H i column densities. Requiring the observed and predicted Hα emission to match, as shown in Figure 7 for core AIV, we compared the properties of the resultant clouds. The predicted Hα emission is derived using Equation (4), such that $L_{{\rm H}^+}=N_e/\left(n_{{\rm H}}\times {\rm volume\ filling\ fraction\ of\ ionized\ H}\right)$, where N_e is the electron column density and n_H is the total hydrogen number density. Table 4 lists the predicted properties of Complex A using this model.

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In general, the Cloudy model produces warm cores with temperatures of log (T/K) ∼ 4.1. The configuration with well-mixed ionized and neutral gas produces low-density cores, with electron densities between −4.0 < log (n_e/ cm⁻³) < −1.7; the scenarios where the ionized gas and neutral gas are either in pressure equilibrium or imbalance are defined by fixing n_e compared to n₀. The path length solutions for the neutral gas, determined through observations of the H i gas, are either equivalent to or slightly less than the predicted path length for the ionized gas for the well-mixed and pressure imbalance cases, but greatly differ for the pressure equilibrium configuration. This indicates that the neutral and ionized gas phases are probably well mixed or in pressure imbalance. However, scenarios where the predicted path length for the ionized gas exceeds a kiloparsec—compared to the smaller path length of the neutral gas that is only a few hundred parsecs long (see Table 2)—could be explained if the Galactic halo provides pressure confinement as hypothesized by Spitzer (1956), which would reduce their extent. Spitzer (1956) shows that a low-density, hot, Galactic corona can greatly confine and substantially reduce the path length of a cloud.

Could the Milky Way and the extragalactic background supply a large enough Lyman continuum flux to produce the observed Hα emission? Bland-Hawthorn & Maloney (1999, 2001) model the ionizing flux radiating from the Milky Way by assuming that the 90–912 Å radiation is dominated by O-B stars confined to spiral arms;⁷ this model predicts the shape and strength of both the soft and hard radiation field emitted by the Milky Way. Haardt & Madau (2001) predict the ionizing flux from the extragalactic background radiation by assuming that the radiation is dominated by quasi-stellar objects, active galaxy nuclei, and active star forming galaxies. We approximate the extragalactic background contribution of ionizing photons as a constant flux with 3.22 × 10⁴ photons  cm⁻²  s⁻¹ along the entire complex. Any attenuation of the extragalactic background flux should be minimal as the cloud is located above the Galactic disk. Using the incident ionizing flux from these models, we investigate which distances would reproduce the observed Hα emission. Figure 8 illustrates these results for a cloud at a constant distance of 9  kpc from the Sun, for a cloud inclined through (1477, 350) at 8.1  kpc and (1600, 433) at 9.9  kpc, and for a cloud at a constant height of z = 5.7  kpc as defined by placing the midpoint of cores AIII and AVI at a distance of 9.0  kpc. The solid diagonal line represents the locations where the predicted ionizing fluxes from the observed Hα emission and the Milky Way and extragalactic background flux models match.

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The solutions for Complex A at a constant distance of 9.0  kpc underpredict the ionizing flux for most of the H i cores. The ionizing flux solutions at a constant distance of z = 5.7  kpc underpredict fluxes for cores A0 and A1 and overpredict fluxes for the remaining cores. The Lyman continuum solutions for the inclined complex produce a better match, but do not adequately predict the necessary fluxes for every core. Figure 9 shows that the expected incident Lyman continuum flux from these models varies very little between each core with distance from the Sun. If photoionization from the Milky Way is the dominant ionization source, then the ionizing continuum from both the Milky Way and the extragalactic background can be used to predict the distance that each core would need to reproduce the observed Hα emission. Table 4 lists these distances. These predicted distances agree with the distance constraints found through absorption-line studies; specifically, the distance to core AIII is greater than 8.1  kpc, the distance to core AV is greater than 4.1 ± 1  kpc, and the distance to core AVI is less than 9.9 ± 1  kpc.

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Although the Bland-Hawthorn & Maloney (1999, 2001) model predicts enough escaping ionizing radiation from the Milky Way to produce reasonable cloud properties, this model might underpredict the ionizing flux at small distances above the Galactic midplane. Wood et al. (2010) argue that this model underpredicts the ionizing flux because it confines all ionizing sources to the Galactic midplane and is attenuated by a uniform density slab of dust. Instead, Wood et al. (2010) suggest that three-dimensional simulations are needed to account for low-density paths and voids that are produced in a turbulent ISM. These voids and low-density paths allow the ionizing photons from the midplane to penetrate and ionize the Galactic halo.

The source of the ionization can influence the morphology of Complex A and of the individual cores. Brüns et al. (2000) suggest that HVCs interacting with their surrounding ambient medium could have a head-tail morphology, similar to that of a comet, where the tails corresponds to material stripped from the HVC core. Using H i observations from the Leiden/Dwingeloo survey (Hartmann & Burton 1997), Brüns et al. (2000) find that many of the dense H i cores in Complex A exhibit this head-tail morphology, as does the Smith Cloud (e.g., Lockman et al. 2008). Bland-Hawthorn et al. (2007) find that as clouds travel through the halo, some of their leading gas can become stripped and trail behind. The trailing gas can then shock the downstream gas, resulting in an ionized skin and fragmentation. The elongated multi-core structure of Complex A could indicate that this cloud has became ionized and fragmented as it passed through the Galactic halo. The collisionally excited gas will produce variations in the [S ii]/[N ii] ratio along the length of the cloud (Haffner et al. 1999). Unfortunately, the signal-to-noise ratio of the [S ii] and [N ii] lines is too low to constrain the contribution of collisional ionization. Although Lyman continuum fluxes predicted by the Bland-Hawthorn & Maloney (1999, 2001) and Haardt & Madau (2001) models of the ionizing photons originating from the Milky Way and the extragalactic background can produce the observed Hα emission and realistic cloud properties, the morphology of Complex A suggests that interactions with the halo might also contribute.

Reynolds (1985) derived a method for calculating the temperature of Hα emission using its width (FWHM_Hα) and the velocity profile:

$$\begin{equation} \frac{T}{10^4\, \mathrm{K}}\approx \left(\frac{\mathrm{FWHM}_{\mathrm{H} \alpha }}{21.4\, \mathrm{ {\rm km\, s^{-1}}}}\right)^2-\left(\frac{v_{\mathrm{p,\, {\rm non-therm}}}}{12.8\, \mathrm{ {\rm km\, s^{-1}}}}\right)^2-0.070, \end{equation} \tag{ 8 }$$

where v_{p, non-therm} is the most probable speed (mode) of the non-thermal distribution of gas particles. Ideally, we would calculate the v_{p, non-therm} by comparing the width of the Hα line with the line width of much heavier elements like sulfur or nitrogen, since bulk motions equally affect gas in equilibrium but thermal motions influence the lighter particles more than the heavy ones. Unfortunately, the low signal-to-noise ratio of the [S ii] and [N ii] observations make measuring their widths difficult. Neglecting non-thermal broadening mechanisms, we calculate the upper limit of the electron temperature due to thermal broadening effects alone. Only a few sightlines exhibit high enough signal to noise to accurately measure the width of the Hα line: AII, AIII, AIV, A₄₁, and two pointings just off the centers of cores AIII and AIV. The average of these solutions, weighted by the error in the FWHM²_Hα, gives a temperature of (3.0 ± 0.3) × 10⁴ K, shown in Figure 10. This method can only place constraints on the maximum thermal contribution on the line widths and places no constraints on the non-thermal broadening mechanisms.

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The source of the ionization in Complex A constrains the lower electron temperature limit. In Section 4, we found that photoionization can produce the observed Hα emission and reasonable cloud properties. If photoionization dominates, then the Cloudy results for the four different inclinations of Complex A included in Table 2 indicate that the lowest reasonable electron temperature consistent with the Hα detections is 8000 K. Note that the Cloudy modeling only provides a rough estimate of this lower limit based on the idealized pure photoionized circumstances described in Section 4. Figure 7 shows that at 8000 K, the expected Hα intensity for core AIV drops rapidly for lower electron temperatures. This trend is consistent for each of the cores.

The Milky Way must be accreting external sources of gas to sustain star formation, as its gas consumption time is only 1–2 Gyr (Larson et al. 1980). Inflowing low-metallicity gas could supply this material and reproduce the stellar abundance patterns in the Milky Way. HVCs may represent much of this inflow. Quantifying both the neutral and ionized mass in circumgalactic gas structures constrains the accretion rate of galaxies. Four effects dominate the uncertainty in accurately calculating the mass of Complex A: the distance to the cloud, the projection angle of the cloud, the morphology of the cloud along the line-of-sight, and the distribution of ionized and neutral gas within the cloud. The distance to the cloud, its projection, and the distribution of the ionized and neutral gas are discussed in Section 3. When estimating the mass of the cloud, we consider the four different cloud projections in Section 3.2 and the three gas distributions in Section 3.3.

Because the Hα emission is proportional to the square of the density, the mass of the ionized gas also depends on the electron density squared. The mass of the ionized gas is given by $M_{{\rm H}^+}=1.4m_{\rm H} n_e D^2 \Omega L_{{\rm H}^+}$, where m_H is the mass of a hydrogen atom, Ω is the solid angle, D is the distance to the cloud from the Sun, and the factor of 1.4 accounts for helium. For a 1° circular beam—the angular resolution of the Hα observations—the mass of the ionized gas is given by (Hill et al. 2009)

$$\begin{equation} \left({\frac{M_{{\rm H}^{+}}}{M_\odot }}\right)_{{\rm beam}}=8.26\left(\frac{D}{\textmd {kpc}}\right)^2 \left(\frac{EM}{\mathrm{pc\, cm^{-6}}}\right)\left(\frac{n_e}{\textmd {cm}^{-3}}\right)^{-1}. \end{equation} \tag{ 9 }$$

The emission measure, EM ≡ ∫n²_e dL_H⁺, is given as

$$\begin{equation} EM=2.75\ \left(\frac{T}{10^4\, {\rm K}}\right)^{0.924} \left(\frac{{I_{\rm {H}\alpha }} }{R}\right) \, \mathrm{pc} \; \mathrm{cm}^{-6}, \end{equation} \tag{ 10 }$$

using Equation (4) for the $L_{{\rm H}^+}$ and by assuming that both the electron density and the temperature are constant over the emitting region. Since the more diffuse Hα emission generally follows the H i, we use the neutral core structures to divide the complex into distinct regions where we estimate gas mass. These regions are defined in Table 3 and shown in Figures 2(c) and (d). Table 2 lists the estimated H i and Hα mass for these regions.

Table 3. Region Locations

Region	sq. deg	(l, b)1	(l, b)2	(l, b)3	(l, b)4
Total	433.5	1680, 510	1300, 270	1341, 217	1700, 360
A0	30.4	1350, 300	1300, 270	1335, 225	1375, 240
AI	50.0	1410, 340	1360, 300	1380, 230	1440, 260
AII	42.0	1450, 365	1410, 350	1435, 260	1480, 280
AIII	31.7	1468, 382	1450, 365	1480, 287	1525, 300
AIV	72.5	1530, 420	1470, 380	1528, 302	1592, 326
AV	29.5	1570, 440	1530, 418	1575, 356	1602, 388
AVI	39.1	1628, 479	1563, 445	1598, 394	1649, 428
B	64.4	1690, 447	1600, 394	1633, 338	1702, 363

Notes. The (l, b)_n indicates the corner positions for the regions and are shown graphically in Figure 2.

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To determine the ionized mass of Complex A, we exclude the faint Hα emission more than 25 from the 3 × 10¹⁸  cm⁻² H i column density contours because a definitive association is less certain between the faint H i and Hα gas. Therefore, the calculated Hα mass should be treated as a minimum. In several of the sightlines that are close to the H i contours, absorption associated with Complex A is absent; this is true for both highly ionized ions, such as O vi, and for low-ionization species, such as C ii (Fox et al. 2006). As a result, the extended ionized envelope around Complex A may be patchy.

The largest uncertainty in determining the mass of Complex A comes from the uncertainty in distance for each of the high H i column density cores. Section 3.2 discusses the four projections used to estimate the distance to each of these regions. The H⁰ mass estimate for Complex A ranges from 1.6 to 2.3 × 10⁶M_☉ depending on the projection used. The H⁺ mass estimate has a larger variation due to the unknown distribution of the ionized gas. One of these distributions, where the skin is in pressure equilibrium with the H i such that n_e = 1/2n₀, seems unphysical as the solutions give line-of-sight distances on the order of a few kiloparsecs. The H⁺ mass ranges from 1.3 to 2.5 × 10⁶M_☉ depending on the projection angle and the distribution of gas—excluding the distribution where the Hα skin is in pressure equilibrium with its surroundings. From these estimates, the mass of the H⁺ gas appears to be at least comparable to the neutral gas of Complex A.

Determining the metallicity of Complex A limits the possible formation mechanisms that created this cloud and provides information on the material that the Milky Way accretes. Four sightlines along the length of Complex A constrain the composition of the cloud. The sightlines toward Mrk 106 and core AIII constrain the nitrogen abundance; the sightlines toward Mrk 116 and core AIV restrict the sulfur abundance. These four sightlines are the only directions with >3σ detections of emission in metal lines.

Hydrogen recombination produces Hα emission and collisional excitation produces [N ii] λ6583 and [S ii] λ6716 emission lines; these interactions make these three spectral lines sensitive to the electron temperature, the ionization fraction of the gas, and the electron density. The intensity ratios eliminate the geometry dependency by removing the electron density—assuming that the emission originates from the same region. The [N ii]/Hα intensity ratio toward the same sightline is given by (Haffner et al. 1999)

$$\begin{eqnarray} \frac{\rm{[N\,{ {\mathsc{ii}}}]}}{\mathrm{H} \alpha } &=& 1.63 \times 10^5 \left[\left(\frac{\mathrm{H}^+}{\mathrm{H}}\right)^{-1} \frac{\mathrm{N}^+}{\mathrm{N}} \right]\nonumber\\ &&\times \left(\frac{\mathrm{N}}{\mathrm{H}}\right) \left(\frac{T}{10^4\, {\rm K}}\right)^{0.426} e^{\left[-2.18/\left(T/10^4\, {\rm K}\right)\right]}, \end{eqnarray} \tag{ 11 }$$

where N⁺/N and H⁺/H are the ionization fractions and N/H is the gas-phase abundance by number. Similarly, the [S ii]/Hα intensity ratio is given by

$$\begin{eqnarray} \frac{\rm{[{S\,{ {\mathsc{ii}}}}]}}{\mathrm{H} \alpha } &=& 7.64 \times 10^5 \left(\frac{\mathrm{H}^+}{\mathrm{H}}\right)^{-1} \left(\frac{{\rm S}^+}{{\rm S}} \frac{{\rm S}}{\mathrm{H}} \right)\nonumber\\ &&\times \left(\frac{T}{10^4\, {\rm K}}\right)^{0.307} e^{\left[-2.14/\left(T/10^4\, {\rm K}\right)\right]}, \end{eqnarray} \tag{ 12 }$$

where S⁺/S is the ionization fraction and S/H is the gas-phase abundance by number.

When the ionization fractions of the singly ionized species and the gas temperature are known, Equations (11) and (12) can be used in conjunction with our observations to constrain the gas-phase abundances. Figures 11 and 12 show this relationship for a reasonable range of ionization fractions and temperatures constrained by our best-determined ratios: [S ii]/Hα toward core AIV and Mrk 116 and [N ii]/Hα toward core AIII and Mrk 106. The symbols in these figures denote estimates for the ionization fractions at a fixed temperature and configuration and are summarized in Table 5. Cloudy modeling of core AIV, using the input geometry discussed in Section 3.2, determines five of these values. The gas temperature in the emitting region is assumed to be 10⁴ K in all cases except one, where we use 10^4.1 K reflecting the discussion in Section 4. We also show a solution where the singly ionized nitrogen, sulfur, and hydrogen ionization fractions are equal. While N⁺/N  ∼  H⁺/H is a reasonable assumption for diffusely ionized gas with similar ionization potentials and a weak charge–exchange reaction, this assumption is likely an oversimplification for sulfur as this ratio can vary in warm ionized gas due to the low second ionization potential (23.4 eV) of sulfur (e.g., Haffner et al. 1999; Madsen et al. 2006).

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As Figures 11 and 12 show, without tighter constraints on the ionization fraction and temperature, this current data set does not place tight constraints on the nitrogen and sulfur abundances. Previous studies suggest that this cloud has an abundance of roughly a tenth solar (e.g., Kunth et al. 1994; Schwarz et al. 1995; Wakker et al. 2001, 1996; van Woerden et al. 1999). The abundance solutions, determined with the observed line ratios, become consistent with previous studies when the gas has a temperature above 10⁴ K or when the gas has a high singly ionized fraction of nitrogen and sulfur (see Table 5 and Figures 11 and 12).

The metallicity of HVCs provides one of the tightest constraints on the possible origins of the cloud. This study finds that many of the possible cloud configurations have a sub-solar metallicity, which drops rapidly with electron temperature (see Figures 11 and 12). The Cloudy modeling of a cloud bathed in Lyman Continuum determined by the Hα emission suggests that the electron temperature is above 8000 K to be consistent with the measured Hα intensities. The Hα line widths of the bright targeted observations suggest that the electron temperature is less than 3.3 × 10⁴ K, as determined from the weighted average of the temperature determined for six sightlines. Many of the cloud configurations place the Complex A abundances below solar, which may indicate that the cloud originated from somewhere other than the Milky Way disk.

Other studies also suggest a sub-solar composition for Complex A (e.g., the oxygen abundance is between 0.03 and 0.4 solar: Kunth et al. 1994 and Wakker et al. 2001; the magnesium abundance is greater than 0.035 solar: Wakker et al. 1996; $N_{{\rm Ca}\,{\mathsc{ii}}}/{N_{\rm {H}\, \mathsc { i}}} = 19\times 10^{-9}\pm 5\times 10^{-9}$: Schwarz et al. 1995 and van Woerden et al. 1999), which indicates that the cloud probably originated from material stripped off a nearby satellite galaxy or from low-metallicity intergalactic gas; however, no complementary stellar stream has been found to suggest that this complex has been stripped from a dwarf galaxy. Complex A does lie in the projected orbital path of the Orphan Steam (Belokurov et al. 2007), but the kinematics of are not consistent with an association (Newberg et al. 2010). Though this and previous studies investigate the metallicity of Complex A, none tightly constrain its metallicity and further studies are needed to constrain the origin of this cloud.

The ionized gas is a major component of the total mass in Complex A. The incident radiation from the Milky Way and the extragalactic background can produce the observed Hα emission. However, the long multi-core morphology of Complex A suggests that interactions with the halo also contribute. The morphology could indicate that the outer layers of the cores are being stripped and are shocking the trailing gas; this could cause the cloud to fragment while traveling through the halo (Bland-Hawthorn 2009). The shock model presented by Raymond (1979) predicts the production of a range of low-ionization emission lines, such as [S ii] and [O i]; the signal-to-noise ratios of the observations of [S ii] and [O i] are too low to identify shocks as a major ionization source of these lines. The two sightlines with detected [S ii] show a large variation in [S ii]/Hα, possibly indicating that these two regions experience large variations in ionization or excitation conditions (Reynolds et al. 1999). Furthermore, a shock excitation scenario could explain the non-uniform Hα intensities along the length of the cloud as the Hα flux would vary strongly with the shock and ambient density (Tufte et al. 1998).

Though the distance to Complex A has been constrained to be about 8–10 kpc toward one foreground star and one background star (Ryans et al. 1997; van Woerden et al. 1999; Wakker et al. 2003), the morphology of the complex makes its projection uncertain and creates a large ambiguity in determining the total mass of the cloud. To anchor the projection angle, more locations along the length of the cloud need their distances measured. This discrepancy must be resolved to understand how much replenishment this cloud offers the Milky Way and to understand how this cloud interacts with the Galactic halo, since the density of the halo varies with distance from the Galaxy.

Populations of mostly neutral, partially ionized, and highly ionized HVCs exist around other galaxies (e.g., M 101, NGC 891, NGC 2403, NGC 6946, M 83, M 33; see Sancisi et al. 2008 for a review), but little is known about the extent of the 10⁴ K ionized gas. Though many studies have investigated the hot (10⁶ K) component of HVCs, these studies require background sources to study this highly ionized medium; this makes quantifying the extent of the hot gas difficult. Further investigations of the ionized component of these clouds will help discern the extent and the source of this ionized gas. Understanding all of the gas phases in HVCs is essential to unraveling how these clouds affect galaxy evolution.

Using WHAM to observe the warm gas phase in Complex A, we mapped the Hα emission over 1350 deg². These kinematically resolved observations—over the velocity range of −250 to −50 km s⁻¹ in the LSR reference frame—include the first full Hα intensity map of Complex A. We compare these observations of the warm ionized gas phase with the H i 21 cm emission in the LAB survey. Additionally, we include 31 deep targeted observations in Hα and 8 in [S ii] λ6716, [N ii] λ6584, and [O i] λ6300 toward H i dense regions, background quasars, and stars to investigate the physical properties of this cloud. This study finishes with five main conclusions from the observations and Cloudy modeling of the warm gas component in Complex A:

• 1.  
  Ionizing sources. The properties of a purely photoionized cloud, modeled with Cloudy, can reproduce clouds with reasonable properties (see Table 4). For a purely photoionized cloud, the Bland-Hawthorn & Maloney (1999, 2001) and Haardt & Madau (2001) Lyman continuum models of the Milky Way and extragalactic background, respectively, place the distances to dense H i cores between 8.1 and 11.5  kpc, just within the distance bounds inferred through absorption-line studies.
• 2.  
  Ionized skin. The Hα morphology follows the global H i distribution, but the Hα emission does not closely trace the H i emission on small scales (see Figure 2). At the H i cores, the Hα emission often has a lower intensity and an offset velocity distribution. This indicates that the Hα and H i emission trace different paths through the clouds—warm ionized gas probably surrounds cold cores. This skin is likely not in pressure equilibrium with the H i because that equilibrium would result in extreme line-of-sight lengths for the ionized gas.
• 3.  
  Ionized gas mass. The total mass of the ionized gas in Complex A depends on four still uncertain factors: the distance to the cloud, the projection angle of the cloud, the morphology of the cloud along the line of sight, and the distribution of the neutral and ionized gases within the cloud. The distance to the high latitude end of Complex A is between 8 and 10  kpc; however, the distances to the lower latitude H i cores are not yet constrained by direct distance measurements. The distribution of the ionized gas either envelops the neutral gas—where the ionized gas is not in pressure equilibrium with the H i—or partially mixes with the neutral gas. Accounting for each of these factors, the total mass of the ionized gas could range from 1.3 to 2.5 × 10⁶M_☉, compared to 1.6 to 2.3 × 10⁶M_☉ for the neutral component; these mass estimates exclude the extended Hα emission that is more than 25 off the 3 × 10¹⁸  cm⁻² H i column density contour. As a result, the ionized component makes up a significant fraction of the overall composition of Complex A.
• 4.  
  Temperature of the ionized component. The Hα line width constrains the maximum kinetic electron temperature of the gas. Comparing Hα line widths toward sightlines with bright emission, we find an upper limit of 10^4.5 K for this temperature.
• 5.  
  Sulfur and nitrogen abundance. The sulfur and the nitrogen detections toward four sightlines reveal a sub-solar composition over a wide range of possible electron temperatures and ionization fractions, as shown in Figures 11 and 12; however, the [S ii] and [N ii] detections presented in this study do not place tight constraints on the abundance. These figures illustrate that different assumed projection angles of Complex A cause variations in the metallicity solution. These solutions combined with previous abundance studies of Complex A suggest that many configurations are only plausible for gas above 10⁴ K or with a high singly ionized fraction of nitrogen and sulfur.

Table 4. Properties of Photoionized Regions with ϕ_LC(Hα) Estimated from Hα Observations

Region	Observed			Predicted
	〈log $N_{\rm {H}\, \mathsc { i}}$〉a	〈Hα〉a,b	log ϕLC(Hα)c	log nHd	log ned	$\log N_{{\rm H}^+}$d	log Ted	$\log L_{{\rm H}^+}$e	$\log L_{{{\rm H}\,\mathsc { i}}}$e	df
	( cm−2)	(mR)	($\# \, \mathrm{cm}^{-2} \, \mathrm{s}^{-1}$)	( cm−3)	( cm−3)	( cm−2)	(K)	(kpc)	( kpc)	( kpc)
A0	19.4	52 ± 2	5.1	−2.8 to −2.3	−2.8 to −2.4	20.6 to 20.0	4.1 to 4.1	2.0 to 0.9	2.0 to 0.9	6.3 to 6.5
AI	19.6	42 ± 1	5.0	−2.6 to −2.3	−2.6 to −2.5	20.2 to 20.0	4.1 to 4.1	1.5 to 1.0	1.4 to 1.0	6.8 to 8.1
AII	19.3	27 ± 2	4.9	−2.1 to −1.9	−2.3 to −2.1	19.6 to 19.4	4.0 to 4.0	0.4 to 0.1	0.4 to 0.0	8.5 to 10.3g
AIII	19.6	36 ± 2	5.0	−2.3 to −2.2	−2.6 to −2.4	20.1 to 20.0	4.1 to 4.1	1.3 to 0.8	1.2 to 0.8	8.0 to 8.6
AIV	19.6	29 ± 1	4.9	−2.6 to −2.3	−2.5 to −2.4	19.9 to 19.7	4.1 to 4.0	1.0 to 0.7	0.9 to 0.6	8.6 to 11.3
AV	19.4	36 ± 3	5.0	−2.4 to −1.9	−2.5 to −2.1	20.0 to 19.6	4.1 to 4.0	1.1 to 0.2	1.0 to 0.2	8.3 to 11.1 g
AVI	19.4	45 ± 2	5.1	−2.4 to −2.1	−2.5 to −2.2	20.1 to 19.8	4.1 to 4.0	1.2 to 0.5	1.2 to 0.5	6.7 to 9.3 g
B	19.2	30 ± 3	4.9	−2.0 to −1.6	−2.1 to −1.9	19.5 to 19.2	4.0 to 4.0	0.3 to −0.3	0.2 to −0.4	8.5 to 10.1

Notes. ^aAverage value for the region. ^bExtinction corrected. ^cCalculated by assuming all the observed Hα emission comes from photoionization, Equation (7), with a log (T/K) = 4.1. ^dCompatible properties of a cloud, with log (n_H/cm⁻³) > −4.0, that produce the observed Hα emission. Quantities are ordered in increasing n_H, where $n_{{\rm H}}=n_{{\rm H}_2}+n_{{\rm H}^0}+n_{{\rm H}^+}$. ^eNeutral and ionized line-of-sight depth, where $L_{{\rm H}\,\mathsc { i}}=N_{{\rm H}}/n_{{\rm H}}$ and $L_{{\rm H}^+}=N_e/\left(n_{{\rm H}}\times {\rm fraction\ of\ ionized\ H}\right)$. N_H and N_e are the electron and hydrogen column densities and n_H is the total hydrogen number density. ^fCalculated using the Bland-Hawthorn & Maloney (1999, 2001) photoionization model of the Milky Way and the Haardt & Madau (2001) model of the extragalactic background radiation. If no value is given, then these models are unsuccessful at predicting a flux that matches log ϕ_LC(Hα) any distance. ^gFrom absorption-line studies, the distance to core AIII is greater than 8.1 kpc, the distance to core AV is greater than 4.0 ± 1.0 kpc, and the distance to core AVI is less than 9.9 ± 1.0 kpc (Wakker et al. 1996, 2003; Ryans et al. 1997; van Woerden et al. 1999).

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The authors acknowledge helpful discussions with Bob Benjamin and Joss Bland-Hawthorn and the anonymous referee for comments and suggestions, which greatly improved the paper. We thank Joss Bland-Hawthorn for providing us with the model for the ionizing radiation emitted from the Milky Way and Kurt Jaehnig for his outstanding technical support in the continuing operation of the WHAM instrument. The National Science Foundation supported WHAM through grants AST 0204973, AST 0607512, and AST 1108911. A.K.D. received support through REU site award AST-0453442. The infrastructure at Kitt Peak is made possible by National Optical Astronomy Observatory and the Tohono Oodham Nation. Kitt Peak National Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation.

Facility: WHAM - Wisconsin H-Alpha Mapper