Solo dwarfs III: Exploring the orbital origins of isolated Local Group galaxies with Gaia Data Release 2
Alan W. McConnachie, Clare R. Higgs, Guillaume F. Thomas, Kim A. Venn, Patrick Côté, Giuseppina Battaglia, Geraint F. Lewis
MMNRAS , 1– ?? (2020) Preprint 16 December 2020 Compiled using MNRAS L A TEX style file v3.0
Solo dwarfs III: Exploring the orbital origins of isolated Local Groupgalaxies with Gaia Data Release 2
Alan W. McConnachie ★ , Clare R. Higgs , Guillaume F. Thomas , Kim A. Venn , Patrick Côté ,Giuseppina Battaglia , , Geraint F. Lewis . NRC Herzberg Astronomy & Astrophysics, 5071 West Saanich Road, Victoria, British Columbia, Canada V9E 2E7 Physics & Astronomy Department, University of Victoria, 3800 Finnerty Rd, Victoria, B.C., Canada, V8P 5C2 Instituto de Astrofísica de Canarias, Calle Via Láctea s/n, E-38206 La Laguna, Tenerife, Spain Universidad de La Laguna, Avda. Astrofísico Fco. Sánchez, La Laguna, 38200 Tenerife, Spain Sydney Institute for Astronomy, School of Physics, A28, The University of Sydney, NSW 2006, Australia
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We measure systemic proper motions for distant dwarf galaxies in the Local Group and investigate if these isolated galaxies haveever had an interaction with the Milky Way or M31. We cross-match photometry of isolated, star forming, dwarf galaxies inthe Local Group, taken as part of the
Solo survey, with astrometric measurements from Gaia Data Release 2. We find that NGC6822, Leo A, IC 1613 and WLM have sufficient supergiants with reliable astrometry to derive proper motions. An additionalthree galaxies (Leo T, Eridanus 2 and Phoenix) are close enough that their proper motions have already been derived using redgiant branch stars. Systematic errors in Gaia DR2 are significant for NGC 6822, IC 1613 and WLM. We explore the orbits forthese galaxies, and conclude that Phoenix, Leo A and WLM are unlikely to have interacted with the Milky Way or M31, unlessthese large galaxies are very massive ( (cid:38) . × 𝑀 (cid:12) ). We rule out a past interaction of NGC 6822 with M31 at ∼ . <
10% chance that NGC 6822 has had an interaction with the Milky Way. We examine the likelyorigins of NGC 6822 in the periphery of the young Local Group, and note that a future interaction of NGC 6822 with the MilkyWay or M31 in the next 4 Gyrs is essentially ruled out. Our measurements indicate that future Gaia data releases will providegood constraints on the interaction history for the majority of these galaxies.
The isolated dwarf galaxies of the Local Group are the ideal systemsfor understanding the galactic-scale consequences of physical dis-tancing. There seems little doubt that these dwarfs are not currentlyexposed to the level of interactions that are relatively common-placewhen orbiting in the more densely populated satellite systems of theMilky Way and M31. What is unclear, however, is if all these galax-ies have forever been as isolated as they are now, or if an interactionearly in the life of the dwarf caused it to travel to the outskirts of theLocal Group in which it is now found.While there are approximately 100 dwarf galaxies known withinthe Local Group, most are satellites of the Milky Way or M31. Onlyabout a dozen dwarfs are not clearly associated with one of thesetwo systems, insofar as they are found more than ∼
300 kpc (theapproximate virial radii of the halos of these two galaxies, e.g., Klypinet al. 2002; Posti & Helmi 2019) from both these large galaxies.It seems unlikely that these dozen galaxies are the totality of allisolated galaxies in the Local Group, and selection effects are likelyimportant. While there has been a concerted efforts to find newsatellites of the Milky Way and M31 in recent years (for a list ofMilky Way discoveries, see Drlica-Wagner et al. 2020 and referencestherein; for a list of M31 discoveries, see McConnachie et al. 2018 andreferences therein), the same is not true for more isolated Local Groupmembers. Such searches are difficult because of their large distances(rendering member stars relatively faint in comparison to Milky Waysatellites) and the fact that they could be found anywhere in the sky (in comparison to the relatively small area of sky around M31 in whichits satellites are found). To the best of our knowledge, the searchfor new Local Group dwarf galaxies using the Palomar ObservatorySky Survey and ESO/Science Research Council survey plates byA. Whiting and colleagues remains the most comprehensive searchto-date for which completeness estimates are available. This searchled to two new galaxies (Antlia and Cetus) out of 206 candidates(Whiting et al. 1997, 1999). Whiting et al. (2007) estimate that theirby-eye searches for Local Group dwarfs are essentially completedown to a surface brightness of 26 −
27 mags arcsec − away fromthe plane of the Milky Way. This surface brightness is comparable tothat of Sextans, the lowest surface brightness “classical” satellite ofthe Milky Way. In this case, Leo T (Irwin et al. 2007) - at a surfacebrightness of around 25 mags arcsec − - would be one of only a fewgalaxies at these surface brightnesses that was not already identified.Clearly, a new search for distant Local Group galaxies (not satellitesof M31 and the Milky Way), using the extensive digital sky surveysaccumulated since the days of the Palomar Sky Survey, is overdue.Isolated dwarf galaxies in the Local Group have long been noted toexhibit some general differences to the satellite populations (Einastoet al. 1974). The former generally host younger, bluer, populations,and have significant gas fractions. The latter generally lack signif-icant young populations and have low or negligible gas fractions.Many exceptions to this trend exist (e.g, the LMC, SMC, M33, Ce-tus, Tucana, Andromeda XVIII). Detailed star formation histories ofgalaxies throughout the Local Group (e.g., Weisz et al. 2014 and ref-erences therein) suggest that in large part the star formation histories © a r X i v : . [ a s t r o - ph . GA ] D ec Alan W. McConnachie et al. of both satellites and isolated systems are generally similar over mostof cosmic time, and that their star formation histories differ mostsignificantly only in the last gigayear or so. Thus, much of the differ-ence in these populations connects back to the fact that the isolateddwarfs have generally been able to retain their gas to the present day,whereas many satellites have not.The position–morphology relation that has been identified in theLocal Group is seen elsewhere in the Universe (e.g., Bouchard et al.2009; Geha et al. 2012), and prompts consideration of the influ-ence of nearby large galaxies on the evolutionary paths of dwarfs.Mechanisms at play may include ram pressure stripping (e.g., Mori &Burkert 2000; Vollmer et al. 2000; Boselli et al. 2014), tidal stripping(e.g., Peñarrubia et al. 2008), tidal stirring (e.g., Mayer et al. 2006;Kazantzidis et al. 2011), induced star formation, and/or strangulation(Kawata & Mulchaey 2008 and references therein). Comparison ofthe properties of isolated dwarfs to satellites could therefore shedlight on the importance and interplay of several complex physicalprocesses.An essential element of these considerations is the acquisition ofcomparable datasets for isolated dwarfs as exist for satellite dwarfsin the Local Group. It is with this in mind that we constructed the
Solitary Local (Solo) Dwarfs survey, where our intent is to providehomogeneous, high-quality, wide-field optical characterization of theclosest, isolated dwarf galaxies (see Higgs et al. 2016, hereafter PaperI). These dwarfs have been identified based on their current locations,namely that they are more than 300 kpc from either the Milky Wayor M31, and are within 3 Mpc. The full sample includes, but isnot limited to, the Local Group. For that subset that are within theLocal Group, an important consideration is whether or not the presentpositions of these dwarfs are enough to indicate that they have alwaysbeen isolated.There are some dwarf galaxies in the Local Group, such asDDO210 or the Sagittarius dwarf irregular galaxy (Sag DIG), thatare more than a megaparsec from either of the dominant two-some.In these extreme cases, then barring pathological velocities (whichare not implied by their heliocentric radial velocities), there is simplynot enough time in the Universe for these galaxies to have previouslyinteracted with M31 or the Milky Way, and then to have reachedtheir current positions (e.g., see Figure 8 of McConnachie 2012).But for systems that are of order 300 kpc – 1 Mpc distant from thelarge galaxies, it is quite conceivable that they have had a previousinteraction (and so potentially been subject to a whole gamut of com-plex environmental processes), and have since travelled to apocenterfar from their host.Identification of these so-called backsplash systems is importantsince, unlike truly isolated systems, their properties cannot neces-sarily be attributed only to secular processes. Early numerical workby Gill et al. (2005) on backsplash galaxies concluded that half ofthe dwarfs at 1 − 𝑅 𝑣𝑖𝑟 from an 𝐿 ★ galaxy could actually be back-splash systems. More recent work by Teyssier et al. (2012) and Bucket al. (2019) reinforce this finding, and attempt to identify which Lo-cal Group dwarfs are most likely backsplash systems based on theirpositions and/or radial velocities and/or velocity dispersions. Bothstudies conclude that there is more than a 50% of NGC6822 and LeoT having passed close to the Milky Way. Of the remaining isolatedLocal Group galaxies, Andromeda XXVIII, Cetus, Eridanus 2, IC1613, Pegasus DIG, Phoenix and Tucana are highlighted as possiblebacksplash systems (more than a 50% chance) by one of the studies.Determination of a galaxy’s orbit is the most robust method toidentify if it is a backsplash system. Observationally, this requiresits position on the sky, its distance, its radial velocity and its propermotion. The first three are all relatively simple measurements. The fourth is not. The first proper motion of a Local Group galaxy that wasnot in the Milky Way subgroup was made 15 years ago. Brunthaleret al. (2005) identified a water maser in M33, and were able to usethe Very Large Baseline Interferometer (VLBI) to obtain a systemicproper motion after correction for M33’s rotation. Water masers areonly associated with intense star formation, and the most intenselystar forming galaxy in the Local Group is the dwarf starburst galaxyIC10. Brunthaler et al. (2007) were able to measure its proper motionusing an identical methodology as for M33. M31 itself is a relativelyquiescent galaxy in comparison to these two satellites (e.g., Davidgeet al. 2012 and references therein), and its proper motion has sincebeen derived from observations with the Hubble Space Telescope(HST; Sohn et al. 2012). Proper motions have also just recently beenmeasured by HST for NGC147 and 185 (Sohn et al. 2020).The advent of Gaia Data Release 2 (DR2; Gaia Collaboration et al.2018a) has been a watershed moment for dynamical studies of theMilky Way satellite system, with a large number of papers dedicatedto the measurement of almost all the dwarf galaxy satellites of theMilky Way (Gaia Collaboration et al. 2018b; Massari & Helmi 2018;Simon 2018; Simon et al. 2020; Fritz et al. 2018, 2019; Kallivayalilet al. 2018; Pace & Li 2019; Longeard et al. 2018, 2020b,a; Mauet al. 2020; McConnachie & Venn 2020). This sample includes threegalaxies - Phoenix, Eridanus II and Leo T - that are in the Solo sample (all located at (cid:46)
450 kpc). In addition, Gaia DR2 has beenused to independently confirm the previous measurements of theproper motions of M31 and M33 (van der Marel et al. 2019), albeitwith less accuracy than HST or VLBI. Here, we explore the utility ofGaia data - now and in future data releases - for obtaining the propermotions of the more distant isolated Local Group dwarf galaxies in
Solo , to better determine their orbital histories.Section 2 discusses the datasets that are used in our analysis andthe identification of the dwarf galaxies for which we are able tomeasure proper motions. These measurements are made in Section3. Section 4 uses these new measurements to explore the orbitalparameter space of these galaxies (including analysis for the threedwarf galaxies for which literature estimates of the proper motionare available). Specifically, we examine the likelihood that thesesystems are backsplash galaxies. Section 5 discusses these findingsand summarises our results.
Solo is a volume limited, wide field imaging survey of all nearbyand isolated dwarf galaxies, and a general introduction to the surveyis given in Paper I. Briefly,
Solo targets all known dwarf galaxiesfainter than the Magellanic Clouds which are within 3 Mpc of theSun and more than 300 kpc from either M31 or the Milky Way(for a current total of 44 galaxies). Galaxies are observed with eitherCFHT/Megacam (Boulade et al. 2003) in the northern hemisphere orMagellan/Megacam (McLeod et al. 2015) or IMACS (Dressler et al.2011) in the southern hemisphere. Some targets are observed withmultiple instruments for calibration purposes. The total survey areaper galaxy is approximately one square degree, regardless of tele-scope/instrument (for Magellan, multiple pointings are used to coverthis area, whereas only a single pointing is required for CFHT). Alldwarfs were observed in the 𝑔 − and 𝑖 − bands, and some galaxies alsohave 𝑢 − band (although in what follows we do not use the 𝑢 − band).Table 1 lists the 16 Solo dwarf galaxies in the Local Group (that is,at or within the zero-velocity survey; see Higgs et al. 2020, hereafterPaper II), ordered by distance modulus. Parameters are taken from
MNRAS , 1– ?? (2020) roper motions of isolated Local Group galaxies Galaxy RA (degs) Dec (degs) ( 𝑚 − 𝑀 ) (mags) 𝑀 𝑉 (mags) 𝑣 ℎ (km s − ) 𝑑 𝑀𝑊 (kpc) 𝑑 𝑀 (kpc) Recent SF?Eridanus 2 56.0879 -43.5333 22 . ± . . ± . . ± .
12 -9.9 − . ± . . ± . . ± . . ± .
08 -15.2 − . ± . . + . − . -8.5 − . ± . . ± .
12 -15.2 − . ± . . ± .
07 -11.3 − . ± . . ± .
18 -10.3 — 779 349 NLeo A 149.8604 30.7464 24 . ± .
12 -12.1 24 . ± . . ± .
12 -9.5 194 . ± . . ± .
07 -12.2 − . ± . . ± .
08 -14.3 − . ± . . ± .
18 -11.5 − . ± . . ± .
08 -10.7 − . ± . . + . − . -9.2 − . ± . . ± .
04 -12.5 − . + . − . Table 1.
All
Solo dwarf galaxies in the Local Group and relevant parameters, including their equatorial coordinates, distance moduli, absolute magnitudes,heliocentric velocities and approximate distances from the Milky Way and M31. Parameters are taken from the updated, online compilation from McConnachie(2012). Also indicated is whether the galaxy has any significant recent star formation ( (cid:46) . − the updated, online compilation from McConnachie (2012) . Theirdistances from the center of the Milky Way and from M31 are alsogiven in Table 1 assuming that the Sun is at a distance of 8.122 kpc(Gravity Collaboration et al. 2018) from the Galactic Center, andthat M31 is at a distance of 783 kpc (McConnachie et al. 2005). Foreach of the galaxies in Table 1, we have wide-field, ground-basedphotometry, the majority of which was presented in Paper II. Thereader is referred to Papers I and II for details of all data acquisition,reduction and processing.For the three closest galaxies (Eridanus 2, Phoenix and Leo T), thebrightest red giant branch stars in these systems are luminous enoughto have reliable astrometry in Gaia DR2, and proper motions for thesethree systems have previously been measured (Fritz et al. 2018; Pace& Li 2019; McConnachie & Venn 2020, hereafter MV2020). For theremaining systems, the tip of the RGB is fainter than the Gaia DR2detection limit. For those galaxies with only old or intermediate-agestellar populations - specifically Andromeda XXVIII, Cetus, An-dromeda XXXIII (Perseus), Tucana, and Andromeda XVIII - none oftheir stars are bright enough to have reliable astrometry in Gaia DR2.However, for those galaxies which also have recent star formation,it is possible for both blue and red supergiants to be (significantly)more luminous than the tip of the RGB, depending on their massand age (e.g., see the original spectroscopic studies of supergiants inNGC 6822 and WLM by Venn et al. 2001, 2003). Indeed, this traithas allowed the determination of the proper motions of M31 and M33using Gaia DR2 (van der Marel et al. 2019), despite both galaxiesbeing located at approximately 800 kpc from the Milky Way.For the 8 galaxies in Table 1 which have some evidence of youngerstellar populations (e.g., see Paper II, Weisz et al. 2014) and whichdo not already have derived proper motions, we cross-match ourground-based photometry to Gaia DR2. Specifically, we only selectthose cataloged objects that are classified as stellar (i.e., within 2 − 𝜎 of the locus of point sources) in each of the 𝑔 and 𝑖 − bands. In all cases,sources are matched to within a few tenths of an arcsecond or better.For the Gaia parameters, we only consider stars with full 5 parameterastrometric solutions, and high quality astrometry as defined via the renormalised unit weighted error ( ruwe ; see Lindegren et al. 2018and discussion in the Gaia DR2 Documentation Release 1.2). Weadopt ruwe < .
4. We also only consider stars whose parallaxes areconsistent with them being located at a similar distance to the galaxy.That is, the 3 − 𝜎 parallax range measured by Gaia DR2 must overlapthe 3 − 𝜎 parallax range implied by the distance modulus of thedwarf as given in Table 1. We correct for the global zero-point of theparallax in Gaia DR2 of -0.029mas (Lindegren et al. 2018).The ground-based photometry is presented in Figure 1. Here, theleft panel of each pair of plots shows the ground-based CMD forthe inner regions of each field centered on each galaxy. The rightpanel of each pair shows those sources that are also in Gaia DR2, andwhich pass the cuts described above. All photometry is extinction-corrected with the reddening maps from Schlegel et al. (1998) usingthe python interface dustmaps (Green 2018). We use the extinctioncoefficients derived using the Padova isochrone (Girardi et al. 2002)web-tool , 𝐴 𝑔 = . × 𝐴 𝑉 and 𝐴 𝑖 = . × 𝐴 𝑉 , where 𝐴 𝑉 = . × 𝐸 ( 𝐵 − 𝑉 ) (Schlafly & Finkbeiner 2011).In contrast to MV2020, we do not apply any cuts to the Gaia DR2data based on the quality of the Gaia photometry, since we rely in-stead on the ground-based data for our photometric selection. This isan important point: experimentation with the Gaia DR2 photometryshows that the formal quality of the Gaia photometry for many of thesources being examined is quite poor (as quantified via the flux-excess parameter; see Lindegren et al. 2018). We expect this is todo with the relatively high degree of crowding in these distant dwarfgalaxies (see also discussion of this point in van der Marel et al.2019 as it relates to the centers of M31 and M33). Of course, theground-based data can also be crowded in the very central regionsof the dwarfs, especially at faint magnitudes. However, the gener-ally good or excellent image quality of our ground-based data, inmultiple bands, combined with the relative brightness of the sourcesunder consideration (with respect to the limiting magnitude of theground-based data) means that the photometric quality of Gaia DR2is not a limiting factor for this analysis, so long as the astrometricquality of the data is sufficient (as parameterized by ruwe ).For the 8 galaxies in Figure 1, blue supergiants are easily visible http://stev.oapd.inaf.it/ MNRAS , 1– ????
4. We also only consider stars whose parallaxes areconsistent with them being located at a similar distance to the galaxy.That is, the 3 − 𝜎 parallax range measured by Gaia DR2 must overlapthe 3 − 𝜎 parallax range implied by the distance modulus of thedwarf as given in Table 1. We correct for the global zero-point of theparallax in Gaia DR2 of -0.029mas (Lindegren et al. 2018).The ground-based photometry is presented in Figure 1. Here, theleft panel of each pair of plots shows the ground-based CMD forthe inner regions of each field centered on each galaxy. The rightpanel of each pair shows those sources that are also in Gaia DR2, andwhich pass the cuts described above. All photometry is extinction-corrected with the reddening maps from Schlegel et al. (1998) usingthe python interface dustmaps (Green 2018). We use the extinctioncoefficients derived using the Padova isochrone (Girardi et al. 2002)web-tool , 𝐴 𝑔 = . × 𝐴 𝑉 and 𝐴 𝑖 = . × 𝐴 𝑉 , where 𝐴 𝑉 = . × 𝐸 ( 𝐵 − 𝑉 ) (Schlafly & Finkbeiner 2011).In contrast to MV2020, we do not apply any cuts to the Gaia DR2data based on the quality of the Gaia photometry, since we rely in-stead on the ground-based data for our photometric selection. This isan important point: experimentation with the Gaia DR2 photometryshows that the formal quality of the Gaia photometry for many of thesources being examined is quite poor (as quantified via the flux-excess parameter; see Lindegren et al. 2018). We expect this is todo with the relatively high degree of crowding in these distant dwarfgalaxies (see also discussion of this point in van der Marel et al.2019 as it relates to the centers of M31 and M33). Of course, theground-based data can also be crowded in the very central regionsof the dwarfs, especially at faint magnitudes. However, the gener-ally good or excellent image quality of our ground-based data, inmultiple bands, combined with the relative brightness of the sourcesunder consideration (with respect to the limiting magnitude of theground-based data) means that the photometric quality of Gaia DR2is not a limiting factor for this analysis, so long as the astrometricquality of the data is sufficient (as parameterized by ruwe ).For the 8 galaxies in Figure 1, blue supergiants are easily visible http://stev.oapd.inaf.it/ MNRAS , 1– ???? (2020) Alan W. McConnachie et al.
Figure 1.
Extinction corrected, ground-based colour magnitude diagrams (CMDs) for each of the galaxies listed in Table 1 that do not already have Gaia DR2systemic proper motions, but which have some evidence of younger stellar populations. The left panel of each pair of CMDs shows the ground-based CMDs forthe inner regions of each field centered on each galaxy. The right panel of each pair shows those sources that are also in Gaia DR2, and which pass the qualitycuts described in the text. as a broad vertical plume of stars generally blueward of ( 𝑔 − 𝑖 ) = ( 𝑔 − 𝑖 ) (cid:39) We adopt a similar methodology to MV2020, and we refer the readerto Section 3 of that paper for a full description of the method. Inbrief, we seek to maximize the likelihood of the data, where the totallikelihood is given by L = 𝑓 dwarf L dwarf + ( − 𝑓 dwarf )L 𝑀𝑊 (1) MNRAS , 1– ?? (2020) roper motions of isolated Local Group galaxies Figure 2.
The spatial and colour-magnitude distributions of Gaia DR2 sources in each field surrounding NGC 6822, IC 1613, Leo A and WLM. The left panelsshow the distribution in the tangent plane of all Gaia DR2 sources that lie within the shaded regions (blue and red supergiant regions) of the CMD in the rightpanels. The right panel shows the CMD of all Gaia DR2 sources that lie within the dashed red circles in the left panels. where L dwarf and L 𝑀𝑊 are the likelihoods for the dwarf galaxyand MW foreground, respectively, and 𝑓 dwarf is the fraction of starsin the satellite. L dwarf can be broken down as L dwarf = L 𝑠 L 𝐶𝑀 L 𝑃𝑀 (2)where L 𝑠 , L 𝐶𝑀 and L 𝑃𝑀 are the likelihoods from the spatial in-formation, colour-magnitude information, and proper motion infor-mation, respectively. L 𝑀𝑊 can similarly be broken down into theproduct of its three constituent likelihoods.We therefore need to define likelihood functions for the spatial andcolour-magnitude distribution of sources in the dwarf. We also needto define spatial, colour-magnitude and proper motion likelihoodfunctions for the Milky Way foreground population. Using these,we find the systemic proper motion of the dwarf that maximisesthe probability of the data given these models, with the adoption ofsuitable priors on the unknown parameters ( 𝜇 𝛼 cos 𝛿, 𝜇 𝛿 ) dwarf and 𝑓 dwarf .Figure 2 shows the spatial and colour-magnitude distributions ofGaia DR2 sources in each field surrounding NGC 6822, IC 1613,Leo A and WLM. Specifically, the left panels show the distributionin the tangent plane of all Gaia DR2 sources that lie within the shadedregions of the CMD in the right panels. The right panel shows theCMD of all Gaia DR2 sources that lie within the dashed red circles inthe left panels. The grey regions are defined empirically to be simplepolygons that enclose the blue and red supergiants in each galaxy.For Leo A, we only consider blue supergiants due to the absence ofany clear red supergiant sequence. For the blue supergiants, the rededge of the selection box is placed bluer than the edge of the MilkyWay foreground (that is delineated by the main sequence turn-off ofstars around ( 𝑔 − 𝑖 ) ∼ . MNRAS , 1– ????
The spatial and colour-magnitude distributions of Gaia DR2 sources in each field surrounding NGC 6822, IC 1613, Leo A and WLM. The left panelsshow the distribution in the tangent plane of all Gaia DR2 sources that lie within the shaded regions (blue and red supergiant regions) of the CMD in the rightpanels. The right panel shows the CMD of all Gaia DR2 sources that lie within the dashed red circles in the left panels. where L dwarf and L 𝑀𝑊 are the likelihoods for the dwarf galaxyand MW foreground, respectively, and 𝑓 dwarf is the fraction of starsin the satellite. L dwarf can be broken down as L dwarf = L 𝑠 L 𝐶𝑀 L 𝑃𝑀 (2)where L 𝑠 , L 𝐶𝑀 and L 𝑃𝑀 are the likelihoods from the spatial in-formation, colour-magnitude information, and proper motion infor-mation, respectively. L 𝑀𝑊 can similarly be broken down into theproduct of its three constituent likelihoods.We therefore need to define likelihood functions for the spatial andcolour-magnitude distribution of sources in the dwarf. We also needto define spatial, colour-magnitude and proper motion likelihoodfunctions for the Milky Way foreground population. Using these,we find the systemic proper motion of the dwarf that maximisesthe probability of the data given these models, with the adoption ofsuitable priors on the unknown parameters ( 𝜇 𝛼 cos 𝛿, 𝜇 𝛿 ) dwarf and 𝑓 dwarf .Figure 2 shows the spatial and colour-magnitude distributions ofGaia DR2 sources in each field surrounding NGC 6822, IC 1613,Leo A and WLM. Specifically, the left panels show the distributionin the tangent plane of all Gaia DR2 sources that lie within the shadedregions of the CMD in the right panels. The right panel shows theCMD of all Gaia DR2 sources that lie within the dashed red circles inthe left panels. The grey regions are defined empirically to be simplepolygons that enclose the blue and red supergiants in each galaxy.For Leo A, we only consider blue supergiants due to the absence ofany clear red supergiant sequence. For the blue supergiants, the rededge of the selection box is placed bluer than the edge of the MilkyWay foreground (that is delineated by the main sequence turn-off ofstars around ( 𝑔 − 𝑖 ) ∼ . MNRAS , 1– ???? (2020) Alan W. McConnachie et al. giants by Dohm-Palmer et al. 2002). Instead, we instead use a simple,empirical model of the expected CMDs, which is that the relevantstars are expected to lie somewhere in the grey regions of the CMDsin Figure 2. A uniform likelihood is assumed over these regions.In MV2020, two different sets of priors were imposed on thesystemic proper motion of the dwarf. The first was that the tangentialvelocity could not be unrealistically high compared to the Milky Way;the second favored systemic motions where stars that appeared to beradial velocity members were more likely to be assigned membership.In the current analysis, there are no radial velocities to consider, andwe do not have any expectation on the tangential velocity of thegalaxy with respect to the Milky Way. As such, the prior requiresonly that the systemic proper motion in each direction is less than10 mas/yr, with a uniform likelihood over this range. We adopt auniform prior for 𝑓 dwarf in the interval 0 ≤ 𝑓 dwarf ≤
1, the same asMV2020.
For NGC 6822, IC 1613, Leo A and WLM, we construct the spatial,colour-magnitude and proper motion likelihood maps as describedin the previous section and explore parameter space using emcee (Foreman-Mackey et al. 2013, 2019) for those values of 𝑓 dwarf and ( 𝜇 𝛼 cos 𝛿, 𝜇 𝛿 ) dwarf that maximise the probability of the data.Table 2 lists the resulting median values and 16th and 84thpercentiles for the three unknown parameters for each of ourfour galaxies. We also list the proper motions for Eridanus 2,Phoenix and Leo T, as derived in MV2020 . We also list thecorresponding Galactocentric tangential velocity components as-suming ( 𝑅 (cid:12) , 𝑉 𝑐 ) = ( .
122 kpc, 229 km s − ) and ( 𝑈 (cid:12) , 𝑉 (cid:12) , 𝑊 (cid:12) ) = ( . , . , . ) km s − (Gravity Collaboration et al. 2018; Schön-rich et al. 2010), for the distance moduli given in Table 1.All error bars in Table 2 describe random errors only, and sys-tematic uncertainties in the proper motions are not included. GaiaCollaboration et al. (2018b) analyse the systematic uncertainties inthe proper motions of stars in the Sagitarrius dwarf spheroidal us-ing Gaia DR2, and conclude that on spatial scales of around 0.2degrees (the approximate spatial scale of the supergiant distribu-tions in NGC 6822 and IC 1613), the systematic uncertainty is ∼ .
035 mas/year. Lindegren et al. (2018) analyse the spatial co-variance of the proper motions of quasars, and conclude that onscales less than 0.125 degrees (the approximate spatial scales of allthe other galaxies in Table 2, excluding NGC 6822 and IC 1613), thesystematic uncertainty is ∼ .
066 mas/yr. It is worth emphasising thescale of these uncertainties for the galaxies under consideration. Atthe distances of NGC 6822 (462 kpc) and WLM (933 kpc), a system-atic uncertainty of [0.035/0.066] mas/year corresponds to an uncer-tainty in the tangential velocity of these dwarfs of [73/138] km s − and [148/280] km s − , respectively, in each direction. As a referencevalue, a simple estimate of the expected velocity dispersion of theLocal Group gives 𝜎 𝐿𝐺 (cid:39) (cid:16) 𝑀 𝐿𝐺 × 𝑀 (cid:12) (cid:17) (cid:16) 𝑘 𝑝𝑐𝑅 𝐿𝐺 (cid:17) km s − .Figure 3 shows the spatial, colour-magnitude, and proper motiondistributions for member stars in NGC 6822, IC 1613, Leo A and Note that the relative foreground for these three galaxies is much higherthan that for the dwarf irregulars studied here due to differences in the tracerpopulation that is used (RGB stars versus supergiants). This results in verydifferent values for 𝑓 dwarf between the two studies. WLM (magenta stars). Here, we use the fact that the probability ofany star being a member of the dwarf is given by 𝑃 dwarf = 𝑓 dwarf L dwarf 𝑓 dwarf L dwarf + ( − 𝑓 dwarf )L 𝑀𝑊 . (3)We define members as those stars with 𝑃 dwarf ≥ .
5. Inspection ofFigure 3 shows that the probable members of these galaxies appearto cluster appropriately in all three parameter spaces, although thevery few stars in Leo A mean that there is not as obvious a cluster ofpoints in proper motion space as for the other three galaxies.
Here, we consider the orbits of our target dwarf galaxies within theLocal Group to better understand what constraints the newly derivedsystemic proper motions place on their orbital histories. In particular,we examine the likelihood that these dwarfs have ever passed within300 kpc of either M31 or the Milky Way.
We explore the orbits of each of the dwarf galaxies backwards in timewithin the Local Group. All our orbital calculations use gyrfalcON (Dehnen 2000). Our intent is to determine only if the dwarf haspassed within 300 kpc of either the Milky Way or M31. Each of thedwarf galaxies starts well outside the virial radius of either the MilkyWay or M31: 𝑅 𝑀𝑊 ,𝑣𝑖𝑟 ∼
287 kpc assuming an NFW profile with atotal mass of 𝑀 𝑀𝑊 ,𝑣𝑖𝑟 (cid:39) . × 𝑀 (cid:12) (Posti & Helmi 2019), andthis should be compared to the present-day distances of the closestdwarfs (for the MW – Eridanus 2, 𝑑 𝑀𝑊 (cid:39)
382 kpc; for M31 – IC1613, 𝑑 𝑀𝑊 (cid:39)
520 kpc). As such, we model each large galaxy as apoint mass. gyrfalcON does not allow for the use of tracer particles,so we instead set the mass of the dwarf to be tiny in comparison toeither of the two large galaxies.We adopt the distance modulus of M31 to be 𝑑 𝑚𝑜𝑑 = . ± . 𝑣 ℎ = − ± − (van den Bergh 2000). We adopt the systemicproper motion of M31 derived using Hubble Space Telescope obser-vations (Sohn et al. 2012) as given in van der Marel et al. (2012a),namely 𝜇 𝛼 cos 𝛿 = . ± .
013 mas/year, 𝜇 𝛿 = − . ± . 𝜎 𝑠𝑦𝑠 = .
035 mas/year (GaiaCollaboration et al. 2018b) given the relatively large angular sizesof these system. For the remaining galaxies, we use 𝜎 𝑠𝑦𝑠 = . (cid:46)
40 kpc) radius. Moredifficult to constrain is the mass at large radius, where there arefewer tracers and generally poorer data, and many estimates rely onextrapolation of results obtained at smaller radius, given some modelassumptions. Bland-Hawthorn & Gerhard (2016) provide a goodreview of the relevant literature, and calculate the average of a rangeof studies based on analysis of the kinematics of the stellar halo. They
MNRAS , 1– ?? (2020) roper motions of isolated Local Group galaxies Galaxy 𝜇 𝛼 cos 𝛿 (mas/yr) 𝜇 𝛿 (mas/yr) 𝑓 dwarf 𝑣 𝛼 cos 𝛿 (km s − ) 𝑣 𝛿 (km s − ) 𝑣 𝑡 (km s − ) 𝑣 𝑟 (km s − ) SourceEridanus 2 0 . + . − . − . ± .
25 0 . + . − . + − − ±
451 473 -73 MV2020Phoenix 0 . ± . − . ± .
18 0 . ± . − ±
291 3 ±
349 3 -114 MV2020Leo T 0 . + . − . . + . − . . ± .
001 227 + − + −
328 -63 MV2020NGC 6822 − . ± .
02 0 . ± .
02 0 . ± .
01 5 ±
44 212 ±
44 212 51 This paperIC 1613 0 . + . − . − . ± .
03 0 . ± .
01 141 + − ±
107 145 -150 This paperLeo A 0 . ± . − . ± .
28 0 . + . − . ± − ± . ± . − . ± .
05 0 . + . − . ± − ±
216 425 -70 This paper
Table 2.
Median, 16th and 84th percentiles of the probability density functions for the three unknown parameters for all
Solo dwarf galaxies in the Local Groupfor which derivation of a systemic proper motion is currently possible (Table 4 of MV2020 presents values for Eridanus 2, Leo T and Phoenix; the currentpaper derives values for NGC 6822, IC 1613 and WLM using a modification of the same method). The corresponding tangential velocity components in aGalactocentric frame of reference are listed, as well as the overall tangential velocity (v 𝑡 ). The implied Galactocentric radial velocities are listed in the lastcolumn for comparison, and are converted from the heliocentric radial velocities listed in Table 1 (see text for details). Figure 3.
The spatial (left panels), colour-magnitude (middle panels), and proper motion (right panels) distributions for member stars (magenta stars) in NGC6822, IC 1613, Leo A and WLM. Grey points show all Gaia DR2 sources that pass our quality-control criteria described in the text. MNRAS , 1– ????
The spatial (left panels), colour-magnitude (middle panels), and proper motion (right panels) distributions for member stars (magenta stars) in NGC6822, IC 1613, Leo A and WLM. Grey points show all Gaia DR2 sources that pass our quality-control criteria described in the text. MNRAS , 1– ???? (2020) Alan W. McConnachie et al. find that 𝑀 𝑀𝑊 (cid:39) ( . ± . ) × 𝑀 (cid:12) . This is an identical value tothat obtained by Posti & Helmi (2019), on extrapolation of the massthat they measure within 20 kpc, based upon Gaia DR2 kinematicsof globular clusters. A different analysis of globular cluster data- including but not limited to Gaia DR2 - by Eadie & Jurić (2019)favors a slightly lighter mass, 𝑀 𝑀𝑊 (cid:39) ( . + . − . ) × 𝑀 (cid:12) (wherethe uncertainties describe the 95% credible intervals). Cautun et al.(2020) estimate 𝑀 𝑀𝑊 = ( . + . − . ) × 𝑀 (cid:12) from analysis ofthe Gaia DR2 rotation curve and other data.For M31, its integrated properties generally suggest that it ismore massive than the MW (e.g, Hammer et al. 2007). Watkinset al. (2010) analysed the satellite kinematics and determined that 𝑀 𝑀 = ( . ± . ) × 𝑀 (cid:12) . Fardal et al. (2013) examined thedynamics of the Giant Stellar Stream (Ibata et al. 2005) and con-cluded that 𝑀 𝑀 (cid:39) ( . ± . ) × 𝑀 (cid:12) . Patel et al. (2017)combine astrometric studies with cosmological simulations to esti-mate that 𝑀 𝑀 = ( . + . − . ) × 𝑀 (cid:12) (where they also estimatethat 𝑀 𝑀𝑊 = ( . + . − . ) × 𝑀 (cid:12) ). A direct measurement of themass ratio between M31 and the MW was made by Peñarrubia et al.(2014), who found that 𝑓 = 𝑀 𝑀𝑊 / 𝑀 𝑀 = . + . − . by analysisof the effect of the Local Group mass on the Hubble expansion of itsnearest neighbours. Here, we run a suite of simulations for each dwarf in which werun their orbits back in time, varying their two tangential velocitycomponents across a grid, to determine which combinations yieldinteractions with the Milky Way and/or M31. We then compare thisparameter space to the actual measured proper motions of the dwarfs.We vary the Galactocentric tangential velocity of each dwarf inthe range − − ≤ 𝑣 𝛼 cos 𝛿, 𝑣 𝛿 ≤ − , searchingthe full grid of values in 5 km s − increments. We note that thevelocity dispersion of the Local Group is expected to be of or-der 𝜎 𝐿𝐺 (cid:39) (cid:16) 𝑀 𝐿𝐺 × 𝑀 (cid:12) (cid:17) (cid:16) 𝑘 𝑝𝑐𝑅 𝐿𝐺 (cid:17) km s − , and so this gridsearch extends out to velocities that would certainly make these galax-ies unbound to the Local Group. All other positional and dynamicalparameters of the dwarf and M31 are fixed to their preferred valuesas described above. For the masses of the Milky Way and M31, weuse three different combinations:(i) LG1: 𝑀 𝑀𝑊 = . × 𝑀 (cid:12) , 𝑓 = . 𝑀 𝑀𝑊 = . × 𝑀 (cid:12) , 𝑓 = . 𝑀 𝑀𝑊 = . × 𝑀 (cid:12) , 𝑓 = . −
40 km s − or so for each dwarf would movethe galaxy into the family of orbits which have not had an interaction.For WLM and IC 1613, no solutions are found in which they haveinteracted with the Milky Way. For WLM, it is only possible for itto have interacted with M31 in the scenarios where M31 is relativelymassive. There is a reasonably large region of parameter space inwhich IC 1613 could have interacted with M31.It is interesting to note that NGC 6822, Leo T and Leo A couldhave interacted with either the Milky Way or M31, depending ontheir tangential velocities. For the latter two, M31 interactions canonly have occured in a relatively small region of parameter space forthe setup with the most massive M31 ( ∼ . × 𝑀 (cid:12) ). For NGC6822, there is a reasonably large area of parameter space for M31 orMilky Way interactions for all three setups.Figures 4 and 5 provide a simple context to understand the useful-ness, or otherwise, of the current proper motion measurements foreach of the dwarfs: • Eridanus 2:
This dwarf can only have passed within 300 kpcof the Milky Way if its Galactocentric tangential velocity is less than ∼
90 km s − . This is at the 1 − 𝜎 edge of the current proper motionmeasurement. The allowable parameter space for a backsplash solu-tion is consistent with a similar study by Blaña et al. (2020), whoconsider the orbits of Eridanus 2, Phoenix, Leo T and Cetus; • Phoenix:
Of the explored setups, the only way for Phoenix tohave ever passed with 300 kpc of the Milky Way if it has a small( (cid:46)
35 km s − ) tangential velocity and the total mass of the MilkyWay is relatively massive (as in LG3; at the upper end of the massrange to which it has been constrained by recent measurements).This is also consistent with the study by Blaña et al. (2020). If theMilky Way is really this massive, then the uncertainties on the currentproper motion are currently a factor of a few too large to distinguish abacksplash scenario from a more isolated orbit. As Phoenix requiresthe Milky Way to be massive in order for an interaction to occur,tightening constraints on the Milky Way’s total mass will likely provevaluble in definitely ruling out a backsplash origin for Phoenix; • Leo T:
If Leo T has a tangential velocity less than ∼
80 km s − ,then it is probably a Milky Way backsplash system, as also concludedby Blaña et al. (2020). Interestingly, in the case of a very massive M31(as in LG2), there is also a small region of parameter space in whichLeo T could be a M31 backsplash system (this is also the case forLeo A; see later). However, the current proper motion measurement MNRAS , 1– ?? (2020) roper motions of isolated Local Group galaxies Figure 4.
Results of the search through orbital parameter space for Eridanus 2, Phoenix, Leo T and NGC 6822. The different panels for each dwarf correspondto the LG1, LG2 and LG3 setups (left to right, respectively; see text for details). Red dashed lines delineate the regions of parameter space where the orbits bringthe dwarf within 300 kpc of the Milky Way. Blue dotted lines delineate the regions of parameter space where the orbits bring the dwarf within 300 kpc of M31.If no dotted or dashed lines are present, it means there is no region of parameter space that brings the dwarf within 300 kpc of these galaxies. Overlaid on eachpanel is the measured proper motion of the dwarf as given in Table 2. Black lines show random errors, and grey lines also include the systematic uncertainties. is utterly useless for providing any meaningful constraints in thisrespect. It is worth noting that the member stars of Leo T (and to alesser extent, Leo A) have not been observed as frequently as in otherdwarf galaxies as a result of the Gaia scanning law. In particular,the average number of “along-scan” measurements by the spacecraft for the member stars of Leo T is astrometric_n_obs_al (cid:39) astrometric_n_obs_al (cid:39)
127 for Leo A). For comparison, NGC6822 and IC 1613 have around 50% more measurements on average( ∼ − MNRAS , 1– ????
127 for Leo A). For comparison, NGC6822 and IC 1613 have around 50% more measurements on average( ∼ − MNRAS , 1– ???? (2020) Alan W. McConnachie et al.
Figure 5.
Same as Figure 4, for IC 1613, Leo A and WLM. Note that the measured systemic proper motion of Leo A falls outside of the proper motion spaceexplored (although it is consistent with zero at less than 2 𝜎 ). ( ∼ − • NGC 6822:
In principle, NGC 6822 could have had interactionswith either the Milky Way or M31, but the relatively precise propermotion measurement means that an M31 interaction is unlikely atmore than 4 − 𝜎 . A Milky Way interaction requires NGC 6822 tohave a Galactocentric tangential velocity of less than ∼
110 km s − ,and this is at the edge of the 1 − 𝜎 proper motion uncertainties. Itis worth noting the importance of systematic errors for NGC 6822,since these contribute more than random uncertainties. We examinethe orbit of NGC 6822 in more detail in the next section; • IC 1613:
The current proper motion measurement of IC 1613is inconsistent at approximately 2 − 𝜎 with ever having an interactionwith M31, under the assumption that M31’s mass is only around1 . × 𝑀 (cid:12) (as in LG1). The region of parameter space in whichan interaction can occur corresponds broadly to IC 1613’s currentspace velocity pointing away from M31, and aligned within ∼ • Leo A:
There is only a tiny regime of parameter space in whichLeo A could have interacted with either the Milky Way or M31. Forthe latter, M31 must be massive (as in LG2; around twice the mostlikely mass for the Milky Way). For the former, the Milky Way mustalso be relatively massive (as in LG3; at the upper end of the currentpreferred mass range) and the relative tangential velocity of the twomust be less than around 40 km s − . Like Leo T, the current estimatefor the proper motion of Leo A is completely useless for distin-guishing these scenarios, but the relatively tiny regions of parameterspace that need to be excluded means that future improvements in thesize of the uncertainities associated with the proper motion may putmeaningful constraints on the likelihood or otherwise of a backspashorigin;x • WLM:
Within the setups explored, this dwarf can only haveinteracted with M31, and can only have done so if M31 is rela-tively massive (as in LG2 and LG3). Those orbits which lead to aninteraction require WLM to be close to apocenter, and with rela-tive velocities between the two less than ∼
60 km s − . This region MNRAS , 1– ?? (2020) roper motions of isolated Local Group galaxies of parameter space overlaps with our current estimate of its propermotion. While several of the galaxies listed in Table 2 have good propermotion measurements in an angular sense (better than a few tenthsof a mas/yr), only NGC 6822 has a tangential velocity constrainedto much better than 100 km s − or so (even after systematic uncer-tainities are taken into account). Thus, compared to any of the othergalaxies in Figures 4 and 5, the volume of likely parameter spaceallowed by the proper motion measurement of NGC 6822 is consid-erably smaller than the volume of parameter space probed by ourprevious grid search. As such, we decided to conduct a more detailedanalysis of the possible orbits of NGC 6822 within the Local Group.Figure 6 shows the orbital path of NGC 6822 in the Local Groupover the last 10 Gyrs, for the LG1 realisation. The first three panelsshow projections in the x-y-z space, and the fourth panel shows theseparation of the dwarf as a function of time from the Milky Wayand M31 (red and blue lines, respectively). Solid points indicate thecurrent positions of the three galaxies. The coordinates are based onthe Galactocentric frame, but rotated so that M31 lies on the x axis,and centered on the midpoint of the Milky Way - M31 positions.Here, we have set the radial velocity, proper motion and distance ofM31 to the values used earlier. We have also set the radial velocity anddistance of NGC 6822 to the values used earlier, and we have set theproper motion of NGC 6822 to the measured value. In this idealisedscenario, NGC 6822 is clearly on its first infall into the Local Groupand has had no interaction with either of the big galaxies. For mostof its history, it has been falling nearly radially into the Local Group,and 10 Gyrs ago it was approximately 1.9 Mpc away from the MilkyWay (3.3 Mpc away from M31).To better understand the range of orbits consistent with the ob-servational parameters, we use the three Local Group setups, withthe different values of 𝑀 𝑀𝑊 and 𝑓 , described previously. For eachsetup, 10 realisations of the Milky Way, M31 and NGC 6822 areevolved backwards in time for 10 Gyrs. For each realisation, val-ues for the distance modulus, the heliocentric radial velocity andthe proper motion of both NGC 6822 and M31 are selected fromGaussian distributions. These are centered on the relevant measuredvalues and have a standard deviation equal to the uncertainty on themeasured value.Out of the three sets of 10 realisations, only eight orbits are foundthat involve NGC 6822 passing within 300 kpc of M31, in line withour findings from the grid search, and essentially ruling out a pastM31 interaction for NGC 6822. In constrast, 6 −
9% of the realisationsinvolve a ≤
300 kpc passage between NGC 6822 and the Milky Way.This too is broadly in line with the results from the grid search, whichdid not take into account the uncertainties in all the other measuredparameters for NGC 6822 and M31.More specifically, for each set of 10 realisations:(i) LG1: 6631 ±
81 orbits (6 . ±
81 orbits (6 . ±
91 orbits (8 . ∼ .
99% confidence and better than 90% confidence, respectively. We also note that themass of M31 does not have any significant impact on the likelihoodthat NGC 6822 is a backsplash galaxy or not.Given that NGC 6822 appears to be on its first infall into the LocalGroup, a natural question to ask is “infall from where?”. Figure 7shows a contour map of the predicted positions of NGC 6822 10 Gyrsago, in celestial coordinates, for those orbits in which NGC 6822 didnot pass within 300 kpc of the Milky Way. The LG1 realisation wasused to make this figure, although all three realisations are qualita-tively similar. Further, the distribution of points is similar whetherthe plot is made for 10 Gyrs ago or 8 Gyrs ago, as is expected giventhat at these early times NGC 6822 is far from the Galaxy and fallingmostly radially towards it. 2 × 𝛿 . Counts were smoothed bya Gaussian with 𝜎 = 𝛼 ∼ ◦ , 𝛿 ∼ − ◦ ) on the sky is not necessarilya good indicator of its historic position. It is well known that all theclosest galaxy groups are found along a great circle path, indicativeof the Local Group being embedded in a “local sheet” of nearbystructures (e.g., Tully et al. 2008 and references therein).There is clearly a reasonably-well defined locus on the sky fromwhich NGC 6822 likely originated. This locus is assiduous in avoid-ing any overlap with the locations of any of the nearest galaxy groups.This is perhaps to be expected: should NGC 6822 have originated ina dark matter halo in the vicinity of any of the other galaxy groups,then it would likely have ended up as a satellite in one of these groups.So this appears consistent with the idea that NGC 6822 formed inrelative isolation in the periphery of the structure now known as theLocal Group of galaxies, close enough that the gravity of the LocalGroup won out over the Hubble expansion. Over the course of aHubble time, it has fallen in to the Local Group, and is now in rela-tively close proximity to the Milky Way. We note that there have beensuggestions that NGC6822 may have undergone a recent interactionwith another small stellar system (e.g., see de Blok & Walter 2000;Demers et al. 2006, but see also Cannon et al. 2012; Thompson et al.2016), in which case perhaps NGC 6822 had a dwarf-like companionat earlier times.And what of the immediate future of NGC 6822? Integratingforward the orbital realisations from LG1 for which there was nota previous interaction suggests that it has only a 0.04/0.6% chanceof having an interaction (i.e., passing within ∼
300 kpc) with theMilky Way/M31 in the next 4 Gyrs. But this uneventful future forNGC 6822 is not shared by the Milky Way and M31. For in about4 Gyrs, these two large galaxies will be within about 100 kpc of eachother, in the midst of a near head-on collision (e.g., see van derMarel et al. 2012b). The most likely fate for NGC 6822 over the next4 Gyrs is shown with the dotted line in Figure 6. In this realisation,NGC 6822 is currently near pericenter with the Milky Way, and willcontinue on its relatively uneventful path through space, oblivious tothe imminent formation of the massive galaxy formerly known as theLocal Group.
MNRAS , 1– ????
MNRAS , 1– ???? (2020) Alan W. McConnachie et al.
Figure 6.
First three panels show the projection of the most likely orbit of NGC 6822 (green) relative to the Milky Way (red) and M31 (blue) over the last10 Gyrs (solid lines), and for the next 4 Gyrs (dashed lines), using the LG1 potential. Solid points indicate current positions of the galaxies. The coordinatesystem is centered on the mid point of the Milky Way - M31 positions, and aligned so that the x-axis connects the Milky Way and M31. The fourth panel showsthe separation of the dwarf as a function of time from the Milky Way (red line) and M31 (blue line). Present day is indicated by the dotted line. The grey shadedregion corresponds to a separation of less than 300 kpc from either large galaxy
The parameter space probed in Figures 4 and 5 gives a good handle onthe current usefulness of the orbital constraints for the dwarf galaxiesprovided by the new measurements of their proper motions. Fromthese considerations, and our orbital analysis, we conclude that theproper motion measurement of NGC 6822 in Table 2 is interesting,even including systematic uncertainties. IC 1613 and WLM both havegood measurements of their proper motions in an angular sense, butgiven their distances, their tangential velocities are less interesting.The current proper motion measurement for the remaining galaxiesare not particularly useful. While smaller uncertainties are needed,we note that the currently derived proper motions are generally within2 − 𝜎 of the predicted proper motions by Shaya & Tully (2013).It is important to recognise the impact future Gaia data releaseswill have on these measurements. Firstly, it is unlikely that any ofthe galaxies listed in Table 1 but not in Table 2 will ever have anymeaningful measurements of their proper motion using Gaia data:there are simply not enough bright stars visible to Gaia in thesegalaxies. Secondly, random errors in all these measurements willdecrease significantly as the baseline ( 𝑡 ) of the Gaia observations increases and the signal to noise of the observations increases, leadingto a proportionality of 𝑡 − / . For example, the imminent release ofGaia Data Release 3 in December 2020 will be based on 34 monthsof observations compared to 22 months for Data Release 2, andproper motions are expected to be a factor of 2 better than DR2 .This should mean that the tangential velocities of IC 1613, WLM andpossibly Phoenix will be able to be constrained at an interesting level,especially if systematic uncertainties also decrease. By the end of thecomplete mission in 2022, with an 8 year baseline, it seems likely thatthe random uncertainties on the tangential velocities should decreaseby a factor of 9 in comparison to these DR2 results. In this case, allthe galaxies in Table 2 except possibly Leo T and Leo A should haveuncertainties in their tangential velocities of several tens of km s − in each direction or better. By this point, the velocity components ofNGC 6822 should be measured with exquisite precision. So what of Leo T, Leo A, and the
Solo dwarfs listed in Table 1 that donot have (m)any stars visible in Gaia? More sensitive observatories MNRAS , 1– ?? (2020) roper motions of isolated Local Group galaxies Figure 7.
Contour map of the predicted positions of NGC 6822 10 Gyrs ago, in celestial coordinates, for those orbits in which NGC 6822 did not pass within300 kpc of the Milky Way, in the LG1 realisation. 2 × 𝛿 . Counts were smoothed by aGaussian with 𝜎 = are clearly required to detect a sufficient number of their stars, butcombining sensitivity with high spatial resolution and low systematicerrrors means there are only a few facilities in the optical and IRregimes that could make these measurements in the next decade.There are many large aperture facilities on the ground. Most no-tably, the Legacy Survey for Space and Time, to be conducted bythe Vera C. Rubin Observatory, will be conducted over a period of adecade. Its repeated observations of the entire southern hemispherewill make it very suitable for proper motion studies, and its dataacquisition strategy and heavy focus on data processing will likelyensure a good understanding of systematic errors. However, as aseeing-limited facility, its spatial resolution will likely not generallybe sufficient for many proper motion studies beyond the Milky Waysub-group. In comparison, the very high spatial resolution of theThirty Meter Telescope (TMT) and the Extremely Large Telescope(ELT) equipped with multi-conjugate adaptive optics systems, willcertainly provide very high spatial resolution (e.g., see Evslin 2015for the science that can be enabled). Here, however, the challenge willbe to obtain a sufficiently detailed understanding and characterisa-tion of the systematic uncertainties which will otherwise dominate,and which are contributed to by residual spatial distortions from theadaptive optics system (e.g., see Taheri et al., 2020, submitted, andreferences therein).Space-based observatories will therefore provide the most promis-ing avenue for more Local Group proper motions. It is worth high-lighting the proven utility of HST for these types of measurements.HST has been used to conduct proper motion studies of dwarf galax-ies for many years, with early ground-breaking work that utilisedbackground quasars to define the absolute reference frame (e.g., Pi-atek et al. 2002, 2003, 2005, 2006, 2007; Kallivayalil et al. 2006a,b,2013). Later adoption of a reference frame defined by backgroundgalaxies reduced the restriction in field selection caused by the re-quirement for there to be a background quasar. Since then, propermotion measurements beyond the Milky Way subgroup have beenmade for M31 (Sohn et al. 2012), NGC147 and NGC185 (Sohn et al.2020). Proper motion measurements also exist for M33 and IC10 from VLBI observations (Brunthaler et al. 2005, 2007). We note thatGaia DR2 has also been used to independently obtain the propermotions of M31 and M33 (van der Marel et al. 2019), although atthese distances the Gaia DR2 accuracy is significantly less than forHST (and, of course, VLBI).Upcoming space missions in the next decade with the potentialto provide new Local Group proper motion measurements includethe James Webb Space Telescope (JWST), the Nancy Grace RomanSpace Telescope, and the Euclid space mission. These observatorieswill all be active by mid-decade, and all operate at longer wave-lengths than HST. Taking into account their apertures, their spatialresolutions will either be similar or slightly poorer than HST (butstill very good in an absolute sense). However, a major advantageof HST for proper motion studies is the very long baseline of obser-vations that exist given the maturity of this facility. In this regard,it is very likely that, even using data on these dwarfs from JWST,Roman or Euclid, first epoch observations will be from HST. Indeed,programs are already underway with HST to obtain first epoch obser-vations of Local Group dwarf galaxies where none currently exist,or to obtain second-epoch observations where first-epoch alreadyexist. Significant survey datasets in this regard include the AdvancedCamera for Surveys Local Cosmology from Isolated Dwarfs (ACSLCID) survey for isolated dwarfs (e.g., Cole et al. 2007; Monelliet al. 2010a,b; Hidalgo et al. 2011; Skillman et al. 2014), the
InitialStar formation and Lifetimes of Andromeda Satellites (ISLANDS) forM31 dwarf spheroidals (Monelli et al. 2016; Skillman et al. 2017;Martínez-Vázquez et al. 2017), and work on fainter members of theM31 satellite system (Martin et al. 2017; Weisz et al. 2019).
In this paper, we have measured systemic proper motions for dis-tant ( 𝑑 ∼ −
900 kpc) dwarf galaxies in the Local Group usingCFHT and Gaia Data Release 2 and investigated if these (currently)isolated galaxies have ever had an interaction with either the MilkyWay or M31. We find that NGC 6822, Leo A, IC 1613 and WLM
MNRAS , 1– ????
MNRAS , 1– ???? (2020) Alan W. McConnachie et al. have a sufficient number of bright stars with reliable astrometry toderive proper motions for these four galaxies. We apply a variant ofthe methodology described in MV2020 to obtain estimates of theirsystemic proper motions. The results for NGC 6822, IC 1613 andWLM are good in an angular sense - systematic errors in Gaia DR2proper motions either dominate or are major contributers to the errorbudgets. However, the large distances of IC 1613 and WLM meanthat the resulting constraint on their orbits are still relatively weak.We explore the orbital parameter space for these isolated galaxiesin light of these new measurement, and also include Leo T, Eridanus2 and Phoenix, which have recent proper motion estimates fromMV2020. We conclude that Phoenix, Leo A and WLM are unlikelyto have ever interacted with the Milky Way or M31, unless thesegalaxies are very massive (at the upper end of any recent estimates oftheir masses). We rule out a past interaction of NGC 6822 with M31at ∼ .
99% confidence, and find there is less than a 10% chancethat NGC 6822 has had an interaction with the Milky Way. We alsoexplore the origins of this galaxy in the periphery of the young LocalGroup. For the remaining dwarfs under consideration, the currentproper motions do not yet rule out the possibility that these galaxiesmay be backsplash systems. However, our results indicate that futuredata releases from Gaia will provide good or excellent constraintson the interaction history of these seven galaxies, with the possibleexceptions of Leo A and Leo T. These last two galaxies suffer froma combination of only a few bright stars being visible to Gaia, anda relative dearth of visits by the spacecraft as a result of the Gaiascanning law.
ACKNOWLEDGEMENTS
We thank the anonymous referee for comments that improved thepaper. We also thank Matías Blaña and Tony Sohn for their comments.AWM and KAV would like to acknowledge funding from the Na-tional Science and Engineering Research Council Discovery Grantsprogram. GB acknowledges financial support through the grants(AEI/FEDER, UE) AYA2017-89076-P, as well as by the Ministe-rio de Ciencia, Innovación y Universidades (MCIU), through theState Budget and by the Consejer a de Economia, Industria, Comer-cio y Conocimiento of the Canary Islands Autonomous Community,through the Regional Budget.Based on observations obtained with MegaPrime/MegaCam, ajoint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Re-search Council (NRC) of Canada, the Institut National des Sciencede l’Univers of the Centre National de la Recherche Scientifique(CNRS) of France, and the University of Hawaii. The observationsat the Canada-France-Hawaii Telescope were performed with careand respect from the summit of Maunakea which is a significantcultural and historic site.
DATA AVAILABILITY
Some of the data underlying this article were accessed fromthe Gaia Archive ( https://gea.esac.esa.int/archive/ ). TheCFHT data underlying this article are available through the CFHTarchive hosted by the Canadian Astronomy Data Center ( ). De-rived data products will be shared on reasonable request to the cor-responding author.
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