The Diffuse Ionized Gas Halo of the Small Magellanic Cloud

After pre-processing the observations with the standard WHAM pipeline (Haffner et al. 2003), the spectra span a 200 $\mathrm{km}\,{{\rm{s}}}^{-1}$ velocity window with 2 $\mathrm{km}\,{{\rm{s}}}^{-1}$ bins in an arbitrary velocity frame. Figure 3(i) highlights the wing of the OH line, centered at a geocentric velocity of +272.44 $\mathrm{km}\,{{\rm{s}}}^{-1}$. This wing dominates the red edge of the velocity window. We use the OH line in combination with an estimated velocity shift based on multiple observations to find the velocity offset.

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We assume that our background continuum level is linear over our 200 $\mathrm{km}\,{{\rm{s}}}^{-1}$ window at all velocities. However, when a foreground star is present, the spectra will be elevated and contain stellar absorption lines. Beams that contain stars with m_V < 6 within a 0.55 radius (∼9% of our observations) are excluded from this survey to minimize this foreground contamination and are replaced with an average of the uncontaminated observations within 1°.

Night-to-night changes in the atmosphere cause variations in the strength of the bright and faint atmospheric lines. The OH line (Meriwether 1989) is produced from interactions between solar radiation and Earth's upper atmosphere and varies in strength with the direction and the time of the observation based on the Earth–Sun geometry. Therefore, we always fit the OH line at ${v}_{\mathrm{geo}}=+272.44\,\mathrm{km}\,{{\rm{s}}}^{-1}$ separately from the faint atmospheric lines, which vary due to the air mass (see Section 3.3). There are two main sources that alter the shape of the bright atmospheric lines: (1) the "tuning" of the dual etalons, where the precision in aligning the dual-etalon transmission functions can have slight night-to-night variations in the instrument profile. These effects are only detectable in narrow, bright lines. (2) A geocoronal "ghost." The "ghost" lies under the lies underneath the OH line at v_geo = +272.44 $\mathrm{km}\,{{\rm{s}}}^{-1}$. As described in Haffner et al. (2003), it is the result of incomplete suppression of the geocoronal line at v_geo = −2.3 $\mathrm{km}\,{{\rm{s}}}^{-1}$ from a neighboring order in the high-resolution etalon. In the velocity window observed in this study ($+50\leqslant {v}_{\mathrm{LSR}}\leqslant +250\,\mathrm{km}\,{{\rm{s}}}^{-1}$), some of the SMC emission may lie under the OH wing. However, because the velocity in this window only contains a portion of the OH line, it is difficult to fit well. To minimize over-subtracting the SMC emission, we assign a width of 10 $\mathrm{km}\,{{\rm{s}}}^{-1}$ to the narrow OH line Gaussian fit to prevent inclusion of lower velocity emission not attributed to the OH line. However, removal of some higher-velocity SMC emission is unavoidable. We therefore integrate our emission maps over a $+90\ \leqslant {v}_{\mathrm{LSR}}\leqslant +210\ \mathrm{km}\,{{\rm{s}}}^{-1}$ to avoid the contaminated regions. All H i emission maps and mass calculations are integrated over the same range for consistency.

While the OH line dominates over the other atmospheric emission, faint atmospheric lines are present throughout the entire spectrum with intensities of ∼0.1 R. The strength of these lines is correlated with the air mass. BHB13 created a synthetic atmospheric spectra to describe the faint atmospheric lines observed at Cerro-Tololo International Observatory (CTIO) by observing two faint directions multiple times over a 10 day period. Properties of the atmospheric lines can be found in Table 1 and Figure 3 of BHB13, and the template creation and subtraction process is also described by Hausen et al. (2002) and Haffner et al. (2003). Our averaged spectrum consists of numerous 30 and 60 s observations, totaling 4.5 hr, toward $({\ell },b)=(60\buildrel{\circ}\over{.} 0^\circ ,-67\buildrel{\circ}\over{.} 0)$ and $(89\buildrel{\circ}\over{.} 0,-71\buildrel{\circ}\over{.} 0)$. These are "faint" directions that appear to have no strong ${\rm{H}}\alpha$ emission, so the atmospheric lines can be identified. To account for changes in the flux due to the air mass and daily fluctuations, we scale the synthetic template to match the emission present in a high signal-to-noise ratio (S/N) block-averaged spectrum. We then subtract the scaled atmospheric template from the observation. The total integrated intensity of the template over the SMC window is ∼0.07 R.

3.4.1. Foreground Extinction

The ${\rm{H}}\alpha$ intensity emitted from the SMC is attenuated by foreground dust from the MW, as well as dust from within the SMC itself. To correct for foreground MW extinction, we used the method outlined in BHB13 (their Section 3.4.1):

$$\begin{eqnarray}&&{I}_{{\rm{H}}\alpha ,\mathrm{corr}}={I}_{{\rm{H}}\alpha ,\mathrm{obs}}{e}^{A({\rm{H}}\alpha )/2.5},\end{eqnarray} \tag{ 1 }$$

where,

$$\begin{eqnarray}&&A({\rm{H}}\alpha )=5.14\times {10}^{-22}\left\langle {N}_{{\rm{H}}{\rm{I}}}\right\rangle {\mathrm{cm}}^{2}\,\,{\mathrm{atoms}}^{-1}\,\,\mathrm{mag}.\end{eqnarray} \tag{ 2 }$$

We integrate the total H i intensity over the −100 to +100 $\mathrm{km}\,{{\rm{s}}}^{-1}$ velocity range. The extinction correction is important to the mass calculations in Section 4.4. We use three different methods to estimate the mass. In one, called the ellipsoidal scenario, we calculate the extinction per beam. In the other two, we use the extinction averaged over the area to stay consistent with the mass calculation methods. Accounting for the dust attention due to the foreground materials results in a 12.9%–14.4% increase in ${I}_{{\rm{H}}\alpha }$ resulting from the foreground extinction for the SMC region, a 14.6%–16.6% and 13.7%–15.8% increase in the H i and ${\rm{H}}\alpha$ Tail regions, and a 6.4%–7.6% increase from the SMC-filament foreground (Table 1).

Table 1.  Extinction

Region	Foreground Extinction			Internal Extinction
	log $\left\langle {N}_{{\rm{H}}{\rm{I}}}\right\rangle$	$A({\rm{H}}\alpha )$ a	${ \% }_{\mathrm{corr}}$	log $\left\langle {N}_{{\rm{H}}{\rm{I}}}\right\rangle$	$A({\rm{H}}\alpha )$	${ \% }_{\mathrm{corr}}$
SMC	20.5	0.15–0.14	12.9%–14.4%	21.0	0.24–0.27b	20–23%
H i SMC Tail	20.6	0.17–0.20	14.6%–16.6%	20.5	0.06–0.03	6.0%–5.6%
${\rm{H}}\alpha$ SMC Tail	20.6	0.17–0.19	13.7%–15.8%	20.7	0.11–0.6	10.0%–9.7%
SMC filamentc	20.2	0.07–0.08	6.4%–7.6%	⋯	⋯	⋯

Notes.

^aThe first listed value was determined by averaging $\left\langle {N}_{{\rm{H}}{\rm{I}}}\right\rangle$ in the region used to calculate masses in all scenarios other than the ellipsoidal scenario (see Section 4.4). The second value is a result smoothing HI4PI to a 025 pixel grid similar to match the smoothed WHAM maps and was only applied to the ellipsoidal scenario. ^bInternal extinction correction for the SMC is only applied to ${\rm{H}}\alpha$ regions, which coincide spatially with ${N}_{{\rm{H}}{\rm{I}}}$ $\geqslant {10.0}^{20.0}$ cm⁻². ^cNo internal extinction values were available for the SMC filament region.

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3.4.2. SMC Extinction

The extended envelope of the SMC has not been thoroughly studied for dust content. However, the bar of the SMC was sampled in Gordon et al. (2003). They find an ${R}_{V}=2.74,{A}_{V}\,\backsimeq 7.6\times {10}^{-23}\ \langle {N}_{{\rm{H}}{\rm{I}}}\rangle$ cm² mag and an average E (B − V) = 0.179 mag. To estimate the ${\rm{H}}\alpha$ extinction in the SMC, we combine Equations (1) and (4) from Gordon et al. (2003) to describe how the dust-attenuated ${\rm{H}}\alpha$ emission scales with ${N}_{{\rm{H}}{\rm{I}}}$:

$$\begin{eqnarray}&&A({\rm{H}}\alpha )=\left(\displaystyle \frac{E({\rm{H}}\alpha -V)}{E(B-V)}\right){R}_{V}^{-1}\langle {N}_{{\rm{H}}{\rm{I}}}\rangle {\mathrm{cm}}^{2}\ \mathrm{mag}.\end{eqnarray} \tag{ 3 }$$

We calculate the value using results listed in Gordon et al. (2003) Tables 2 and 3 for the SMC, $E({\rm{H}}\alpha -V)=0.197$ mag, and the resulting equation is $A({\rm{H}}\alpha )=1.057\times {10}^{-22}\left\langle {N}_{{\rm{H}}{\rm{I}}}\right\rangle \,{\mathrm{cm}}^{2}$ mag. We apply the extinction correction only on the central region of the SMC for observations (or beams) with an ${N}_{{\rm{H}}{\rm{I}}}$ > 1.0 × 10²⁰ cm⁻² over an integrated velocity range of $+90\leqslant {v}_{\mathrm{LSR}}\leqslant +210\,\mathrm{km}\,{{\rm{s}}}^{-1}$, where the gas is coincident with the visible stellar component of the galaxy. ${N}_{{\rm{H}}{\rm{I}}}$ is determined using the H i 4π (HI4PI) survey smoothed to 025 pixels to match our angular resolution when calculating the extinction in our ellipsoidal scenario (HI4PI Collaboration et al. 2016). Our ionized skin and cylindrical scenarios use the average ${N}_{{\rm{H}}{\rm{I}}}$ of the region to calculate the extinction for the regions in the SMC where ${N}_{{\rm{H}}{\rm{I}}}$ > 1.0 × 10²⁰ cm⁻². All areas of the SMC with lower column than our cutoff were only foreground-extinction corrected. Correcting the ${\rm{H}}\alpha$ intensities for the dust within the structure results in an average 21%–23% increase for the region of the SMC where ${I}_{{\rm{H}}\alpha }\gt 0.5$ R. Because the ${\rm{H}}\alpha$ emitting regions lie throughout the SMC and not necessarily behind the full dust extent, our correction provides an upper limit for the ${\rm{H}}\alpha$ intensities.

BHB13 included an analysis of the ${\rm{H}}\alpha$ and H i Tail of the SMC (see the region designated in Figure 2). Based on their WHAM observations, the region was integrated over $+100\leqslant {v}_{\mathrm{LSR}}\leqslant +300\,\mathrm{km}\,{{\rm{s}}}^{-1}$. They calculated a mass estimate using the same methods described in Section 4.4. We use an updated data reduction and intensity correction method compared to BHB13. The previous WHAM reduction pipeline included a standard 0.93 intensity correction applied universally to each night. The new pipelines calculates a night-to-night intensity variation based on the seeing conditions for a night and uses a standard calibrator (λ Ori) to calculate the transmission. In addition to the night-to-night variation, we include the transmission degradation WHAM optics in our corrections. On average, this results in a ∼20% correction to the intensity used in the BHB13.

Outside the core of the SMC, the brighter ${\rm{H}}\alpha$ emission does not appear to directly correlate with the densest H i regions. Toward the Stream, there is a bright region of ${\rm{H}}\alpha$ emission starting at $({\ell },b)=(305\buildrel{\circ}\over{.} 5,-50\buildrel{\circ}\over{.} 0)$ in a region we will refer to as the SMC–Stream interface. Conversely, the dense neutral filament from $b=-47^\circ$ to $-55^\circ$ has little ${\rm{H}}\alpha$ emission. The faint ${\rm{H}}\alpha$ emission reaches several degrees beyond the boundaries of the H i gas to the south, extending out toward the Magellanic Stream. ${\rm{H}}\alpha$ emission above 0.16 R can be observed in areas without bright H i emission, such as the H i gap from $({\ell },b)=(315\buildrel{\circ}\over{.} 5,-50\buildrel{\circ}\over{.} 0)$ to $(307\buildrel{\circ}\over{.} 0,-47\buildrel{\circ}\over{.} 5)$. While WHAM is reliably sensitive to emission lines at ${I}_{{\rm{H}}\alpha }$ ≥ 25 mR, WHAM can detect continuous emission above 10 mR.

In Figure 5, we present ${N}_{{\rm{H}}{\rm{i}}}$ and ${I}_{{\rm{H}}\alpha }$ maps at several velocity ranges, $+90\leqslant {v}_{\mathrm{LSR}}\leqslant +130\,\mathrm{km}\,{{\rm{s}}}^{-1}$, $+130\leqslant {v}_{\mathrm{LSR}}\,\leqslant +170\,\mathrm{km}\,{{\rm{s}}}^{-1}$, and $+170\leqslant {v}_{\mathrm{LSR}}\leqslant +210\,\mathrm{km}\,{{\rm{s}}}^{-1}$. The channel maps show the wide distribution of ${\rm{H}}\alpha$ emission at several velocities in the same spatial location. In contrast, the H i channel maps show the neutral component stays coherent in both velocity space and location.

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We find a region of ionized gas extending out from the SMC, which is marked by the black box in Figure 4 (bottom right). This region begins at $({\ell },b)=(303\buildrel{\circ}\over{.} 0,-47\buildrel{\circ}\over{.} 0)$ and extends down to the edge of the observed region at (3030 , −550 ). The ionized filament is marked by the black arrow. This ionized filament runs parallel to two neutral filaments discovered in Nidever et al. (2008), as marked by the solid red and dashed red lines. Figure 6 focuses on the region of the extended SMC containing the ionized SMC filament, with several spectra from the region in Figure 7. While there is detectable ${\rm{H}}\alpha$ on the order of 0.1 R along the H i filament marked by the solid red line, similar emission is also present in the extended region beyond the filament and does not appear directly related to the H i filament. In contrast, along ${\ell }=305^\circ$ ionized filament, there is an ${\rm{H}}\alpha$ enhancement, with intensities of 0.2–0.5 R. This filament is spatially coincident with several H i clouds with column densities of $(0.5\mbox{--}1.0)\times {10}^{20}\,{\mathrm{cm}}^{-2}$. However, no extended filamentary structure comparable to the H i filament exists at lower longitudes.

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Gas in the SMC has a wide velocity distribution. The first moment of the H i gas ranges from +120 km s⁻¹ near the SMC–Stream interface to +190 km s⁻¹ near the Bridge. These trends can be seen in Figure 8.

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Previous studies have shown that the H i component has a strong gradient, suggesting that the large scale motions of the H i gas is dominated by rotation (Stanimirović et al. 2004; Di Teodoro et al. 2019). In contrast, the ${\rm{H}}\alpha$ rotation is less pronounced. We picked two pointings along the greatest velocity gradient line as measured in Stanimirović et al. (2004). Comparing mean velocities from $({\ell },b)=(299\buildrel{\circ}\over{.} 3,-45\buildrel{\circ}\over{.} 2)$ and $({\ell },b)=(306\buildrel{\circ}\over{.} 0,-43\buildrel{\circ}\over{.} 0)$, we find a velocity gradient of +67 $\mathrm{km}\,{{\rm{s}}}^{-1}$ for the neutral gas and +15 $\mathrm{km}\,{{\rm{s}}}^{-1}$ for the ionized gas. The appearance of weaker rotation is partially due to the broader nature of the ${\rm{H}}\alpha$ lines. WHAM measures the total integrated emission along the line of sight and cannot distinguish a singular cloud with a broad velocity range from several clouds in the halo of the galaxy imposed over clouds embedded in the interior or multiple halo clouds at different velocities. Additionally, with our 1° beam, the small scale structure is blended together. This convolution broaden the lines, shifting the mean velocity.

We calculated the mass of ionizing gas following Hill et al. (2009) and BHB13. We assume a uniform density distribution to estimate a characteristic line-of-sight depth:

$$\begin{eqnarray}&&\mathrm{EM}=2.75{\left(\displaystyle \frac{T}{{10}^{4}{\rm{K}}}\right)}^{0.924}\left(\displaystyle \frac{{I}_{{\rm{H}}\alpha }}{{\rm{R}}}\right)\,{\mathrm{cm}}^{-6}\,\mathrm{pc}.\end{eqnarray} \tag{ 4 }$$

The resulting mass in each beam is then

$$\begin{eqnarray}&&\left(\displaystyle \frac{{M}_{{{\rm{H}}}^{+}}}{{M}_{\odot }}\right)=3.4\times {10}^{4}\,{\rm{\Omega }}{\left(\displaystyle \frac{D}{\mathrm{kpc}}\right)}^{2}\left(\displaystyle \frac{\mathrm{EM}}{{\mathrm{cm}}^{-6}\,\mathrm{pc}}\right){\left(\displaystyle \frac{{n}_{e}}{{\mathrm{cm}}^{-3}}\right)}^{-1},\end{eqnarray} \tag{ 5 }$$

where n_e is the electron density, which we estimate from several scenarios described below, and Ω is the solid angle over which the mass is calculated. In our case, the solid angle is a $1^\circ$ WHAM beam or a $0\buildrel{\circ}\over{.} 25$ pixel in the resampled images. ${M}_{{{\rm{H}}}^{+}}$ is the total gas mass where H is ${{\rm{H}}}^{+}$ since we include a factor of 1.4 to account for helium as in Hill et al. (2009) and BHB13. The distance to any section of the SMC is taken as the average distance of the SMC, or 60 kpc (Hilditch et al. 2005), with the exception of the SMC Tail region marked in Figure 2, where the mass is calculated with a distance of both 55 kpc and 60 kpc. All mass calculations were determined by integrating the emission over the $+90\leqslant {v}_{\mathrm{LSR}}\leqslant +210\,\mathrm{km}\,{{\rm{s}}}^{-1}$ velocity range. We use the methods described in BHB13 to calculate the mass of the H i and include a factor of 1.4 to account for helium. In all cases, we smooth the H i emission to match WHAM's resolution, integrating over the same velocity range as the ${\rm{H}}\alpha$ emission.

To determine the ionized mass of the SMC and its extended system, we must make assumptions for either the line-of-sight depths or the electron density. While there are line-of-sight depths in the literature (Subramanian & Subramaniam 2009, 2012; Scowcroft et al. 2016; Ripepi et al. 2017), these depths are for the stellar component of the SMC. As is apparent from the extent of the gas, and from MW studies of the WIM, the ${\rm{H}}\alpha$ gas likely has a larger line-of-sight depth than the stellar line of sight. For our mass estimates, we assume three different scenarios. The first scenario assumes the ionized gas is in a skin around the neutral gas. For the second and third scenarios, we assume the gas is well-mixed and the H i line of sight is equal to the ${\rm{H}}\alpha$ line of sight. These line-of-sight depths must be assumed, as there is no comprehensive model of H i or ${\rm{H}}\alpha$ line-of-sight depths. Our second and third scenarios use a "cylindrical" and an "ellipsoidal" geometry, respectively. We define the third scenario as our ellipsoid scenario, where we assume a standard shape and create a model of the structure of the galaxy. For the mass calculations, we partitioned the galaxy into four different regions: the SMC Tail, the central galaxy, the SMC–Stream interface, and the extended ionized gas (Figure 2). The SMC Tail is divided into two regions in order to directly compare to deeper observations made of the same regions in BHB13. Values for each region can be found in Table 2. M_ionized/M_{ionized+neutral} values are listed in Table 3.

Table 2.  Neutral and Ionized Properties

Region		Neutral Properties
		$\mathrm{log}\left\langle {N}_{{\rm{H}}{\rm{I}}}\right\rangle$	${M}_{{{\rm{H}}}^{0}\mathrm{avg}}$ a	${M}_{{{\rm{H}}}^{0}\mathrm{beam}}$ b	${L}_{{{\rm{H}}}^{+}}$	$\mathrm{log}\left\langle {n}_{0}\right\rangle$
		(cm${}^{-2})$	(106 ${M}_{\odot }$)	(106 ${M}_{\odot }$)	(kpc)	(cm−3)
SMCd		21.0	841c	683c	9.0	−1.4
H i SMC Taild, g		20.5	160–243	166–198	1.9	−1.3
${\rm{H}}\alpha$ SMC Taild, g		20.7	112–170	114–136	1.9	−1.0
SMC filamentd		19.7	42	34	3.3	−2.3

Region		Ionized Properties
		Ionized Skin		Cylinder		Ellipsoid
	$\left\langle {EM}\right\rangle$	${L}_{{{\rm{H}}}^{+}}$	${M}_{{{\rm{H}}}^{+}}$	${L}_{{{\rm{H}}}^{+}}$	${M}_{{{\rm{H}}}^{+}}$	${L}_{{{\rm{H}}}^{+}}$	${M}_{{{\rm{H}}}^{+}}$
	(10−3 cm−6 pc)	(kpc)	(106${M}_{\odot }$)	(kpc)	(106 ${M}_{\odot }$)	(kpc)	(106${M}_{\odot }$)
SMCd	8488	6.6	738e	9.0	788e	14–20f	671–802e
H i SMC Taild, g	771	0.2–0.3	26–34	1.9–2.0	74–91	1.9	76–90
${\rm{H}}\alpha$ SMC Taild, g	1284	0.1–0.1	11–14	1.9–2.0	39–48	1.9	42–50
SMC filamentd, h	698	⋯	⋯	3.3	128	3.3	61

Notes.

^aMass range calculated using the column density average, applied to ionized skin and cylinder scenarios. ^bMass range calculated using per beam column densities, applied only to ellipsoid scenario. ^cIn all cases, our masses calculated reduces the resolution of the H i to match the WHAM resolutions. This results in an overestimation of the H i mass and our results do not match previously published results in Brüns et al. (2005). ^dRegions defined by an ellipsoid (SMC) centered at ${\ell }=301\buildrel{\circ}\over{.} 6$ and $b=-44\buildrel{\circ}\over{.} 8$ and polygons with the following corners: ${\ell }=(301\buildrel{\circ}\over{.} 8,295\buildrel{\circ}\over{.} 9,289\buildrel{\circ}\over{.} 1,295\buildrel{\circ}\over{.} 7)$ and $b=(-39\buildrel{\circ}\over{.} 4,-36\buildrel{\circ}\over{.} 2,-43\buildrel{\circ}\over{.} 0,-46\buildrel{\circ}\over{.} 5)$ for the H i SMC Tail, ${\ell }=(300\buildrel{\circ}\over{.} 5,294\buildrel{\circ}\over{.} 5,292\buildrel{\circ}\over{.} 0,297\buildrel{\circ}\over{.} 0)$ and $b=(-41\buildrel{\circ}\over{.} 0,-39\buildrel{\circ}\over{.} 5,-42\buildrel{\circ}\over{.} 0,-45\buildrel{\circ}\over{.} 0)$ for the ${\rm{H}}\alpha$ SMC Tail, and ${\ell }=(309\buildrel{\circ}\over{.} 0,299\buildrel{\circ}\over{.} 0,299\buildrel{\circ}\over{.} 0,309\buildrel{\circ}\over{.} 0)$ and $b=(-48\buildrel{\circ}\over{.} 0,-48\buildrel{\circ}\over{.} 0,-55\buildrel{\circ}\over{.} 0,-55\buildrel{\circ}\over{.} 0)$ for the SMC filament. ^eNot including the internal extinction of the SMC results in a mass range of 692 $\times \,{10}^{6}$ ${M}_{\odot }$ for the ionized skin scenario, 763 $\times \,{10}^{6}$ ${M}_{\odot }$ for the cylindrical scenario, and (571–698) × 10⁶ ${M}_{\odot }$ for the ellipsoidal scenario. ^fLine-of-sight depth at the maximum depth. We use 14 kpc from Subramanian & Subramaniam (2012) and 20 kpc from Scowcroft et al. (2016). Minimum depth of 3 kpc. ^gTwo different distances are used, 55 and 60 kpc. The average distance to the Bridge is 55 kpc; however, the SMC is measured at 60 kpc. Both distances are used to provide a range of possible masses and to provide a more direct comparison to results from BHB13. ^hIonized skin method is not applied here due to little to no H i column density.

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Table 3.  Ionization Mass Fraction: M_ionized/M_{ionized+neutral}

	Ionized Skin (ne = n0)	Cylinder	Ellipsoid
SMC	46%	48%	50%–54%
H i SMC Tail	12%–14%	27%–32%	29%–31%
${\rm{H}}\alpha$ SMC Tail	8%–9%	22%–26%	24%–27%
SMC filamenta	⋯	79%	65%

Note.

^aIonized mass fraction not calculated using ${n}_{e}={n}_{0}$ due to little to no H i column density.

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In the first ionized skin scenario, we assume that the ionized gas lies in a skin around the H i features. This assumes a relation between the neutral gas density and the density of the electrons. This results in two possibilities, n_e = n₀ and n_e = n₀/2. If the neutral and ionized components are separated, but are in pressure equilibrium, then the electron density of an ionized skin would equal half the neutral hydrogen density (Hill et al. 2009). However, because the recombination time (∼1 Myr) is much shorter than the sound crossing time (a few hundred Myr), we expect that n_e ≈ n₀ is more likely and only consider this case. We assume the H i column densities from HI4PI to calculate the electron column densities. This method is more reasonable outside the center of the galaxy, in regions where there is significant H i emission. Since we use the average column density over each region to calculate the mass, we use the averaged extinction over the same region to be consistent. The ionized hydrogen mass estimate for the SMC using this first method is then $\sim 7.4\times {10}^{8}\,{M}_{\odot }$.

Our second scenario assumes a cylindrical geometry. In this scenario, we assume ${L}_{{{\rm{H}}}^{+}}={L}_{{{\rm{H}}}^{0}}$. This treats the ionized and neutral gas as components occupying similar mixed volumes/regions along the line of sight. In this case, the line of sight of the neutral component is similar to the line of sight of the ionized component, and each region is assumed to have the same path length, effectively a cylindrical geometry. The intensity is then averaged over the region, and treated as if it is in a single flat layer, with a depth equivalent to the width of the semimajor axis of the H i feature. This scenario uses the average extinction for the region. This results in a mass estimate of $\sim 7.9\times {10}^{8}\,{M}_{\odot }$.

The third scenario is our ellipsoid scenario. Similar to our cylindrical scenario, we assume that neutral and ionized gas lies along the same line of sight. However, we model the shape of the SMC as a simple ellipsoid, in order to estimate the line-of-sight depth of the gas. Similar to the BHB13 method for the Bridge, we assume that the maximum depth is equivalent to the width of the galaxy. We define the width as the semimajor axis. We chose two points on the edge of the ${N}_{{\rm{H}}{\rm{I}}}=1.0\,\times {10}^{20}\,{\mathrm{cm}}^{-2}$ contour to define the semimajor axis, centered at the radio kinematic center as defined in Stanimirović et al. (2004). The projected ellipse can be seen in Figure 2, with a semimajor axis of 6 kpc and a semiminor axis of 4.55 kpc. We then assume that the line-of-sight depth of the ellipse is from 14 kpc (Subramanian & Subramaniam 2012) to 20 kpc (Scowcroft et al. 2016), based on measurements from red clump stars, RR Lyrae stars, and Cepheids. We constrained the minimum depth for the model to be no less than 1.9 kpc, again using the assumption that the width of the extended areas are similar to the depths. While there are estimates of the SMC's inclination, we chose to leave more extensive models for future work. Sightlines with intensities below 0.01 R were excluded in the mass calculations. In this scenario, we calculate the extinction correction and mass within individual smoothed 025 pixels to stay consistent with the mass calculation methods. Using this model, we found the ionized content of the SMC to be $\sim 6.7\times {10}^{8}\,{M}_{\odot }$ using a depth of 14 kpc and $\sim 8.0\times {10}^{8}\,{M}_{\odot }$ using a depth of 20 kpc.

These simplified scenarios allow us to make estimates of the extended ionized gas mass but do not include many effects that would be important for higher-resolution data. The gas is more likely to be clumpy and discontinuous, with varying densities and components at different distances. These models also do not consider the inclination of the SMC nor how that would change the projected line of sight. Our calculations assumed an average distance of 60 kpc. However, gas toward the Stream is more distant, and gas toward the Bridge is closer to 55 kpc. In all regions, the H i resolution is reduced to match the WHAM resolution to consistently compare emission along the same line of sight. The results of this approximation, along with a different defined area for the galaxy, is a higher calculated H i mass than previously measured in Brüns et al. (2005). All three scenarios give ${M}_{{{\rm{H}}}^{+}}\sim 6\times {10}^{8}{M}_{\odot }$. We do not quantify the uncertainties in the many assumptions involved, but the consistency of the estimates gives us confidence that they are realistic.

BHB13 uses neutral column densities from the Leiden/Argon/Bonn (LAB) H i survey (Kalberla et al. 2005) data set for the mass calculations of the region; here, we use HI4PI. The use of HI4PI results in ∼4%–7% increase in H i in the ${\rm{H}}\alpha$ and H i Tail, which in turn decreases the mass ${\rm{H}}\alpha$ calculated for the assumed case in which we set the density of the electrons, n_e, equal to that of the neutral gas, n₀. By also included a 20% correction which accounts for degradation in the WHAM instrument and using HI4PI instead of LAB, we find similar mass results for the velocity range of +100 ≤ v_LSR ≤ +210 $\mathrm{km}\,{{\rm{s}}}^{-1}$.

The trailing Magellanic Stream was first discovered by Mathewson et al. (1974). Putman et al. (2003) provided higher-resolution observations that strongly suggest a bifurcated, filamentary structure. Through a Gaussian decomposition of the H i emission, Nidever et al. (2008) traced these two filaments to the LMC and the Magellanic Bridge. The "LMC" filament is marked in Figure 4 with a dashed red line. However, the right filament in solid red has a less certain origin. Fox et al. (2010) found that quasar sightlines within the shorter filament have abundances of roughly 0.1 solar metallicity. Such measurements match the expected metallically of the SMC 2.5 Gyrs ago (Pagel & Tautvaisiene 1998; Harris & Zaritsky 2004), further suggesting an SMC origin for the filament.

The origin of the filament appears to be the lower left side of the SMC, toward the Stream, which is marked in Figure 4 (bottom right). This could suggest that the ${\rm{H}}\alpha$ filament is a shock, similar to shocks presented in Bland-Hawthorn et al. (2007). The ${\rm{H}}\alpha$ filament is near the SMC H i filament and could be the leading edge of the neutral SMC filament (solid red), pulled out similarly to the Stream filaments, and ionized by shocks. In Mastropietro et al. (2005), simulations were run with the LMC and MW, where even a low-density halo removed significant gas from the system. While the simulations did not include the SMC, if similar conditions strip gas out of the SMC, proper motions from Kallivayalil et al. (2013) suggest gas stripped would trail the SMC in the direction of the Stream. Overtime, this filament may have become more highly ionized, leaving only a few scattered H i clouds intact. Or, if the SMC has a puffy, ionized halo, interactions could be stripping outer gas directly. Confirming the extent of the ${\rm{H}}\alpha$ beyond the $b\,=\,55^\circ$ edge of our survey will help give a clearer picture, and line ratios could also help point to the origins of the ${\rm{H}}\alpha$ enhancement. A recent study by McClure-Griffiths et al. (2018) found a neutral outflow centered at $(\alpha ,\delta )\approx {00}^{{\rm{h}}}{49}^{{\rm{m}}},-71^\circ 15^{\prime}$, near the origin of the ionized filament. While the extent of the ionized filament is longer then the neutral outflow and offset spatially, exploring a possible relationship between the two features could help identify the origins of the structure. Extended observations of the filament is part of the ongoing WHAM Magellanic Stream Survey in ${\rm{H}}\alpha$.

The diffuse ionized gas of the SMC extends beyond the traditionally defined extent of the neutral gas. The morphology, kinematics, and environment of this gas have been explored in several studies.

The COS/UVES survey compared five sightlines along the Magellanic system with WHAM observations (Fox et al. 2014). Along one sightline, FAIRALL9, they found an offset in velocity between the neutral emission at v_LSR = +190 $\mathrm{km}\,{{\rm{s}}}^{-1}$ and the ${\rm{H}}\alpha$ emission at v_LSR = +156 $\mathrm{km}\,{{\rm{s}}}^{-1}$, with the ${\rm{H}}\alpha$ offset confirmed by the detection of C ii* at v_LSR = +150 $\mathrm{km}\,{{\rm{s}}}^{-1}$. While the location of FAIRALL9 is just outside the SMC map, we find a similar offset along a significant number of our observations for the SMC and the surrounding material, which can be seen in Figure 8. They suggest this could indicate that ionized gas exists as a boundary layer that is compressed by ram pressure as the neutral gas moves through an ionized medium. Diaz & Bekki (2011) modeled the Magellanic System and found the bifurcation of the Magellanic Stream was sensitive to drag from the hot halo, limiting the velocity dispersion of the Magellanic Stream structures. While this model is not able to reproduce the detailed kinematic and spatial structure of the Magellanic Stream, it does suggest that interactions with the surrounding coronal gas affect the morphology of the Stream. Similarly, in Barger et al. (2017), an analysis of a sample of ${\rm{H}}\alpha$ observations throughout the Stream suggests that halo–gas interactions likely affect morphology even if they are not the primary source of ionization.

The effect of the MW corona on the MCs is also discussed in Salem et al. (2015). They find the interaction between the MW coronal gas and the LMC results in a sharp drop-off in the radial gas profile. While they are not able to similarly constrain the SMC, they find that interactions with the corona would result in a truncated halo ≈3.5 kpc in size. Their study only considered the neutral gas in the SMC with a correction for the ionized gas mass, but we find that the denser neutral gas ends more closely to the main body of the galaxy and does not extend out as far as the diffuse ionized gas. This picture is more consistent with Wang et al. (2019) as their models trace the morphology of the warm and hot gas independently from the neutral component. Modeling the formation of the Magellanic Stream and including effects of ram pressure stripping on the Clouds, they find a large, extended envelope of ionized gas while the neutral gas is concentrated near the galaxies.

Pairing the WHAM observations of the extended SMC with further absorption studies and dynamical models may help to constrain and explore the effects of the MW corona and ram pressure stripping on the system.

We have measured diffuse emission in the halo of the SMC with sensitivity an order of magnitude better than other studies that have looked at the DIG in external galaxies. Observations from Rossa & Dettmar (2000) and Dettmar (1990) use a similar method to estimate the total DIG mass of edge on galaxies. In both studies, a filling factor is assumed and applied to the emission measure and a line-of-sight distance is assumed  with a correction factor included for helium. The resulting masses are on the order of ${10}^{6}\mbox{--}{10}^{8}\ {M}_{\odot }$. For the galaxy with the largest observed diffuse gas mass, NGC 891, the total calculated diffuse gas mass is $4.0\times {10}^{8}\ {M}_{\odot }$ (Dettmar 1990). This can be compared to its neutral halo mass of ${M}_{{{\rm{H}}}^{0}}\approx 1.2\times {10}^{9}\ {M}_{\odot }$ (Oosterloo et al. 2007). In this case, the measured mass contribution of the low-ionization species is lower than the comparable neutral component. However, in our study, we are able to look through the galaxy and measure both diffuse gas in the halo as well as in the disk. In addition to the difference in sightlines, Rossa & Dettmar (2000) were able to detect the DIG down to a few Rayleighs, compared with WHAM's ∼25 mR sensitivity for singular pointings and ∼10 mR for continuous emission. To directly compare our observations to the detection limits of the previous studies, we can limit our mass calculations to bright emission. When only measuring the mass of regions with emission 5.0 R and over, which coincides with regions in the SMC with ${N}_{{\rm{H}}{\rm{I}}}$ > 5.0 × 10²⁰ and is comparable to the extent of MCELS, we see the ionized mass of the SMC reduced by ∼50%.

Several other studies have looked at the fraction of ${\rm{H}}\alpha$ emission originating from the WIM compared to H ii regions (Ferguson et al. 1996; Hoopes et al. 1996; Wang et al. 1999; Oey et al. 2007). These studies find the total contribution of ${\rm{H}}\alpha$ emission from the WIM ranges from 30% to 59%. If we use this guidance to estimate the fraction of observed emission arising from WIM within the core of the galaxy, the mass of ionized gas in this region is reduced by about 25%–45%. While we cannot separate these contributions easily due to our large beam size, such estimates still result in a substantial WIM mass for the SMC, even within its traditional boundaries.

In this work, we present the first detection of the extended ionized halo of the SMC and the first measurements of its associated mass. While some spectra show evidence for emission outside the range we focus on ($+90\leqslant {v}_{\mathrm{LSR}}\,\leqslant +210\,\mathrm{km}\,{{\rm{s}}}^{-1}$), confusion with MW ${\rm{H}}\alpha$ emission and OH skyline emission prevents us from including these regions using this first data set. Nidever et al. (2008) use Gaussian decomposition to trace extended H i structures carefully through velocity regions where the Magellanic Stream blends with other sources. Combining our knowledge of MW emission from the WHAM Sky Survey (Haffner et al. 2003) and these methods may help to isolate SMC emission in the future.

While Gaussian decomposition may help with emission at lower velocities, we are limited at higher velocities due to our window only including the edge of the OH lines. BHB13 was able to recover some Magellanic emission (with reduced sensitivity) in spectra where the OH line was more completely sampled within their velocity window. We would need to obtain additional observations to attempt similar extractions in the areas of this study that are affected.