Identifying H i Emission and UV Absorber Associations near the Magellanic Stream

We obtain the H i emission data from N08, which is primarily based on the Leiden/Argentine/Bonn (LAB) all-sky H i survey (Kalberla et al. 2005). The LAB all-sky H i survey is a combined data set between the Leiden/Dwingeloo Survey that covers the northern sky over decl. > − 30° (Hartmann & Burton 1997) and the Instituto Argentino de Radioastronomía Survey that covers decl. ≤ − 25° (Arnal et al. 2000; Bajaja et al. 2005). The combined data set has a velocity and spatial resolution of 1.3 km s⁻¹ and 36', respectively. The velocity range is from −400 to 400 km s⁻¹, and its rms noise is 0.09 K.

With the LAB survey, N08 decomposed the H i emission in the vicinity of the MS into Gaussian components and grouped the H i emission based on the phase structures of the gas (Field et al. 1969; McKee & Ostriker 1977; Ferrière 2001). Their Gaussian decomposition disentangles the MS from the MW gas and preserves the continuity of MS's H i filamentary structures in position and velocity space. For each H i data point from N08, which we define as an H i element, the Gaussian decomposition provides the amplitude of the H i emission, the centroid velocity v_{H I} in the local standard of rest (LSR), and the velocity dispersion σ_{v,H I}. Our distance model will be based on the (v_{H I}, σ_{v,H I}) measurements from N08, which we elaborate on in Section 3.

We utilize the all-sky catalogs of nearby galaxies within the Local Volume provided by Karachentsev et al. (2013, hereafter K13), Putman et al. (2021, hereafter P21). We work with an underlying assumption that, if a galaxy in the Local Volume does not have detectable H i gas in its main body, then it is unlikely to have an associated gaseous absorption line in its CGM. We adopt the galaxies detected in H i by P21 and additional galaxies from the K13 catalog whose H i gas mass is above 10⁵ M_⊙ and within the velocity range ± 500 km s⁻¹. The K13 catalog encompasses various observed properties of nearby galaxies, including apparent magnitudes, K-band luminosities, H i fluxes, radial velocities, distances, and derived properties such as H i masses and M26, which are the dynamical masses within Holmberg radii. In cases where there are discrepancies in the reported H i masses between the K13's and P21's catalogs, we preferentially rely on the values from P21. Figure 1 displays all galaxies that surpass the H i mass threshold and are located at Galactic latitudes less than 0° (GLAT ≤ 0°).

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We compile our UV absorber data set from five sources. We begin with recently observed data from our Hubble Space Telescope (HST) program (Program ID: 16301) and conduct a search in the Mikulski Archive for Space Telescopes (as of 2022 November) for QSO sight lines within 1000 kpc of the Sculptor Group; hereafter, we refer to this set of data as the archive sample. Further details on our archive sample regarding the sight line selection, spectral coaddition, and absorption line analyses can be found in Appendix A.

We also compile sight lines from four published works, including (1) R17 that characterized the UV absorption of high-velocity clouds in the MW and Local Group toward 270 sight lines, (2) Fox et al. (2020, hereafter F20) that modeled the kinematic structure of ionized absorbers near the MS (within 30°) toward 31 sight lines, (3) K22 that examined the ambient medium of the LMC within 35 kpc for evidence of a Magellanic corona using a sample of 28 sight lines located within 45° from the LMC, and (4) L20 that surveyed 43 sight lines at impact parameters (b) between 25 and 569 kpc from M31. L20 further identified the MS absorbers to be located within 20° of the MS latitude. From these literature works, we only select sight lines with UV absorbers that are near the MS and located at GLAT ≤ 0°.

The unique aspect of this work is that we implement a comprehensive statistical technique to evaluate the UV absorber associations with the MS using both kinematic and spatial information, and we identify the associations quantitatively. This is in contrast to the aforementioned UV studies, which mainly used simple cuts in sky locations and velocities to identify absorber associations.

All QSO sight lines that we have compiled, including our archive sample and literature values, were observed with the Cosmic Origins Spectrograph (COS) on board the HST with G130M and/or G160M gratings, covering a wavelength range of λ ∼ 1150–1450 Å and λ ∼ 1405–1775 Å, respectively. For UV absorber measurements used in this work, we denote the absorbers' centroid velocities in the LSR as v_ion. We only collect absorbers with v_ion within a velocity range of [−500, 500] km s⁻¹.

We focus on a set of common absorption lines from silicon and carbon ions, including Si ii, Si iii, Si iv, C ii, and C iv. More specifically, we consider the following UV transition lines: C ii λ1334, Si ii λ1193, Si iii λ1206, Si iv λ1393, and C iv λ λ 1548. While many of these ions have multiple transition lines (e.g., the 1393/1402 Å doublet for Si iv), we mostly adopt the stronger lines, which yield higher signal-to-noise ratios (S/Ns). For Si ii, we choose a weaker Si ii λ1193 line instead of λ1260, because Si ii λ1260 is often heavily saturated and blended with S ii λ1259 from potential high-velocity clouds in the MW along the same line of sight. Following Fox et al. (2014), λ1260 is used in lieu of Si ii λ1193 at positive absorption velocities where the MW's S ii λ1259 is not a concern. When certain lines are either saturated or contaminated, we instead take the other available transition lines of the same ions, such as Si ii λ1526, Si iv λ1402, or C iv λ λ 1550.

Table 1 presents the absorber data for a total of 870 UV absorbers collected from 92 QSO sight lines near the MS. Amongst the 870 absorbers, 372 are from L20, 242 are from K22, 106 are from F20, 76 are from the archive, and 74 are from R17. We assign a numerical ID to each sight line and show the sight lines with the corresponding IDs in Figure 1. For the QSO sight lines in our archive sample, we calculate the column density of each absorber using the apparent optical depth (AOD) method (Savage & Sembach 1991), consistent with the method adopted in R17 and L20. Meanwhile, F20 and K22 measured their absorber column densities by identifying distinct velocity components in the absorption line data and fitting them with Voigt profiles (VP). The different techniques may result in variation in the assessment of an absorber's column density and velocity range. We elaborate on the main differences between the AOD and VP methods as follows, and discuss our approach to combine the data sets from different sources.

The AOD-based method as adopted by R17, L20, and this work (the archive sample) identifies absorption velocity ranges mainly through visual inspection, and calculates total column densities by integrating the normalized line profiles over the designated velocity ranges using Equation (A1). The R17 data set and our archive sample identify all metal absorbers that occur over a velocity range from v_LSR ∼ −500 km s⁻¹ to ∼ +500 km s⁻¹. L20 instead focused on −510 ≲ v_LSR ≲ − 150 km s⁻¹ for absorption related to M31; we adopt L20's full data set without considering the M31 or MS membership that they assign to their absorbers. In Section 5.2, we compare our association results to L20's association result.

For the VP-based method, F20 modeled both the low (∣v_LSR∣ < 100 km s⁻¹) and high (∣v_LSR∣ > 100 km s⁻¹) velocity components simultaneously in their VP fits to better constrain the physical parameters of the MS-associated components. In contrast, K22 exclusively considered absorbers with ∣v_LSR∣ > 150 km s⁻¹ to exclude absorbers with velocities associated with known MW intermediate-velocity and high-velocity clouds in the region (Wakker & van Woerden 1997; Putman et al. 2012).

In Table 1, for absorber data calculated based on the AOD method, we adopt the minimum and maximum velocity ranges (${v}_{\min }$, ${v}_{\max }$) of the absorbers directly from the corresponding references. For those that are based on the VP method, we first convert each velocity component's Doppler width to the 1D velocity dispersion (σ_v,ion) as ${\sigma }_{{\rm{v}},\mathrm{ion}}\equiv \mathrm{Dopper}\,\mathrm{width}/\sqrt{2}$ (Draine 2011); for these absorbers, the (${v}_{\min }$, ${v}_{\max }$) values in Table 1 reflect the extents of the velocity components' full width at half-maximum (FWHM ≡2.355σ_v,ion). Furthermore, all S/Ns per resolution element listed in Table 1 are directly sourced from the original literature. R17 calculated their S/N averaged over an absorption-free spectral range of 1208–1338 Å, F20 estimated theirs near S ii 1250 Å, and L20 estimated theirs near Si iii 1206 Å. The S/N values of the sight lines in our archive sample are estimated over a wide spectral range of 1150–1750 Å (see Zheng et al. 2023). As the K22 sample did not provide S/N values for their published absorbers, we leave these entries empty in Table 1. We also exclude absorbers from K22 that yield what they refer to as poor component fits. We adopt absorbers from the four published literature references as they are and do not implement S/N cuts in these data.

We cross-match the QSO sight lines among the five sources (our archive sample, R17, L20, F20, and K22) and identify the common sight lines that are included in more than one study. For these sight lines, measurements of their absorption line features may vary among different works depending on the particular methods being used. For absorbers of the same ions with centroid velocities within the COS resolution limit (≈25 km s⁻¹) from different works (James 2022), we favor the VP-based data over the AOD-based data. If an absorber appears in both F20 and K22, which both applied VP fitting in their analyses, we prioritize the measurement from F20 for its known S/N. Similarly, if multiple AOD data exist for the same absorber, we adopt the most recent measurement in the order of our archive, L20, and then R17.

By design, the absorbers that we compile in this work are in the region near the MS and at a Galactic latitude of GLAT ≤ 0°. To determine the primary association of an absorber, we follow the methodology outlined in Sections 3 and 4. The absorbers are categorized into one of four distinct groups: MS associated (labeled "MS"), secondary MS associated (labeled "UMS"), galaxy associated ("G"), and uncertain ("U"). The UMS absorbers are initially classified as uncertain but are assigned secondary association to the MS because of their closer proximity to the MS compared to other nearby galaxies (see Section 4.3 for further details).

In this section, we calculate the WDs that characterize the H i within the MS in both spatial and velocity dimensions. This procedure is analogous to determining the radius of a cluster, if we consider the MS as a single cluster. However, our approach differs slightly from conventional clustering techniques. Typically, a cluster radius serves as a hard cutoff to distinguish between cluster members and nonmembers. Instead of adopting this hard classification, we develop a score function that provides conditional probabilities and perform classification based on estimated probabilities.

In the velocity dimension, we calculate the WD between the velocity distribution of the entire MS and the empirical velocity distribution of each H i element. In Figure 2, the velocity distribution of the entire MS is depicted in gray, while the velocity distribution of a single H i element is shown in red. The empirical velocity distribution of an H i element is modeled as a Gaussian distribution, ${N}\,({v}_{{\rm{H}}\,{\rm\small{I}}},{\sigma }_{{\rm{v}},{\rm{H}}\,{\rm{I}}}^{2})$ with v_{H I} as the centroid velocity and σ_{v,H I} as the velocity dispersion. We denote the velocity WD computed between the entire MS and a single H i element as W_v,global, in units of kilometers per second. We repeat this process for all available H i elements and obtain a distribution of all W_v,global, which is illustrated as a blue histogram in the left panel of Figure 3.

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Next, we compute the angular separation between the spatial coordinates of the entire MS and each H i element, and define this spatial WD as W_θ,global in the unit of degrees. We begin by computing the angular separation between an individual H i element and the entire MS and subsequently calculate the WD between this angular separation and the positional uncertainty induced by the LAB data. This uncertainty due to the beam is modeled as a Gaussian distribution, N(0, θ_beam), with θ_beam(≈06) representing the full width at half-maximum (FWHM) of the beam. The effect of the beam is almost negligible when contrasted with the angular separation between an H i element and the entire MS. We repeat this process for all available H i elements within the MS and generate a distribution of all W_θ,global, which is illustrated as an orange histogram in the right panel of Figure 3.

The global WD (W_v,global and W_θ,global) distributions, presented in Figure 3, provide an overview of how the H i elements are distributed in velocity and spatial dimensions. The peaks in the W_v,global and W_θ,global distributions signify relative clustering distances among the H i elements. Higher values of W_v,global and W_θ,global (moving farther away from the peaks) indicate that a particular H i element is more distant from the majority of H i in the MS. As shown in Figure 3, the majority of H i elements are located near the peaks of the distributions, and decrease at larger W_v,global and W_θ,global values beyond the peaks. We leverage the decreasing trends in the global WDs to create the score functions.

To ensure the continuity and completeness of the scores, we fit probability distribution functions (PDFs) to both distributions in Figure 3. We choose the best-fit PDF for each distribution as the one that has the highest score in the Kolmogorov–Smirnov goodness-of-fit test, which is conducted between the histogram distribution and the PDFs available in the scipypackage. We find that the PDF of the W_v,global distribution can be best fit by a Birnbaum–Saunders distribution function expressed as

$$\begin{eqnarray*}&&g\,(x,c)=\displaystyle \frac{x+1}{2c\sqrt{2\pi {x}^{3}}}\;\exp \;\left(-\displaystyle \frac{{\left(x-1\right)}^{2}}{2{{xc}}^{2}}\right),\end{eqnarray*}$$

where x is a variable greater than 0, and c is a shape parameter greater than 0. And the distribution of W_θ,global can be best represented by another PDF, Kappa 3 distribution expressed as

$$\begin{eqnarray*}&&h{\,(x,\alpha )=\alpha \,(\alpha +{x}^{\alpha })}^{(-(\alpha +1)/\alpha )},\end{eqnarray*}$$

where α is a shape parameter.

The smaller the WD, the more likely an H i element is associated with the MS. Therefore, the scores should be the highest for relatively small WD values and gradually decrease as W_v,global and W_θ,global increase. We define the most densely populated W_v,global and W_θ,global values as ω_v,global (=134.6 km s⁻¹) and ω_θ,global (=227), and assign the highest scores of unity (1) at these values (near the peaks in Figure 3). We employ the best-fit PDFs to transform the remaining global WD values into normalized scores. These modified best-fit PDFs become the score functions (f_v and f_θ ), which are represented as solid lines in Figure 3. More specifically, we define the velocity score function as

$$\begin{eqnarray}{f}_{v}\,({W}_{v})=\left\{\begin{array}{ll}1, & \mathrm{if}\ {W}_{v}\leqslant {\omega }_{{\rm{v}},\mathrm{global}}\\ g\,({W}_{v})/\max \,(g\,({W}_{v})), & \mathrm{otherwise}\end{array}\right.\end{eqnarray} \tag{ 2 }$$

where W_v is any velocity WD, and g(W_v ) is the Birnbaum–Saunders distribution function evaluated at a given W_v . We define the spatial score function as

$$\begin{eqnarray}{f}_{\theta }\,({W}_{\theta })=\left\{\begin{array}{ll}1, & \mathrm{if}\ {W}_{\theta }\leqslant {\omega }_{\theta ,\mathrm{global}}\\ h\,({W}_{\theta })/\max \,(h\,({W}_{\theta })), & \mathrm{otherwise}\end{array}\right.\end{eqnarray} \tag{ 3 }$$

where W_θ is any spatial WD, and h(W_θ ) is the Kappa 3 distribution function evaluated at a given W_θ .

Thus far, we have constructed the score functions by calculating the WDs between individual H i elements and the entire MS. The score functions quantify the relative level of association of each H i element with the MS. In the subsequent section, we evaluate the scores of all H i elements in the MS in an unbiased way to further refine the characteristic WDs and construct the distance metric Σ to evaluate the level of association near the MS.

The H i score functions are designed to quantify H i associations. For instance, we can quantify the association in velocity space between one H i element and the whole H i extent of the MS based on a measured velocity WD, W_v , and a normalized velocity score f_v (W_v ), where a higher score indicates higher association. However, we do not directly assign scores based on individual W_v,global and W_θ,global values that we show in Figure 3. The global WDs measure the WD between an H i element and all H i emission in the MS. If we were to naively determine the level of association solely based on scores derived from W_v,global or W_θ,global, elements in the regions with the highest H i covering factor would consistently score the highest, while elements in the regions with the lowest H i covering factor would score the lowest in association. This is due to the morphological asymmetry and uneven distribution of H i emission within the MS, as illustrated in Figure 1. A high coverage may be a sufficient, yet not necessary, condition for the association.

To mitigate these H i covering factor biases, we only build the score functions upon the global WDs (W_v,global and W_θ,global; Section 3.1) and separately derive two local WDs (hereafter W_v,local and W_θ,local) when quantifying the association of an H i element. The local WD minimizes the biases due to the covering factor variation across the MS while conserving the general characteristics of the MS. This approach not only prevents the bias introduced by the uneven distribution of H i in the MS but also provides robust constraints on the scoring metric. Any structures, including gaseous media, are more likely to be strongly coupled kinematically and spatially at a short range. Consequently, a distance measured between an object and its kinematically and spatially local areas is likely to be smaller than a distance measured between the same object and the entire gaseous structure to which it belongs, even if the representation is unbiased. By determining the level of association in a local area using the score function derived from the overall structure, our model becomes more resilient to data outliers.

In Figure 4, we illustrate our definition of a spatial local region for an H i element. The H i element is shown as a blue "X," and the sky blue pixels around the "X" demonstrate a spatial local region, defined as an annulus of two concentric circles, both centered at the location of the H i element "X." The inner concentric circle has a radius of ${r}_{\min }$ that indicates the minimum angular distance to the nearest H i element from the H i element "X"; because of the prevalent presence of H i, ${r}_{\min }$ is always 0 for any H i element. Note that this is different from the ${r}_{\min }$ values set for UV absorbers (green pixels) that we discuss in Section 4.1.

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The outer concentric circle has a radius of ${r}_{\min }+{r}_{\theta }$, where r_θ is an arbitrary radius that captures a sufficient number of H i elements (sky blue pixels) to preserve the characteristics of the MS. Naturally, the spatial local region of an H i element, such as "X," becomes the area enclosed by the circle with the radius r_θ , which is the sky blue patch surrounding "X." We initially set r_θ to 2° to capture a sufficient number of H i elements at most locations within the MS. We increase r_θ when at least 1% of the total H i area of the MS is not collected, but keep the maximum r_θ at 7°. Beyond 7°, we observe a significant increase in the velocity variance within the collected H i patch.

We further demonstrate a kinematic local region shown as a red "+" and surrounded by a patch of red pixels in Figure 4. A kinematic local region of an H i element covers all neighboring H i elements that have velocities within the velocity range of the given H i element v_{H I} ± σ_{v,H I}, where v_{H I} and σ_{v,H I} indicate the central velocity and velocity dispersion of a chosen H i element, respectively. We only consider H i elements within a radius of 40° of the given H i element to avoid selecting unassociated H i elements that happen to have similar velocities but are spatially at large distances. The search radius of 40° corresponds to a W_θ,global value with a normalized score of 0.1, or ${f}_{\theta }^{-1}\,(0.1)$, as shown in the right panel of Figure 3.

After defining the spatial and kinematic local regions for each H i element, we compute the statistical distances, denoted as local WDs W_θ,local and W_v,local, between the H i element and its local regions. We compute the local velocity WD (W_v,local) by measuring the WD between the empirical velocity distribution of one H i element and the velocity distribution of its spatial local region. This is similar to the two histogram distributions shown in Figure 2, but with the gray histogram representing the velocity distribution of a local patch instead of the whole H i extent of the MS. Similarly, we evaluate the local spatial WD (W_θ,local) by measuring the angular separation between one H i element and its kinematic local region. The left panel of Figure 5 demonstrates the empirical velocity distribution of the "X" element in dark blue that we model as a Gaussian model ${N}\,({v}_{{\rm{H}}\,{\rm\small{I}}},{\sigma }_{{\rm{v}},{\rm{H}}\,{\rm{I}}}^{2})$ (same as in Figure 2), and the velocity distribution of its spatial local region (the sky blue patch in Figure 4) is shown in sky blue. The computed local WDs are indicated in the corresponding panels. The W_v,local between the empirical velocity distribution of "X" (dark blue distribution) and the velocities of its spatial local region (sky blue distribution) is 24.65 km s⁻¹. The right panel of Figure 5 displays the angular separation (Δθ) between the "+" element and its kinematic local region in the red distribution, along with the angular separation between "+" and the positional uncertainty induced by the telescope beam in orange. The W_θ,local between these two distributions is 492.

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After calculating the W_v,local and W_θ,local for all H i elements in the MS, we determine the association scores for these local WDs using the score functions (Equations (2) and (3)) developed in the previous section. Figure 6 presents the distributions of the velocity scores f_v (W_v,local) in blue and the spatial scores f_θ (W_θ,local) in orange. The normalized scores in velocity and θ allow us to evaluate the association of H i elements in both velocity and position space simultaneously, which is not possible when comparing the global or local WD values. A vast majority of the H i elements score one, indicating that most H i elements' local WDs are smaller than the most populated global WDs. This is expected because local regions often have more directly associated H i emission. Additionally, we observe a clear break in both score distributions at the 0.9 mark. Since this trend is evident for both scores, we consider the WD values at the score 0.9, ${f}_{v}^{-1}\,(0.9)$ and ${f}_{\theta }^{-1}\,(0.9)$ (117.7 km s⁻¹ and 25°, respectively) as the characteristic velocity and angular size of the H i in the MS.

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For clarity, we define the local WDs corresponding to the score 0.9 as ω_v,local and ω_θ,local. These characteristic distances also represent the size of the MS as a cluster.

We define a generic, dimensionless distance metric Σ as follows:

$$\begin{eqnarray}&&{\rm{\Sigma }}=\sqrt{{\left(\displaystyle \frac{{W}_{v,\mathrm{local}}}{{\omega }_{{\rm{v}},\mathrm{local}}}\right)}^{2}+{\left(\displaystyle \frac{{W}_{\theta ,\mathrm{local}}}{{\omega }_{\theta ,\mathrm{local}}}\right)}^{2}},\end{eqnarray} \tag{ 4 }$$

where the characteristic distances (ω_v,local and ω_θ,local) now serve as normalization constants. Hereafter, we will refer to the distance metric used to evaluate the association of an H i element to its local environment as Σ_{H I}; this is to distinguish the distance metric Σ that we develop in Sections 4.1–4.2 for UV ion absorbers. We only consider an H i element to be associated with the MS if it meets the threshold of ${{\rm{\Sigma }}}_{{\rm{H}}\,{\rm\small{I}}}\leqslant \sqrt{2}$, and lower Σ_{H I} values indicate higher levels of associations. The threshold of ${{\rm{\Sigma }}}_{{\rm{H}}\,{\rm\small{I}}}\leqslant \sqrt{2}$ is set such that the W_v,local and W_θ,local are at the MS characteristic distances of 117.7 km s⁻¹ and 25°, respectively. We summarize all the steps to derive the characteristic distances of the H i in the MS and the Σ metric in Figure 7.

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We estimate the H i score PDF uncertainties using bootstrapping (Efron 1979). Because all score metrics are evaluated based on the H i data from N08, we apply bootstrapping by randomly discarding 20% of all the H i data, then draw at random a sample with replacement until the number of the new drawing in each bootstrap realization is equal to the total number of the H i elements in the original data set. For each realization, we fit PDFs to the sampled velocity and angular separation WD distributions, then reevaluate the scores based on the bootstrapped PDFs. The mean and variance of the velocity and spatial scores are estimated from 1000 bootstrap realizations, and are found to be insensitive to increasing or decreasing numbers of bootstrap realizations.

With the H i distance metric Σ_{H I} and local WDs evaluated in Sections 3.1 and 3.2, we now quantify the level of associations of individual H i elements to the main body of the MS. In Figure 8, we show the velocity scores f_v (W_v,local) in the left panel and the spatial scores f_θ (W_θ,local) in the right panel for all H i elements available in N08's data set.

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An H i velocity score (on the left panel) indicates the kinematic proximity between an H i element and its spatially local region. It measures the extent to which the velocity characteristics of an H i element align with the overall velocity distribution of the MS. Lower-velocity scores mean weaker associations, which suggest the presence of complex dynamics or interactions in local areas. Notably, regions with low-velocity scores are often associated with specific features, such as the intersection of two H i flows near the south Galactic pole (located at the center of the polar map) as previously noted by Putman et al. (2003b). Additionally, some areas with low-velocity scores are found in close proximity to the LMC and SMC near the bottom of the polar-projected map.

A spatial score (on the right panel) reveals the spatial proximity between an H i element and its kinematic local region. It offers insights into the relative spatial scales of kinematically homogeneous H i elements. The main body of the MS displays a transverse velocity gradient from the head (near the LMC and SMC) to the tail (near M31; see Figure 1). Naturally, segmented clouds situated distant from the main body tend to have low spatial scores because their kinematic characteristics deviate from the prevailing trend, such as the clouds located near the head of the MS with Galactic latitudes between −30° and 0° in the right panel of Figure 8 (lower section of the polar map). Interestingly, H i elements near the tail region of the MS exhibit a higher degree of kinematic consistency with uniformly high spatial scores, even though the area is known to be more fragmented.

In the middle panel of Figure 8, the H i elements with low combined scores are depicted in red, while the rest are shown in blue. We define H i elements with low combined scores as those with both velocity and spatial scores below 0.9 and with Σ_{H I} values greater than $\sqrt{2}$. The H i elements with low combined scores are found in regions with inhomogeneous spatial and kinematic distributions that are indicative of increased complexity, such as the intersection of colliding H i flows, in proximity to the LMC and SMC, or within fragmented clouds with greater kinematic complexity compared to the MS.

When assessing the association between an absorber and its local H i environment, we follow a procedure that closely resembles the one outlined in Section 3.2. We first filter out H i elements in the N08 data that are unlikely to be associated with the MS, which is quantified as those with both spatial and velocity scores less than 0.9 and Σ_{H I} greater than $\sqrt{2}$ (red pixels in the middle panel of Figure 8; see Section 3.4 for further details). Hereafter, the main body of the MS or H i extent of the MS refers to those H i elements that our algorithm identifies to be associated with the MS, shown as blue pixels in the middle panel of Figure 8.

We define a spatial local H i region of a UV absorber as the set of H i elements enclosed within an annulus formed by two concentric circles; we show an example of a spatially local H i region for an absorber in green pixels in Figure 4. Unlike the steps outlined for H i associations in Section 3.2, ${r}_{\min }$ for UV absorbers are not necessarily zero because most absorbers are located beyond the H i extent of the MS. While we initiate with r_θ = 2°, we do not enforce a maximum limit at 7° as we did in Section 3.2. Instead, we progressively increase r_θ until we collect at least 1%, the minimum flux that captures local properties without imposing any biases, of the total H i area in the MS.

We identify a kinematic local H i region of a UV absorber as the area within which the H i elements all have velocities within the velocity range defined by the absorber's minimum and maximum velocities that we tabulate in Table 1. We collect at least 5% of the H i elements in the MS, which is more than the percentage (1%) collected for spatial local H i regions to better reflect the MS's local morphology. Again, unlike the case of H i, we do not set a specific maximum limit in area sizes.

We use the same method as described in Section 3.2 to compute the spatial WD between a UV absorber and its kinematic local H i region, and the velocity WD between the absorber and its spatial local H i region. The key difference from Section 3.2 is the modeling of the absorber's empirical velocity distribution depending on whether the absorber's data are calculated based on the AOD or the VP methods. For absorbers originating from VP data sets (e.g., F20 and K22), we model the empirical velocity distributions as N(v_ion, σ_v,ion), where v_ion is the fitted centroid velocity of an absorber in the LSR frame, and σ_v,ion is the velocity dispersion. For absorbers from the AOD data sets (e.g., R17, L20, and our archive sample), we model the velocity distributions as continuous uniform distributions bound by the absorbers' minimum and maximum velocities, i.e., ${ \mathcal U }\,({v}_{\min },{v}_{\max })$ for each ion. We denote the velocity WD between an absorber and its spatial local H i region as W_v,ion, and the spatial WD between an absorber and its kinematic local H i region as W_θ,ion. The distance metric to quantify the associations between UV absorbers and the main body of the MS, Σ_MS, is calculated based on the absorbers' spatial and velocity WDs (W_v,ion, W_θ,ion) using Equation (4).

Additional sources of absorption, apart from the MS, are the metals in the CGM of nearby galaxies that are farther than the MS in distances but appear to be in close projection. In this section, we use the distance metric Σ to evaluate possible associations between our UV absorbers and nearby galaxies. We refer to the Σ calculated between an absorber and the modeled dark matter halo of a galaxy as Σ_G.

To determine the association of an absorber with a galaxy, we first need to quantify a galaxy's physical influence by computing its virial radius and escape velocity from the galaxy's stellar mass.

We estimate the galaxy's stellar mass by employing the K-band luminosity (K_L ), which is an indicator of the stellar mass of a galaxy due to its insensitivity to internal extinction and young stellar populations (Bell et al. 2003). We adopt K_L values from K13 and convert them into stellar masses using the unity relation (Bell et al. 2003). We compute the halo masses using a stellar-to-halo mass relation from Behroozi et al. (2013), and define the halo masses based on two density contrast definitions: one relative to the mean matter density of the Universe (ρ_m) and another relative to the critical density (ρ_c) (Davis et al. 1985). We consider both density definitions to provide a more conservative assessment of an absorber's association with a galaxy. Using the virial theorem, we derive two types of virial radii (R_200m & R_200c ∈R_vir) and their respective escape velocities (V_200m & V_200c ∈V_esc) for a galaxy. For galaxies without K_L values, we directly adopt the halo masses and virial radii from P21 and L20.

Next, we evaluate the spatial and velocity WDs based on the two sets of virial radii and escape velocities. The velocity WD is computed between the empirical velocity distribution of an absorber (as discussed in Section 4.1) and the velocity distribution of a galaxy N(V_G, V_esc), where V_G represents the radial velocity of the galaxy in the LSR frame, and V_esc denotes the galaxy's escape velocity.

Before computing the spatial WD, we model the angular distribution of the halo of a galaxy, which is computed as the area enclosed within the virial radius (R_200m or R_200c ) projected to the distance to the galaxy. We then evaluate the spatial WD between the angular separation of an absorber and the effective angular distribution of the galaxy's halo. We note that the positional uncertainty due to the size of the COS aperture (25) is negligible.

So far, we have calculated Σ values relative to the MS (Σ_MS) and nearby galaxies (Σ_G). In this section, we compare the Σ values to identify the dominant association of each absorber.

Figure 9 provides an overview of the process we use to determine the dominant association of an absorber. We identify an absorber as MS associated when Σ_MS < Σ_G for all nearby galaxies (Criterion A in Figure 9). To be conservative in identifying galaxy associations, we recognize an absorber as galaxy associated only when Σ_MS > Σ_G and all of the following three conditions are met (Criterion B):

• 1.  
  An absorber's impact parameter b is less than the virial radius of a galaxy, b < R_vir.
• 2.  
  The absolute difference between the velocity centroid of an absorber and the velocity of a galaxy is less than the escape velocity of the galaxy, δ V ≡ ∣v_ion − V_G ∣ < V_esc.
• 3.  
  The above conditions are satisfied for the pairs of virial radius and escape velocity values derived based on both ρ_m and ρ_c as we describe in Section 4.2.

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When multiple galaxies are found with Σ_MS > Σ_G and Criterion B is met, we consider the absorber to be primarily associated with the galaxy that has the smallest Σ_G, velocity offset δ V, and impact parameter b. However, if all these galaxies show similar Σ_G, δ V, and b values such that a primary association cannot be determined, we recommend all possible galaxy associations for the absorber.

Since we cross-examine between two virial radius and escape velocity definitions and impose rather strict conditions in Criterion B, the numbers of galaxy-associated absorbers and its associated galaxies are relatively small, as shown in Table 2. Many absorbers that may well be associated with either the MS or nearby galaxies may not have any associations assigned by our algorithm. For such absorbers, we implement Criterion C to consider the physical distance between an absorber and the MS's H i content or nearby galaxies. Assuming a distance to the MS of 100 kpc (Besla et al. 2012), we compare the physical distance (D_MS) between an absorber and its spatial local H i region, and the physical distance (D_G) between the absorber and all galaxies that yield Σ_G < Σ_MS. If an absorber's D_MS is smaller than all the D_G values and W_v,ion < ω_v,local, we assign a secondary MS association (labeled as "UMS") to the absorber. We group the primary and secondary MS-associated absorbers as the Magellanic absorbers and proceed with further analyses in later sections. The remaining absorbers that do not pass any criterion are labeled as "uncertain."

Table 1 and Figure 10 show all absorbers with their identified associations: MS associated ("MS," blue), galaxy associated ("G," orange), secondary MS associated ("UMS," light blue), and uncertain ("U," white). Each sight line is identified with a unique numerical ID (see Table 1) and is shown as a circle color-coded based on the associations of the absorbers detected along the sight line. Additionally, for absorbers that are associated with galaxies, we assign the galaxies with unique letter labels in Table 2 and show the galaxies in Figure 10.

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We consider a sight line with complete associations if all absorbers along the sight line have the same associations. If a sight line contains absorbers with multiple associations, we consider it with partial associations. For instance, we consider the sight line PHL2525 (ID 54 in Table 1) to have two partial associations because it contains a group of ions (C ii, C iv, Si iii) at v_ion ∼ −200 km s⁻¹ that are associated with the MS, and another group of ions (C ii, C iv, Si ii, Si iii, Si iv) at v_ion ∼ −140 km s⁻¹ that are associated with the galaxy Wolf–Lundmark–Mellote (WLM; labeled as I in Table 2). It is noteworthy that multiple sight lines in the vicinity of the LMC, SMC, and the head of the MS have more than one association, suggesting intricate kinematics in gas within this region that is likely due to complex interplay among the LMC, SMC, the MS, and the MW's CGM.

In general, when an absorber is associated with satellite galaxies of M31, our algorithm is likely to associate this absorber with M31 itself because of the large virial radius and escape velocity. To determine which is the dominant association (M31 or its satellites), we further compare three distance-related metrics (Σ_G , δ V, b), and find a handful of absorbers solely associated with M31's satellites rather than those of M31. For example, toward sight line IRAS-F00040+4325 (ID 25), the absorbers at velocities from ∼ −281 km s⁻¹ to ∼ −125 km s⁻¹ are associated with M31's satellite galaxy NGC 205.

Sometimes we do not find dominant associations based on the three distance metrics (Σ_G , δ V, b). For example, the absorbers along sight lines HS0033+4300 (ID 22), HS0058+4213 (ID 23), IO-AND (ID 24), MRK352 (ID 42), RX-J0043.6+3725 (ID 72), RX-J0050.8+3536 (ID 73), and Zw535.012 (ID 92) are listed to be associated with M31 and either NGC 185 or NGC 205 or sometimes all three simultaneously.

The multiple associations of absorbers in the direction of M31 imply a spatial and kinematic proximity between M31 and its satellites NGC 185 and NGC 205. Yet, M33-associated absorbers are relatively well separated in position and velocity space from M31. Among the three sight lines with absorbers associated with M33, all absorbers along 3C48.0 (ID 2) and RXS-J0155.6+3115 (ID 77) are completely associated with M33, while those along MRK352 (ID 42) are partially associated. Specifically, along MRK352, the absorbers at more negative velocities from ∼ −350 km s⁻¹ to ∼ −225 km s⁻¹ are kinematically closer to M31 but spatially closer to M33; these absorbers are considered to be associated with M31 because the kinematic proximity overrules the spatial proximity for Σ_G evaluation. However, the absorbers at less negative velocities from ∼ −267 km s⁻¹ to ∼ −155 km s⁻¹ are classified to be solely associated with M33 because they exhibit lower b, δ V, and Σ_G values to M33 compared with those with respect to M31.

We treat the LMC and SMC as galaxies separate from the MS despite their known relations to examine which part of the Magellanic System the absorbers are most likely to be associated with. We find ten sight lines containing absorbers associated with either the LMC or SMC. However, only one of the ten sight lines (HE0226-4110, ID 15) has complete associations—all the absorbers detected along this sight line are classified as associated with the SMC. For the rest of the sight lines, the spatial proximity between the LMC, SMC, and the MS causes our algorithm to classify them with partial associations, i.e., some sight lines have some absorbers associated with the LMC or SMC, and others have absorbers with the MS depending on the absorbers' velocities. For example, HE0435-5254 (ID 19) has absorbers with two associations: absorbers at v_ion ∼ 130 km s⁻¹ are associated with the MS, while those with v_ion > 200 km s⁻¹ are associated with the LMC.

Apart from sight lines in the vicinity of M31 and the LMC/SMC, we also find some sight lines near nearby galaxies with absorbers with multiple/partial associations. For example, the absorbers at velocities ∼100–180 km s⁻¹ along HE0056-3622 (ID 13) are associated with NGC 300, but those at negative velocities from ∼ −220 to −50 km s⁻¹ are classified as uncertain (U) or with secondary MS association (UMS).

Our algorithm assigns a significant number of absorbers to be uncertain (not associated with the MS or any galaxies). These absorbers are located closer to nearby galaxies than to the MS in terms of physical distance and WD, yet positioned outside the halos of the galaxies. Even though some of these absorbers may have been classified as associated with known structures such as the MS (e.g., F20) or the M31 (L20) in previous studies, our algorithm provides the most conservative estimates by systematically considering a range of distance metrics (see Figure 9).

Many sight lines with absorbers classified as uncertain are located in the vicinity of M31 (at 90° ≤ GLON ≤ 180° and −50° ≤ GLAT ≤ −30°), as shown in Figure 10. The presence of abundant satellites near M31 increases the probabilities of some absorbers to have lower Σ_G compared to Σ_MS, causing these absorbers to be not associated with the MS (Criterion A in Figure 9). However, these absorbers are not considered to be associated with M31 or any of its satellites either, because the absorbers' velocities with respect to the galaxies are larger than at least one of the galaxies' escape velocities, or the absorbers' impact parameters are larger than at least one of the galaxies' virial radii. As a result, these absorbers are classified as uncertain.

Lastly, we observe that absorbers are more likely to be labeled as uncertain if they are located near complex kinematic regions. Our model relies on the average statistics of the H i emission within the MS. Naturally, regions with unique kinematic or spatial complexities may not be well represented by our model. For instance, the region near the South Galactic Pole (270° < GLON < 360°, −90° < GLAT < −70°), is unusually complex and shows the coexistence of gas structures with both positive and negative H i velocities. If the W_v,local were measured in this region, the velocity distribution would be bimodal. Since a bimodal distribution is atypical for most local regions in the MS, the W_v,local measured from this region may not accurately represent the velocity distribution.

In this section, we highlight the disparities between our absorber associations and the associations identified from previous studies for the same set of sight lines.

F20 associated an absorber with the MS if it is detected along a sight line within 30° of the 21 cm emission from the MS (defined by Morras et al. 2000), and the velocity of the absorber is consistent with the general kinematics of the H i. Their sample includes 21 sight lines with MS-associated absorbers. Among these absorbers, we find the absorbers along 11 sight lines from F20's MS sample are either completely or partially associated with the MS. In the remaining ten sight lines, half of them are with absorbers that have uncertain associations, including MRK1044 (ID 34), MRK1513 (ID 39), PG0026+129 (ID 48), SDSSJ015530.02-085704.0 (ID 82), and UGC12163 (ID 87). The other half are with absorbers associated with nearby galaxies, including HE0226-4110 (ID 15; SMC association), IO-AND (ID 24; M31 and NGC 205), LBQS0107-0235 (ID 31; IC 1613), PG0044+030 (ID 49; IC 1613), and PHL2525 (ID 54; WLM).

K22 considered sight lines that are located within 45° from the LMC, which corresponds to an impact parameter of 35 kpc from the galaxy. K22 eliminated components linked to the MW or known intermediate-velocity clouds or high-velocity clouds by comparing absorber velocities with those of nearby known gaseous structures. In our analysis, we only consider absorber components identified as attributed to the Magellanic System in K22. Notably, all 26 sight lines from K22 are either completely or partially associated with the MS, LMC, or SMC. For instance, HE0439-5254 (ID 19) absorbers with velocities below 200 km s⁻¹ are associated with the MS, while the absorbers with velocities above 200 km s⁻¹ are associated with LMC. While most absorbers demonstrate such partial associations with the MS and magellanic clouds (MCs), five sight lines including HE0246-4101 (ID 16), HE2305-5315 (ID 20), HE2336-5540 (ID 21), IRAS-F21325-6237 (ID 26), UKS0242-724 (ID 88) demonstrate complete association with the MS (including UMS). Although a handful of absorbers from K22 are classified uncertain, all of the corresponding sight lines are partially associated with either the MS or MCs at different velocity ranges.

L20 analyzed 43 sight lines to investigate the CGM of the Andromeda galaxy (M31) within an impact parameter range of 25–569 kpc. Our algorithm shows that about half of their absorbers are associated with either M31 or its satellites, while the other half are classified differently because of their relative closeness to the MS. While L20 considered absorbers within ≲1.9 virial radius to be also associated with the M31, our algorithm uses a stricter criterion of one virial radius and also considers the influence of M31's satellite galaxies.

Apart from M31-associated absorbers, L20 also identified absorbers that are likely to be contaminated by the MS by examining whether the absorbers's positions and velocities are within the extent of the MS's H i emission as studied by Nidever et al. (2010). In general, these MS-contaminated absorbers are also classified as MS associated in our algorithm, except for those along seven sight lines. We find that absorbers along sight lines HS0033+4300 (ID 22), IO-AND (ID 24), IRAS-F00040+4325 (ID 25), KAZ238 (ID 30), RBS2055 (ID 67), and Zw535.012 (ID 92) are associated with M31 rather than the MS. On the other hand, while L20 flagged all absorbers with velocities near ∼ −370 km s⁻¹ along RX-J0028.1+3103 as not contaminated by the MS, our algorithm identifies them as MS associated.

Our algorithm also classifies all absorbers along 13 sight lines from L20's sample as uncertain, including IRAS01477+1254 (ID 28), MRK1014 (ID 33), MRK1148 (ID 35), MRK1179 (ID 36), MRK1502 (ID 38), MRK595 (ID 44), PG0026+129 (ID 48), PHL1226 (ID 52), SDSSJ011623.06+142940.6 (ID 80), SDSSJ014143.20+134032.0 (ID 81), SDSSJ015952.95+134554.3 (ID 83), UGC12163 (ID 87), and UM228 (ID 89). Additionally, our algorithm identifies absorbers along nine sight lines—3C 454.3 (ID 1), MRK1501 (ID 37), MRK304 (ID 40), MRK335 (ID 41), NGC 7469 (ID 45), PG0003+158 (ID 47), PG2349-014 (ID 51), RX-J0023.5+1547 (ID 70), SDSSJ225738.20+134045.4 (ID 84)—from L20 to be primarily associated with the MS.

Some sight lines have partial associations, with some absorbers associated with the M31 halo and others associated with the MS. For example, the absorbers from sight line RBS2005 (ID 66) at v_LSR ∼ −340 km s⁻¹ are classified as MS associated, while the rest at different velocities are labeled as uncertain, indicating their proximity to the nearby galaxies. Similarly, RX-J0028.1+3103 (ID 71) has both MS and M31-associated absorbers: absorbers with velocities below v_LSR ∼ −350 km s⁻¹ are classified as MS associated, while those with absorption velocities above −350 km s⁻¹ are associated with M31. For the absorbers from sight line PG0044+030 (ID 49) in L20's sample, our algorithm classifies them as associated with IC 1613 rather than M31.

In this section, we investigate the physical conditions of the MS using the MS-associated absorbers classified by our algorithm. We consider both the primary and secondary MS-associated absorbers as MS absorbers. We consider the MS absorbers in the Magellanic coordinate system, which sets the equator along the spine of the MS parallel to a great circle in the Galactic coordinate system (N08). The Magellanic longitude, MLON, describes the location of an absorber along the MS from the head (near the LMC and SMC) to the tail. And the Magellanic latitude, MLAT, describes the distance of an absorber from the MS perpendicular to the long axis of the MS. The MS is mostly confined at MLON ≤0 and −20 ≤ MLAT ≤20, and MLON decreases along the MS (toward its tail).

Figure 11 shows the column densities of absorbers as a function of MLON (top row) and MLAT (bottom row). In the background, we show 2D histograms representing the column densities of absorbers for the selected ion, with different colors denoting their associations: blue for MS absorbers, orange for galaxy-associated absorbers, and green for uncertain absorbers. The blue solid line represents the binned average trend for the MS absorbers, with vertical bars indicating the standard deviations of column densities within the corresponding bins. We apply a minimum of two counts threshold per each bin. Notably, the mean column densities of the MS absorbers are ∼0.5 dex higher than those of non-MS absorbers across the entire length and width of the MS.

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The top panels of Figure 11 also show that the column densities of low ions like C ii and Si ii decrease toward the Magellanic tail (more negative MLON values), while the column densities of C iv tend to increase toward the tail. These trends indicate that gas in the tail region is likely to be more highly ionized. While the binned averages for the MS absorber may appear to decrease at MLON < −120, this trend is influenced by only a few MS absorbers, as indicated by a high standard deviation. The mean column densities of the MS-associated absorbers remain relatively flat for Si iii and Si iv.

Figure 12 shows the spatial trends of the low-to-high ion ratios, C ii/C iv, which we calculate only for absorbers adopted from the same data reference and with centroid velocity differences less than the COS resolution (25 km s⁻¹). We show MS absorbers as circles, galaxy-associated absorbers as squares, and those with uncertain associations as triangles. Near the head of the MS, we find that the MS absorbers exhibit higher ion ratios, which is consistent with the trend seen in Figure 11 that the column densities of C ii are higher toward the head. The ion ratios of MS absorbers decrease toward the tail with more negative MLON, consistent with Bland-Hawthorn et al. (2019). This trend is driven by higher C iv column densities at the tail of the MS as evident in Figure 11. We observe a similar trend with low-to-intermediate ion ratios (such as Si ii/Si iv), but with more scatter.

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We calculate centroid velocity offsets for different pairs of ions, including the low–high ion pairs of C ii–C iv and Si ii–C iv, and the low–intermediate ion pairs of C ii–Si iv and Si ii–Si iv to understand whether these ions trace gas in the MS with similar kinematics. The centroid velocity offsets are computed for pairs of MS absorbers from the same data reference, and we only consider absorbers with velocity offsets within 50 km s⁻¹ from each other to avoid outliers. We find that the distributions of velocity offsets for all ion pairs are centered around zero, and the widths of the distributions are consistent among ion species within the same low–high or low–intermediate groups. The velocity offset distributions between low-to-intermediate ions are narrower than those of low-to-high ions, consistent with the findings by F20 (see the left panel in their Figure 6).

In this paper, we have gone beyond simple virial radius and velocity offsets for associating absorbers to galaxies. Our approach is primarily guided by relative comparisons, and all details are found in Sections 4.2 and 4.3. Figure 13 presents the distribution of absorbers' impact parameters b normalized by the corresponding galaxy's virial radius (b/R_200c ) for individual associated galaxies listed in Table 2. Each circle represents an ion absorber with its color showing the velocity offset between the absorber and the galaxy's systemic velocity, normalized by the galaxy's escape velocity (V_200c ). Approximately 60% of the galaxy-associated absorbers are found in the CGM of M31. This is likely due to M31 being the most massive nearby galaxy, and also the fact that at least half of the absorbers in our sample are adopted from L20, which primarily focused on M31. In Table 3, we list the impact parameters b and velocity offsets δ V for all absorber–galaxy pairs shown in Figure 13. In the subsequent sections, we discuss individual galaxies and their associated absorbers.

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Table 3. Associated QSO-galaxy Pairs

Galaxy Name	QID	QSO Name	Ions	b	$\overline{| \delta V}|$
				(kpc)	(km s−1)
(1)	(2)	(3)	(4)	(5)	(6)
IC1613	31	LBQS0107-0235	Si iii	61.9	11.7
			C ii	⋯	26.4
			C ii, Si iii	⋯	45.7
	49	PG0044+030	C ii, Si ii, Si iii, Si iv	60.7	21.8
LMC	18	HE0435-5304	C iv	15.3	18.8
			C ii, Si ii, Si iii	⋯	28.6
	19	HE0439-5254	C iv, Si ii	15.4	25.8
			C iv, Si iv	⋯	37.1
	56	PKS0355-483	Si ii, Si iii	20.7	0.2
	64	RBS1992	Si ii, Si iii	24.2	50.2
	69	RBS567	Si ii, Si iii	15.1	1.5
			Si ii	...	38.4
			C ii, Si ii, Si iii	⋯	86.8
M31	3	3C66A	C ii, C iv, Si ii, Si iii, Si iv	248.0	38.4
			Si iii	⋯	127.4
			C iv	⋯	154.9
			C ii, Si ii	⋯	159.9
	4	4C25.01	C ii, C iv, Si ii, Si iii, Si iv	213.7	14.1
	9	FBS0150+396	C iv, Si ii, Si iii, Si iv	179.7	120.9
	22	HS0033+4300	C iv, Si ii, Si iii, Si iv	31.3	68.4
			C ii, C iv, Si ii, Si iii, Si iv	⋯	94.1
	23	HS0058+4213	C ii, C iv, Si ii, Si iii, Si iv	49.8	48.4
			C ii, C iv, Si ii, Si iii, Si iv	⋯	100.9
	24	IO-AND	C ii, C iv	25.6	38.4
			Si ii	⋯	43.2
			Si iii	⋯	50.4
			Si iv	⋯	63.9
			Si ii, Si iii	⋯	80.8
			Si iv	⋯	91.8
			C ii, C iv	⋯	106.7
			Si ii	⋯	114.0
			C ii, C iv	⋯	118.36
			Si iv	⋯	123.6
	25	IRAS-F00040+4325	C ii, C iv, Si ii, Si iii, Si iv	95.2	41.1
			C ii, C iv, Si ii, Si iii, Si iv	⋯	136.6
	30	KAZ238	C ii, C iv, Si ii, Si iii	153.8	105.9
			C ii, C iv, Si ii, Si iii	⋯	139.1
	42	MRK352	C ii, C iv, Si iv	134.9	15.1
			C ii, C iv, Si ii, Si iii, Si iv	⋯	47.4
			C ii, C iv, Si ii, Si iii, Si iv	⋯	102.4
	50	PG0052+251	C ii, C iv, Si ii, Si iii	214.9	4.9
			C ii, C iv, Si ii, Si iii, Si iv	⋯	103.4
	67	RBS2055	C ii, C iv, Si ii, Si iii, Si iv	244.3	30.9
			C ii, C iv, Si ii, Si iii, Si iv	⋯	134.1
	71	RX-J0028.1+3103	C ii, C iv, Si ii, Si iii, Si iv	142.5	8.4
	72	RX-J0043.6+3725	C ii, C iv, Si ii, Si iii, Si iv	51.8	6.6
			C ii, C iv, Si ii, Si iii, Si iv	⋯	108.4
	73	RX-J0050.8+3536	C ii, C iv, Si ii, Si iii, Si iv	78.9	48.4
	74	RX-J0053.7+2232	C ii, C iv, Si ii, Si iii, Si iv	252.5	40.9
	76	RXS-J0118.8+3836	C ii, C iv, Si ii, Si iii, Si iv	99.5	20.9
			C ii, C iv, Si ii, Si iii, Si iv	⋯	75.9
	92	Zw535.012	C ii, C iv, Si ii, Si iii, Si iv	61.1	68.4
			C ii, C iv, Si ii, Si iii, Si iv	⋯	91.6
			C ii, C iv, Si ii, Si iii, Si iv	⋯	118.4
M33	2	3C48.0	C iv, Si ii, Si iii	42.7	4.0
	42	MRK352	C ii, C iv, Si ii, Si iii, Si iv	119.2	7.5
			C ii, C iv, Si ii, Si iii, Si iv	⋯	62.5
	77	RXS-J0155.6+3115	C ii, C iv, Si ii, Si iii, Si iv	76.3	21.5
NGC 185	22	HS0033+4300	C iv, Si ii, Si iii, Si iv	58.5	25.8
	92	Zw535.012	C ii, C iv, Si ii, Si iii, Si iv	31.2	24.2
			C ii, C iv, Si ii, Si iii, Si iv	⋯	25.8
NGC 205	22	HS0033+4300	C iv, Si ii, Si iii, Si iv	24.5	6.8
	23	HS0058+4213	C ii, C iv, Si ii, Si iii, Si iv	55.9	25.7
			C ii, C iv, Si ii, Si iii, Si iv	⋯	26.8
	24	IO-AND	Si iv	34.9	11.3
			Si iii	⋯	24.8
			Si ii	⋯	32.0
			Si iii	⋯	35.8
			C ii, C iv	⋯	36.8
			Si ii	⋯	38.8
			C ii, C iv	⋯	43.2
			Si iv	⋯	48.4
	25	IRAS-F00040+4325	C ii, C iv, Si ii, Si iii, Si iv	91.0	19.8
			C ii, C iv, Si ii, Si iii, Si iv	⋯	58.2
	72	RX-J0043.6+3725	C ii, C iv, Si ii, Si iii, Si iv	60.2	33.2
	73	RX-J0050.8+3536	C ii, C iv, Si ii, Si iii, Si iv	89.4	26.8
	92	Zw535.012	C ii, C iv, Si ii, Si iii, Si iv	56.5	6.8
			C ii, C iv, Si ii, Si iii, Si iv	⋯	43.2
NGC300	13	HE0056-3622	C ii, Si iii	63.8	1.0
			C iv	⋯	3.0
			Si ii,	⋯	6.2
SMC	14	HE0153-4520	Si iii	29.7	45.3
	15	HE0226-4110	C ii	35.0	5.4
			C iv	⋯	16.8
			Si ii	⋯	26.6
			Si iii	⋯	32.1
			C ii	⋯	36.3
			Si iii	⋯	53.1
			C ii	⋯	55.2
			C ii	⋯	65.4
	18	HE0435-5304	C ii	31.5	3.9
			Si ii	⋯	19.1
	56	PKS0355-483	C iv	33.0	54.0
	57	PKS0552-640	C iv, Si iv	27.8	39.7
			C ii, Si ii, Si iii	⋯	48.8
	68	RBS563	C ii, Si ii, Si iii	24.1	26.6
	69	RBS567	C ii, Si ii, Si iii	31.5	22.4
			Si ii, Si iii	⋯	85.6
	75	RX-J0503.1-6634	C iv	22.4	8.4
			Si ii	⋯	11.4
			C ii	⋯	19.4
			Si iii	⋯	21.9
WLM	54	PHL2525	C ii, C iv, Si iii, Si iv	46.6	21.2
			C iv, Si ii	⋯	16.4

Note: Column (1): galaxy names. Column (2): unique IDs assigned to QSO sight lines as listed in Table 1. Column (3): QSO names. Column (4): ion absorbers detected along the QSO sight lines. Column (5): impact parameters in unit of kiloparsecs. Column (6): absolution velocity difference in LSR between an ion absorber and the systemic velocity of its associated galaxy. If multiple absorbers of the same ions are detected along the same sight lines and they are with centroid velocities within 1 km s⁻¹, the velocity difference reflected the mean of these absorbers.

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6.1.1. M31 and Its Satellites

The Andromeda galaxy (M31) is the closest massive galaxy to our MW (located approximately 700 kpc apart) and is home to a rich system of satellite galaxies. Tidal features observed in M31's vicinity suggest that it has undergone multiple significant interactions with its satellites (Hodge 1973; McConnachie et al. 2009). Although M31 boasts a variety of dwarf companions, we exclude the majority of M31's dwarf companions due to their lack of H i gas (P21). Two dwarf elliptical companions of M31, NGC 185 and NGC 205, have only small amounts of gas relative to their total mass and given their proximity to M31 are identified to be potentially associated with some absorbers.

NGC 205 lies at a projected distance of only 37' (∼9 kpc) from M31 and shows evidence of distortion in its outer isophotes that are presumed to be the result of tidal interaction with M31 (Hodge 1973; Sato & Sawa 1986; Choi et al. 2002). Another dwarf companion, NGC 185, lies at a projected distance of 7° (∼140 kpc) from M31 and shows less evidence for dynamical interactions with M31 (Held et al. 1992), but the star formation history of NGC 185 implies an earlier infall time into the M31 environment (Geha et al. 2015). A recent proper-motion measurement shows the connection between NGC 185 and M31 through the alignment of rotation planes (Pawlowski & Sohn 2021).

A vast majority of galaxy-associated absorbers near M31 are classified to be associated with M31. With L20's deliberate selection of sight lines, systematically probing azimuthal variations near M31, the absorbers associated with M31 and its satellites demonstrate good coverage in both impact and velocity ratios compared to other galaxies. Although not all L20 absorbers are M31 associated as mentioned in Section 5.2, all M31-associated absorbers, except IO-AND (ID 24) from F20, are originated from L20. Details of our association comparisons with L20 are found in Section 5.2.

Figure 14 displays the logarithmic column density values for individual ion absorbers as a function of impact parameters from M31. The M31-associated absorbers are represented with square markers, while the MS-associated absorbers are marked with circles. The filled markers denote detections or lower limits (with upward pointing arrows), while the empty markers indicate upper limits. We show carbon ions on the left and silicon ions on the right. As shown, we find contrasting trends between the M31-associated and MS-associated absorbers for all available ions. In general, the column densities of M31-associated absorbers decrease as the impact parameter increases, indicating a decrease in gas content with radial distance, a signature of a diffuse CGM (Tumlinson et al. 2017). In contrast, the column densities of MS-associated ion absorbers increase as the distance to the MS decreases, and the impact parameter of M31 increases. Two sight lines, 4C25.01 (ID 4) and RX-J0028.1+3103 (ID 71) located at b_M31 ∼ 213 and 142 kpc respectively, are partially associated with both the MS and M31 with two groups of absorbers at different velocities. Our algorithm classifies that their absorbers with velocities ∼ −400 to ∼ −330 km s⁻¹ are associated with the MS, while the rest of the absorbers above this velocity range are classified as M31 associated.

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To investigate the general trend further, we perform a linear regression on the column densities and impact parameters of the M31-associated absorbers with only detection and lower-limit measurements. In Figure 14, a solid line represents the actual data range, while a dashed line is an extrapolation based on the fit. The Pearson correlation coefficient r values range from -0.55 to -0.21, suggesting negative correlations between the column densities and impact parameters for M31-associated absorbers. The correlation for C ii yields a p-value of 0.01 (<0.05), suggesting that the correlation is significant. However, the p-values for other ions are greater than 0.1, suggesting that given the current data sample and the large scatters we are unable to rule out the null hypothesis that there is no strong correlation between the ion (C iv, Si ii, Si iii, Si iv) column densities and impact parameters related to M31. As shown, the slope of the C ii and Si ii profiles are the steepest, and the slope of the Si iii profile is the shallowest. We also find that the standard deviations of the column densities for the silicon ions are roughly twice as high as those for the carbon ions due to large scatter.

Similar to L20, we find it challenging to discern a clear trend in ion ratios as a function of b_M31 due to the large scatter. For absorbers along the same sight lines but from different data sets, we consider them to be different absorbers if their centroid velocities are offset by more than the COS resolution limit, regardless of the overlaps in their velocity ranges. For this reason, absorbers with wider velocity ranges would have higher column densities than those with narrower ranges, even though they are partially probing the same gas structures along the line of sight. The large scatter may also be caused by ion absorbers likely associated with M31 and its satellites. Although we do not detect much of a radial trend in most directions around M31, we do find a notable increase in the ion ratios in the direction of NGC 185 from M31 and near M33, especially in low-to-high ion ratios (C ii/C iv and Si ii/Si iv).

6.1.2. M33

6.1.3. LMC and SMC

The Magellanic Clouds (LMC and SMC) are dwarf irregular (dIrr) satellites of the MW. The LMC is located at 50 ± 1 kpc (Walker 2012) from us, and the SMC is at 61 ± 1 kpc (Graczyk et al. 2014). The MCs are interacting with both each other and the MW, which results in a very complex gaseous environment. Despite having different association labels, the ions from the MCs and the MS overlap significantly in the column density–impact parameter space compared with M31. Figure 15 shows the logarithm of column densities of individual ion absorbers around the SMC as a function of b_SMC on the left and the column densities of ion absorbers around the LMC as a function of b_LMC on the right. We show either LMC- or SMC-associated absorbers with squares and mark the MS-associated absorbers with circles. As before, the lower-limit measurements are indicated with upward-pointing arrows. We note that Figure 15 does not include sight lines with upper-limit column density measurements that were reported by K22. This is due to the lack of velocity information for upper-limit data points in K22's published data (see their extended data Table 1). Given that our work relies on both position and velocity information to quantify possible associations for ion absorbers, we are unable to process those absorbers with only upper-limit column density values from K22.

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Unlike the M31 radial trend shown in Figures 14, Figure 15 does not demonstrate a discernible trend between the MS-associated absorbers and those associated with the SMC (left panel) or the LMC (right panel). This is consistent with previous studies that found the MCs and the MS are part of the larger Magellanic System (Wannier & Wrixon 1972; Mathewson et al. 1974; Putman et al. 2003b; Fox et al. 2013; D'Onghia & Fox 2016). It is also consistent with the fact that gas emanates continuously from the SMC into the MS, and the absorbing gas is likely associated.

K22 reported a possible detection of a Magellanic corona hosted by the LMC. Their model suggests the corona of the LMC is a collisionally ionized, warm-hot gaseous halo at a virial temperature of T ∼ 10 ^5.3−5.5 K that extends to the virial radius of the LMC (∼100–130 kpc). In their analysis, K22 excluded the fractions of Si iv, C iv, and O vi column densities due to photoionization and found that the rest of the ion column densities due to collisional ionization decline as a function of impact parameters from the LMC, which they interpreted as evidence for the presence of a Magellanic corona.

Although K22 considered all absorbers within 35 kpc of the LMC to be part of its corona gas, our algorithm shows that a large fraction of these K22 absorbers are instead closer to either the MS or the SMC when considering the absorbers' proximity in both position and velocity space (see Section 5.2 and Table 1). In fact, Figure 15 shows that most absorbers within b_SMC ≲ 20 kpc of the SMC (left panel) or b_LMC ≲ 15 kpc of the LMC are kinematically closer to the MS and thus classified to be associated with the MS by our algorithm. There is a large scatter, but the absorbers in the general area of the LMC, SMC, and the MS show similar column densities, and there is no obvious trend in $\mathrm{log}\;N$ vs. b_SMC or b_LMC. Similar to what K22 suggested, our result finds that the absorber environment in this area is complex, and the ion absorbers from the LMC's corona, if it exists, may not be as cleanly separated from the MS and SMC gas.

6.1.4. NGC 300

6.1.5. IC 1613

6.1.6. WLM

In the Magellanic coordinate system, all of our Magellanic-associated absorbers are located between −118° ≤ MLON ≤6° and −28° ≤ MLAT ≤22°. Out of a total of 605 Magellanic absorbers in the area mentioned above, 248 absorbers are associated with the MS, 61 absorbers are assigned with the secondary association to the MS (UMS), 209 absorbers are labeled uncertain, and the rest is galaxy associated. We find a covering fraction of 78% when we exclude the uncertain absorbers from the calculation.

Based on our association and UV absorber detection rate, we estimate the cross section of the Magellanic gas using the same method used by Fox et al. (2014). By multiplying the covering fraction and the area on the sky in which the Magellanic UV absorbers are detected, we obtain a total cross section of ∼4820 deg². In contrast, Fox et al. (2014) estimated the effective area of the MS by summing the area of the nonshaded grid cells in their Figure 1(b). Since Fox et al. (2014) considered the entire Magellanic System, we capture the relevant area from their figure for the comparison and multiply by their covering fraction 81% to estimate their relevant cross section as ∼7047 deg². Because the strict association algorithm that we implement in this work and our MS extent is inferred by H i emissions, the Magellanic cross section that we derive is only ∼70% of what Fox et al. (2014) suggested. Assuming that the cross section of the whole Magellanic System (including the Leading Arm) is reduced by the same rate, our work suggests that the total ionized mass of the MS inferred by Fox et al. (2014) should be scaled down by ∼30%. We note that our value may grow if deeper H i observations significantly extend the H i emission of the MS (e.g., Stanimirović et al. 2008; Westmeier & Koribalski 2008).

Our results are consistent with the finding that the MS contains a substantial amount of ionized gas, and also highlight some unique aspects of the ionized gas. Figure 11 suggests the mean ion column density of the MS is generally higher (∼0.5 dex) than absorbers not associated by our algorithm with the MS in all directions. With the exception of C iv, the region with the highest ion column densities coincides with the two H i filamentary structures connecting the SMC and the LMC, with a gradient along the length of the MS. This gradient is also seen in the H i column densities (Mathewson et al. 1977; Mirabel 1981; Putman et al. 2003b; Brüns et al. 2005) and strength of Hα emission (Putman et al. 2003a; Barger et al. 2017) along the MS. The gradient is more pronounced in the low ions, consistent with the colder gas representing the more recently stripped material from the Magellanic Clouds and the gas being more highly ionized farther along the MS.

From Figure 12, we see direct evidence of the gas associated with the MS being more ionized toward the tail of the MS. We also examine a similar trend for other ion ratios, but the gradient is not as obvious as that for C ii/C iv. The increased amount of highly ionized gas toward the MS tail is likely due to the gas there being more fragmented and optically thin, which is consistent with previous findings that the H i debris clouds near the tail are likely to represent the cold peaks of a largely ionized structure (Westmeier & Koribalski 2008; Kumari et al. 2015). The Hα emission along the MS is too bright in regions to be sourced by photoionization from the MCs, MW, or the extragalactic background (Putman et al. 2003a; Bland-Hawthorn et al. 2013; Barger et al. 2017; Fox et al. 2020). The ionization of the MS is likely due to a combination of its interaction with another medium and radiation from the Galactic disk (Moore & Davis 1994; Bland-Hawthorn et al. 2007). Future work on the ion ratios, combined with deeper H i emission observations, should provide further insights into the ionization mechanisms of the MS.