The Gas Content and Stripping of Local Group Dwarf Galaxies

The gas content of the complete compilation of Local Group dwarf galaxies (119 within 2 Mpc) is presented using H i survey data. Within the virial radius of the Milky Way (224 kpc here), 53 of 55 dwarf galaxies are devoid of gas to limits of M H i < 104 M ⊙. Within the virial radius of M31 (266 kpc), 27 of 30 dwarf galaxies are devoid of gas (with limits typically <105 M ⊙). Beyond the virial radii of the Milky Way and M31, the majority of the dwarf galaxies have detected H i gas and H i masses higher than the limits. When the relationship between gas content and distance is investigated using a Local Group virial radius, more of the nondetected dwarf galaxies are within this radius (85 ± 1 of the 93 nondetected dwarf galaxies) than within the virial radii of the Milky Way and M31. Using the Gaia proper-motion measurements available for 38 dwarf galaxies, the minimum gas density required to completely strip them of gas is calculated. Halo densities between 10−5 and 5 × 10−4 cm−3 are typically required for instantaneous stripping at perigalacticon. When compared to halo density with radius expectations from simulations and observations, 80% of the dwarf galaxies with proper motions are consistent with being stripped by ram pressure at Milky Way pericenter. The results suggest that a diffuse gaseous galactic halo medium is important in quenching dwarf galaxies, and that a Local Group medium also potentially plays a role.


Introduction
The smallest galaxies in the universe today provide a window into how the first galaxies that formed in the universe have evolved. These small galaxies can only be detected locally and have been found to have a range of properties, from objects that appear to harbor only dark matter and just thousands of stars, to gas-rich dwarf galaxies with a range of stellar populations. It remains unclear what dictates the properties of the dwarf galaxies and, in particular, what quenches their gas content and star formation. This understanding is key to making progress on how these small galaxies evolve and proceed to build up larger galaxies.
In the Local Group, the gas content of dwarf galaxies has been shown to have a clear correlation with distance from the primary spiral galaxy (e.g., Einasto et al. 1974;Blitz & Robishaw 2000;Grebel et al. 2003;Grcevich & Putman 2009, hereafter GP09;Spekkens et al. 2014). This suggests that the environment of the dwarf galaxy plays an essential role in its evolution. Beyond the Local Group, however, the situation is not as clear. The SAGA survey of Milky Way analogs finds more star-forming dwarf galaxies in the halos of most of these galaxies than for the Milky Way or M31 (Geha et al. 2017). Other work finds more consistency with the Local Group, with evidence for the gas content of dwarf galaxies increasing with isolation (Bradford et al. 2015;Stierwalt et al. 2015) and a similar distribution of dwarf galaxies around spirals in a deep optical survey (Carlsten et al. 2020).
There are numerous mechanisms that can rob a dwarf galaxy of its cold gas. In the early universe, reionization is thought to be effective at removing cold gas in the smallest dark matter halos (Tollerud & Peek 2018;Kang & Ricotti 2019;Rodriguez Wimberly et al. 2019). It is possible that this mechanism is patchy in its effectiveness, and the exact redshift is still debated, but the star formation histories of some of the oldest local dwarf galaxies are consistent with this being a quenching mechanism (Weisz et al. 2014). Another mechanism is through some type of interaction with another galaxy. There is no strong evidence that a dwarf-dwarf interaction removes the cold gas from the resulting pair (Pearson et al. 2016(Pearson et al. , 2018, but the proximity of the pair to a larger galaxy is often found to result in quenched galaxies (Geha et al. 2012;Stierwalt et al. 2015). Supernova explosions and stellar winds can also act to remove gas, particularly during periods of intense star formation, but this appears to be insufficient for the complete removal of gas in typical systems (Agertz et al. 2013;Emerick et al. 2016).
In the Local Group, dwarf galaxies within the virial radius of the Milky Way or Andromeda are largely devoid of gas, while those beyond typically have gas. This relationship suggests that the distance to a larger galaxy is an important factor in dwarf galaxy quenching. Though tidal forces can be important for those galaxies that have plunged deep into the host dark matter halo in the past, this has been shown to affect only a very small  The method indicates whether the 1σ was obtained with a method consistent with the source being resolved (Res.) or unresolved (Unres.) in the data. If the source does not have a velocity (no V), then the 1σ is an average from all of the channels without significant Galactic emission. For HI4PI resolved, the 1σ values tend to be lower, as they are the standard deviation of the flux sum divided by the area of the optical galaxy for nine regions surrounding the galaxy (see text). c The H I mass is calculated using 5σ, the noted distance, and a fixed velocity width of 10 km s −1 . The errors are from the distance errors shown. d This column notes the references for the positions, velocities, and distances, respectively. e The limit is only for the core of this tidally extended galaxy. f The limit is calculated with twice the median flux in the region of the galaxy due to strong Galactic contamination (see text). g Sculptor has been claimed as a detection in previous publications, but the H I clouds are offset from the stellar position of the galaxy, and there is abundant surrounding emission at similar velocities. h Fornax is at velocities that confuse any associated H I with Galactic emission. The limit at the stellar position and velocity is given. i This galaxy is unlikely to exist based on observations by Cantu et al. (2020). j Phoenix has confusion with Galactic emission, but the H I cloud is at the position and velocity of the stellar component. k Lacerta I is Andromeda XXXI in (M12). l Perseus I is Andromeda XXXIII in (M12). m Cassiopeia III is Andromeda XXXII in (M12).
(2) S19.  Bouchard et al. (2005) found a velocity of 159 km s −1 , but we do not note that here, as this could not be confirmed by Westmeier et al. (2017) or Koribalski et al. (2018). Koribalski et al. (2018) found emission with a similar flux and velocity width at 36 km s −1 , so we leave the H I mass.
(This table is available in machine-readable form.) fraction of the Local Group dwarfs (e.g., Mateo et al. 2008;Simpson et al. 2018;Iorio et al. 2019). The results thus far have been consistent with a diffuse gaseous halo medium playing an important role in stripping the gas from the dwarf galaxies given the range of distances for the dwarf galaxies and the assumption of instantaneous stripping (GP09; Gatto et al. 2013). This can be tested with the discovery of new dwarf galaxies, further information about the orbital histories of the dwarf galaxies, and deeper limits on the H I content of the dwarf galaxies.
One aspect that has not been commonly considered is the role of a diffuse group medium of the Local Group in stripping dwarf galaxies. Groups are thought to harbor a hot halo medium at temperatures of ∼10 5-6 K (Osmond & Ponman 2004;Nuza et al. 2014;Stocke et al. 2019), and dwarf galaxies falling through this medium with a fast enough velocity are likely to be partially stripped. Simulations also show support for some dwarf galaxies being more easily quenched in a Local Group environment compared to the equivalent satellite of an isolated spiral (Garrison-Kimmel et al. 2019). However, the role of a large-scale environment, instead of that of an individual host galaxy, in dictating a galaxy's gas content continues to be debated (Tollerud et al. 2016;Luber et al. 2019).
In this paper, we provide new limits on the gas content of the Local Group dwarf galaxy population for galaxies discovered within 2 Mpc as of 2020 (Simon 2019, hereafter S19; McConnachie 2012, hereafter M12). This work is motivated by the discovery of large numbers of new Local Group dwarf galaxies, the availability of deeper H I survey data, and uncertainty about the cause of dwarf galaxy quenching. Gas content can be used to describe the H I results, as molecular and ionized gas are only detected in those galaxies with H I and are generally a small fraction of the H I Buyle et al. 2006;Schruba et al. 2012). In Section 2, we describe the data and methods we use to set the H I mass limits. A model for the structure of the Local Group is presented in Section 3.1, and the Milky Way model used for orbit integration of the dwarf galaxies is described in Section 3.2. In Section 4, we present the H I results in the context of the distance to the Milky Way or Andromeda and relative to a virial radius of the Local Group. We discuss our results in Section 5 in terms of the recent Gaia proper-motion measurements for Milky Way dwarf galaxies and the potential role of a Local Group medium. The paper is briefly summarized in Section 6.

Data and H I Mass Limit Derivations
The dwarf galaxies included in this study are listed in Table 1, sorted by their heliocentric distance. This distance is also used to calculate the H I mass limit. Additional properties of the dwarf galaxies are listed in Table 2. The dwarf galaxies and their properties are primarily taken from the updated online catalog 6 of the M12 paper and the S19 review. The online M12 catalog contains those dwarf galaxies within 3 Mpc that have distances measured from resolved stellar populations. Here we include only those galaxies within 2 Mpc to aim for greater completeness and avoid nearby groups. This catalog includes some galaxies that are clearly not dwarf galaxies, so we exclude galaxies with stellar masses >2 × 10 9 M e . Note that this limit results in the inclusion of the Magellanic Clouds. We also exclude Canis Major from the M12 list, as it is primarily defined as a stellar stream (Martin et al. 2004). We add to the list additional ultrafaint dwarf galaxies tabulated in S19 and Antlia 2 (Torrealba et al. 2019). For all of the ultrafaint dwarf galaxies, we prioritize the more recent S19 values for their properties over M12. We examined the catalog of Karachentsev et al. (2013) as a check of our dwarf galaxy completeness within 2 Mpc and found anything additional in their catalog to be consistent with being unconfirmed or a globular cluster.
There are three main sources of H I data we used to set limits on the dwarf galaxy H I content: Galactic Arecibo L-band Feed Array HI (GALFA-H I DR1; Peek et al. 2011), GALFA-H I DR2 7 HI4PI (HI4PI Collaboration et al. 2016). These are referred to as GALFA1, GALFA2, and HI4PI in Table 1. The starting point for all of the GALFA-H I data were cubes with a resolution of 4′ and a channel spacing of 0.754 km s −1 . GALFA-H I DR2 covers the entire sky observable with the Arecibo 300 m radio telescope, or all right ascensions for declinations between approximately −1°and +37°(approximately one-third of the sky). GALFA-H I DR1 has the same resolution as DR2 but only covers approximately half of the Arecibo sky in noncontinuous regions. We used the DR1 data in a few cases because they are deeper in some regions with the inclusion of additional commensal data (see Peek et al. 2011Peek et al. , 2018. The HI4PI survey combines the southern GASS data taken with the Parkes 64 m radio telescope (McClure-Griffiths et al. 2009) and the northern EBHIS survey taken with the Effelsberg 100 m telescope to cover the entire sky (Winkel et al. 2016). The combination results in an all-sky H I survey with 16 2 spatial resolution and a channel spacing of 1.29 km s −1 .
To determine if a dwarf galaxy was detected and obtain the limits on the H I masses, we first applied Hanning smoothing on each cube that contains the position of a dwarf galaxy to ∼10 km s −1 . Since the channel spacing is different for GALFA-H I and HI4PI, the closest value to 10 km s −1 was used; 13 channels were smoothed for GALFA-H I and 7 for HI4PI. We then examined the smoothed data cube at the position and velocity of the source in both the data cube and the spectrum for a possible detection. In all cases where there was no previous detection, there was no detection at the position and velocity of the galaxy, and we proceeded to extract a noise level to determine the H I mass limit.
The method to obtain the quantitative H I mass limit differed depending on whether the gas in the dwarf was likely to be resolved or not. We used the optical half-light radius (r h ) as a guide to whether this was likely. In all cases, the noise values were checked to be consistent across several channels, and, with the exception of the rare cases when the dwarf was resolved with HI4PI data, the standard deviation was calculated within a 30′ diameter region at the position and velocity of the dwarf. The 30′ window is designed to be an area larger than the beam size but not large enough to potentially encompass nearby structures at the velocity of the dwarf (i.e., Galactic emission in some cases or high-velocity clouds). None of the dwarf galaxies were close enough to the edges of the cubes for this to influence the analysis. If the dwarf was in the GALFA-H I sky and the optical diameter was smaller than 4′-5′, the limit was obtained from the standard deviation within a 30′      Table 1 with data = GALFA1 or 2). If the dwarf was in the GALFA-H I sky and had an optical diameter between approximately 5′ and 12′, we did this same procedure with GALFA-H I data smoothed to 8′ (Res. in Table 1 with data = GALFA1 or 2). This generally resulted in a better limit on the H I mass than going to the HI4PI data, though for the three dwarf galaxies with optical diameters >9′, it does assume that the H I is more centrally concentrated (Coma Berenices, Andromeda XIX, and Andromeda II). There are several dwarf galaxies for which we adopt the HI4PI limit even though the dwarf is in the GALFA-H I sky: Hercules and Canes Venatici I because of their large optical size and Canes Venatici II, Andromeda XI, Leo I, and Leo II due to their location in a noisier region of the GALFA-H I data (i.e., on a basket-weave remnant and/or near the outer regions of the survey). The HI4PI data were used for the majority of the dwarf galaxies due to their greater sky coverage. The limits were obtained with a 30′ region (Unres. in Table 1 with data = HI4PI), as was used for the GALFA data, with the exception of those galaxies that have optical sizes larger than the 16 2 HI4PI beam. For these galaxies, we took the sum of the flux within a region that was the optical size of the galaxy at its position and did the same for eight regions surrounding the central position of the galaxy. We divided the summed flux values by the area of the optical size and calculated the standard deviation of the nine values. We then checked that the value was consistent with the values taken from surrounding channels (Res. in Table 1 with data = HI4PI). The exceptions to using this method for large-extent galaxies are the disrupted Sagittarius dSph and Boötes III galaxies. For these galaxies, we quote the limit in the core with the unresolved technique rather than attempt to cover their full extent. The 1σ values from these methods are listed in Table 1, while 5σ is used in the H I mass calculations. The conversion factors from the kelvin σ values to janskys are 0.6 Jy K −1 for HI4PI, 0.11 Jy K −1 for GALFA-H I, and 0.44 Jy K −1 for the GALFA-H I data smoothed to 8′ resolution. Several dwarf galaxies are at velocities that are contaminated by Galactic emission. In most cases, five times the standard deviation calculated with the relevant method above is sufficiently high to represent a limit on the H I gas in the dwarf over the background. In the case of Willman 1, its low heliocentric velocity led to strong Galactic emission and the standard deviation not being suitable for determining the H I mass limit. For this galaxy, we calculated the median flux in 30′ regions surrounding the dwarf position in the 10 channels centered on the dwarf velocity and found that twice the median of these values was a conservative value to choose for a limit on what would be a detectable H I mass.
Ultimately, 5σ H I mass limits are quoted in Table 1, and they are calculated using a velocity width of 10 km s −1 and the distance to the dwarf galaxy: M H I (M e ) = 2.36 × 10 5 5σ (Jy) 10 km s −1 D 2 (Mpc). We debated whether to use the stellar dispersion values for each galaxy instead of a fixed 10 km s −1 , but given the variations on availability and errors, we chose the fixed value. Errors on the mass limits are given based on the distance errors. If the systemic velocity of the dwarf galaxy was not available, we measured the standard deviation every 10 km s −1 for |v LSR | < 500 km s −1 in a 30′ region at the position of the dwarf (all are unresolved and labeled Unres. no V) and used the average of those values, excluding those channels that were contaminated by Galactic or Magellanic-related emission. The dwarf galaxies without velocities at the time of paper submission were Cetus II, Horologium II, Reticulum III, Pictoris 1, Columba I, Sagittarius II, Indus II, Phoenix 2, Eridanus 3, Indus I, Cetus III, DES J0225+0304, Pictor II, and Virgo I.
Though we checked some of the H I masses for previously detected dwarf galaxies for consistency, we did not remeasure the H I masses and largely adopted values from the references in M12 and adjusted the value if an updated distance was available. The only exceptions to adopting the M12 detections are Sculptor and Fornax. We do not include them because the H I clouds detected are not centered on the optical component of the galaxies, and there is abundant nearby H I that makes the  References.
(2) S19.  (2005). (21) The σ is from Bouchard et al. (2005) and is consistent with the detection at the lower velocity by Koribalski et al. (2018). (22)  association highly uncertain. Instead, we adopt H I limits at the stellar position of these galaxies. Sculptor formed the vast majority of its stars in the distant past and is in a region where there are multiple high-velocity clouds; therefore, we think it is unlikely that the nearby gas is associated. Fornax has formed stars in the past few gigayears (Weisz et al. 2011), but its velocity makes confusion with Galactic H I emission a huge issue, and the potentially associated extended H I is not centered on the galaxy. The Phoenix dwarf galaxy was considered highly uncertain as well, but with the improved stellar velocities of Kacharov et al. (2017) and the H I clump at the stellar heliocentric velocity and overlapping with the stellar component (St-Germain et al. 1999;Young et al. 2007), we adopt this H I clump as a detection.

Local Group and Milky Way Mass Models
In this section, we define the mass models for the Milky Way and M31 that we use to define a Local Group virial radius or "surface." We then describe how we numerically computed orbits for the satellites of the Milky Way that have propermotion measurements.

Defining a Local Group "Bounding Surface"
We first define a Local Group coordinate system with an origin at the approximate center of mass of the Milky Way and M31 (computed using models specified below). We define the x-axis of this coordinate system by the line connecting the Galactic center to the center of M31 and place the origin at the center of mass along this axis. Because our models are symmetric about the x-axis, the orientations of the y-and z-axes are arbitrary; with our definition, the z-axis is aligned with (α, δ) ICRS = (193.327, 48.585)°, and the y-axis is aligned with (α, δ) ICRS = (102.219, 0.977)°. We assume that the heliocentric distance to M31 is 779 kpc (Conn et al. 2012), the heliocentric distance to the Galactic center is 8.122 kpc (Gravity Collaboration et al. 2018), and the coordinates of the Galactic center are taken from Reid & Brunthaler (2004).
As a simplified representation of the total density distribution of the Local Group, we define a prolate spheroidal surface bounding the Local Group in order to distinguish satellite systems that are within or outside of the Local Group. We first construct a mass model for the total mass distribution of the Milky Way and M31 by representing each galaxy with a spherical Navarro-Frenk-White (NFW; Navarro et al. 1996) density profile such that the total Local Group density is given by the sum of two independent NFW profiles. For the Milky Way, we use virial mass and halo concentration values of M 200,MW = 1.2 × 10 12 M e and c = 10, motivated by a number of recent mass determinations that use satellite galaxy and globular cluster kinematics to infer the mass of the Galaxy To determine the axis ratio of the total Local Group density distribution, q LG , we compute the xx and yy components of the inertia tensor given by the above mass model and use them to compute the axis ratio q LG = I yy /I xx . We define the Local Group-bounding prolate surface (in Local Group Cartesian coordinates x, y, z) to be LG 2 2 ( ) where r e ≈ 733 kpc is defined such that the surface fully encloses the virial sphere around M31. For each satellite galaxy in our sample, we compute the minimum distance between the galaxy and the Local Group-bounding surface. Figure 1 (solid gray ellipse) shows a projection of this bounding surface in both the x LG , y LG and x LG , z LG planes, along with the positions of all dwarf galaxies in our sample (blue squares for H Idetected galaxies and red upside-down triangles for nondetections) and projections of the virial spheres around the Milky Way and M31 (left and right black circles, respectively). We note that there is substantial uncertainty and potentially large (up to a factor of ∼2) biases on the measurements of both the Milky Way and M31 virial masses (e.g., from the presence of the Magellanic Clouds in the case of the Milky Way; , so this bounding surface should be interpreted qualitatively as a "soft" boundary. To emphasize this point and assess how our conclusions and results are affected by uncertainties on the global properties of the Milky Way and M31 dark matter halos, we also construct two additional Local Group models and bounding surfaces with varied masses for the two galaxies. Since the total Local Group mass is fairly well constrained (van der Marel et al. 2012), we only vary the masses of the Milky Way and M31 to keep the total Local Group mass constant at M LG = 3.2 × 10 12 M e . As the virial masses of the Milky Way or M31 are not individually well constrained, and the scatter in the existing mass measurements for either galaxy are likely underestimated due to biases in the individual measurements (e.g., Kafle et al. 2018), we choose to vary the Milky Way mass by 25% up and down (adjusting the mass of M31 to keep the Local Group mass fixed). Our models therefore have M MW = (0.9, 1.2, 1.5) × 10 12 M e , M M31 = (2.3, 2.0, 1.7) × 10 12 M e , R vir,MW ≈ (204, 224, 242) kpc, and R vir,M31 = (279, 266, 252) kpc. The Local Group-bounding surfaces for the two other models are shown in Figure 1 as gray dashed ellipses, and the thickness of the virial circles reflects the range of virial radii for the two galaxies.
In Table 2, we include estimates of the closest distance between each dwarf galaxy and the Local Group surface, D LG , as estimated in our fiducial mass model. We use the two other mass models to estimate the bounds on the D LG values for each source and note these as error bars. We note that in some cases (e.g., Pisces II, Pegasus III), the Local Group surface distance in the fiducial mass model is not the central value; this is expected and happens when a dwarf galaxy is near enough to the Local Group-bounding surface such that the change of ellipticity of the surface in the different Local Group mass models causes unintuitive changes.

A Milky Way Model for Orbit Integration
We numerically integrate orbits for the Milky Way dwarf galaxies that have distances, radial velocities, and propermotion measurements. For computing these orbits, we use a three-component mass model to represent the Milky Way composed of a Hernquist bulge (Hernquist 1990), Miyamoto-Nagai disk (Miyamoto & Nagai 1975), and spherical NFW halo (Navarro et al. 1997). We fix the parameters of the disk and bulge models to be consistent with the model defined in Bovy (2015). For our fiducial model, we adopt a more massive halo such that the enclosed mass within 250 kpc is M enc ≈ 1.2 × 10 12 M e in order to fit a compilation of mass-enclosed measurements (see the gala documentation 8 for more information) and be consistent with the model assumed to define the Local Group boundary surface above.
The mass model is implemented in gala (Price-Whelan 2017), which we then also use to numerically integrate the orbits of the dwarfs, treating the satellite galaxies as test particles. We cross-match our catalog of Milky Way satellites with recent proper-motion measurements of a subset of the dwarfs (Fritz et al. 2018;Pace & Li 2019) that make use of astrometry from the Gaia Data Release 2 (Gaia Collaboration et al. 2018b; Lindegren et al. 2018). We compute initial conditions (i.e., at present day) by generating random samples from the error distributions over all kinematic measurements for each of the 38 dwarf galaxies in this subset. For each error sample, we additionally vary the Milky Way halo enclosed mass by sampling a uniform random value between 0.9 and 1.5 × 10 12 M e , following the discussion in Section 3.1, in order to include uncertainty in the Milky Way mass in our derived orbital quantities. 9 We transform these samples into a galactocentric reference frame assuming a Sun-Galactic center distance of R e ≈ 8.122 kpc (Gravity Collaboration et al. 2018) and using solar-motion values from Drimmel & Poggio (2018). We then numerically integrate each orbit sample for each dwarf backward from the present day for 2 Gyr with a time step of 1 Myr using Leapfrog integration. We ignore the gravitational influence of the Magellanic Clouds, which likely affects the orbits of a small subset of the dwarf satellites of the Milky Way Patel et al. 2020). We use these orbits (in particular, pericentric distances and velocities at pericenter) later to determine the minimum Milky Way gas density needed to strip the satellites of their own gas reservoirs. Table 3 includes the orbital parameters for the satellites for which this is done.

Results
The results of the new H I measurements are presented in Table 1 and shown in Figures 4 and 5. All of the newly discovered dwarf galaxies without previous H I measurements are nondetections, and all previous nondetections remain as nondetections. The limits presented here are generally deeper than those previously published. Notable other limits are the deeper limits published for some of the Milky Way dwarf galaxies in Spekkens et al. (2014) and preoptical velocity limits for some of the new ultrafaint dwarf galaxies by Westmeier et al. (2015). To ensure consistency across the complete set of Local Group dwarfs, our limits here depend only on the GALFA-H I and HI4PI data described in Section 2. Figure 2 shows the relationship between the H I mass limit or H I mass of a dwarf galaxy versus distance from the Milky Way or M31, whichever is closer. The virial radii of the Milky Way and M31, as defined in Section 3, are 224 and 266 kpc, respectively. These virial radii are not presumed to be exact but rather give a guideline to consider the detections and nondetections. A range of possible virial radii for each galaxy is shown by the shaded regions, as described in Section 3.1. The Milky Way and M31 are described individually below, but it can be seen from Figure 2 that the vast majority of the galaxies are nondetections within these radii, and beyond, the vast majority are H I detections. Though we code each dwarf galaxy by whether the Milky Way or M31 is closer, we note that beyond a certain radius, a clear association with either galaxy is uncertain without orbit information. Thus, the majority of the H I detections cannot be directly associated with either the Milky Way or M31. Beyond the virial radii of these galaxies, the detections Leo T, Phoenix, and NGC 6822 could be associated with the Milky Way, and LGS 3, Pegasus dIrr, and IC 1613 could be associated with M31. The other 15 detections beyond the virial radii in this plot are >750 kpc from either galaxy. The average H I mass of the 26 detected dwarf galaxies within 2 Mpc of the Milky Way is 7.5 × 10 7 M e , and the median H I mass is 7.4 × 10 6 M e .
Using the virial radius of 224 kpc for the Milky Way, 53 dwarf galaxies have 5σ limits on their H I mass of <10 4 M e within this radius. These are the strongest H I limits due to their proximity and the D 2 dependency for the H I mass. This dependency also results in the arc of increasing mass limit with increasing distance, since we use survey data that do not vary substantially in sensitivity at a given position. For the Milky Way dwarf nondetections beyond 224 kpc, Leo II has an H I mass limit <10 4 M e and, at 233 kpc, is within the range of the possible Milky Way virial radii we consider here, Leo I and Cetus III have H I limits of ∼10 4 M e and are at 254 and 251 kpc, and Eridanus II is at 366 kpc with an H I mass limit of <2 × 10 4 M e . Tucana is a nondetection with a limit of <10 5 M e at 887 kpc from the Milky Way and should be considered a field object. The lowest H I mass of a detected dwarf galaxy is above 10 5 M e , so the results strongly indicate that none of the Milky Way dwarf galaxies with limits are likely to have H I. The only two H I detections within the virial radius of the Milky Way are the Magellanic Clouds, which were not included in GP09 due to their large mass and are currently being stripped of their gas (Putman et al. 2003b;Salem et al. 2015). A radius of 260 kpc would optimize the numbers, with the Milky Way having 56 dwarf galaxies with  Notes. a This is the median halo density required to strip the dwarf at this position. The errors should be multiplied by the same factor of 10 noted for the median density. b This galaxy is not included in Figures 6 and 7 because of its very small pericenter. c Phoenix is the only galaxy in this list with gas.
(This table is available in machine-readable form.) no gas and two massive dwarf galaxies with gas within this radius. We note that for Sculptor and Fornax, if the offset H I gas was associated (see Section 2), they would be clear outliers in being small dwarf galaxies within 150 kpc of the Milky Way that have H I gas.
The virial radius for M31 from the model in Section 3.1 is 266 kpc. Using this radius as a guide, 27 dwarf galaxies are undetected with limits 10 5 M e . These limits do not vary as much as the Milky Way limits due to the similar distance of these satellites. This count includes M32, And XXV, and And XIX, which have limits slightly above 10 5 M e due to some confusion with emission from M31 or the Milky Way. The nondetected dwarf galaxies beyond 266 kpc that can be considered satellites of M31 are And VI at 268 kpc, And XXII at 276 kpc, And XVI at 319 kpc, Perseus I at 348 kpc, And XXVIII at 365 kpc, and And XVIII, which is at a distant 457 kpc. Cetus is a nondetection at 678 kpc from M31 and is in the same category as Tucana, where its large distance makes a direct association with either galaxy uncertain. At close to 2 Mpc from either galaxy, KKR 25 is a nondetection that clearly cannot be associated with either galaxy. The H I detections within the 266 kpc radius for M31 are its dwarf elliptical satellites (NGC 205 and NGC 185) and IC 10. The dwarf ellipticals have smaller amounts of H I relative to their luminosity and dynamical mass compared to other dwarf galaxies (Figures 4 and 5; see also Geha et al. 2006), and IC 10 is at 252 kpc from M31 and has irregular/disturbed H I, similar to LGS 3 at 267 kpc (Hunter et al. 2012;Ashley et al. 2014). This may indicate that the H I gas of these galaxies is beginning to be removed. As can be seen from Figure 2, the outer range of possible M31 virial radii (279 kpc) considered for our Local Group model results in 29 dwarf galaxies within this radius without gas and four with gas. Figure 3 shows the H I measurements in the context of the dwarf galaxy's distance from a Local Group surface or an approximate virial radius of the Local Group. As outlined in Section 3.1, this surface was defined using the Milky Way and M31 mass and concentration parameters, and variation in this surface was calculated by varying the mass of the Milky Way and M31. The range of distances relative to the variation in the Local Group surface is shown by the line through each symbol, with our fiducial model represented by the position of the symbol and noted in Table 2. It is immediately apparent that, as with the Milky Way and M31, the nondetections are largely located within the Local Group surface (zero on the plot), while those with detected H I are beyond this Local Group surface. There are six detected exceptions within the surface, three of which are the most optically luminous dwarf galaxies in the sample (LMC, SMC, and NGC 205), and two others are in the top 11 most luminous (IC 10 and NGC 185). These detection exceptions are the same as for the Milky Way and M31, with the addition of LGS 3, which is right at the edge of M31ʼs virial radius and very close to the edge of the Local Group surface. The nondetections beyond the Local Group surface are And XVIII, Perseus I, Eridanus II, Leo I, and Leo II. Cetus, Tucana, and the very distant KKR 25 remain odd nondetections at large radii similar to the Milky Way and M31. As can be seen, some dwarf galaxies move inside or outside of the Local Group surface with higher or lower Milky Way and M31 masses. With a 25% lower Milky Way mass but higher M31 mass to obtain the same total Local Group mass, seven (instead of eight) nondetections would be beyond the surface; and with a 25% higher Milky Way mass and correspondingly lower M31 mass, nine nondetections would be beyond the Local Group surface. If the Local Group is more massive than the 3.2 × 10 12 M e used here, the surface would easily encompass the four nondetections within 50 kpc of the surface. Using our fiducial model as the primary comparison point, we find that the Local Group surface has eight nondetections beyond the surface, and the Milky Way and M31 have a total of 13 nondetections beyond their virial radii. This value of 13 does not change with the changes in the masses of the Milky Way and M31. The Local Group surface therefore encompasses more of the galaxies without gas.
The completeness of the optical surveys in finding dwarf galaxies at various radii should be considered when assessing the results for both the virial radii of the Milky Way and M31 and the Local Group surface. Most of the dwarf galaxies were discovered in the Sloan Digital Sky Survey, DES, Pan-STARRS, or PANDAS (e.g., Willman et al. 2005;Martin et al. 2006;Belokurov et al. 2007;Bechtol et al. 2015;Koposov et al. 2015;Laevens et al. 2015), and though the completeness has been partially assessed for some of these surveys (Walsh et al. 2009;Newton et al. 2018), none cover the complete sky. If one adopts the all-sky survey of Whiting et al. (2007), which is noted to be 77% complete for objects brighter than 25 mag arcsec −2 in R and one to several arcminutes in size, all of the galaxies within 275 kpc of the Milky Way or Andromeda are devoid of gas. Likewise, galaxies within the Local Group surface or close to the surface used here (e.g., Leo I and Leo II) are devoid of gas. Beyond these distances, things are less clear, with four galaxies detected in H I and three galaxies with H I mass limits. Though the Whiting et al. (2007) sample is very limited in the number of dwarf galaxies, it may suggest that additional faint galaxies without gas will be detected at larger radii.
Figures 4 and 5 examine whether the H I limits for the dwarf galaxies are significant when scaled by their luminosity or dynamical mass. In other words, one might expect the amount of gas in a dwarf galaxy to correlate with the stellar or total mass, and therefore the limits should be lower than the detected galaxies when normalized. The V-band luminosity can be considered as a proxy for the stellar mass, consistent with the stellar mass-to-light ratio of 1 used in M12. While the stellar mass-to-light ratio will vary for different dwarf galaxies, we do not address that here, as these estimates can have many complications and do not span more than an order of magnitude. Figure 4 shows this scaling of the H I content of the dwarf galaxies by V-band luminosity (see Table 2). The scaled H I limits remain significant; however, there are a number of undetected dwarf galaxies around M H I /L V = 1. The median value of M H I /L V for the H I-detected dwarf galaxies is 0.93 (blue line in Figure 4), and the average value is 1.2. The undetected dwarf galaxies near these values are dominated by ultrafaint dwarf galaxies with very small stellar populations and some Andromeda dwarf galaxies that are faint but also influenced by slightly higher H I mass limits. All of the undetected Milky Way dwarf galaxies with M H I /L V ∼ 1 have L V < 10 4 L e . Leo T is the best H I-detected comparison point for these galaxies and has an M H I /L V higher than most of these galaxies. Stronger limits on their H I masses would be useful, but the dwarf galaxies near M Hi /L V = 1 have ancient stellar populations and are highly unlikely to have gas that can support star formation. The dynamical mass estimates for the dwarf galaxies were calculated within the half-light radius (r h ) using the same method adopted by M12 in most cases. This involves using the measured stellar velocity dispersions and r h values and the equation from Walker et al. (2009) . When values of r h and σ å were not in M12, they were added from S19 or the literature, and upper limits were used when necessary (see Table 2). Many of the dwarf galaxies with gas are more distant and do not have a measured stellar velocity dispersion. For these galaxies, we adopt the dispersion calculated from the FWHM of the H I line and calculate the total mass within r h using The use of the gas dispersion will result in a larger dynamical mass than if the internal stellar velocity dispersion was used. These masses are not designed to be representative of the true total mass of the dwarf galaxies but are used throughout for consistency. Figure 5 shows the results of scaling the H I mass limits and masses by this dynamical mass estimate. It shows that the H I limits are significant when scaled by the total mass interior to r h , since the vast majority of the detected dwarf galaxies lie above the nondetections. The nondetections with higher M H I /M dyn values are largely faint Andromeda dwarf galaxies whose H I limits are not as deep. We exclude the Sagittarius dwarf spheroidal galaxy and Boötes III from this plot, since their stellar components are clearly not in equilibrium. For the detections, besides the dwarf ellipticals, Phoenix is somewhat of an outlier in that it is lower than other detections in both this and the M H I /L V plot. Phoenix is at a velocity of −13 km s −1 and confused with Galactic emission. This location on the plot may indicate more of the gas mixed in with Galactic gas should be associated with the dwarf galaxy, that it is in the process of being stripped, or possibly that the gas is not actually associated with the dwarf.

Discussion
In this section, we discuss the results in the context of the likely methods of gas removal from Local Group dwarf galaxies. We separate the discussion into the effect of a Milky Way (or M31) gaseous halo medium (Section 5.1) and the potential role of a diffuse Local Group gaseous medium in removing gas from dwarf galaxies (Section 5.2). We briefly discuss other methods to potentially remove gas from dwarf galaxies in Section 5.3.

Stripping by a Spiral Galaxy Halo Medium
The halo media of the Milky Way and M31 have been thought to play a dominant role in setting the relationship between the gas Figure 4. The H I mass or mass limit of the dwarf galaxies divided by the V-band luminosity (log scale) against the distance from the Local Group surface. Detections are filled diamonds, and nondetections are open diamonds. The lines through the symbols represent the range of possible Local Group surfaces by varying the mass of the Milky Way and M31. We exclude the Sag dSph from this plot as M H I /L V = 5.7 × 10 −6 due to its large V-band luminosity and low H I mass limit. The blue solid line represents the median M H I /L V for the detected dwarf galaxies. content of dwarf galaxies and their distance from these large spirals (GP09; Blitz & Robishaw 2000;Spekkens et al. 2014). Numerous dwarf galaxies without gas have now been added within the virial radii of the Milky Way and M31, and this provides additional support for a diffuse halo medium playing an important role in quenching the dwarf galaxies. The few exceptions of H I detections within the virial radii of these galaxies were already known and consistent with being more massive galaxies that can more easily retain their gaseous reservoirs (e.g., Simpson et al. 2018;Garrison-Kimmel et al. 2019). These galaxies also often have gas that is disturbed in nature and may be in the process of being removed. The below discussion focuses on the halo medium of the Milky Way; however, we note that M31 has a halo medium that is likely to be similarly effective at stripping dwarf galaxies (Lehner et al. 2020).
We can freshly examine the required gas density to ram pressure strip Milky Way dwarf galaxies for those that have proper-motion measurements from Gaia (see Table 3; Fritz et al. 2018;Gaia Collaboration et al. 2018a;Simon 2018;Pace & Li 2019). The criterion to ram pressure strip a galaxy of its gas was originally derived by Gunn & Gott (1972). The equation that describes the complete stripping of a homogeneous medium can be written as where n halo is the ambient gas number density in the halo in cm −3 , σ is the stellar velocity dispersion of the dwarf, v sat is the relative motion of the dwarf through the medium, and n gas is the average gas density of the dwarf in the inner regions. Some comparisons with numerical simulations have found that this equation tends to underestimate the halo density required for stripping. Gatto et al. (2013) completed 2D simulations of the stripping of classical dwarf galaxies and found that the equation gives values that are approximately a factor of 5 too low. Salem et al. (2015) also found a somewhat lower value for the analytical calculation for the stripping effect on the LMC, but the value is within the errors found with the numerical simulation. We leave a more detailed examination of the required halo density to future simulation work but account for this potential large systematic by including large error bars on our calculations. The internal velocity dispersions (σ) for the Milky Way dwarf galaxies with proper motions are measured in most cases, albeit with large error bars. For Hydra II and Triangulum II, the measured upper limits are used (see Table 2). A dwarf galaxy's dispersion may be similar to its value at earlier times if the dwarf has not been significantly affected by tidal forces and has not grown substantially.
The correct gas density in the inner regions of the dwarf galaxies at the time of stripping is a difficult value to pinpoint. The central densities from model fits to the H I gas profiles depend on the dark matter profiles used and tend to be very high (Faerman et al. 2013;Emerick et al. 2016). On the other hand, star formation can be triggered when gas is compressed as it interacts with a diffuse medium, which can result in a decrease in the gas density. This decrease in the central regions is seen in several galaxies in our sample (e.g., IC 1613 and Sextans A; Hunter et al. 2012). An estimate for the central gas density can be obtained using the current gas distribution in Leo T. Adams & Oosterloo (2018) found a peak column density in the central regions of 4.6 × 10 20 cm −2 in their 117 × 32 pc beam and an H I extent of 400 pc for the dwarf. This results in an average gas density of 0.37 cm −3 , which is within the range of values used in GP09 and similar to the typical values found in models within the central 100 pc (Emerick et al. 2016). This value is also consistent with what has been found for some larger dwarf galaxies, with central density measurements more typically approaching 10 21 cm −2 and extents of a few kiloparsecs (Hunter et al. 2012).
Since a dwarf galaxy will be moving at the highest velocity and most likely through the densest halo medium at perigalacticon, we can assume that this would be the point at which the galaxy would be subject to maximal ram pressure stripping. We therefore compute the minimum halo gas density, n halo , required to strip the dwarf at perigalacticon using Equation (2), assuming all of the stripping happens at this orbital phase for each dwarf. We note that this is strictly an upper limit on the minimum value, as it does not account for the steady ram pressure stripping from the extended gaseous halo during its orbit. We determine the velocity at perigalacticon for those dwarf galaxies with proper-motion estimates using the Milky Way model and orbit calculations described in Section 3.2. We compute estimates of n halo and uncertainties on this quantity by Monte Carlo sampling from the error distributions over the velocity dispersion measurements (as compiled from other work) and pericentric velocity for each dwarf galaxy. The error samples in pericentric velocity are computed by sampling from the observed error distribution over distance, proper motion, and radial velocity and numerically integrating the orbits of each dwarf galaxy for the range of Milky Way masses described in Section 3.2. We then compute the median (over samples) value of n halo (plotted as points in Figure 6) and report upper and lower error bars by computing the 16th and 84th percentiles of our samples over n halo . We do not account for uncertainty on the gas density of each dwarf because we use a fixed value of n gas . The orbital values and resulting halo densities are tabulated in Table 3.
We note that whether all of the dwarf galaxies with measured proper motions are bound remains dependent on the mass of the Milky Way and their potential association with the Magellanic Clouds. In particular, Hyd I, Hor I, Car II, and Car III are likely Magellanic satellites (Simon 2018;Patel et al. 2020) that may be coming in for the first time. In any case, these satellites do not stand out in pericenter or halo density compared to other satellites.
The results of the calculation of the minimum halo density at perigalacticon required to strip the galaxy are shown in Figure 6. For the majority of the dwarf galaxies, the requisite halo gas densities are between 10 −5 and 5 × 10 −4 cm −3 out to 200 kpc. The exceptions are two ultrafaint dwarf galaxies that require < 10 −5 cm −3 to be stripped and Fornax, which requires ∼10 −3 cm −3 to be stripped. Phoenix and Eridanus have perigalacticons >300 kpc; the former has gas, though it may show some signs of initial stripping, and the latter requires densities of only 2 × 10 −5 cm −3 to be stripped. All galaxies with dispersions < 6 km s −1 require halo densities < 1.5 × 10 −4 cm −3 to be stripped at perigalacticon. Though direct measures of the density of the Milky Way's halo medium are not available, this type of halo density is easily attainable within 50 kpc with the observational constraints that exist (Sembach et al. 2003;Stanimirović et al. 2006;Hsu et al. 2011;Putman et al. 2011;Miller & Bregman 2015;Salem et al. 2015;Nidever et al. 2019). At larger radii, we do not have solid observational constraints on the halo density of the Milky Way, but absorption line observations indicate that a halo medium is prevalent out to the virial radius of galaxies (Tumlinson et al. 2013;Liang & Chen 2014;Werk et al. 2014). The halo densities required for stripping that are derived here are consistent overall with the values derived from previous related work for some classical dwarfs given the differences in orbital information and central gas densities (e.g., GP09; Gatto et al. 2013).
The derived halo densities can be compared to the halo density with radius values found in simulations, as shown in Figure 7. There are numerous simulations from which the halo gas density can be compared, though most do not plot the data in terms of gas atoms per cubic centimeter verses radius Ford et al. 2016;Salem et al. 2016;van de Voort et al. 2019). When the data are made available in this form, the mean is often adopted, which is biased by clumpy higher-density values and results in higher halo densities at a given radius (Kaufmann et al. 2009;Nuza et al. 2014). Indeed, Simons et al. (2020) found that the effect of ram pressure stripping on a satellite galaxy can be highly stochastic owing to the broad dynamic range in density and velocity of the Figure 6. Minimum halo density (n halo ) required to completely strip the dwarf galaxies with proper-motion measurements when at orbital perigalacticon (r per ). The median n halo is plotted given the errors on the quantities in Equation (2), with the upper and lower error bars representing the 16th and 84th percentiles. See text and Table 3 for details. The velocity dispersions of the dwarf galaxies are color-coded here to provide an estimate of which galaxies are easiest to strip based on this variable. Tucana III is not included on this plot, as it has a pericenter of only 2 kpc and requires only 3.5 × 10 −7 cm −3 to be stripped. We do include the Sag dSph, though its dispersion is confused by its tidal disruption. Phoenix (Phe, the outlier to the upper right) is the only galaxy on this plot that has gas. circumgalactic medium (CGM). Therefore, in Figure 7, we choose to show the volume-weighted median and include the 5th and 95th percentiles 10 to highlight the broad range of densities the dwarf galaxies may experience. The simulations shown are two ENZO cosmological simulations of Milky Way analogs: Joung et al. (2012), which has a total mass of 1.4 × 10 12 M e at z = 0 within 250 kpc (red), and the Tempest halo from the FOGGIE simulation (Peeples et al. 2019;Zheng et al. 2020), which has a mass of 4.9 × 10 11 M e at z = 0.1 within R 200 = 161.5 kpc (blue). The Tempest halo from FOGGIE shows lower median values and a broader density spread than the other halo. This difference is likely due to Tempest's lower halo mass and FOGGIE's new refinement scheme that uniformly resolves the CGM of the simulated galaxy in more detail.
We focus on the Joung et al. (2012) simulation (red) for most of the direct comparison to the dwarf galaxies, given that the Tempest halo from FOGGIE is not as massive as we expect the Milky Way to be. The FOGGIE simulation has higher resolution, and though the spread of properties increases with resolution, the average halo densities remain similar (Peeples et al. 2019;Corlies et al. 2020). The halo densities from Joung et al.'s (2012) simulation are consistent with the majority of the dwarf galaxies being completely stripped as they move through perigalacticon. This is consistent with the simulations of Fillingham et al. (2019) that find that the majority of the galaxies were quenched rapidly on infall. As mentioned previously, Phoenix still has gas, so the fact that it has not passed through a halo medium dense enough to strip it makes sense. There is a group of dwarf galaxies with perigalacticons clustered roughly around 100 kpc that are not as easily stripped by this simulated z = 0 halo medium. Most of these are more massive, with velocity dispersions of 6.6-11.7 km s −1 , and Fornax and Carina have longer quenching timescales and more circular orbits consistent with them being less likely to have instantaneous stripping (Fritz et al. 2018;Fillingham et al. 2019). Some of the dwarf galaxies may have been stripped as they passed through an overdense region of halo gas, or star formation triggered by the compression of the gas may have helped to loosen the gas for stripping (Fillingham et al. 2016;Wright et al. 2019;Simons et al. 2020). The halo densities required for stripping are also likely to be more easily reached at earlier times, as cosmological simulations indicate the gaseous surroundings were denser and colder in the past Rahmati et al. 2016). Early stripping is consistent with the fact that these galaxies ceased their star formation at early times.
Given the low densities required for stripping the lowestmass dwarf galaxies at perigalacticon, we checked the required densities to strip the dwarf galaxies at apogalacticon (see Table 3). This indicates whether these dwarf galaxies could have been stripped early in their orbit or even on entry into the Local Group (see next section). The orbital values at apogalacticon are more uncertain, but generally, gas densities >10 −4 cm −3 are required; these are densities that are unlikely to be reached at large radii. The exceptions are a group of small galaxies at apogalacticons >1 Mpc that have required densities of only ∼10 −5 cm −3 . The level of stripping that a dwarf galaxy experiences throughout its orbit will depend on star formation loosening the gas and the orbital direction of the dwarf galaxy relative to the movement of the halo medium. There are clear indications that the halo medium of a galaxy rotates (Hodges-Kluck et al. 2016;Oppenheimer 2018;Martin et al. 2019;DeFelippis et al. 2020;Simons et al. 2020), and this would potentially make stripping more (or less) effective via the addition of another velocity component between the gaseous medium and the dwarf galaxy.

Stripping by a Local Group Medium
As shown in Figure 3, the Local Group dwarf galaxies with and without gas follow a relationship not only with distance from the Milky Way and Andromeda but also with distance from a Local Group virial radius or surface. The relationship with the Local Group is potentially better in the sense that 8 nondetections are beyond the Local Group surface, while 13 are beyond the virial radii of the Milky Way or M31. Dwarf galaxies close to the Local Group surface line can change to be beyond or within this line with reasonable choices of the model parameters (see Section 3.1), but the Local Group surface was defined using the Milky Way and M31 mass models that define their virial radii for Figure 2. We find that at most one galaxy moves inside or outside the Local Group surface with variations in the mass of the Milky Way and M31, while the number inside or outside the virial radii of these galaxies remains the same. It should also be noted that timing argument masses for the Local Group are generally higher than the 3.2 × 10 12 M e used here, and any increase in the total mass of the Local Group would easily bring the four nondetections  Joung et al. (2012;red). The cold gas with T  10 4.2 K is excluded from this plot to remove the dense disk interstellar medium and satellite gas. The profiles are overlaid with the minimum gas density required to strip a given dwarf galaxy at perigalacticon from Figure 6. The FOGGIE Milky Way analog (blue) has a mass of 4.9 × 10 11 M e at z = 0.1 within R 200 = 161.5 kpc, while the Joung et al. (2012) simulation has a total mass of 1.4 × 10 12 M e at z = 0 within 250 kpc. For each simulation, the solid line denotes the volume-weighted median value, and the colored bands show the 5th and 95th volume-weighted percentiles. 10 To calculate the volume-weighted median density and percentiles, we first rank all of the CGM cells in ascending order according to their volume densities. Then we sort the cells' volumes using the rank and calculate the cumulative distribution function (CDF) of the sorted cells. The volumeweighted median, 5th, and 95th percentiles are the halo densities at which the CDF is equal to 0.5, 0.05, and 0.95, respectively. close to the Local Group surface within that surface (Li & White 2008;van der Marel et al. 2012). The virial radii of the fiducial Milky Way and M31 used here (224 and 266 kpc, respectively) are such that the halos of the two large spirals are within 289 kpc of touching each other. On one hand, this makes the relationship with the Local Group surface not surprising; on the other hand, this indicates the importance of considering the effect of a group medium in stripping gas from dwarf galaxies.
The Local Group is a fairly low-mass group, and there are limited predictions for the properties of an intragroup medium at this mass scale. One comparison point is the Local Group simulation of Nuza et al. (2014), where the two galaxies are embedded in an elongated distribution of hot (>10 5 K) gas with ∼ 20% below this temperature range. The mean gas density declines below 10 −5 cm −3 beyond 300 kpc from the Milky Way in most directions, with the distinct exception of the direction toward M31, where the density is 4 × 10 −5 cm −3 at its lowest point and then increases again. It is unlikely that the orbits of the dwarf galaxies have changed greatly with redshift (Wetzel 2011), but unfortunately, the orbital information derived from the observations is insufficient to indicate how many have passed through the denser region between the Milky Way and M31 in the past. The typical Local Group densities in simulations are unlikely to completely strip most dwarf galaxies but will loosen the gas (Emerick et al. 2016), and there are a few possible exceptions for complete stripping in our sample. Hydra II, Leo IV, Leo V, Pisces II, and Eridanus II are fast-moving small dwarf galaxies that would only require densities of ∼10 −5 cm −3 to be completely stripped along most of their orbit (see Table 3).
Though the Local Group medium may not be able to completely strip most dwarf galaxies, it is likely to be able to strip away any diffuse halo medium, thus leading to a gradual starvation of the galaxy. This starvation of gas that could have accreted to feed star formation is found for satellites in massive halos in the EAGLE simulation (van de Voort et al. 2017). In particular, the more massive the host halo, the greater the starvation of the satellites. Marasco et al. (2016) found the same thing for removal of H I from galaxies, that more massive host halos are more effective with the removal, although this is for galaxies with stellar masses of the LMC and greater. The group environment may have also led to more satellite-satellite interactions that helped to loosen the gas (Marasco et al. 2016;Pearson et al. 2018). Furthermore, any dwarf galaxies that came in with the Magellanic System are likely to have been preprocessed at some level (Patel et al. 2020). In summary, the simulation results indicate that the halo of the Local Group would be expected to have a larger quenching role than an individual Milky Way mass galaxy (see also Garrison-Kimmel et al. 2019). The group environment therefore may help to explain why some observed isolated Milky Way analogs do not show the same large fraction of quenched satellites (Geha et al. 2017).
Direct evidence for a Local Group medium, or diffuse hot gas filling the volume beyond the virial radii of the Milky Way and Andromeda, is not available, but there are some indirect suggestions that this medium exists. The H I structure of some of the galaxies close to the edge of the Local Group but beyond the virial radius of the Milky Way or M31 has been claimed to be affected by ram pressure stripping by a diffuse gaseous medium (e.g., Leo T, Pegasus, and possibly Phoenix; St-Germain et al. 1999;McConnachie et al. 2007;Young et al. 2007;Adams & Oosterloo 2018). In addition, the H I structure of the Magellanic System can be more easily explained with the presence of a Local Group medium. The Clouds are modeled to be coming into the Milky Way halo for the first time and are currently at 50-60 kpc (Besla et al. 2010), yet a huge amount of ionized and neutral gas trails behind the Clouds, with less on the leading side of the Clouds (Putman et al. 1998(Putman et al. , 2003aFox et al. 2014). The gas is thought to have been initially loosened from the interaction of the Clouds with each other, but a more prolonged passage through a gaseous medium would help create the >100 kpc massive tail of gas. Finally, there are detections of ultraviolet absorption lines that remain mysterious in origin (e.g., velocities not easily connected to nearby denser structures and very low derived pressures) that may be related to a Local Group medium (Sembach et al. 2003;Richter et al. 2017). This would be consistent with the UV Cosmic Origins Spectrograph results of Stocke et al. (2019), who found a bias for intragroup gas detections in the lower-mass, more spiral-rich groups. They only probe groups with mass >10 13.5 M e but predict from their results that Local Group mass-scale groups will have a 100% covering fraction of diffuse gas out to a couple of virial radii.

Other Methods of Gas Removal
As mentioned in the Introduction, there are several mechanisms besides ram pressure stripping that could play a role in removing gas from dwarf galaxies, including stellar feedback, tidal forces, and reionization. There is no strong evidence that stellar feedback or tidal forces are dominant mechanisms given the distance-dependent effect shown here and the strength of the tidal force during the orbit of the dwarf galaxies and lack of stellar tidal features (Blitz & Robishaw 2000;Mayer et al. 2006;Mateo et al. 2008;Emerick et al. 2016;Simpson et al. 2018, GP09). However, given that many dwarf galaxies without gas are likely to have lost it in the early universe (Weisz et al. 2014), reionization needs to be considered at the lowest mass scales (Gnedin 2000;Kang & Ricotti 2019;Rodriguez Wimberly et al. 2019). The finding of Leo T, a small dwarf galaxy with gas, cast doubt on the effectiveness of reionization, but the lack of additional galaxies with gas at this mass scale is supportive of it (e.g., Tollerud & Peek 2018). The finding of more small dwarf galaxies without gas beyond the edges of the Local Group will provide support for reionization being an important quenching mechanism. The proper-motion measurements find fewer dwarf galaxies at apocenter than pericenter, and this indicates that additional dwarf galaxies are likely to be found at larger distances (Fritz et al. 2018). Simulations also expect there to be additional dwarf galaxies in the Local Group beyond the virial radii of the Milky Way and M31 (Klypin et al. 2015;Fattahi et al. 2020).
Thus far, the gasless dwarf galaxies at larger distances (e.g., Tucana, Cetus, And XVIII, and Eridanus II) may belong to a population of backsplash galaxies, or galaxies predicted by simulations to have fallen in at early times and been subsequently flung out to larger distances (Teyssier et al. 2012;Fillingham et al. 2018;Simpson et al. 2018;Blaña et al. 2020). In the study of simulated Milky Way analogs by Simpson et al. (2018), 41% of the systems beyond the virial radius and within 1 Mpc are backsplash galaxies, indicating that more gasless dwarf galaxies may be discovered at large radii that are not necessarily linked to reionization (see also Wetzel et al. 2014). It may be possible to obtain proper motions for gasless dwarf galaxies that are currently beyond the virial radius in the future (e.g., Eridanus II) to determine if they are likely to have been relatively deep within the Local Group in the past. The galaxy KKR 25 is a larger (i.e., too big for reionization quenching) dwarf galaxy at a large distance for which the quenching mechanism is unknown, and it is joined by two others at distances greater than 2 Mpc (Karachentsev et al. 2014;Sharina et al. 2017). In any case, at early times, a combination of quenching mechanisms is likely to have played a role; however, reproducing the distance dependency shown here is likely to be difficult without ram pressure stripping. Future observations of the field galaxy population will help to further distinguish between stripping mechanisms.

Summary
We have placed limits on the gas content of the dwarf galaxies within 2 Mpc of the Milky Way and examined the relationship of gas content with distance from the Milky Way and M31 and relative to their location in the Local Group. The findings can be summarized as follows.
1. The H I gas mass limits for the vast majority of the nondetected dwarf galaxies are less than 10 5 M e (5σ). This is less than the H I mass of any of the detected dwarf galaxies. This limit improves to <10 4 M e for the dwarf galaxies within the virial radius of the Milky Way. Scaling by stellar (i.e., optical luminosity) or total (within the stellar component) mass, the limits are consistent with the gas content of the dwarf galaxies being far suppressed from where they were when they formed their stars. 2. The number of dwarf galaxies within 2 Mpc has doubled in the last 10 yr, but there is a distinct lack of new dwarf galaxies with gas. This suggests that galaxies like Leo T are either rare or only at distances where current surveys struggle to detect them (see Tollerud & Peek 2018;DeFelippis et al. 2019). Future surveys capable of detecting low-mass dwarf galaxies at large distances in gas (e.g., WALLABY; Koribalski et al. 2020) and stars (e.g., LSST; Ivezić et al. 2019) will provide important insight into the dwarf population and quenching mechanisms. 3. There is a clear relationship that those dwarf galaxies with gas are largely beyond the virial radii of the Milky Way and Andromeda, while nondetections are largely within these radii. This relationship of gas content versus distance is also found when the distance from a Local Group surface, or virial radius, is used. More of the nondetected dwarf galaxies are within the Local Group surface than the virial radii of the Milky Way and M31 (85 ± 1 versus 80, respectively), which may indicate that a Local Group medium plays a role in the gas stripping. 4. The relationship of gas content with distance suggests a distance-dependent quenching mechanism such as ram pressure stripping by a diffuse gaseous medium. Using the proper motions available from Gaia, the orbits of 38 dwarf galaxies are calculated, and the minimum required densities for stripping at perigalacticon are typically between 10 −5 and 5 × 10 −4 cm −3 . Compared to the halo densities found in simulations, 80% of these dwarf galaxies are consistent with being stripped at perigalacticon. Continuous stripping throughout their orbit is likely to play an important additional role in starving and quenching the dwarf galaxies.