H i IN LOCAL GROUP DWARF GALAXIES AND STRIPPING BY THE GALACTIC HALO

3.1.1. Newly Discovered Milky Way Satellites

3.1.2. New and Previously Known M31 Satellites

The H i environment of both the previously known and newly discovered M31 satellites were examined. This section describes only those satellites with nondetections that have been clearly defined as M31 satellites. Upper limits for the H i mass were determined with LAB data for Andromeda IX, X, XI, XII, XIII, XIV, XV, XVI, and XVII. We also confirm H i nondetections for Andromeda I, II, and VII with LAB data and And VI with HIPASS data (Blitz & Robishaw 2000; hereafter BR00). Nondetection of H i toward And III was confirmed by Robishaw et al. (2000), and the velocity measured by Harbeck et al. (2001) of Andromeda V indicates that the detection in BR00 is false.

The H i upper limits for undetected M31 satellites are listed in Table 2. We list the 5σ detection limits for the LAB data, except for the case of And VI, in which we use the 5σ HIPASS limit, and for NGC 147 and M32 whose limits come from other sources. Andromeda IV is not included because it is not associated with M31 (Ferguson et al. 2000), and Andromeda VIII is excluded because its existence is in dispute (Merrett et al. 2006). Andromeda XI, XII, and XIII have uncertain distances; for the purpose of calculating an H i mass upper limit they are assumed to be at the distance of M31 (784 kpc, Stanek & Garnavich 1998), but the limits listed in Table 2 for these dwarfs are approximate and they are excluded from Figure 2.

Table 2. H i Mass of Andromeda Satellites

Object	α	δ	D☉ (kpc)	DM31 (kpc)	H i Mass (106M☉)	References
	(J2000)
And I	00h45m398	+38°02'28''	745	59	<0.35	a,b,c
And II	01h16m298	+33°25'09''	652	185	<0.27	a,b,c
And III	00h35m338	+36°29'52''	749	76	<0.35	a,b,c
And V	01h10m171	+47°37'41''	774	110	<0.37	b,d
And VI	23h51m463	+24°34'57''	783	269	<0.015	a,b,c,e
And VII	23h26m31s	+50°41'31''	763	219	<0.36	b,d,f
And IX	00h52m53s	+43°11'45''	765	42	<0.37	b,g
And X	01h06m337	+44°48'16''	783	112	<0.38	b,i
And XI	00h46m200	+33°48'05''	⋅⋅⋅	103	<0.38	j
And XII	00h47m270	+34°22'29''	⋅⋅⋅	95	<0.38	j
And XIII	00h51m510	+33°00'16''	⋅⋅⋅	116	<0.38	j
And XIV	00h51m350	+29°41'49''	740	167	<0.34	l
And XV	01h14m187	+38°07'03''	630	170	<0.25	k
And XVI	00h59m298	+32°22'36''	525	270	<0.17	k
And XVII	00h37m070	+44°19'20''	794	45	<0.39	m
M32	00h42m42s	+40°51'54''	805	22	<2.7	a,n
NGC 147	00h33m12s	+48°20'12''	725	115	<0.005	a
NGC 185	00h38m58s	+48°20'12''	620	185	0.13	a
NGC 205	00h40m22s	+41°41'24''	815	32	0.38	a

References. a: Mateo (1998), b: van den Bergh (2006), c: van den Bergh (1972), d: Armandroff et al. (1998), e: Armandroff et al. (1999), f: Karachentsev & Karachentseva (1999), g: Zucker et al. (2004b), h: Morrison et al. (2003), i: Zucker et al. (2007), j: Martin et al. (2006), k: Ibata et al. (2007), l: Majewski et al. (2007), m: Irwin et al. (2008), n: Grebel et al. (2003).

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3.1.3. Other Previously Known Local Group Dwarfs

Prior studies have examined the H i environment of the previously known dwarf galaxies. In the case of Cetus, an H i cloud within 1°.5 of the optical center was found at a velocity of −280 km s⁻¹ (BCS06). Since that time the optical velocity of Cetus has been measured by Lewis et al. (2007) as being −87 km s⁻¹, so the cloud is not associated with the galaxy. A detection of low significance near the position and optical velocity of the Sextans dwarf galaxy was found using data with less sensitivity and resolution than the HIPASS data (BR00), but no cloud was found after inspection of the HIPASS cubes. A cloud reported near the position of Leo I at a velocity 26 km s⁻¹ from the optical velocity of the dwarf (BR00) was also not found upon inspection of the HIPASS data, in agreement with BCS06.

Three clouds were reported near the Carina galaxy by BCS06. Of the three clouds, two are near the optical edge of the galaxy at a distance of about 80' (2.3 kpc) from the optical center, and have velocities close to the optical velocity of Carina. There is no H i within the optical radius of the galaxy and the clouds lie outside the tidal radius, so it is unlikely that the gas and the dwarf are physically associated (BCS06).

H i in the general direction of Tucana was first detected by Oosterloo et al. (1996) who claimed it was associated with the Magellanic Stream. BCS06 also detect this cloud at a velocity of about 130 km s⁻¹, and offset from central position of the dwarf by ∼18'. The optical velocity for Tucana has been found by Tolstoy et al. (2004) to be 182 km s⁻¹, so the difference in velocity between the H i cloud and the optical dwarf is 52 km s⁻¹. Figure 1 shows the average velocity along the line of sight with the integrated intensity contours overlaid for the vicinity of the Tucana Dwarf. The optical position of the dwarf is marked with a plus sign. Due to its proximity to the Magellanic Stream and the offset velocity of the cloud near the Tucana dwarf, we consider it a nondetection.

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To summarize our findings for the nondetections of previously known Local Group dwarfs, we confirm the nondetections or improve H i mass limits with HIPASS for Leo I and Leo II (Knapp et al. 1978), Cetus, Carina, Sextans (BCS06), and the core of the Sagittarius stream (Koribalski et al. 1994) and find that the gas in the vicinity of Tucana is unlikely to be associated. We confirm nondetections in the LAB data for Ursa Minor and Draco (Knapp et al. 1978), and NGC 147 (Young & Lo 1997). The H i limits for previously known Local Group dwarfs except the Andromeda dwarfs are given in Table 3.

Table 3. H i Mass of Additional Local Group Satellite Galaxies

Object	α	δ	Optical Velocity (km s−1)	D☉ (kpc)	H i Mass (106 M☉)	References
	(J2000)
WLM	00h01m58s	−15°27'48''	−78	925	61	a,j
IC 10	00h20m25s	+59°17'30''	−344	825	153	a
Cetus	00h26m11s	−11°02'40''	−87	755	<0.014	a,f,h
SMCa	00h52m44s	−72°49'42''	175	60	402	a,i
Sculptorb	01h00m09s	−33°42'33''	102	88	(0.234)	a,b,h,v,z
LGS3	01h03m55s	+21°53'06''	−287	810	0.16	a,d,h,o,p
IC 1613	01h04m54s	+02°08'00''	−237	700	54	a,q,r
Phoenix	01h51m06s	−44°26'41''	−13	445	0.17	a,b,l
Fornaxb	02h39m59s	−34°26'57''	53	138	(0.15)	a,h,aa
UGCA 092	04h32m01s	+63°36'24''	−99	1300	16	a
LMCa	05h23m34s	−69°45'24''	324	50	500	a,b,i
Carina	06h41m37s	−50°57'58''	224	101	<0.00021	a,h,bb
Leo A	09h59m24s	+30°44'42''	22.3	690	8	a,k
Sextans B	10h00m00s	+05°19'42''	300	1345	45	a,m,r
Antlia	10h04m04s	−27°19'52''	351	1235	0.72	a,b,e
Leo I	10h08m28s	+12°18'23''	286	250	<0.0015	a,h,bb
Sextans A	10h11m06s	−04°42'30''	328	1440	78	a,s,w
Sextans	10h13m03s	−01°36'53''	140	86	<0.00018	a,h
Leo II	11h13m29s	+22°09'17''	76	205	<0.01	a,v
GR8	12h58m40s	+14°13'00''	214	1590	4.5	a,p,t,r
Ursa Minor	15h09m08s	+67°13'21''	−247	66	<0.04	a,v
Draco	17h20m124	+57°54'55''	−293	82	<0.00016	a
Sagittarius	18h55m03s	−30°28'42''	140	24	<0.00014	a,u,bb
SagDIG	19h29m59s	−17°40'41''	−75	1060	8.8	a,d,p,n
DDO 210	20h46m518	−12°50'53''	−141	800	1.9	a,b,p
IC 5152	22h02m42s	−51°17'42''	122	1590	67	a,m,x
Tucana	22h41m50s	−64°25'10''	182	880	<0.015	a,b,c,h
UGCA 438	23h26m27s	−32°23'18''	62	1320	6.2	a,m,n
PegDIG	23h28m36s	+14°44'35''	−183	760	3.4	b,g

Notes. ^aThe LMC and SMC are included here for reference, but are not included in the figures. ^bThe H i mass given is that of the nearby H i cloud which may or may not be associated with the galaxy. References: a: Mateo (1998) and references therein, b: Grebel et al. (2003) and references therein, c: Tolstoy et al. (2004), d: Young & Lo (1997), e: Tolstoy & Irwin (2000), f: Lewis et al. (2007), g: Huchra et al. (1999), h: Bouchard et al. (2006), i: Brüns et al. (2005), j: Humason et al. (1956), k: Brown et al. (2007), l: Irwin & Tolstoy (2002), m: Huchtmeier & Richter (1986), n: Longmore et al. (1982), o: Thuan & Martin (1979), p: Lo et al. (1993), q: Lake & Skillman (1989), r: Hoffman et al. (1996), s: Huchtmeier & Richter (1988), t: Carignan et al. (1990), u: Koribalski et al. (1994), v: Knapp et al. (1978), w: Skillman et al. (1988), x: Blitz & Robishaw (2000), y: Oosterloo et al. (1996), z: Carignan et al. (1998), aa: Bouchard et al. (2006), bb: This paper.

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In the case of two of the dwarfs, it is unclear if a cloud is associated with the dwarf galaxy or has a separate origin. We refer to these as ambiguous detections, but note the mass of the cloud at the distance of the galaxy in Table 3. One of these is the Sculptor Dwarf, near which two H i clouds were discovered by Carignan et al. (1998). The velocity of the H i (∼105 km s⁻¹) and the optical velocity of the dwarf galaxy (102 km s⁻¹) agree. Despite this, the Sculptor dwarf is in the same direction as the Magellanic Stream and another complex of H i clouds in the general direction of the Sculptor Group (Putman et al. 2003), and numerous clouds near that velocity are found in this region that could be mistaken for gas associated with the Sculptor dwarf (see Figure 1). For these reasons, as well as the offset of the clouds from the optical center and the lack of recent star formation in this dwarf, we consider the Sculptor detection ambiguous.

Another ambiguous case is that of the Fornax dwarf. The Fornax dwarf has an optical velocity of 53 km s⁻¹. The cloud in question suffers from contamination from Galactic H i emission in the HIPASS data and is offset 28' from the optical center of Fornax. In the analysis by BCS06 the removal of the Milky Way's spectrum was incomplete, and it was unclear if the cloud was part of the Milky Way, a cloud of separate origin, or associated with the Fornax dwarf. We confirm that the origin of the cloud is unclear from the HIPASS data, which is shown in its environment in Figure 1.

Clear detections of H i at the position and velocity of the dwarf have been made for Antlia, Phoenix, Pegasus, DDO 210, WLM, IC 5152, UGCA 438, LGS3, Sextans B, IC1613, Sextans A, GR8, Sagittarius, and SagDIG. We confirm all of these detections in the HIPASS data, although the Phoenix dwarf blends into Galactic emission. The H i masses of these and additional Local Group dwarfs as well as references are listed in Table 3.

The H i detection of LGS3 (Hulsbosch & Wakker 1988; BCS06) is unusual in that it has one cloud at the optical position of the dwarf and two clouds offset from the optical center which have diffuse H i connecting them. Only the cloud aligned with the position of LGS3 has a velocity which agrees closely with the optical velocity of LGS3, so only the mass of that cloud is considered.

Leo T is one of the newly discovered Sloan Digital Sky Survey (SDSS) dwarf galaxies and is a particularly interesting object due to its low luminosity, recent history of star formation, and gas content. The HIPASS data show a compact H i cloud in the direction of the Leo T dwarf which was first reported by Irwin et al. (2007), and confirmed by Ryan-Weber et al. (2008) with synthesis data. Leo T has a velocity of about 35 km s⁻¹, and in the HIPASS data a maximum velocity of about 46 km s⁻¹. The lower velocity cutoff and the total width in velocity are uncertain due to Galactic interference. Our reanalysis of the H i cloud as it appears in the HIPASS data reduced to recover extended emission indicates Leo T has a total H i mass of about 4.3 × 10⁵M_☉ assuming a distance of 420 kpc.⁴ Ryan-Weber et al. (2008) found a total H i mass of 2.8 × 10⁵ M_☉ and a peak H i column density of 7 × 10²⁰ cm⁻². Our higher total mass may be due to extended emission of Leo T not recovered in the synthesis maps and/or some level of diffuse Galactic emission included in the integrated intensity map.

Figure 2 shows the H i mass or upper limit of each Local Group dwarf versus the distance to the center of the Milky Way or Andromeda from the dwarf, whichever is closer to the given satellite. Nondetections are associated with upper limits in H i mass, and are marked with downward arrows. Confident detections are marked with diamonds and the two ambiguous detections with plus signs. The apparent lines of upper limits in Figure 2 arise due to the distance dependence of the H i mass limits.

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As illustrated in Figure 2, there is a cutoff in the distance to the Milky Way or Andromeda within the range of 260 to 280 kpc (which corresponds to log values of 2.41 and 2.45) within which galaxies are undetected in H i to low levels, and beyond which the majority of galaxies have significant amounts of H i. A similar type of relationship was noted by other authors (Einasto et al. 1974; Lin & Faber 1983; Blitz & Robishaw 2000; Grebel et al. 2003). There are only two satellite galaxies with significant amounts of H i at galactocentric radii less than 270 kpc: NGC 185 and NGC 205. These galaxies are dwarf ellipticals that have total masses between 10⁸–10⁹ M_☉, much greater than that of the typical satellites in our sample. The two ambiguous detections, Sculptor and Fornax, are at intermediate Galactocentric distances of 88 and 138 kpc, respectively. Of those galaxies beyond 270 kpc, 19 galaxies are detected confidently at masses greater than 10⁵ M_☉, and two are not detected (Tucana and Cetus). The H i mass of galaxies detected beyond 270 kpc ranges from 4.3 × 10⁵ M_☉ (Leo T), which is significantly greater than all of our upper limits for Milky Way satellites, to H i masses as high as 1.5 × 10⁸ M_☉ (IC 10). The mean H i mass of detected galaxies beyond 270 kpc is 2.8 × 10⁷ M_☉, and the median H i mass is 6.1 × 10⁶ M_☉.

Figure 3 shows H i mass normalized by total mass versus galactocentric distance for those dwarfs with measured dynamical masses. All of the dwarfs with measured total masses within 270 kpc, with the exception of Canis Venetici II and possibly Sculptor, have limits on their gas fractions that are less than any galaxy beyond 270 kpc. We have also plotted the H i mass normalized by V-band luminosity (in L_☉) in Figure 4. All dwarfs except possibly Fornax within 270 kpc have M$_{\rm H\, {\sc I}}$/L_V limits approximately at or below the values of those beyond 270 kpc. Figures 3 and 4 indicate that our limits on H i mass are significant even accounting for a simple scaling by total mass or luminosity. The fact that the main outliers in these plots are the two ambiguous detections suggests the H i clouds are less likely to be directly associated with the galaxies.

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Proposed methods by which dwarf satellites have their gas removed include ram-pressure stripping, tidal stripping, feedback from supernovae or stellar winds, and the effects of reionization. In the process known as ram-pressure stripping, as a satellite moves through the halo medium it experiences a pressure whose strength depends on the satellite's velocity, total mass, and gas density and the properties of the ambient gas (Gunn & Gott 1972). If the orbit of a dwarf brings it into a region of sufficient density the pressure will be great enough to allow the gas to escape the potential well of the satellite. If ram-pressure stripping is taking place, we can estimate the density of the diffuse hot halo gas that a satellite has experienced. The general equation describing the condition necessary for stripping to take place is

$$\begin{equation} n_{\rm halo} \sim \frac{\sigma ^{2}\,n_{\rm gas}}{3\,v_{\rm sat}^{2}} \; {\rm cm}^{-3}, \end{equation} \tag{ 1 }$$

where n_halo is the ambient gas number density, σ is the central 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. It should be noted that this equation assumes that stripping is instantaneous, occurs in a homogeneous medium, and does not trigger star formation which can heat the gas and increase stripping efficiency; some of these factors may play an important role (e.g., Mayer et al. 2006).

Another way to strip a galaxy of its gas is via the effects of massive star evolution. Internal mechanisms such as stellar winds and supernovae may cause gas loss from the shallow potential wells of the dwarfs. Though star formation and the resulting feedback may play a role in heating the gas and making it easier to strip, it is unlikely to result in the distance-dependent mass loss shown in Figure 2. This is emphasized by Figures 3 and 4, which show the limits on the gas content of the dwarfs is significant even when scaling by total mass and stellar content. If gas loss due to stellar feedback was dominant, a relationship between gas content and the quantity of stars and/or the total mass of the galaxy (depth of the potential well) may be apparent. Strigari et. al. (2008) have shown that both the newly discovered and previously known dwarf spheroidals have similar total mass of ∼10⁷ M_☉ interior to 300 pc. Since the gas would not escape more easily from the nearby dwarfs, there is no evidence that stellar feedback is the dominant gas loss mechanism. Though the products of stellar evolution can potentially also contribute H i to galaxies (van Loon et al. 2006; Bouchard et al. 2005), it would not create the distance-dependent effect seen in Figures 2–4.

An additional gas loss mechanism is photoionization during the epoch of reionization (Gnedin & Kravtsov 2006; Dijkstra et al. 2004; Madau et al. 2008; Ricotti & Gnedin 2005). The effects of reionization inhibit the ability of the lowest mass halos to accrete gas. It has been proposed that the smallest dwarf galaxies of the Local Group formed their stars before reionization when they were still capable of accreting gas (Gnedin & Kravtsov 2006). The mass scale for the halos that are able to accrete gas from the intergalactic medium after reionization is somewhat uncertain (Dijkstra et al. 2004); however, the gas-rich, low-mass Leo T is difficult to explain unless its dark matter halo extends out to much larger radii than the observed baryons. In the case of reionization it may be possible that galaxies further from the main source of ionization would be more likely to retain gas. If the Milky Way and Andromeda were major sources of ionization at early times and there is a correlation with the current and past galactocentric distances of the dwarfs, then reionization may play a role in the H i distance trend. Given the amount of time for the Local Group galaxies to evolve since reionization (e.g., Moore et al. 2006), it seems unlikely that reionization could lead to the present day H i distance effect.

The lack of significant H i in nearby dwarfs is due to a distant-dependent mechanism. The two most widely studied distance-dependent gas-loss mechanisms are tidal and ram-pressure stripping, with simulations showing that the combination of tides and ram pressure is more effective than either mechanism alone. Ram pressure stripping is the dominant gas loss mechanism in the simulations (Mayer et al. 2006), with tides enhancing the effectiveness of ram-pressure stripping by lowering the depth of the satellite's potential well. The limited effect of tidal forces in stripping the gas from the satellites is evident from calculations of tidal radii of the dwarf galaxies and studies of the galaxies stellar components. The tidal radius for a 10⁷ M_☉ dwarf galaxy at a distance of 20 kpc from the center of the Milky Way is on the order of 1 kpc, and increasing the total mass of the satellite galaxy only serves to increase the tidal radius (Battaner & Florido 2000). This is significantly larger than the extent of H i in Leo T and is three times the average stellar extent of the newly discovered dwarf galaxies (Strigari et al. 2008). The stellar component of 18 Local Group dwarf galaxies was examined by Strigari et al. (2008) to search for the current effects of tidal forces on individual dwarfs. They searched for gradients in the line of sight stellar velocities across the face of the galaxies (including Willman I, Coma Berenices, and Ursa Major II, which are all within 44 kpc of the Milky Way) and found no significant detection of streaming motions indicative of tidal disruption. The dominant gas loss mechanism is likely to be ram-pressure stripping for the dwarf satellites in the Local Group, as also concluded by BR00, and we address this further below.

Leo T still has a significant amount of H i and does not appear to have been affected by ram-pressure stripping or tidal disruption (Ryan-Weber et al. 2008; Strigari et al. 2008). Given the total mass of Leo T and its diffuse stellar component, it is likely similar to the progenitors of the newly discovered dwarfs which do not have H i. The diffuse halo component required to completely strip this type of galaxy can be calculated. We assume a Leo T-like value for σ of 7.5 km s⁻¹ (Simon & Geha 2007). We also estimate a range of possible dwarf gas densities; for the low end of the range, we take the mean gas density in the central region of Leo T, n_gas = 0.12 cm⁻³, and for the high limit we take the central density calculated from fitting a Plummer model to the column density profiles in Ryan-Weber et al. (2008), which yields n_gas = 0.44 cm⁻³. We approximate the value of v_sat as the one-dimensional velocity dispersion of 60 km s⁻¹ for Local Group dwarfs (van den Bergh 1999). Using these values and assuming the dwarfs are on circular orbits or experiencing their initial infall, we find that the newly discovered, gas-free dwarfs likely experienced a halo density greater than n_halo∼ 0.6–2.3 × 10⁻³ cm⁻³ at the distance limit where the dwarfs have H i, or ∼270 kpc. Observations indicate densities on the order of 10⁻³ cm⁻³ are extremely unlikely at this distance (Gaensler et al. 2008; Sembach et al. 2003; Putman et al. 2004; Peek et al. 2007), as do simulations and calculations of the hot halo density profile (Kaufmann et al. 2007, 2008; Peek et al. 2007; Sommer-Larsen 2006; Maller & Bullock 2004). Figure 5 shows several of the hot halo density profiles from the simulations drop towards 10⁻⁵ cm⁻³ at distances greater than 200 kpc.

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The most likely solution to the above is that the dwarf orbits have brought them closer to the center of the parent galaxy than we see them today, and they therefore experienced a much higher halo density than that present in their current environment. In addition, they would have attained a much greater velocity through the halo medium as they approached the galaxy, and because the required density for stripping scales as v⁻², they would require lower densities for stripping during this portion of their orbit. It is also possible they have traveled through their parent galaxy's disk before arriving at their current position. Eccentric orbits could cause an overestimate of the typical stripping radius based on Figure 2, since the satellites would spend more time at apogalacticon than perigalacticon.

Several dwarfs do have proper motion measurements which give an estimation of their space velocity and orbital characteristics. The velocity at perigalacticon can be calculated by using the current radius and velocity in the galaxy rest frame to find the specific angular momentum of the orbit, J = vR. Using angular momentum conservation, the velocity at perigalacticon is v_peri = J/R_peri. We calculated v_peri for the dwarfs with proper motions and orbital analyses, Carina (Piatek et al. 2003), Ursa Minor (Piatek et al. 2005), Sculptor (Piatek et al. 2006), and Fornax (Piatek et al. 2002; Walker et al. 2008). We assume typical values for the central stellar velocity dispersion, σ = 10 km s⁻¹(Mateo 1998), and a central density, n_gas = 0.5 cm⁻³. For all of the dwarfs with proper motions there is a range of possible orbits and perigalacticons, and thus a range in the densities required for stripping. The 90% confidence range for the distance at perigalacticon from the proper motion references as well as the maximum and minimum density required for stripping within that range is listed for each dwarf in Table 4. In the case of Carina, we calculate a lower limit for the halo density of 8.5 × 10⁻⁵ cm⁻³ at the most likely perigalacticon of 20 kpc. For Ursa Minor, the calculated lower limit for the density of the halo at the most likely perigalacticon of 40 kpc is 2.1 × 10⁻⁴ cm⁻³. Using the Sculptor orbital characteristics we calculate a halo density of 2.7 × 10⁻⁴ cm⁻³ at the most likely perigalacticon of 68 kpc. The case of Fornax is interesting because at 137 kpc, it may be near perigalacticon (Piatek et al. 2002). The most likely perigalacticon for Fornax is 118 kpc and at that distance the required density for stripping is ∼3.1 × 10⁻⁴ cm⁻³. We note that these calculations of the halo density do not include tidal effects which may play a small role in contributing to the effectiveness of ram-pressure stripping for the closest perigalactica (as previously discussed).

Sculptor and Fornax are the most distant dwarf galaxies in Table 3 and are also labeled as ambiguous detections indicating there are clouds in the vicinity of these galaxies which may or may not be associated (see Figures 1 and 2). Since in both cases the H i clouds are offset from the optical center of the dwarf, even if the gas is associated with the dwarf galaxies it appears to have been partially removed. We also note the discrepant position of Sculptor and Fornax in Figures 3 and 4, possibly indicating the H i clouds may not be associated. The halo density estimate holds for these two galaxies if the gas has been stripped or is not associated with the dwarf.

We can now come back to the newly discovered dwarf galaxies (with a Leo T-like progenitor) and give them a velocity at perigalacticon that is closer to that obtained by the above dwarf galaxies to estimate a more likely density required to strip them. We do not know the actual perigalactica of these galaxies, but if they were moving at velocities between 200–400 km s⁻¹halo densities of ∼1.0–4.2 × 10⁻⁴ cm⁻³ would be required to strip them. This is much closer to the expected halo densities at the current distance of many of the newly discovered dwarf galaxies.

The densities of the halo derived from the dwarf galaxies with proper motion estimates can be compared to theoretical models of hot gas confined within a Milky Way-sized dark matter halo. Figure 5 shows halo density versus Galactocentric distance with the range in distances and halo densities for the dwarf galaxies taken from Table 4. The solid line is the theoretical density profile for gas whose initial distribution traces the central cusp in the NFW halo, while the dotted line represents the density profile which results from an initial gas distribution with a central core of high entropy (Kaufmann et al. 2007, 2008). The cored model is expected for haloes which have experienced pre-heating feedback early in their histories, and implies a more extended distribution for the hot halo gas, as well as an extended cloud population (Rasmussen et al. 2006; Li et al. 2007). The remaining density model plotted on Figure 5 is from Sommer-Larsen (2006) and is from high resolution cosmological SPH simulations of a Milky Way-like galaxy in a ΛCDM cosmology. The densities derived from the stripping of the dwarf galaxies are broadly consistent with the theoretical profiles. The exception is the value calculated with Fornax which predicts a halo density that is higher than the models in most cases. If the gas clouds in the vicinity of Fornax are in the process of being stripped, an overestimate could be due to the calculation of the halo density being for the complete stripping of the gas from the dwarf.

It is possible, given a halo model and a typical range of dwarf galaxy characteristics, to calculate the velocity required to strip a satellite galaxy at a given radius. This is plotted in Figure 6 for the three halo density models previously discussed and using a range in dwarf galaxy velocity dispersions (σ = 5–12 km s⁻¹) and central densities (n_gas = 0.1–0.8 cm⁻³). As additional proper motions are determined this plot can be used to check consistency between the ram-pressure stripping scenario and the halo density models. Also, if there is independent evidence that a dwarf is being stripped at its current radius (e.g., a head–tail structure; Quilis & Moore 2001), Figure 6 could be used to estimate a lower limit on the velocity of the satellite.

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