Free Access
Issue
A&A
Volume 657, January 2022
Article Number A54
Number of page(s) 49
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/202141528
Published online 07 January 2022

© ESO 2022

1. Introduction

Knowledge of the bulk motions of galaxies residing in the Local Group (LG) is a precious resource for a wealth of galaxy evolution and near-field cosmology investigations, for example, inferences of the mass, barycentre position, and velocity of the LG (e.g. Kahn & Woltjer 1959; Peebles et al. 2001; Li & White 2008; van der Marel et al. 2012b; González et al. 2014; Peñarrubia et al. 2014, to mention a few); studies of the possible history of past interactions between the Milky Way (MW) and the M31 system and its future fate (e.g. Loeb et al. 2005; van der Marel et al. 2012a; Salomon et al. 2021, and references therein); determinations of the mass of the MW through dynamical modelling of tracers of its gravitational potential, such as its satellite galaxies (e.g. Wilkinson & Evans 1999; Battaglia et al. 2005; Boylan-Kolchin et al. 2013; Patel et al. 2018; Callingham et al. 2019; Fritz et al. 2020, see references in Fritz et al. 2020 for an overview on the works on this topic); group infall as well as the significance and stability of the vast polar structure (e.g. Metz et al. 2008; Pawlowski & Kroupa 2013; Fritz et al. 2018a; Kallivayalil et al. 2018; Li et al. 2021a); and considerations on the missing satellite problem (e.g. Simon 2018; Fritz et al. 2018a). The orbital history of MW satellite galaxies is also very likely to influence several aspects of their evolution, through, for example, the impact of ram-pressure stripping and tidal effects onto their gas content, star formation history (SFH), morphology, and dark matter (DM) halo properties (e.g. Mayer et al. 2006; Muñoz et al. 2008; Kazantzidis et al. 2011; Battaglia et al. 2015; Hausammann et al. 2019; Iorio et al. 2019; Miyoshi & Chiba 2020; Ruiz-Lara et al. 2021; Rusakov et al. 2021; Di Cintio et al. 2021; Genina et al. 2020, and references therein).

Before the second data release (DR2) of the Gaia mission (Gaia Collaboration 2016, 2018a), measurements of the systemic proper motions (PMs) of galaxies in the LG were essentially limited to the Magellanic Clouds, the so-called classical MW dwarf spheroidal galaxies (dSphs), one ultra faint dwarf (UFD, Fritz et al. 2018b), M31, M33, and IC 10, mostly from Hubble Space Telescope (HST) observations, and a few very-long-baseline interferometry (VLBI) observations of OH masers (see Brunthaler et al. 2007, and references in Sect. 6). In fact, some of them have become available surprisingly recently (in the case of the Sextans MW dSph, the first such measurement was published by Casetti-Dinescu et al. 2018).

Since April 2018, the situation has seen a dramatic improvement, starting with the Gaia science verification article (Gaia Collaboration 2018b). Multiple determinations of the systemic PM of a large number of MW satellite galaxies and galaxy candidates blossomed in a matter of weeks after Gaia DR2, led by several groups in the community, and using a variety of techniques, for example focussing only on stars with prior spectroscopic information (Simon 2018; Fritz et al. 2018a) or including the full set of stars with astrometric information (Kallivayalil et al. 2018; Massari & Helmi 2018). It is now also becoming routine to use Gaia astrometric data to remove contaminants, as well as to attempt systemic proper motion determinations along with the study of other properties of the systems (e.g. Longeard et al. 2018; Torrealba et al. 2019). Surveys of the MW stellar halo and sub-structures within are and will make plentiful use of Gaia astrometry to boost the success rate in target selection (e.g. Conroy et al. 2019; Li et al. 2019; Allende Prieto et al. 2020, but also the surveys to be carried out with 4MOST and WEAVE, to mention some of the upcoming ones). Interestingly, the use of Gaia DR2 data has also been pushed beyond the MW system, with determinations of the tangential motions of M31 & M33 (van der Marel et al. 2019), as well as of a few LG dwarf galaxies such as NGC 6822, IC 1613, WLM, and Leo A (McConnachie et al. 2021).

The methodologies applied in the early Gaia DR2 works mentioned above were rather simple ones, being based on iterative cleanings of the data sets via σ-clipping and no statistical treatment of the foreground and background contamination. Later on, more sophisticated methods were used, for example with simultaneous statistical modelling of the properties of the dwarf galaxy and the contamination. For instance, Pace & Li (2019) used the spatial and PM information of stars preselected to have a magnitude and colour lying on an isochrone and adopted a multi-variate Gaussian in proper motion for both the dwarf galaxy and the MW, while McConnachie & Venn (2020a) used all the observables at once and adopted the empirical distribution of the contaminant stars in the PM and the colour-magnitude (CM) planes.

The early third data release (eDR3) of Gaia data (Gaia Collaboration 2021a) has implied more precise and accurate astrometric measurements; in particular, for PMs the precision has increased by a factor of two and systematic errors have decreased by a factor ∼2.5 (Lindegren et al. 2021b). McConnachie & Venn (2020b) provide updated systemic PMs for the 58 MW satellites previously considered by the same team with DR2 data, with the improved astrometry now allowing one to detect the systemic PM of Boötes IV, Cetus III, Pegasus III, and Virgo I. Li et al. (2021a) have recently provided an independent determination of systemic PMs for 46 MW satellites, and they integrated the 3D motions in four isolated MW potential models, with a total mass from 2.8 × 1011 to 15 × 1011M. Martínez-García et al. (2021) combined the astrometric and spectroscopic information available for 14 MW satellites to study their internal kinematics and quantify the presence of velocity gradients.

In this work we aim to provide a comprehensive determination of systemic proper motions based on Gaia eDR3, not only for MW satellites, but for LG dwarf galaxies in general1 and to push these determinations to even larger distances for the first time, that is to say reaching out to the NGC 3109 association at ∼1.4 Mpc. We are making use of the best techniques in the literature, McConnachie & Venn (2020a) and McConnachie et al. (2021), inspired by Pace & Li (2019), since these techniques take full advantage of the observables available for the largest number of stars with full astrometric and photometric information (location on the sky with respect to the dwarf galaxy centre, on the colour-magnitude diagram, and on the proper motion planes), and model them in a Bayesian way with a mixture model accounting for contaminant sources. We have introduced a few modifications to these techniques, mainly aimed at making an even more realistic treatment of the stellar population content of the dwarf galaxies and its distribution on the colour-magnitude plane, also accounting for the photometric completeness of Gaia eDR3 data; this allowed us also to determine the probability of memberships for stars in different evolutionary phases, which we make available to the community2.

Finally, we study the orbital properties of the galaxies surroundings of the MW by integrating their bulk motions in a set of gravitational potentials, bracketing a 0.9–1.6 × 1012M range for the mass of the MW. Motivated by the work by Patel et al. (2020), who show that the orbits of MW satellites can significantly differ between a gravitational potential including only the MW and one where the gravitational influence of the LMC (and SMC) are taken into account (and all galaxies are free to move in response), we integrated the bulk motions also in the triaxial time-varying MW potential made available by Vasiliev et al. (2021), where the infall of a massive LMC and the response of the MW to this infall are modelled. In this context, we also revisit the association of the dwarfs surrounding the MW with the LMC system.

In Sect. 2 we introduce the sample of galaxies analysed and, in Sect. 3, the data sets used and the quality selection criteria applied. In Sect. 4 we present the methodology for the systemic proper motion determinations, and discuss the output and the tests performed to tackle the robustness of the method; in Sect. 5 we complement the results with a determination of the zero-points and additional errors due to systematics in the Gaia eDR3 data, using quasars (QSO). Our systemic proper motions are compared to those in the literature in Sect. 6. In Sect. 7 the bulk motions are integrated in the three gravitational potentials and the resulting orbital trajectories and parameters are then used to address the impact of the LMC on the reconstructed orbital history as well as to make considerations as to the too-big-to-fail problem, the system of MW and LMC satellites, and the observed properties such as SFHs. We discuss other potential applications of our work in Sect. 8 and present our conclusions and summary in Sect. 9.

2. Sample

The 74 systems considered in this work are listed in Table B.1, together with their main global properties (see also Fig. 1). The sample is the union of the dwarf galaxies studied in Fritz et al. (2018a), Fritz et al. (2019), and some other recently discovered satellites of the MW. We also included isolated LG dwarf galaxies within ∼1.4 Mpc.

thumbnail Fig. 1.

Line-of-sight (l.o.s.) velocity of heliocentric distance for the galaxies in the sample (circles). The systems without a literature measurement of the l.o.s. velocity are assigned a null value, exclusively for the purpose of this figure, and are indicated as crosses. The colour-coding is based on the uncertainty in heliocentric transverse velocity, derived from the statistical uncertainties in the systemic proper motions and distance modulus (see Sect. 4).

Due to the large distance of the isolated LG dwarf galaxies, in terms of resolved or partially resolved sources, only H II regions, young main sequence, blue super-giants, red super-giants, and asymptotic giant branch (AGB) stars brighter than the tip of the red giant branch (RGB) are potentially detected above the magnitude limit for Gaia astrometric measurements. Therefore not all isolated dwarf galaxies will have enough (or any) Gaia eDR3 sources with full astrometric solution.

In order to select which systems to consider on a first pass, we gave priority to those galaxies within 1.5 Mpc with an H I detection, as listed in McConnachie (2012), and hence likely to host young stars and/or H II regions. The systems that showed to have a clear enough detection in Gaia eDR3 of centrally concentrated sources (after a first, rough, spatial, parallax and proper motion selection) were retained. We exclude IC 10 because, apart from being only marginally detected, its analysis is complicated by the very high and patchy extinction in its direction. The borderline systems such as LGS3, Antlia, NGC 205, NGC 185 were excluded but the closer galaxy Leo T was retained.

We exclude the Magellanic Clouds, M 31 and the Sagittarius (Sgr) dwarf galaxy, because we are neglecting internal motions in our analysis, while they might be relevant for the systemic PM determination of these systems. These galaxies have anyway already been the subject of very detailed analyses based on Gaia data (see Gaia Collaboration 2021b; Salomon et al. 2021; del Pino et al. 2021, the latter using DR2). We note that in their Gaia DR2-based study, van der Marel et al. (2019) found no difference in the centre-of-mass proper motion when explicitly modelling M33 rotation or neglecting it. This means we include the following galaxies outside the virial radius of the MW: Eridanus II, Leo T, Phoenix, NGC 6822, WLM, IC 1613, Leo A, M33, Peg-dIrr, UGC 4879, Sgr-dIrr, Sextans A, Sextans B, NGC 3109.

We caution the reader that, even for those galaxies for which a determination of the systemic PM is possible, depending on the distance, the error in the transverse velocity is still too large for scientific applications (see Fig. 1). We refer the reader to Sect. 5 to learn about which galaxies have their error budget dominated by random or statistical errors.

3. Data sets

Gaia eDR3 astrometric and photometric measurements for stars with full astrometric solutions constitute the bulk of the data over which the analysis is performed. For the distant systems (i.e., those beyond 400 kpc) we complement Gaia photometry with the deeper data set from the Pan-STARRS1 Surveys (PS1, Chambers et al. 2016); this will be used to identify the regions in the colour-magnitude plane where to select candidate massive blue stars and red super giants stars and to determine their spatial distribution, in some cases. We refer to Sect. 4.1 for a detailed explanation of the methodology. We download Gaia eDR3 and PS1 data over an area centred on the systems under consideration, with a radius such to guarantee at least 2000 objects where we expect contaminants to be clearly dominant over stars from the galaxy under consideration, i.e. beyond 5 half-light radii, Rh3.

We concentrate exclusively on those Gaia eDR3 detected objects that are not flagged as duplicated source, have a full astrometric solution (astrometric_params_solved ≥ 31), high-quality astrometry (renormalised unit-weighted error, ruwe, < 1.4, see e.g. Lindegren et al. 2018) and reliable photometric measurements. For this last factor, we retain the measurements with an absolute value of the corrected excess factor within 5 times the standard deviation expected at the corresponding G-mag (see Eqs. (6), (18) and Table 2 in Riello et al. 2021). In order to exclude sources seen as extended or not isolated by Gaia, we retain objects with ipd_frac_multi_peak ≤ 2 and ipd_gof_harmonic_amplitude < 0.2; this latter cut is less restrictive with respect to what adopted in Fabricius et al. (2021) but adjusts better to the distribution of values seen for the sources around the galaxies under consideration. Objects with source_id with a match in the Gaia AGN catalogue are excluded.

We exclude clear foreground stars by requiring the parallax of each individual source to be consistent with the parallax expected at the dwarf distance modulus within 3σπ; here σπ is the sum in quadrature of the parallax error on the individual measurements and that due to the uncertainty of the galaxy distance modulus. We apply a global zero-point offset of −0.017 mas to the parallax measurements of the individual stars (Lindegren et al. 2021a). We do not correct for the Gaia parallax zero-point as a function of location, magnitude and colour, because of its negligible effect on our analysis: even at the brightest magnitudes considered here (mG ∼ 13.4 mag for the tip of the RGB of Delve 1, the closest system in the sample), the maximum difference between the zero-point applied and that expected at mG ∼ 13.4 mag would be ∼0.03 mas (Lindegren et al. 2021a), smaller than the 3 × σπ range under consideration.

The apparent G-mag for the sources with 6-parameters solutions are corrected as in Riello et al. (2021), with the PYTHON code presented in Gaia Collaboration (2021a). Finally, the apparent G-mag and the BP–RP colour are corrected for extinction using the Schlafly & Finkbeiner (2011) maps interpolated at the position of the stars and using the Marigo et al. (2008) coefficients for the Gaia filters, based on Evans et al. (2018) (see Sestito et al. 2019).

4. Determination of systemic proper motions

4.1. Method

Rather than relying only on Gaia eDR3 sources with previous spectroscopic observations, we adopt the flexible methodology by McConnachie & Venn (2020a, hereafter, MV20a) and McConnachie et al. (2021, hereafter, Mc21), inspired by Pace & Li (2019), which allows to make use of all the stars with Gaia astrometric and photometric measurements (aside from the quality cuts detailed in the previous section). We refer the reader to the original sources for a detailed explanation of the methodology. Here suffices to say that it is based on a maximum likelihood procedure, which has three free-parameters: the systemic proper motion of the galaxy, μα, *, sys and μδ, sys, and the fraction of stars in the dwarf galaxy under consideration over the total, fgal. It is assumed that the intrinsic dispersion is negligible in the distribution of PM measurements.

The likelihood of a star to belong to the system under consideration, Lgal, or to the contamination, Lc, is estimated taking into account a spatial, colour-magnitude and proper motion likelihood term. After having determined μα, *, sys, μδ, sys and fgal, these, together with the likelihoods, can be used to obtain the probability of membership of each star to a given galaxy (Eq. (5) in MV20a):

(1)

Below we describe the methodology followed to determine the various terms of the likelihood function, and provide an overview of how each galaxy was treated in Table 1.

Table 1.

Methodology used for the spatial and Colour-Magnitude (CM) of the likelihood for stars in the dwarf galaxy (Sect. 4.1).

4.1.1. Spatial distribution

The contaminants are assumed to be uniformly distributed over the areas considered around each system.

The spatial term of the likelihood function for the stars belonging to the dwarf galaxy is based on the 2D structure of the dwarf galaxy stellar component. In order to evaluate it, we adopt two main approaches, depending on the system under consideration: either we parametrise it to have an elliptical shape and an exponentially declining surface number density profile, as done by MV20a, or determine it empirically, as done by Mc21 (“Exp” and “Emp” in column “Spatial” of Table 1). We refer readers to MV20a and Mc21 for the possible caveats concerning this approach.

For the “Exp” case, a 2D look-up map is created by co-adding and then normalising N = 1000 Monte-Carlo realisations of the expected 2D surface number density at a given position on the sky; in each realisation, values for the ellipticity, position angle and half-light radii4 are randomly extracted from a Gaussian distribution centred on the values listed in Table B.1 and with dispersion given by the average of the lower and upper 1-σ uncertainties listed in the same table. For those galaxies where a determination of the ellipticity is missing or only an upper limit is available, we assume the spatial distribution to be circular. This approach is essentially applied to all systems for which the spatial distribution of most of the sources detected by Gaia and used in the analysis have a smooth, spheroidal-looking morphology (i.e. the classical dSphs and the UFDs) or for some late-type systems for which there is not enough statistics for an empirical determination (see below).

For the distant late-type systems, the majority of the sources detected by Gaia will be blue massive stars, red super-giants (RSGs) and AGB stars. Among these, we concentrate on the blue and RSGs as more easily identified on the CMD (see also Mc21). These young stars are those that give an irregular morphology to some of these galaxies, due to asymmetries in their spatial distribution. Therefore, the approach to follow for the late-type systems is decided after a visual analysis of the spatial distribution of stars with colours consistent with being young main-sequence or blue super-giant stars in the PS1 photometry: if their spatial distribution is well defined, then the probability distribution of the spatial term is determined empirically from these stars as a normalised 2D histogram within 3 half-light radii (apart from M33, that is missing this quantity, for which we consider 0.5 deg). For those cases where the statistics of blue stars are not sufficient for an empirical determination, we resort to modelling the spatial term as an exponentially declining profile. In all cases, the spatial distribution of the RSGs is assumed to follow that of the blue stars, which is true to a good approximation.

4.1.2. Distribution on the colour-magnitude plane

We concentrate on sources with −1.0< (BP–RP)0 < 2.5, apart for the late-types, for which we adopt −1.5< (BP–RP)0 < 2.5. We have verified that these colour cuts works also for metal-rich systems such as Fornax, WLM, NGC 6822 etc.

As in MV20a, the distribution of contaminants onto the colour-magnitude plane is determined empirically, from Gaia eDR3 sources at semi-major axis radii larger than 5 × Rh, with the exception of those systems for which this limit exceeded the spatial extension of the catalogue downloaded (e.g., for Antlia II), in which case we assume radii larger than 3 × Rh. For M33 we do not use a value of the half-light radius but define the region by eye, beyond 1 deg.

For the CM probability distribution of stars belonging to the systems of interest, we introduce a few changes with respect to the method of MV20a:

  1. Empirical determination (“Emp” in column “CM” of Table 1). For well populated and nearby systems, such as the classical dSphs, the distribution on the CM-plane is determined empirically, from the region within one half-light radii. The dwarf galaxy’s stellar population within this region dominates over that of the contaminants and the increase in statistics over considering a smaller area is worth the introduction of a few contaminants. While we do not expect the choice of using an empirical determination of the dwarf’s CM likelihood term to cause a significant difference in the determination of the systemic proper motion over e.g., using an isochrone, we wish to factor in the CMD information in the estimate of the probability of membership for stars in different evolutionary phases, since this is one of the products that we make available. Classical dSphs are well-known to display stellar population gradients; however a complete modelling of the CMD as a function of distance from the dwarf centre is outside of the scope of this work, and the CMD of the central regions contains all the features present also in the outer parts.

  2. Synthetic CMD (“Syn” in column “CM” of Table 1). All those galaxies closer than 440 kpc that are not included in the category above do not have enough signal inside their half-light radius for an empirical determination of the CM probability distribution. In addition, many of these systems are very faint and sparsely populated; therefore we wish to adopt an approach that includes all the relevant evolutionary phases and does not exclude a priori possible members, e.g. if they were not to fall on the locus of an isochrone of a given age and metallicity. To this aim, rather than an isochrone as done in MV20a, we use Basti-IAC to create a synthetic CMD in the Gaia eDR3 photometric filters5, based on the stellar evolutionary models presented in Hidalgo et al. (2018). These models include also the He-burning phase, which can be precious in faint systems, since in particular the blue part of the horizontal branch is a region of rather reduced contamination. An advantage of using a synthetic CMD over using an isochrone is that stars are distributed on the magnitude and colour plane in the correct proportion (for a given SFH, chemical enrichment law, initial mass function, …). Given that the systems we are applying this method to are either completely or mostly dominated by ancient stellar populations, we adopt a constant star formation rate between 12 and 13 Gyr ago, and a metallicity centred around [Fe/H] = − 2.3 with a spread of 0.5 dex. This is representative of the metallicity distribution function of stars in UFDs (see review by Simon 2019). One hundred realisations are carried out, where the synthetic CMD is shifted in distance modulus, drawing from Gaussian distributions centred on the values listed in Table B.1 and with dispersion given by the average of the upper and lower 1-σ errors. At the same time, the photometric errors are introduced by scattering the BP–RP colours of the stars in the synthetic CMD according to the photometric errors derived from the Gaia eDR3 catalogue corresponding to each given object, at the appropriate apparent G-mag. Correction for photometric completeness. The synthetic CMD of course does not suffer from photometric incompleteness; on the other hand, it should be considered that the CMD of the contaminants does suffer from this issue, since it is derived empirically from the Gaia eDR3 data, and that the completeness varies depending on the number of transits in a given region of the sky. This might alter the relative probabilities of dwarf galaxy’s stars versus contaminant stars in some regions of the CMD, in favour of the former. In order to introduce an (approximate) correction to take this effect into account, we resort to Gaia Universe Model Snapshot (GUMS, Robin et al. 2012). We download GUMS models from the Gaia archive around the position of each system, and calculate the ratio of the luminosity function of contaminants stars in the observed Gaia eDR3 catalogues (which will be mostly MW stars) and that of model stars, in a representative colour range, 0.5 < (BP–RP)0 < 2.5. In the assumption that the model is a reasonable approximation of the data, at G-mag where Gaia should not suffer from completeness issues, this ratio should be around unity. In practice, there are some deviations; therefore, we normalise the ratio to the median value in the range 17 < G-mag < 20. After this step, the ratio of the two luminosity functions oscillates around one, except at faint magnitudes, where a decline towards zero is observed, which can be assumed to be due to the Gaia photometric completeness. This will be the factor by which we multiply the counts in the CMD look-up map as a function of magnitude6. As we see in Sect. 4.2.1, this correction has a minor effect, but this will be adopted for our baseline results, listed in Table B.2. Even though Phoenix and Leo T do contain a sprinkle of young, blue stars detected in Gaia eDR3, since the majoritarian population in Gaia eDR3 data is by far represented by RGB stars, these systems are treated with the synthetic CMD. This choice does not impact the determination of the systemic PM but it implies that these young stars will be missing from our list of probable members.

  3. Box (“Box” in column “CM” of Table 1). For the distant (> 440 kpc) and well populated galaxies, we follow closely the approach by Mc21, and focus on blue sources and RSGs. The colour and magnitude limits are chosen by visual inspection of the PS1 photometry, and transferred to the Gaia eDR3 bands, using the stars in common between the data sets for each galaxy. We assign a uniform probability inside these boxes.

For both the dwarfs and the contaminants, we construct the CM look-up map in bins of magnitude and colour, smooth it with a boxcar kernel and then proceed to normalising it.

4.1.3. Proper motion

For the distribution on the PM plane, we adopt the same approach as MV20a, that is an empirical determination for the contamination, while assuming a multi-variate Gaussian distribution for the dwarf galaxy, taking into account the correlation terms between the μα, * and μδ of the individual stars. For the MW classical dSphs and UFDs, we restrict the range of the analysis to within ±5 mas yr−1, corresponding to a generous tangential velocity cut of > 470 km s−1 at a heliocentric distance larger than 20 kpc (±3 mas yr−1 for Antlia II, to reduce the overwhelmingly large contamination). For the other systems we filter out sources whose proper motion in each component at the distance of the galaxy would imply tangential velocities 3× in excess of a given velocity dispersion (around the reflex proper motion at the galaxy’s sky location). As dispersion, we consider the square-root of the quadratic sum of the uncertainty given by the proper motion measurements and 200 km s−1, where the latter is the observed scatter in line-of-sight (l.o.s.) velocities for the whole sample of galaxies in Table B.1 (assuming that the scatter in tangential velocities is the same)7.

4.2. Results

The outcome of the analysis is summarised in Table B.2. Examples of the distribution of member stars projected on the tangent plane passing through the galaxy centre, and on the proper motion and colour-magnitude plane are given in Figs. 24, for systems in various regimes, in terms of number of member stars, heliocentric distances, and morphological types.

thumbnail Fig. 2.

Distribution of member stars (large circles) projected on the tangent plane passing through the galaxy centre (left), and on the proper motion (middle) and colour-magnitude plane (right), for systems in the regime of > 500 stars with P > 0.95, in increasing order of distance from top to bottom. The galaxy names are indicated in the figure titles. The colour-coding indicates the probability of membership (only when above > 0.5; the stars with P < 0.5 are shown as grey dots. The ellipses in the left panel have semi-major axes equal to 1× and 3× the half-light radii in Table 1 (apart from M33, that is missing this quantity, for which we consider 0.5 deg), and ellipticity and position angle taken from the same table.

thumbnail Fig. 3.

As in Fig. 2, but for the regime of 50–200 stars with P > 0.95.

thumbnail Fig. 4.

As in Fig. 2, but for the regime of < 50 stars with P > 0.95. Cetus III and Bootes IV are two cases in which the uncertainties in McConnachie & Venn (2020b) are much smaller than in our determination.

For the majority of the systems in the sample, in output there are sizeable numbers of stars with large membership probability (42 and 52 systems with > 10 stars with P > 0.95 and P > 0.5, respectively). In fact, some galaxies are extremely well populated. For example, we obtain > 1000 stars with membership probabilities P > 0.95 in each of the classical MW dSphs (except Leo II) as well as in M33 (> 20 000 for Fornax). Ten systems have between 100–1000 P > 0.95 members, among which several of the distant galaxies (Phoenix, NGC 6822, IC 1613, WLM, NGC 3109).

On the other end of the spectrum, there are systems with only an handful of probable members or none at all. The analysis does not lead to a systemic PM determination for Pisces II and Virgo I, with posterior distribution functions (PDFs) that are essentially flat. Other systems with clearly problematic PDFs are DESJ0225+0304, Pegasus III, Tucana V, with strong lopsidedness and/or very extended wings of high amplitude, and Indus I, with a double peaked PDF. For Pisces II and Tucana V, however, we are able to obtain a systemic PM when including the information about l.o.s. velocities for the stars observed spectroscopically (see Sect. 4.2.1). We would advice against using the systemic PMs for all these cases (whose names are highlighted in red in Table B.2) and advice to use the motions obtained when considering the spectroscopic information for Pisces II and Tucana V. In addition to the above, the shape of the PDFs and of the distribution of probable member stars on the plane of the sky, proper motion and colour-magnitude leads us to advise exerting caution when considering the motions of Cetus III, Indus II, Aquarius II, Delve 1, Reticulum III, Bootes IV (see Sect. A for more details; these are highlighted in orange in Table B.2).

In summary, out of 74 systems analysed, we are able to determine systemic proper motions for 72 systems without considering complementary spectroscopic information (73 when considering the spectroscopic information), and consider certainly reliable 62 (64 with spectroscopy). The majority of these 64 systems are found in the vicinity of the MW, within 300 kpc, but the galaxies for which we provide systemic PMs are as distant as 1.4 Mpc (Sextans A and Sextans B). This is the largest, and most extended in volume, set of systemic proper motions for galaxies and galaxy candidates. Of course, it should be kept in mind that the same uncertainty in proper motion will translate into an uncertainty in transverse velocity 10× larger for a galaxy at 1 Mpc than for one at 100 kpc.

4.2.1. Tests and validations

Photometric completeness. As discussed in Sect. 4.1, a correction for the photometric completeness of Gaia eDR3 data was applied to the CM probability distribution of the galaxies treated with the synthetic CMD (see Table 1). Figure C.1 shows the comparison of the systemic proper motions determined with and without applying this correction: the determinations are always in very good agreement, well within the 1-σ errors, apart from Antlia II, for which a larger difference is seen, but still within 2-σ. The good agreement between the two determinations is likely due to the correction kicking in at faint magnitudes, there were the individual proper motions are less accurate and therefore have a lower weight in the global determination.

For our photometric completeness correction, we are not applying quality cuts to the Gaia eDR3 data to be compared to GUMS, apart from requiring a full astrometric solution. We checked that the change in systemic PM would be negligible if we would apply the same quality cuts as in Sect. 3.

Inclusion of spectroscopy information. MV20a analysed the galaxies in their sample with and without considering additional information on the stars’s membership from spectroscopic observations. Specifically, when including information from spectroscopy, they modified the prior on the systemic proper motion by multiplying it by a bi-variate Gaussian with mean and dispersion given by the weighted mean proper motion and associated uncertainty of the stars with Gaia astrometric measurements that are also probable spectroscopic members. The authors concluded that information from stars with spectroscopic follow-up was not required to obtain reasonable estimates of the systemic PMs; in fact, in only a few systems, the inclusion of this information played an important role: Carina III, Segue 1, Triangulum II and Tucana IV, for which the spectroscopy allowed to go from a bi-modal to a uni-modal PDF (which in the case of Carina III was due to the presence of Carina II in the field-of-view). In general, the inclusion of this prior had the effect of reducing the size of the error-bars, even though in some cases only slightly. The authors also warn about the dangers of including this information for systems with only an handful of spectroscopic members, since interlopers could of course lurk among them too.

We explore the possible improvements due to the use of spectroscopic information in a different way: rather than using the iteratively derived mean proper motion of spectroscopic member stars to modify the prior, we introduce another term in the likelihood, in which the l.o.s. velocity distribution is modelled as the sum of two 1D Gaussians, one for the dwarf galaxy and one for the MW. Since not all the stars with astrometric information do have a l.o.s. velocity measurement, we assign a l.o.s. velocity equal to 0 km s−1 and a l.o.s. velocity uncertainty of 10 000 km s−1 to the stars in the astrometric sample that do not have a spectroscopic match; these arbitrarily large velocity uncertainties have the effect of giving these stars no weight in the estimate, but do allow us to treat the spectroscopic information as a further likelihood term. The value of the peak l.o.s. velocity and l.o.s. velocity dispersion for the dwarf galaxies are fixed to the values in Table B.1, fixing the velocity dispersion to 5 km s−1 when only an upper limit is available. At the same time we solve for the peak l.o.s. velocity and l.o.s. velocity dispersion of the MW component (we have tried also keeping them fixed to 0 km s−1 and 200 km s−1, respectively, and the results do not vary). Table B.3 lists the results and Fig. C.2 shows the comparison of our baseline case with the determinations using a spectroscopic prior for the category for which the largest differences could in principle be expected, i.e. the ultra faint dwarfs. The only two systems with significant differences are Pisces II and Tucana V, where the size of the error-bars reduces drastically. This is due to two stars with high probability of membership found for Pisces II and a PDF with wings of much lower level for Tucana V in the run with spectroscopic information with respect to that without. For the great majority of the other cases, the differences are minor both in terms of systemic motions and associated uncertainties. In Appendix A, we comment on those cases where the difference between the systemic PMs with and without the spectroscopic information is larger than 0.5σ.

As MV20a concluded, it is re-assuring that spectroscopic follow-up is not a necessary condition for systemic PM determinations. Overall, we see a lower degree of improvement than that found by MV20a on Gaia DR2 data. Likely, the main reason is that Gaia eDR3 data, in particular the PMs, have become more precise, which makes it easier for the algorithm to find galaxies even if they have only a few stars above the Gaia magnitude limit. This might make it potentially easier to find galaxies using only Gaia data in the future data releases, but perhaps also already in Gaia eDR3 (see also Darragh-Ford et al. 2021).

RR Lyrae variable stars. As an additional check of the robustness of the results, we compared the systemic PMs with the individual measurements for RR Lyrae variable stars found at projected distances within 5× half-light radii and with magnitudes approximately compatible with the horizontal branch of each system. As catalogue of RR Lyrae stars, we use the union of the Gaia DR2 Specific Objects Study (SOS) catalogue gaiadr2.vari_rrlyrae (Holl et al. 2018; Gaia Collaboration 2019; Clementini et al. 2019), the stars classified as RR Lyrae of ab, c, d type in the general variability catalogues gaiadr2.vari_classifier_result, and the PS1 RR Lyrae of ab or cd type by Sesar et al. (2017)8. The comparison is very good. The only system in which some outliers in the RR Lyrae PMs are found is Hydrus I, but this is not a cause for concern, because a closest examination shows the presence of RR Lyrae to be compatible with belonging to the SMC-LMC system in the background and we made no attempt of statistically account for contamination in the RR Lyrae variables data set.

5. Systematic errors and distance errors

It is known that Gaia PM measurements are affected by systematic errors, which can be thought of as a component on small angular scales, ≲1 deg, and a component on large scales, with a scale-length of ∼16 deg for Gaia eDR3 (see Lindegren et al. 2021b). Given the spatial scales typically involved in our analysis, the effect of the large-scale component should be to act as a zero-point in the observed systemic motions. On the other hand, the small-scale component will average out for some of the systems with the largest angular size, but not for a significant number of them. Therefore we follow two routes: we treat the bias on small-scales as an additional source of noise, while we determine the zero-point from the large-scale component for each galaxy separately from QSOs.

For the small-scale error, we use the determination by Vasiliev & Baumgardt (2021)9, rather than that by Lindegren et al. (2021b), since the former was derived on globular cluster stars, in which there are more close neighbours on smaller scales than among quasars, used by the latter work. As typical scale of our systems, we use the “circularised” half-light radius, θhalf (for M33 we use the radius containing half of the member stars). This leads to errors between 13 and 23 μas yr−1 for both dimensions, σvas(θhalf).

For the other component, we calculate the weighted average of the PMs of QSOs (from the table agn_cross_id provided within Gaia eDR3) within 7 deg around each galaxy. We found this scale to be a good choice in terms of overall error and scatter among the galaxies, among the explored scales of 3–10 deg with 1 deg steps. We concentrate on QSOs with 5p solutions, since they are known to have more precise measurements (Lindegren et al. 2021b; Fabricius et al. 2021), and retain those with G < 19, to reduce statistical errors, and ruwe < 1.4, ipd_gof_harmonic_amplitude < 0.2 and ipd_frac_multi_peak ≤ 2 for ensuring good astrometric measurements. The zero-point, to be subtracted to the systemic PM, is calculated as a weighted mean (and its error as error in the weighted mean) after two iterations. This yields a minimum of 50 QSO, with the median being ∼900.

Since the Vasiliev & Baumgardt (2021) formula includes the effect from the large-scale component, we subtract from σvas(θhalf) the corresponding value from the same formula on the scales of the determination from QSO and account for the error on the weighted mean of QSO PMs. Both the zero-points and additional error per PM component are given in Table B.4 and are used for the orbit integration analysis in Sect. 7 (the PMs and errors in Tables B.2, B.3 do not include these additional errors and corrections).

In general, we find that the dominant10 source of error is the random one for all the galaxies, apart from Fornax, Sculptor, Ursa Minor, Draco, Carina, NGC 6822, Leo I, Sextans, Antlia II, Bootes I, Hydrus I, Reticulum II, Carina II, IC 1613, Crater II, M33. Since Lindegren et al. (2021b) find that the systematic PM error decreases with a similar factor with time as the random error, this is not expected to change.

In the great majority of applications, systemic PMs need to be converted into a velocity, and uncertainties in the distance modulus will contribute to the uncertainties in the physical transverse velocity. Therefore, it is interesting to known in which cases that is the largest source of error (see also Table B.4); these are: Bootes I, Bootes II, Bootes III, Carina, Carina II, Carina III, Cetus II, Coma Berenices, Delve 1, Fornax, Grus II, Horologium I, Hydrus I, Phoenix II, Pictor II, Reticulum II, Sagittarius II, Segue 1, Segue 2, Tucana II, Tucana III, Tucana IV, Tucana V, Ursa Major I, Ursa Major II, Willman 1. It turns out that the majority of galaxies within 100 kpc have their uncertainty in transverse velocity dominated by distance errors, as compared to that due to the statistical and systematic errors in the systemic PM. We note that we are including an additional 0.1 mag error in the distance modulus of galaxies whose published uncertainties are lower than that value; this in order to mimic the typical mismatch between values of distance modulus found from different techniques. If we drop this additional factor, the situation changes only for Fornax and Bootes II, which become dominated by the PM component. Sticking to the published uncertainties, there are systems where the distance factor can be as large as 3 to 7 times the systemic PM one (with the former ranging from 10 to 40 km s−1, while the latter is within 3–12 km s−1), as Carina III, Cetus II, Hydrus I, Reticulum II, Sagittarius II, Segue 1, Tucana II, Ursa Major II. These are all very faint systems, and it will be hard to improve on their distance estimates, but it might be worth the trouble.

6. Comparison with the literature

In this section, we compare our systemic PMs determinations with those in the literature. These were obtained with Gaia DR2 data (Gaia Collaboration 2018b; Simon 2018; Simon et al. 2020; Fritz et al. 2018a, 2019; Carlin & Sand 2018; Massari & Helmi 2018; Kallivayalil et al. 2018; Pace & Li 2019; Pace et al. 2020; Fu et al. 2019; McConnachie & Venn 2020a; Longeard et al. 2018, 2020; Torrealba et al. 2019; Mau et al. 2020; Cerny et al. 2021; Chakrabarti et al. 2019; Gregory et al. 2020; Mutlu-Pakdil et al. 2019), eDR3 (McConnachie & Venn 2020b; Vasiliev & Baumgardt 2021; Jenkins et al. 2021; Martínez-García et al. 2021; Li et al. 2021a; Ji et al. 2021), with HST (Piatek et al. 2003, 2005, 2006, 2007, 2016; Pryor et al. 2015; Sohn et al. 2013, 2017) and VLBI (Brunthaler et al. 2005). For the HST measurements, we ignore older determinations, when newer ones from the same group are available. We compare all measurements in Figs. 5, C.3C.6.

thumbnail Fig. 5.

Comparison of our systemic PM measurements (labelled “This work”, shown as a black star) with literature measurements. The Gaia measurements are from Gaia Collaboration (2018b), Simon (2018), Simon et al. (2020), Fritz et al. (2018a, 2019), Carlin & Sand (2018), Massari & Helmi (2018), Kallivayalil et al. (2018), Pace & Li (2019), Pace et al. (2020), Fu et al. (2019), McConnachie & Venn (2020a,b), Longeard et al. (2018, 2020), Torrealba et al. (2019), Mau et al. (2020), Cerny et al. (2021), Chakrabarti et al. (2019), Gregory et al. (2020), Mutlu-Pakdil et al. (2019), Jenkins et al. (2021), Vasiliev & Baumgardt (2021), Martínez-García et al. (2021), Li et al. (2021a), Ji et al. (2021). Triangles indicate works that used only stars with additional information on membership, usually from spectroscopy, but also RR Lyrae variable stars in some cases, as Simon (2018). HST measurements are from Piatek et al. (2003, 2005, 2006, 2007), Pryor et al. (2015), Piatek et al. (2016), Sohn et al. (2013, 2017). Among them, those indicated by diamonds (pentagons) use background galaxies (QSOs) as references. The smaller error bars include only the random Gaia error, the larger one also the systematic error when they are given as separated in the source. We do not display the correlation between the PMs components here. The ellipses (when in the field of view of the plots) indicate the σ = 100 km s−1 prior (green) of McConnachie & Venn (2020a,b), and the escape velocity (grey) in the 1.6 × 1012M Milky Way of Fritz et al. (2018a) centred on the expected reflex motion for the system. For galaxies at a distance > 500 kpc, we only plot an ellipse (purple) corresponding to 200 km s−1.

The agreement with McConnachie & Venn (2020b, hereafter, MV20b) is in general very good, if not excellent, with the values being within 1- or 2-σ at most, in each component (here we consider the largest of the two error-bars, since the methodology is very similar and the systematics should be directly comparable). There are however a handful of cases for which the μδ component differs by more 2-σ: Antlia II (3.3-σ), Reticulum III (2.5-σ), Carina III (2.3-σ), Segue 1 (2.5-σ) and in principle also for some of the brightest galaxies, as Sextans, when only the statistical error is used. Inspection of the spatial, CM and PM location of the probable members from our code does not reveal hints of specific issues with these galaxies; the differences are likely to be the results of the methodology applied, which for some systems turns out to have a more noticeable effect.

We note that there are cases in which the statistical MV20b uncertainties are much smaller than those we determined, that is in each component separately they are between 10–30% of ours for Bootes IV, Leo T, Cetus III, and as small as 2–3% for Indus I, Virgo I, Pegasus III (there are also cases in which our uncertainties are smaller, but with a reduction of at most 60%). Inspection of the output of our code corroborates the expectation of the large errors we find in these cases, given the small number of probable members with P > 0.5 and their in general faint magnitudes; for example no stars with a probability of membership larger than 0.5 is found for Virgo I, Pegasus III, and only 2 for Cetus III (see Appendix A for more details). MV20b find only one likely member in Cetus III, Pegasus III and Virgo I. Clearly the results for these systems need to be taken with a pinch of salt. The inclusion or not of spectroscopy in the determination does not seem to be the culprit of this difference, since in most cases we do not notice any significant reduction in the random error when we include the l.o.s. velocity likelihood term.

On the other hand, we suspect that the main reason for the difference might be the prior in systemic PM corresponding to a 100 km s−1 velocity dispersion used by MV20b. This can be easily seen for the three most distant galaxies of their sample (Phoenix, Eridanus II and Leo T), where they give also the motions without this prior. For the others, if we model the ratio of ours and MV20b errors as the quadratic sum of one and the ratio of our statistical error over the 100 km s−1 dispersion, then in median our error would be only 3% larger, with excursion in both directions our error is between 53% and 149% of their scaled error, when we exclude Indus I (324%) and Virgo I (201%), for which we do not obtain a reliable measurement. This prior seems to be also mainly responsible for some PM differences, in cases where the absolute value of our PM is larger than in MV20b, such as for Eridanus III and Horologium II.

Unlike MV20b, we do find a motion for Indus II, with 6 stars with P > 0.5 (1 with P > 0.95). Nonetheless, the distribution of the probable members on the various planes does not transmit confidence in the result.

Typically our results compare well with the other works based on Gaia eDR3. Li et al. (2021a) consider only stars that have also spectroscopic observations, removing those that do not have consistent astrometric properties within 5-σ. Their errors (which includes systematics) are nearly always larger than our total errors (in median, about 1.18×, clearly larger for many of the faintest systems). Due to their larger errors, the system with the most noticeable deviation is Bootes I (2.3-σ in R.A. when we do not apply our correction for systematics).

Martínez-García et al. (2021) focus on 14 galaxies and also use a probabilistic approach, with quality cuts likely more conservative than those adopted here. Our statistical errors are in general smaller than their errors, typically by a factor 0.7; the largest differences are found for the fainter and more diffuse galaxies, probably indicating that their method needs more stars to perform well. Their systematic errors are lower, since they also model small scales effects. They also apply a QSO-based zero-point correction on their systemic PMs. Our zero-point correction and that of Martínez-García et al. (2021) differ by 0.009 mas yr−1 on average, with the standard deviation in the (μα, *, μδ, *) zero-points for the galaxies in common being (0.012, 0.012) [mas yr−1] for Martínez-García et al. (2021) and (0.013, 0.008) [mas yr−1] in our work. When comparing our motions before QSO correction, they agree usually within 2.0-σ, the exception is Reticulum II which deviates by 2.9-σ in R.A. (and 2.0 in Dec) from ours and is also different from the other eDR3 determinations.

Finally, Jenkins et al. (2021) focus on Leo IV, Leo V and Boötes I and use only stars with spectroscopy, hence it is not surprising that their uncertainties on the systemic PMs are larger than ours. For Leo IV and Leo V the motions agree within 1-σ and for Boötes I within 2-σ in both dimensions.

A comparison with Gaia DR2 measurements tests mainly the performance of those, due to their larger astrometric errors, but that is still useful to perform. When comparing with Fritz et al. (2018a) for 38 systems in common, the standard deviation of the distribution of differences in systemic PM normalised by the uncertainty11 is 0.96 and 1.05 in the R.A. and Dec component, respectively, thus within expectations. At a closer look, it appears that the standard deviation for most of the sample would be smaller than ∼1 and it is inflated by a few cases with larger deviations (Segue 2, 3.8; Triangulum II, 2.5 and Ursa Major I, 2.8 from the values in this work). The accumulation at small deviation is probably understandable, since we might not be taking the correlation between the data sets well into account. We find good agreement with the preferred values by Fritz et al. (2019), but their sample of 4 UFDs is too small to tackle whether the small deviations found could be the result of chance.

Regarding other estimates, we note that the sub-sample of those by Kallivayalil et al. (2018) for which spectroscopy was not used do not match our motion well. That is not necessarily surprising, since in those cases Kallivayalil et al. (2018) values were based on the assumption that the galaxies were former satellites of the LMC, which is not the case for most, such as Columba I. It is more surprising for Phoenix II which likely is a LMC satellite (Fritz et al. 2019, but see also Sect. 7.2.4). Probably the reason in this case is that the LMC model used in Kallivayalil et al. (2018) does not match reality sufficiently well, as it is likely not massive enough.

The agreement is slightly worse with Massari & Helmi (2018) with a standard deviation between ours and their results of 1.35 in R.A. and 1.06 in Dec. This is mainly driven by Sagittarius II, which deviates by 2.9- and 2.0-σ from our value, despite the large errors; nonetheless, also other of Massari & Helmi (2018) determinations show deviations from other DR2 measurements.

As for the galaxies found beyond the MW virial radius, we can compare with the Gaia DR2 measurement of McConnachie et al. (2021) for NGC 6822, WLM, Leo A and IC 1613. Our statistical errors are between 27% and 47% of theirs, a clear improvement. The standard deviation between the values is 0.67 and 1.20 in R.A. and Dec respectively in the expected range. For M 33 there exist VLBI OH maser and HST measurements by Brunthaler et al. (2005) and van der Marel et al. (2019), with which our determination agrees reasonably well.

It is interesting to compare Gaia measurements to high precision PMs obtained in a completely independent way with other telescopes, such as HST and VLBI. The references used by HST are either QSOs or background galaxies. The accuracy of QSOs based measurements can suffer because of the small number of reference sources, since e.g. systematic errors cannot be well derived from the data. When compared with our errors, it seems that the uncertainties quoted in the literature are underestimated, as four out of five measurements have a deviation of at least 1.8-σ (up to 3.5-σ) in one dimension12. In the cases with galaxies used as reference sources, 3 out of 4 works obtain deviations smaller than 1.6-σ in both dimensions. The only exception is Sculptor (2.5-σ). Our QSO-based shift improves the comparison for Sculptor slightly, although less than the correction adopted by Martínez-García et al. (2021); nonetheless, also with this shift a difference remains with respect to the HST determination. Since Gaia DR2 and EDR3 estimates agree with each other it seems unlikely that Gaia systematics are the only reason for it. Nevertheless, overall HST PMs based on galaxies and Gaia agree well, increasing the confidence in the precision and accuracy of both, see also the example of M 31 (van der Marel et al. 2012b; Salomon et al. 2021).

7. Orbit integration

7.1. Method

Using the PMs derived above with the distance modulus and the l.o.s. velocities from the literature listed in Table B.1, we integrated the orbits of each galaxy for which spectroscopic measurements are available in three MW potentials: in two of them, the MW is treated as an isolated system (hereafter isolated potentials), and we explore a mass for the MW DM halo that brackets the range of likely MW masses (Boylan-Kolchin et al. 2013; Gibbons et al. 2014; Fritz et al. 2020; Wang et al. 2020); in the other potential (hereafter perturbed potential) a 8.8 × 1011M MW is perturbed by a 1.5 × 1011M LMC, as published by Vasiliev et al. (2021). The reason for including the latter case is that, although the mass of the LMC system is still subject to debate (i.e. see Wang et al. 2019), recent observations, such as the rotational velocity of the LMC (van der Marel & Kallivayalil 2014), some perturbation of the MW’s disc (Laporte et al. 2018), the dynamic of the ATLAS, Tucana III, Orphan and Sagittarius streams (Erkal et al. 2018, 2019; Vasiliev et al. 2021; Li et al. 2021b) and the dynamics of distant halo stars (Erkal & Belokurov 2020), are consistent with the idea of a massive LMC, i.e. with a mass of 1 − 2.5 × 1011M, perturbing significantly the gravitational potential of the MW (see Garavito-Camargo et al. 2019, 2021; Cunningham et al. 2020). Therefore, we wish to investigate the impact of a massive LMC on the past orbits of the dwarf galaxies of the MW and on the account of its possible satellites.

The first isolated potential (“Light MW”) is that published by Vasiliev et al. (2021), composed of a spherical bulge of 1.2 × 1010M, an exponential disc of 5 × 1010M and of a triaxial DM halo, with a total mass M(< Rvir) = 8.8 × 1011M within the virial radius of 251 kpc. The second isolated potential (“Heavy MW”) is similar to the massive potential used by Fritz et al. (2018a) and consists of a MWPotential14 (Bovy 2015) with a more massive DM halo so that the system has a total mass of M(< rvir) = 1.6 × 1012M within the virial radius rvir = 307 kpc. Orbits are integrated 6 Gyr backward and forward, with a time step of 3 Myr, through the AGAMA package (Vasiliev 2018). The reason to integrate forward is that some of the most distant galaxies have not yet passed by their pericentre, and therefore we have to integrate their orbit in the future to measure their orbital parameters.

In the perturbed potential, published by Vasiliev et al. (2021), the MW experiences the passage of a LMC with mass MLMC = 1.5 × 1011 M, which enters the MW DM halo virial radius about 1.6 Gyr ago. In this model, the initial MW potential is as the isolated “Light MW” mentioned above, and the initial LMC is represented by a NFW halo with a scale radius of rs = 10.84 kpc and truncated at rtrunc = 108.4 kpc. In this case we integrate the orbits only backward, considering that before 5 Gyr ago the model of Vasiliev et al. (2021) is stationary.

In order to take into account the uncertainties on the different measurements, the systematic errors in the PMs, and the correlations between the PMs along the Right Ascension and the Declination, we integrated the orbits from 100 Monte-Carlo realisations of the current position and velocity of the galaxies. For the galaxies having distance modulus uncertainties lower than 0.1 mag in Table B.1, we added in quadrature 0.1 mag, corresponding to typical systematic uncertainties between different methods of distances determinations. Additionally, we did not integrate the galaxies with heliocentric distances larger than 500 kpc since they are clearly not members of the MW system, and will require taking into account the LG in its globality (see McConnachie et al. 2021).

The current (right-handed) Cartesian Galactoncentric coordinates were calculated with ASTROPY (Astropy Collaboration 2013, 2018). The solar radius is assumed to be R = 8.129 kpc (GRAVITY Collaboration 2018), the circular velocity is of Vcirc(R) = 229.0 km s−1 (Eilers et al. 2019), and the Solar peculiar motion (U, V, W) = (11.1, 12.24, 7.25) [km s−1] (Schönrich et al. 2010).

The orbital parameters, including their uncertainties, for the two isolated MW potentials are listed in Table B.5. The quantities listed in this table are the Galactocentric distance of the pericentre (peri), of the apocentre (apo), the eccentricity (ecc), the orbit period (T), the time since the last pericentre (Tlast, peri), and the fraction of galaxies reaching their apocentre in the last or next 6 Gyr ℱapo. For each of these quantities (except ℱapo), the listed values correspond to the median of that parameter found for the 100 realisation of the orbits, and the uncertainties have been calculated from the 16th and 84th quantiles. When the majority of the orbits do not reach the apocentre within the time range of the integration, the uncertainties on the apocentre, eccentricity and period cannot be computed. Therefore, for those galaxies, we rather give the value of the 16th quantile. Table B.6 lists the most recent pericentric and apocentric distances for the perturbed potential.

It is important to note here that the values given in this table are not free of biases. Indeed, the observed tangential velocity is known to be a biased estimator of the real tangential velocity of a given system (Fritz et al. 2018a; van der Marel & Guhathakurta 2008), where the former is inflated by the measurement uncertainties. Therefore, this bias also reverberates on the different derived parameters, such as the apocentre or the pericentre. The bias on the tangential velocity can be understood with the following idealised experiment. Let us assume that a galaxy is moving radially towards us with a real tangential velocity of exactly 0 km s−1. In this case, the true pericentre is at 0 kpc. In reality, the uncertainties on the systemic PM can only increase the observed tangential motion, this last one being positive by definition, increasing de facto the observed pericentre of the galaxy.

In order to identify the galaxies least impacted by this bias, we follow the guidelines in the appendix of Fritz et al. (2018a), where this effect was estimated with backward Monte-Carlo simulations. According to that study, assuming a typical velocity of ∼100 km s−1 for galaxies in the MW system of satellites, one can expect the observed 3D or the tangential velocity to be < 1.5 the true one for measurements uncertainties ≲70 km s−1 on these quantities. For the rest of the analysis, we therefore mainly focus on systems with uncertainties on the total Galactocentric velocity < 70 km s−1 (those with larger errors have their name in italics in Table B.5).

7.2. Results and discussion

7.2.1. Effect of a massive LMC on the orbital properties

Patel et al. (2020) examined the changes in the orbital properties of 13 UFDs and 5 classical dSphs introduced by the inclusion of the LMC (and SMC), for a range of LMC and MW masses, using Gaia DR2 PMs. The authors found that the orbits of both classical dSphs and UFDs were noticeably affected by the inclusion of the Magellanic Clouds, in particular the LMC for the classical dSphs; the inclusion of the SMC did not have an impact on the number of galaxies potentially classified as satellites of the LMC, but on the longevity of this association.

Although, as we see in Sect. 7.2.4, the large majority of the dwarf galaxies found around the MW that we examine were not bound to the LMC, also in this work we see that the presence of a massive LMC significantly perturbs the MW potential, modifying the orbits of most of the dwarfs. Figure 6 gives a view on how the pericentres and apocentres are impacted within the 68% confidence interval. In Figs. D.1, D.2, D.3 we compare the orbital path of the dwarf galaxies found within 500 kpc from the MW during the last 3 Gyr in the presence of the LMC to the case of the isolated Light MW, which is equal to the former apart from the inclusion of the LMC and the corresponding response of the MW. This is one realisation coming from the integration of the observed systemic motions and l.o.s. velocities. For obvious reasons, the difference between the isolated and perturbed orbits become more important with lookback time since we used the same current dynamical parameters as a starting point. Thus by definition, the orbital shifting is of 0 kpc at t = 0 Gyr.

thumbnail Fig. 6.

Apocentric (top) and pericentric (bottom) distance for the sample of likely MW satellite galaxies (excluding the high likely long-term LMC satellites of the LMC in Table 2) with error in 3D velocity less than 70 km s−1. The filled and open squares show the results for the “Light” and “Heavy” isolated MW potentials and the light blue asterisks for the perturbed potential. The arrows indicate those cases where either the median or the 84th percentiles were undefined. When not even the 16th percentile was defined, the symbols are placed at an apocentric distance = 900 kpc. We only consider cases where the galaxy has already experienced a pericentric passage. The horizontal lines that have a label indicate the virial radius of the DM halo in the corresponding gravitational potential; the line at a distance of 30 kpc is meant to indicate a region potentially dangerous in terms of tidal effects (see main text).

Interestingly, we can see that the orbits of the majority of the galaxies are affected by the presence of the LMC, regardless of their distance to the MW or to the LMC. The influence of the inclusion of a massive LMC can manifest itself in several ways, e.g. as a change in the pericentric and/or apocentric distance, which can become larger or smaller, as well as the timing of the passages, even for systems that are very distant from the LMC and away from its orbital plane.

There are systems that are barely affected or affected in a minor way, e.g. Segue 1, Hydra II, Leo I as there are systems that are very strongly impacted, as e.g. Draco II, Sextans, Sculptor, but even NGC 6822. For example, Sculptor would have been infalling recently onto the MW in the perturbed potential rather than being compatible with having been a long term satellite. This is mainly either due to the proximity of the LMC or to the MW reflex motion to the gravitational wake caused by the LMC infall (also called collective response) (Garavito-Camargo et al. 2021; Petersen & Peñarrubia 2020, 2021; Vasiliev et al. 2021).

The perturbed potential explored here assumes a specific mass for the LMC and, of course, for the MW, but as discussed above, neither values are set in stone. That said, it is clear that if the LMC is indeed massive, the impact on the orbital properties of objects within and around the halo of the MW, and the conclusions one draw from them, can be significant. This is of course true also for individual stars in the MW (outer) stellar halo, a vast number of which will soon have 6D phase-space information thanks to large spectroscopic surveys (e.g. WHT/WEAVE, VISTA/4MOST, PSF etc.).

7.2.2. Too-big-to-fail problem and central DM halo densities

The determination of orbital parameters of MW satellite galaxies has also been used in the literature to examine aspects of the Too-big-to-fail (TBTF) problem and make considerations on the inner DM halo densities inferred. Recently, in their analysis of PHAT-II simulations, Robles & Bullock (2021) found that at a given present-day maximum circular velocity, sub-haloes with small pericentres are more concentrated and have experienced a higher mass loss than those with a larger pericentre. Using Gaia DR2 pericentric distances for the MW classical dSphs, they show that the allowed ranges for the maximum circular and peak velocities are both tightened than without the Gaia DR2 information, with both quantities becoming smaller and going in the direction of exacerbating the TBTF problem.

In comparison with the Gaia DR2 pericentric distances in Fritz et al. (2018a), used by Robles & Bullock (2021), those we derived here for the similar isolated potentials are tighter and towards the upper range of what the DR2 data were suggesting for Draco and Ursa Minor (Draco: “Light MW” eDR3 48 − 56 kpc versus 31–58 kpc in DR2 and “Heavy MW” eDR3 34 − 42 kpc versus 21–40 kpc in DR2), which would go in the direction of slightly alleviating the issue. Interestingly, in the perturbed potential, Draco would have a 1-σ range of pericentric distances of 81–122 kpc, while Ursa Minor would have 65–79 kpc, which would push upwards the estimates of both their maximum and peak circular velocities.

Fornax is another interesting object, as dynamical modelling of the kinematic properties of its stellar component (Walker & Peñarrubia 2011; Amorisco et al. 2013; Pascale et al. 2018) as well as considerations and modelling of its system of globular clusters (e.g. Leung et al. 2020) suggest its DM halo to have a density core; this has sometimes been attributed to DM being heated up by stellar feedback (e.g. Read et al. 2019) and more recently to the possibility of significant mass loss due to tides (Genina et al. 2020). The range of pericentric distances determined here (see Table B.5) is rather similar to that of the Gaia DR2 determinations in Fritz et al. (2018a) for the isolated potentials, probably because in the case of Fornax the uncertainty in the distance measurement plays also a role (Borukhovetskaya et al. 2022); also the values themselves are very similar. The 1-σ range for pericentre in the perturbed potential (66–124 kpc) is in agreement with those given by the isolated potentials. These include orbital trajectories that can significantly reduce the peak circular velocity of the DM halo due to tidal mass loss and reconcile it with the kinematic properties measured at the half-light radius (Genina et al. 2020; Borukhovetskaya et al. 2022).

7.2.3. Relation to the Milky Way

Figure 6 shows the apocentric (top) and pericentric (bottom) distances obtained in the three gravitational potentials for the systems with total Galactocentric velocity error < 70 km s−1. Since here we wish to explore the relation to the MW, we exclude the systems that we find to be likely LMC satellites (which will be discussed in detail see below, in Sect. 7.2.4).

Uncertainties in the MW gravitational potential do cause significant variations in the orbital parameters of some of the galaxies in the sample. Nonetheless, there are some considerations that we can make.

The system of Milky Way satellites. From the top panel, we can see that the 16th quantile of the distribution of apocentres never reaches within the MW virial radius for Leo I and NGC 6822 within the time range of the orbit integration. On the other hand, both galaxies do seem to have experienced one passage around the MW in the past; in particular when the perturbed and the “Heavy MW” potentials are considered for NGC 6822, this galaxy could have reached within ∼100 kpc within the 68% confidence interval, which supports the conclusions of Teyssier et al. (2012) based on a comparison of the Galactocentric distance and radial velocity of LG field galaxies with those of haloes in the Via Lactea II simulations.

If we perform no cut in the total Galactocentric velocity error, there are other galaxies which do not have an apocentre within the MW virial radius, i.e. Eridanus II, Leo T, Phoenix, Pisces II. However, the error in the total velocity is too large to draw meaningful conclusions without correcting for biases. Thus we cannot test yet the claim of Teyssier et al. (2012) that Leo T and Phoenix are backsplash galaxies on the basis of the orbital trajectories13. McConnachie et al. (2021) use systemic PMs to understand which ones of the isolated galaxies studied in that work might have reached within 300 kpc from the MW (or M 31) but our uncertainties on Leo T and Phoenix systemic motions are still too large to exclude this hypothesis in this way either. Nonetheless, the presence of young stars and H I gas in faint systems as Leo T and Phoenix supports the hypothesis that they have never approached the MW before. Also, according to McConnachie et al. (2021), the possibility that Phoenix might have entered the MW virial radius is tiny and possible only if the MW mass is at the high end of the probable range.

Fast-moving galaxies. Fast-moving galaxies are especially useful for placing constraints on the MW mass (Boylan-Kolchin et al. 2013). A clear example is that of Leo I, whose large receding radial velocity and status as bound or unbound to the MW has caused several headaches for determinations of the MW mass since a long time (e.g. Wilkinson & Evans 1999, and references therein). In our determination, Leo I has a slightly smaller bulk PM value and error compared to the HST one (Sohn et al. 2013) used by Boylan-Kolchin et al. (2013). This should cause a likely decrease in the MW mass but minor, since its Leo I total velocity is dominated by the l.o.s. component. Also the impact of the LMC does not change the main conclusions on its orbital history. As for other fast-moving galaxies, most of those for which we can measure reliable PMs are likely to have come in with the LMC (see Sect. 7.2.4), as expected due its high velocity orbit, and are not of interest here.

If we concentrate on objects not classified as likely LMC satellites and that are receding, to exclude those recently infalling: in the “perturbed” potential, Bootes II would fall under this classification and has a large velocity compared to the escape velocity at its distance, as in Fritz et al. (2018a); CanesVenatici I would do so in the “Light MW” but the inclusion of the LMC lowers the chances to have the apocentre beyond the MW virial radius for a 0.9 × 1012M massive MW and makes the values get close to those of the “Heavy MW”. The combined study of CanesVenatici I, Draco II and Hercules might turn out to be useful for considerations on the MW gravitational potential, because for the latter two objects, the likelihood of apocentres well outside of the MW virial radius has the opposite behaviour as for Canes Venatici I, i.e. it increases with the inclusion of the effect of the LMC infall.

Tidal disturbances. Both Bootes III and Tucana III are known to be embedded in stellar streams (Drlica-Wagner et al. 2015; Carlin & Sand 2018). Our analysis fully confirms the expectation that these features are the results of tidal disruption, since these two systems have pericentres in all the three potentials that bring them very close to the central regions of the MW, likely within 10 kpc or less; this is fully in line with the Gaia DR2-based results (see e.g. Fritz et al. 2018a; Simon 2018; Carlin & Sand 2018) and the eDR3-ones by Li et al. (2021a) for Tucana III.

The stellar component of both Antlia II and Crater II has peculiar properties, with an extremely low surface brightness, large half-light radius and low l.o.s. velocity dispersion when compared to other MW satellites of similar stellar mass (Torrealba et al. 2016b, 2019; Caldwell et al. 2017). It has been postulated that also these galaxies have been “sculpted” by tidal disturbances by the MW (Fattahi et al. 2018; Sanders et al. 2018; Torrealba et al. 2019). According to the orbital parameters derived in this work, this hypothesis appears fairly robust for Crater II, confirming the Gaia DR2-based results, while for Antlia II it appears more sound when considering the “perturbed” and “Heavy MW” potentials, than in the “Light MW” one. The pericentric distances obtained for these two models are compatible with that explored by Torrealba et al. (2019) to study whether tidal effects onto a cored DM halo could explain the low surface brightness, large half-light radius and low l.o.s. velocity dispersion of Antlia II.

The spatial distribution of the high probability member stars returned by our method shows an elongation in the outer parts for Carina’s stellar component (Fig. 2), compatible with what seen in previous studies, based on red giant branch stars observed spectroscopically (Muñoz et al. 2006) and deep wide-area photometry (Battaglia et al. 2012a; McMonigal et al. 2014). Even if there are some intervening LMC stars in the Carina’s line-of-sight, it is unlikely the feature is due to that, given that these would be included in our contamination model. Given the orbital parameters that we obtain, it appears very unlikely that this might be the result of a close interaction with the MW, nor with the LMC (see Fig. 10). The second last pericentre in the perturbed potential, about 7 Gyr ago, might have brought Carina as close as 37 kpc at a 1σ level; but even if that would have been sufficient to strip its stellar component, it is highly unlikely that the elongation we see today is due to that, as tidal debris are not expected to be seen anymore after 15–20 crossing times (e.g. Peñarrubia et al. 2009), i.e., between 1 and 2 Gyr in this case.

Within the 68% confidence limit, Segue 1, Segue 2, Triangulum II enter what can be potentially be seen as a dangerous zone, i.e. within 10–30 kpc from the MW centre in all the 3 potentials. We note that the clearly tidally disrupted Sagittarius (not included in this analysis) has had the most recent pericentre at about 16 kpc and the second last at about 25 kpc, (Vasiliev et al. 2021), showing that tidal stripping can be efficient also at those Galactocentric distances. Depending on the potential and/or on the error-bars some galaxies might or might not have suffered strong tidal effects (e.g. CVen I, Hercules, Willman 1, Tucana V and several more).

Especially in the perturbed potential, one can see hints that, excluding the galaxies with clearer tidal effects (streams or a very diffuse stellar component), the smallest galaxies in terms of half-light radius in general have the smallest pericentres, see Fig. 7. Some possible hypotheses are that these systems had a fairly compact stellar structure at birth and have survived tides better than less compact systems, or that this is a different manifestation of the type of features that tidal stripping might imprint on the galaxies it acts upon. A deeper investigation is deferred to the future.

thumbnail Fig. 7.

Pericentric distance compared to the projected semi-major axis half light radius for the sample of likely MW satellite galaxies (excluding the highly likely long-term LMC satellites of the LMC in Table 2) with error in 3D velocity less than 70 km s−1. The filled and open squares show the results for the “Light” and “Heavy” isolated MW potentials and the asterisks for perturbed potential. The arrows indicate those cases where either the median or the 84th percentiles were undefined. We only consider cases where the galaxy has already experienced a pericentric passage.

We have investigated whether the ellipticity of the stellar component could be taken as a sign of strong tidal disturbances. We find no clear trend between ellipticity and pericentric distances, neither in the sense of small pericentres having preferentially large ellipticities nor being preferentially round.

Connection to star formation history (SFH). The dwarf galaxies that inhabit the LG have long been known to exhibit a variety of SFHs (e.g. Mateo et al. 1998; Grebel 1998; Skillman 2005), where this holds also when focussing only on those surrounding the MW. It is natural to ask whether a connection exists between the timing of strong enhancements of the star formation activity, or on the contrary, its quenching, and important times in the orbital history of these galaxies, e.g. infall into the MW halo or pericentric passages.

The star formation histories of the vast majority of the dwarf galaxies that surround the MW halted 8–10 Gyr ago (e.g. Tolstoy et al. 2009; Brown et al. 2014; Gallart et al. 2015). At that time, in a hierarchical formation framework, the DM halo of the MW was still growing rapidly; e.g. according to the formula in Wechsler et al. (2002), around 8 Gyr ago, it would have assembled about half of its mass, while about 3 Gyr ago, already 80% of it would have been in place (this excludes the infall of LMC-like systems, which are rare in the ΛCDM cosmogony). As it can be seen e.g. in Armstrong et al. (2021), the trajectories of MW satellites in a time evolving MW potential start deviating from those in a static potential around 3–4 Gyr ago, with the differences becoming more and more noticeable as a function of look-back time, as expected (see Fig. 4 in their article). Even though, the effect appears to be minor with respect to the mass and mass distribution of the MW, it is an additional source of uncertainty. The time-variation of the potential is even stronger if one takes into account that around 8–10 Gyr ago, the MW accreated Gaia-Enceladus (e.g. Belokurov et al. 2018; Helmi et al. 2018) and potentially there have been other subsequent events (e.g. Myeong et al. 2019; Kruijssen et al. 2019, Sequoia and Kraken, respectively).

Therefore, since the gravitational potentials considered here do not include the growth of the MW DM halo as a function of time, we concentrate on those systems that have experienced star formation activity in the past few Gyr and might have been linked to the MW: Leo I, Fornax, Carina, NGC 6822. We refer the reader to works such as those by Fillingham et al. (2019) and Miyoshi & Chiba (2020) for an analysis of the connection between SFH and Gaia DR2-based orbital trajectories of MW satellites via a comparison with simulations in the former and an analytical treatment of the growth of the MW halo in the latter. Even though both Phoenix and Leo T host young stars, we exclude them since they are currently found beyond the MW virial radius and so far there is no evidence that they might have gone through a pericentric passage. As for Eridanus II, recent SFH determinations seem to exclude the presence of young and intermediate-age stars (Simon et al. 2021; Gallart et al. 2021).

The most detailed SFHs for Leo I, Fornax and Carina were derived in Ruiz-Lara et al. (2021), Rusakov et al. (2021) and de Boer et al. (2014), respectively. The star formation activity of Leo I saw the last episode of enhancement about ∼1 Gyr ago, after which it started decreasing till coming recently to a halt. The authors note that the timing is similar to that of the pericentric passage from HST PM measurements (Sohn et al. 2013) and Gaia DR2 ones (Fritz et al. 2018a; Gaia Collaboration 2018b), possibly indicating that the decrease and then stop of SFH was due to ram-pressure stripping of the gaseous component. Our Gaia eDR3 based analysis confirms the timing of the last (and only) pericentric passage for the 3 potentials explored (see Table B.5 and Fig. D.2). Compared to Fornax and Carina, Leo I is highly likely to have come much closer to the MW centre.

Within the time range considered here, Rusakov et al. (2021) detected intermittent episodes of enhanced star formation activity at ∼0.5, 1, 2 Gyr ago in Fornax. In our analysis, the timing of the last pericentre is at a look-back time of Gyr (the negative sign means 2.8 Gyr ago) with an orbital period Gyr in the “Light MW” and of Gyr with an orbital period Gyr in the “Heavy MW”. While it cannot be excluded that the burst occurring about 2 Gyr ago was due to a pericentric passage in either of the two isolated potentials, the orbital period would exclude that the more recent ones are due to the same cause. We examined the orbits determined for the perturbed potential and in this case, the timing of the last pericentre is similar to that of the “Heavy MW” case, with a period in the past exceeding 5 Gyr, leading to the same conclusions.

As for Carina, in the “Light MW” it has not passed pericentre yet, while in the “Heavy MW” the last pericentre occurred at a look-back time of Gyr, with an orbital period of Gyr. The timing of the last pericentre passage in the perturbed potential is similar to that of the “Heavy MW”, with the previous one occurring more than 7 Gyr ago. de Boer et al. (2014) find a long period of enhanced star formation activity, 4 − 6 Gyr ago, with a strong decrease about 1 Gyr ago, followed by an increase of SFR at the youngest ages probed, 0.25 − 0.5 Gyr, till shut down. Also in this case, the decrease in star formation about 1 Gyr ago is potentially compatible with gas stripping.

Overall, correlation can be found between some of the main features in the recent SFH of Leo I, Fornax, and Carina and their orbital histories (although it is important to note that correlation does not necessarily imply causality). However, the same explanation does not seem to be valid for the intermittent bursts of SFH seen in the past 1–2 Gyr in these galaxies, though those events are less strong than the older star forming events.

Fusco et al. (2014) determined the SFH of NGC 6822 in 6 fields at different distances from the centre, out to 4 kpc. Their shapes differ significantly from each other and there is no unambiguous signature of a drop at a common time. On the other hand, the timing of the pericentric passage has too large uncertainties to indicate anything conclusive. In any case, given the fairly large stellar mass of NGC 6822 in comparison to the other dwarfs, and the fact that it is likely to have kept in the outer regions of the MW halo, probably the expected effect of the pericentric passage on the gas content and distribution of this galaxy should be minor and more in the direction of an outside-in ram-pressure stripping and smooth reduction of the size of the region where the bulk of the star formation has occurred, rather than sharp features in the SFH.

7.2.4. LMC satellites

Here we aim to explore which galaxies were likely part of the cortege of satellites that arrived with the LMC. For this, we used the 100 Monte-Carlo realisations of the orbits obtained in the perturbed MW potential to measure the time evolution of their relative distances to the LMC. As we can see from Fig. 8, the scatter increases with time. This is the consequence of the (un)accuracy of the different dynamical parameters measured for the galaxies (especially on the PMs, but also the distance), leading to a broad range of possible orbits for the galaxies with the least accurate measurements.

thumbnail Fig. 8.

Distance from the LMC -as a function of look-back time for 100 Monte-Carlo realisations of the galaxies’s orbit. The horizontal solid and dashed lines, labelled rs and rt, correspond to the scale and truncation radius of the initial LMC potential, of 10.84 kpc and 108.4 kpc, respectively.

Although the majority of the dwarf galaxies stay far from the LMC (> 60 kpc) at every time step, for 23 of them14, at least one of the 100 orbits went close enough (< 60 kpc, corresponding to ∼6rs) to potentially suggest a physical association. For those 23 galaxies, we increased the number of Monte-Carlo realisations of the orbits to 1000, so we can measure the fraction of orbits that have been linked to the LMC in the past. The relative position and velocity with respect to the LMC at the moment of their closest approach is listed in Table 2 and is shown in Fig. 9. In this figure, we can see that the majority of the galaxies that pass close to the LMC are actually not linked to it, since their relative velocity is too high in comparison to the escape velocity of the LMC at any moment. On the other hand, 6 galaxies are clearly related to the LMC, with relative velocity at the moment of their closest approach significantly lower than the escape velocity: Carina II, Carina III, Hydrus I, Reticulum II, Phoenix II and Horologium I15. A closer-look to the time evolution of the distance of these galaxies from the LMC is given in Fig. 10 and will be provided as a movie16.

thumbnail Fig. 9.

Left panel: relative distance and velocity for the galaxies for which at least one of the 100 orbit realisations in the perturbed potential pass close to the LMC (< 60 kpc). The black line represents the escape velocity of the initial a 1.5 × 1011M LMC represented by a NFW profile with a scale radius rs = 10.84 kpc, while the dashed line shows the escape velocity of the current LMC. Each coloured line shows the evolution of the relative distance and velocity of the galaxies with each point marking 100 Myr of evolution. For the galaxies that are not currently at their closest approach, the triangles show their current position on this diagram. The vertical lines at the bottom of the panel show the location of the Jacobi radius at different epochs. Right panel: same as the left panel but assuming that the LMC follows the orbit of a point mass, and does not modify the MW potential. The black lines represent the escape velocity for a LMC with a mass of respectively 1, 5, 10, 15 and 20 × 1010M and a scale radius that respect the observational constraint following the requirement of Vasiliev et al. (2021).

Table 2.

Galaxies reaching within 60 kpc from the LMC centre and their relation to the LMC or to the MW.

Interestingly, none of those galaxies are currently bound to the Magellanic system. Indeed, assuming that the gravitational potential of the LMC inside the tidal radius is unchanged by the tidal stripping of the external DM halo at any time (but see Errani & Navarro 2021) and that the mass of the MW is constant, one can measure the Jacobi radius (rJ) as a function of time t, such as:

(2)

where DLMC is the Galactocentric distance of the LMC, MLMC is the mass of the LMC inside the Jacobi radius and MMW is the mass of the MW inside DLMC. With this formula, the Jacobi radius a t = 0, 0.5, 1.0, 1.5, 2.0, 2.5 Gyr ago is of rJ = 19, 41, 67, 88, 104 and 106 kpc respectively. One can see that at present-day these 6 galaxies are found outside of the t = 0 Jacobi radius. However, Carina II, Carina III, Hydrus I, Reticulum II and Phoenix II were still bound to the LMC at the time of closest approach, as can also be gauged by the values listed in Table 2. This allows us to conclude that they are very likely related to the LMC.

For Horologium I, the time of its closest approach to the LMC is more recent than the time when it escapes its gravitational attraction. However, over the last 5 Gyr, the distance of Horologium I relative to the LMC oscillates between 35 and 55 kpc with a velocity systematically lower than the escape velocity. Thus, we conclude that Horologium I used to be a satellite of the LMC prior to its escape. This is in agreement with the conclusions drawn by Erkal & Belokurov (2020).

Patel et al. (2020) reached similar conclusions for Carina II, Carina III and Hydrus I, but for Reticulum II and Phoenix II they concluded that both have been recently captured by the LMC. It is likely that the reason for these different conclusions is due to the different method used. The method used in this study is relatively similar to Erkal & Belokurov (2020) who measured the fraction of orbits energetically bound to the LMC, while in Patel et al. (2020), they measured the orbits inside the radius of equi-density between the MW and the LMC. Moreover, the better accuracy on the systemic PMs derived in our study, which impacts significantly the probability of being related to the LMC, can also partly explain the different conclusions, as it is expected that more accurate and precise systemic PMs can deliver a stronger signal of association, when this is present, as noted by Patel et al. (2020).

As for Horologium II, despite having a median velocity relative to the LMC higher than the escape velocity, 56% of its orbits are compatible with having been recently (< 500 Myr) ejected from the LMC system. However, it seems that Horologium II had a velocity relative to the LMC very close to the escape velocity, and this at any time. Thus, with the current precision on its systemic PM17, which dominates the uncertainties on its past orbits, it is not possible to definitively conclude if Horologium II is a former satellite of the LMC or if it has been interacting with it for a long period of time (> 2 Gyr). A visual inspection of the different possible orbits seems to favour the first idea.

Grus II has a relative velocity at its closest approach similar to the escape velocity. However, its orbit clearly shows that the galaxy did not originate in the Magellanic system, but it was just captured by the LMC in the last 200 Myr.

Tucana IV is also potentially linked to the LMC system. Despite its orbit reconstruction suggesting that it has been captured by the LMC about 500 Myr ago, its closest approach is at kpc18, 200 Myr ago with a relative velocity to the LMC lower than the escape velocity at this radius. Moreover, it has to be noticed that at that distance, the orbit of Tucana IV might have been highly perturbed by the SMC, which could have boosted its kinetic energy. Since, our model does not take into account the presence of the SMC, the orbit of Tucana IV likely overestimates its past kinetic energy, especially more than 200 Myr ago. Thus it is very likely that this galaxy has always been bound to the LMC system.

Although the majority of the possible orbits of Tucana II do not present any potential link with the LMC, 19% of its orbits have a relative velocity lower than the escape velocity of the LMC for at least one time step, while the satellite was inside the tidal radius of the LMC at that time19 However, even in that conditions, it is very unlikely that Tucana II is related to the LMC. First because those linked orbits have an inclination of ∼47° compared to the orbit of the LMC. Secondly, those orbits suggest that Tucana II passed through the very outer region of the halo of the LMC more than 2.8 Gyr ago, and being influenced by it ∼4.5 Gyr ago. Taking into account the simplistic potential model for both the MW and the LMC on which our model is based of, it is very unlikely that Tucana II is linked to the LMC.

As for the classical dSphs, 25% of the potential orbits of Carina do pass through the external region of the LMC halo 2.7 Gyr ago, and for ∼70% of them interacted another time with the LMC ∼5 − 6 Gyr (see online video). Moreover, contrary to Tucana II, the orbital plane of the linked orbits of Carina are relatively close to the orbital plane of the LMC, with a typical angular separation between the two planes of 21°. Therefore, we cannot exclude with our study that Carina was orbiting in the external region of the LMC and has been ejected from it more than 5 Gyr, as suggested by Pardy et al. (2020). However, our study tends to indicate that this scenario is unlikely, and a more accurate modelling of the MW-LMC accretion event, and/or better measurement of the current properties of Carina (especially of the distance) are required to definitively conclude something on the potential link between Carina and the Magellanic system. For Fornax the other classical dSphs that could be linked to the LMC, the fraction of linked orbits is even lower than for Carina (4%) and majority of them just pass through the LMC halo 1.8 Gyr and do not show any clear common history with the LMC, at least in the last 6 Gyr, despite having an orbital plane relatively close to the LMC, with a typical separation of of 31°. Therefore, we concluded that it is improbable that Fornax was a part of the Magellanic system.

It has to be noticed here that the fraction of linked orbits of Fornax and Carina that we found (0.04 and 0.25 respectively) is significantly different than the value found by Erkal & Belokurov (2020) (0.128 and 0.004). This is the consequence of the difference in the systemic PMs that we measured above, compared to the values found with Gaia DR2 that they used for their work (see Fig. 5).

For the two others galaxies with non zero fraction of the orbits linked to the LMC, Hydra II and Reticulum III, these orbits are the consequence of the large uncertainties that remain on their systemic PM, which allow a very large range of potential orbits. However, even for the few linked orbits, they pass only once in the external halo of the LMC in the last 5 Gyr, indicating that they are not physically associated with it. For all the other galaxies, we can unambiguously argue that they are satellite of the MW and never used to be satellites of the LMC.

Santos-Santos et al. (2021) identified LMC analogues and their satellites in cosmological simulations and studied their dynamical properties around the MW-like hosts at first infall or pericentre. Guided by the simulations and using Gaia DR2 proper motions, they provide a list of MW satellites that are most-likely associated with the LMC, on the basis of criteria of relative velocity, proximity and orientation of the angular momentum vector. In general there is good agreement between our studies, in terms of what systems are very likely or likely to be associated with the LMC; the most notable exception is Carina II, rejected by Santos-Santos et al. (2021) on the basis of the large velocity relative to the LMC, where this discrepancy might be the result of not including the impact of the infall of a massive LMC onto the observed velocities of the MW satellites (see also below).

Comparison with a non perturbing LMC. As said before, the mass of the Magellanic system is still heavily debated; for example based on hydro-dynamical simulations Wang et al. (2019) argued that a 1011M massive LMC cannot reproduce the Magellanic stream and its associated large amounts of ionised gas (Fox et al. 2014). Their simulations favours a LMC with a mass of 1 − 2 × 1010M, which does not produce strong perturbations of the MW halo (e.g. Law & Majewski 2010; Gómez et al. 2015). Thus we decided to perform the analysis of which galaxies are or were linked to the LMC also by assuming different LMC masses, ranging from 1 × 1010M to 2 × 1011M and assuming that it does not perturb the halo of the MW.

The result is shown on the right panel of Fig. 9. One can see that the number of linked satellites is changing drastically depending on the mass of the LMC, with zero satellites for a LMC of 1 × 1010, 3 (or 4 if Tucana IV is included) for a 5 × 1010. The figure also clearly shows the importance of taking into account the perturbations produced by a massive LMC, since by neglecting them will lead to Carina II not being physically associated with the LMC even for a mass equal to 1.5 × 1011M, while we saw in the previous section that it is unambiguously linked to the LMC if the perturbations produced by a massive LMC are taking into account.

Estimation of the mass of the LMC. We use the number of possible LMC long-term satellites in the context of the gravitational potential perturbed by the LMC infall to estimate the mass-ratio between the Magellanic system and the MW, as done by Fritz et al. (2019). This assumes that the number of LMC or MW satellites is directly related to the mass-ratio between the two objects. Thus, the ratio of satellites between the LMC and the MW (ℛsat) is equal to: where NLMC is the number of LMC satellites, Ntot is the total number of galaxies, whether they are MW’s or the LMC’s, and NMW = Ntot − NLMC the number of MW satellites. Despite being only a rough estimate, the mass so derived is still useful to verify the concordance with the mass of the LMC used to find the number of LMC satellites.

Given that the exact number of NLMC and NMW is still subject to debate, mostly due to the uncertainties on systemic distances and PMs, we made 2 selections for both systems, a generous and a conservative one. For the LMC, the generous sample includes the 9 potential satellites listed in Table 2 as “Highly likely former satellites of the LMC” and “Potentially former satellites of the LMC”, plus the SMC (Murai & Fujimoto 1980; Besla et al. 2012); the conservative sample is composed of the 6 satellites “Highly likely satellites”, plus the SMC. For the MW, we consider satellites those galaxies that have the 16th quantile of their apocentre within the virial radius of the MW in any of the 3 potentials considered in Sect. 7, plus the Sgr dSph and the galaxies not assigned to the LMC; Sagittarius II and Crater I are not taken into account, since they are likely globular clusters (e.g. Laevens et al. 2014; Voggel et al. 2016; Longeard et al. 2021). In the generous MW sample, we also add the galaxies for which spectroscopic measurements are not available. This leads to Ntot = 58 (NMW = 51 − 48 for the conservative and generous LMC samples, respectively). The conservative MW sample is restricted to the galaxies with uncertainties on their total Galactocentric velocity < 70 km s−1 (see Sect. 7), which obviously excludes those without spectroscopic measurements. This leads to Ntot = 37 (NMW = 27 − 30 for the conservative and generous LMC samples, respectively). Doing the 4 possibles combinations that allow these 4 samples, we find a ratio of satellites between the LMC and the MW ranging from 0.14 to 0.37, with a mean of ℛsat = 0.24, consistent with the values found by Peñarrubia et al. (2016) (0.2), Erkal et al. (2019) (0.13–0.19) and Fritz et al. (2019) (). This translates into a mass of the LMC between 1.5 − 4.1 × 1011M with a mean of 2.6 × 1011M for a 1.1 × 1012M MW (Bland-Hawthorn & Gerhard 2016) and between 2.0 − 5.5 × 1011M with a mean of 3.6 × 1011M for a 1.51 × 1012M MW (Fritz et al. 2020). Although with this method the mass range for the LMC is broad, we can see that in all the cases, it is consistent with a value of ∼1.5 × 1011M, but rejects the possibility of the LMC having a mass of ∼1 − 5 × 1010M.

Assuming an extreme scenario, with a number of LMC satellites as low as 2 (i.e. the SMC plus one other), as we found for a low-mass non-perturbing LMC, the ratio of satellites using the conservative and generous MW samples are of ℛsat = 0.057 and 0.036 respectively. Assuming a MW with a mass of 1.1 × 1012M, this correspond to a mass of the LMC of 6.27 × 1010M and 3.93 × 1010M, respectively. This shows a lower level of consistency between the results in the case of a low mass LMC, taking into account that the mass estimated here are those for the most extreme scenario considered. Indeed, if we use the higher mass for the MW found by Fritz et al. (2020), the LMC mass estimated by its number of satellites and the mass assumed to find the number of its satellites will not be consistent anymore. However, it is important to stress that this is a ballpark estimate, since the method is based on is very simplistic. For example, it relies on the assumption that the number of luminous satellites surviving till present day is proportional to the mass of host haloes, something that is not necessarily true (e.g. Jahn et al. 2019, for indications that LMC-like haloes destroy fewer satellites than more massive haloes). What we can say here is that the observations tend to favour a massive LMC of 1.5 − 2.5 × 1011M rather than a 1 − 2 × 1010M LMC.

8. Further applications

The existence of systemic PMs and catalogues of member stars with astrometric properties opens a wealth of possibilities for the study of the internal and orbital properties of LG galaxies, which goes beyond what can be addressed in one article. Below we make a (non-exhaustive) list of the applications that could make use either of the systemic PM measurements derived or of the list of probable member stars and associated quantities provided by this work:

  • It is natural to expect that in the future LG dwarf galaxies will continue being the subject of intensive spectroscopic follow-up for the acquisition of large samples of individual stars with l.o.s. velocities and stellar atmospheric parameters (and chemical abundances). The large field-of-view and multiplex power of instruments such as DESI, WEAVE, 4MOST, MOONS, PFS, MSE, and the collective power of the telescopes they are (or will be) mounted on, makes them particularly suitable for a comprehensive study of these systems. Lists of probable members allow one to enhance the success rate of such observations by reducing the amount of contamination, as well as to assign priorities.

  • The 3D motions of MW satellites, independently on their nature as galaxies or stellar clusters, can be used for determinations of the MW mass, either on their own (for recent works see e.g. Callingham et al. 2019; Fritz et al. 2020; Li et al. 2020) or as a useful addition to samples of other halo tracers, since their predominantly probe the outer parts of the MW gravitational potential and their tangential motions are known with a much higher precision than similarly distant individual MW halo stars. These 3D motions can also be used to determine the velocity anisotropy of the MW system of satellites (see Riley et al. 2019; Fritz et al. 2020, for such determinations based on Gaia DR2), typically an important ingredient for mass modelling and interesting to compare to that of other tracers and to the properties of satellite systems in cosmologically simulated MW-like haloes.

  • The Gaia eDR3 3D motions of MW satellite galaxies can be used to update limits on the density of the MW hot gas corona that would be required to ram-pressure strip them of their gaseous component (see Putman et al. 2021, for a Gaia DR2-based analysis). Since the common assumption is that ram-pressure stripping is most effective at pericentre, it would be interesting to perform this type of analysis both taking into account the growth of the MW DM halo (and possibly of its hot gas corona), since the SFHs of the great majority of MW satellite galaxies would suggest that they had lost their gaseous component already 8–10 Gyr ago, and combining it with models including the recent infall of a massive LMC, for those dwarf galaxies showing star formation activity in the last couple of Gyr.

  • van der Marel et al. (2019) presented the first Gaia-based study of the dynamics of the M 31–M 33 system, resolved the PM rotation of both galaxies, and argued that, thanks for the complete view of these rotating galaxies, the Gaia DR2 PMs determinations allow for an independent assessment of possible biases of the systemic PM measurements based on small field-of-views. The authors found that the motions of M 31 and M 33 support the hypothesis in which M 33 is on its first infall onto M 31. In our determinations of M 33 motion, the statistical errors are a factor 3–4 smaller in the Gaia DR2 based value by van der Marel et al. (2019); but systematic errors still dominate. Nonetheless, these new measurements can be used to revisit the above issues, in conjunction with Gaia eDR3 measurements of M 31 motion (e.g. Salomon et al. 2021).

  • For those systems that enjoy both a determination of the systemic PM and l.o.s. velocity, phase-space information can be used to look for associations among dwarf galaxies, and/or with globular clusters and streams. This will be the subject of a future work. This kinematic information can also be used to determine the orbital poles to further investigates the main plane of satellites around the MW, the vast polar structure of satellites (VPOS) (Pawlowski & Kroupa 2013). The Gaia eDR3 determinations will be particularly useful for the most distant satellites, for which the PMs in DR2 were often not precise enough for a good determination of membership to the VPOS (Fritz et al. 2018a, 2019). Further it is interesting to investigate how many of the members of the VPOS were once satellites of the LMC.

9. Summary and conclusions

In this work we have jointly analysed the spatial distribution and the distributions onto the colour-magnitude and PM planes of individual Gaia eDR3 sources with full astrometric solutions in the direction of 74 Local Group dwarf galaxies to determine systemic PMs of these systems. The sample includes 14 galaxies outside of the virial radius of the MW, out to ∼1.4 Mpc. Our method is largely based on that by McConnachie & Venn (2020a) and McConnachie et al. (2021), to which we have introduced some modifications, aimed at a more realistic treatment of the information on the colour-magnitude diagram of the dwarf galaxies.

We were able to determine systemic PMs for 72 systems when the analysis made no use of complementary spectroscopic information, and for 73 of them when we made use of such additional data. Overall, we consider the measurements for 66 of them to be certainly reliable, including all those for the galaxies outside of the MW virial radius. The output of our analysis, including the list of members and non-members, the plots showing their distribution on the observables used for the maximum likelihood analysis, and the posterior distribution function of the systemic PMs will be made available after publication of the article.

In general, our results are in very good agreement with those in the literature based on Gaia eDR3 data. However, we notice that our measurement uncertainties are larger than those by McConnachie & Venn (2020b) for a few systems. The main explanation for this difference is probably the prior on the velocity dispersion of the MW halo used by the other work and, in a few cases, differences in the quality cuts applied to the Gaia eDR3 data.

We used Gaia eDR3 astrometry for QSOs in the l.o.s. to the dwarf galaxies to calculate the effect of Gaia systematics on the systemic PMs and their uncertainties. These corrections, as well as uncertainties on the distance module, were taken into account for the determination of the 3D velocities used for the reconstruction of the orbital trajectories of the galaxies around the MW (for systems out to the distance of NGC 6822).

In order to tackle the effect of the MW mass onto the orbital history and parameters, we integrated the orbits in two MW static potentials, with a mass between 0.9 and 1.6 × 1012M. In addition, we complemented the analysis by also integrating the orbits in a MW potential perturbed by the infall of a massive LMC, for which we used the model by Vasiliev et al. (2021). In this way, also the reflex motion imprinted onto the objects found in the outskirts of the MW halo was factored in. It should be pointed out that the errors on the transverse and 3D velocities are still very large for several systems, and this can cause biases on the determined orbital parameters. In order to limit the impact of such biases, our considerations based on the results of the orbit integration analysis mainly concern galaxies with uncertainties in the observed 3D velocities < 70 km s−1, which we expect to be inflated with respect to the true 3D velocity of a factor ≲0.5.

The inclusion of a massive LMC, and the response of the MW, is found to modify the orbits of the majority of the MW satellites, regardless of their distance from the MW or the LMC, in a variety of ways, for example increasing and decreasing the pericentric, apocentric distance and the timing of these crucial events. As would be expected, significant differences are also seen in the results from the two isolated potentials.

In general though, orbit integration of the Gaia eDR3-based systemic PMs and literature l.o.s. velocities lead to the following conclusions in the three gravitational potentials used:

  • Leo I and NGC 6822 do not seem to be currently bound to the MW, although both, including NGC 6822, are likely to have entered within its virial radius once in the past.

  • Bootes III and Tucana III are very likely to have reached within 10 kpc from the MW centre, fully confirming the expectations that the streams in which they are embedded are the result of tidal disruption.

  • The orbital properties of Crater II confirm those from Gaia DR2-based systemic PMs and are in line with those explored by models that explain its very low surface brightness, large half-light radius, and low l.o.s. velocity dispersion in the context of strong tidal disturbances from the MW.

  • There are hints that the half-light radius of systems that are likely to have reached within 30 kpc from the MW centre are smaller than those whose orbits kept them in more external regions.

  • Concerning the SFH of MW satellites hosting young stars, that is Leo I, Fornax, and Carina, a correlation can be found between some of the main features seen in their recent SFH, such as bursts or a clear decrease in the activity, the same explanation does not fit all the main features observed.

We also carried out an analysis aimed at identifying which galaxies surrounding the MW might have been or are physically linked to the LMC. We first identified the galaxies that have at least an orbit that brings them within ∼60 kpc from the LMC, and then looked at their total velocity and position, compared to the escape velocity curve of the LMC as a function of time. In the hypothesis that the gravitational potential and time evolution of the MW and LMC system is well represented by the Vasiliev et al. (2021) model, we found six systems that are highly likely to have been satellites of the LMC (Carina II, Carina III, Horologium I, Hydrus I, Phoenix II, Reticulum II), three that might have been potentially associated to it (Horologium II, Tucana IV, Carina), and one that seems to have been recently captured (Grus II). On the other hand, it is unlikely that Fornax was associated with the LMC.

Exploring some generous and conservative estimates in the assignment of satellites to the LMC or the MW, we found that the ratio between the two ranges between 0.14 and 0.37. A simple re-scaling of the number of satellite galaxies with the DM halo mass would suggest the DM halo of the LMC to be in the range 1.5–4.1×1011M for a 1.1 × 1012M MW mass. It should however be pointed out that the number of (and which) galaxies are classified as LMC satellites would change when applying the same methodology using a MW potential not perturbed by the presence of the LMC and allowing for a smaller LMC DM halo mass. It would be interesting to explore further which combinations of the LMC and MW gravitational potential lead to a number of LMC satellites consistent with the expectations of cosmological theories for LMC-like haloes.

The significantly more accurate and precise Gaia eDR3 astrometry has allowed to us to expand and improve our view of the dynamical properties of galaxies in the LG and its immediate surroundings with respect to Gaia DR2. Even though this has only skimmed the surface as to the potential applications of these measurements, we can only eagerly await the fourth data release.


1

For brevity, hereafter we refer to all the systems in the sample as dwarf galaxies, including when they are only “candidates” and even in the case of larger galaxies, such as M33 and NGC 3109.

2

On CDS and on http://research.iac.es/proyecto/GaiaDR3LocalGroup/; at the latter location, we include several other outputs of our analysis (see main text).

3

The colour-magnitude diagrams were inspected for all the systems, to confirm the dominance by contaminant sources in those regions.

4

The ellipticity is defined as 1 − b/a, where b and a are the projected minor and major axes; the position angle increases from north to east; the half-light radius here refers to the projected one on the sky, along the major axis.

5

The synthetic CMD was courtesy of S. Cassisi; the website of Basti-IAC is http://basti-iac.oa-abruzzo.inaf.it/index.html

6

In practice, to avoid introducing noise, we only multiply the counts by this correction factor at G-mag > 19 and if the ratio is < 0.75.

7

We tested the performance when relaxing the cut in tangential velocity and the resulting systemic PMs are always within 1 or at most 2-σ from each other, showing that the method is robust also when removing this condition.

8

With classification score above 0.6.

9

Their equation 2, but with 400/(1 + θ/3), not 400 × (1 + θ/3), which was a typo (Vasiliev, priv. comm.).

10

Here defined as being at least 1.2× larger.

11

We use only the Fritz et al. (2018a) error for normalisation, since the data from the two releases are not independent.

12

In contrast to the previous comparisons with Gaia measurement we apply here our QSO-based shifts, since these independent measurement are not affected by the Gaia systematics.

13

We note however that the radial velocities used by those authors for Phoenix is wrong, see Kacharov et al. (2017).

14

Aquarius II, Böotes III, Canes Venatici II, Carina, Carina II, Carina III, Fornax, Grus II, Horologium I, Horologium II, Hydra II, Hydrus I, Phoenix II, Reticulum II, Reticulum III, Sagittarius II, Sculptor, Segue 1, Segue 2, Tucana II, Tucana III, Tucana IV, Tucana V.

15

The uncertainty on the total Galactocentric velocity of these 6 galaxies is < 70 km s−1.

17

We note that the uncertainty on its total velocity is ∼120 km s−1, exceeding the quality cut of 70 km s−1.

18

We note that for such a small distance the positive bias likely increased the number.

19

Hereafter we refer to this kind of orbits as “linked” orbits.

20

The article Mau et al. (2020) contains a typo, with the μδ being −1.6 mas yr−1, rather than +1.6 mas yr−1 (Mau, private communication).

Acknowledgments

The authors acknowledge support from the State Research Agency (AEI), Spanish Ministry of Science, Innovation and Universities (MICIU), the Agencia Estatal de Investigación del Ministerio de Ciencia e Innovación(AEI-MCINN) and the European Regional Development Fund (ERDF) under grants with reference AYA2017-89076-P (AEI/FEDER, UE) and PID2020-118778GB-I00, and the “Centro de Excelencia Severo Ochoa” program through grants no. CEX2019-000920-S, as well as by the MICIU, through to the State Budget and by the Canary Islands Department of Economy, Knowledge and Employment, through the Regional Budget of the Autonomous Community. GT acknowledges support from the Agencia Estatal de Investigación of the Ministerio de Ciencia e Innovación under grant FJC2018-037323-I. The authors are thankful to Santi Cassisi for kindly providing the simulated Basti-IAC CMD in Gaia eDR3 passbands. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

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Appendix A: Comments on individual galaxies

In the following, unless said otherwise, the comments refer to the results of the ’baseline’ analysis, i.e. with no spectroscopic information for the whole sample, apart from Pisces II and Tucana V. The comments referring to the number of member stars returned by the routine are limited to the trickiest cases, i.e. those in the low statistics regime, ≲10 members.

A.1. Antlia II

For this galaxy the correction for photometric completeness in the determination of the CMD likelihood term has the most noticeable effect. Without this correction our motion is more similar to those by Li et al. (2021a) and McConnachie & Venn (2020b). The systemic PM is in good agreement with that by Ji et al. (2021).

A.2. Aquarius II

There is significant scatter in the PM plane for the P > 0.5 stars; on the other hand, the distribution on the colour-magnitude plane and on the sky seems reasonable. We noticed that for this system the cut ipd_gof_harmonic_amplitude < 0.2 excludes several sources whose spatial, photometric and astrometric properties are perfectly compatible with those of the sources classified as probable members. This is probably the reason for the significantly larger uncertainties in the systemic PM in this work with respect to McConnachie & Venn (2020b).

A.3. Bootes III

The system is clearly detected in the distribution of P > 0.5 stars in the three observables (PMs, CMD< location on the sky). This strongly argues in favour of the actual existence of the system. The resulting spatial distribution is clearly lopsided with respect to the east-west axis, probably a result of tidal disruption, given the very small pericentric distance (7-9 kpc) found in both the potentials explored in this work (see Tab. B.5) and the work by Carlin & Sand (2018) based on Gaia DR2. Our PM determination is in excellent agreement with that by those authors and with the predictions for the retrograde orbit of the Styx stream.

A.4. Bootes IV

Our routine returns only 5 members with P> 0.5 and all very faint. The distribution in PM has 3 stars clumping at μδ around ∼2mas yr−1 and the other 2 stars are found at at 0 mas yr−1 and -2 mas yr−1. The error-bars in this component of the systemic PM are such that within 2σ the clump at 2 mas yr−1 would be included.

It is one of the objects with the most elongated stellar structure, with an ellipticity ∼0.6.

A.5. Canes Venatici I

There seems to be a possible elongation on the N-W side in the spatial distribution of probable members. The pericentric distance could reach 20-30 kpc within the 1-σ uncertainties in both isolated potentials explored; while the results from the perturbed potential tend to suggest larger pericentric distances within the 1-σ confidence interval, we find that 5 out of the 100 realisations have pericentres below 20kpc, hence the results from the perturbed potential do not necessarily go against the possibility of Canes Venatici I having reached quite inward into the MW halo.

Matus Carrillo et al. (2020) model Canes Venatici I as a DM free object and look for orbits that match several of its photometric and kinematic properties, including its ellipticity, half-light radius, position angle, velocity dispersion. Both their PM predictions and the orbital parameters are in line with our values.

A.6. Carina

The spatial distribution of the high probability member stars returned by our routine shows an elongation in the outer parts (Fig. 2), compatible with what seen in previous studies of the spatial distribution of Carina stars, based on red giant branch stars observed spectroscopically (Muñoz et al. 2006) and deep wide-area photometry (Battaglia et al. 2012a; McMonigal et al. 2014). Even if there are some intervening LMC stars in the Carina’s line-of-sight, it is unlikely the feature is due to that, given that these would be included in our contamination model. Given the orbital parameters that we obtain, it seems very unlikely this might be the result of a close interaction with the MW, or with the LMC (see e.g. Fig. 10) as suggested by Fritz et al. (2018a).

thumbnail Fig. 10.

Distance from the LMC as a function of time for the last 3 Gyr. The thicker line gives the median of the 100 random realisations and the thinner lines the 16th and 84th percentiles. The first and second row from the top depict the likely long term satellites of the LMC; the third row the possible long term satellites of the LMC and the last row the recently captured satellites.

It is possible that this galaxy was linked to the LMC.

A.7. Carina II

Highly likely to have been part of the cohort of LMC satellites.

A.8. Carina III

Highly likely to have been part of the cohort of LMC satellites.

A.9. Cetus II

It is possible that there is quite some amount of residual contamination among the stars with high probability of membership: about half are found beyond 3x the half-light radius and they display a large scatter in PM.

A.10. Cetus III

The PDF of systemic PM has extended wings, but of low amplitude. It is one of the objects with the most elongated stellar structure, with an ellipticity ∼0.75.

A.11. Columba I

The Fritz et al. (2019) determination of Columba I systemic PM is well compatible with that obtained in this work; other Gaia DR2-based systemic PMs agree less well with our values (while there is a good agreement between the various eDR3-based measurements).

A.12. Crater I

This object is likely to be a stellar cluster (Kirby et al. 2015; Weisz et al. 2016; Voggel et al. 2016). The distribution of probable members is rather sparse on the PM plane. However, there is a 2-σ agreement between our value of systemic PM in the α, * component and excellent agreement in the δ component with the determination by Vasiliev & Baumgardt (2021).

A.13. Crater II

The systemic PM agrees within 1σ with the determination by Ji et al. (2021).

A.14. Delve 1

It is argued to be a faint halo cluster due to its compactness (Mau et al. 2020) but it lacks spectroscopic information that could validate this classification. The distribution of P> 0.5 stars is quite sparse in PM but well clumped in space. Comparing the PDF and the distribution of members on PM plane, one might be led to think that the error-bars are underestimated. When comparing to the DR2 systemic PM motion by Mau et al. (2020)20, the δ component is found to be in good agreement, while the μα, * component differs by more than 4σ.

A.15. Draco II

The distribution of probable member stars is reasonably well clumped in all properties. The spatial distribution seems asymmetric, although we have not verified whether this is statistically significant. Longeard et al. (2018) find hints of tidal extension along the major axis. Since this system galaxy is currently at 24 kpc from the MW, it can be presently experiencing significant tidal forces, independent of its past orbit.

A.16. DESJ0225+0304

Problematic PDF, with strong lopsidedness and/or very extended wings of high amplitude. It is one of the objects with the most elongated stellar structure, with an ellipticity ∼0.6.

A.17. Eridanus II

Our proper motion PM is in better agreement with a previous entry into the MW halo than the PM in McConnachie et al. (2021). However, the error of about 200 km s−1 in transverse velocity is still so large that forward Monte Carlo simulations do not lead to useful results.

A.18. Eridanus III

It is argued to be a globular cluster due to its compactness (Conn et al. 2018a) but it lacks spectroscopic information that could validate this classification. Its PM suggests a total velocity at the edge of what expected for the escape speed in the ’Heavy MW’ potential at Eridanus III distance. Smaller errors are needed to understand whether Eridanus III is unbound.

A.19. Grus II

Recently captured by the LMC.

A.20. Hercules

This is one of the UFDs for which several features possibly attributable to tidal effects have been detected, see references within the review article by Simon (2019). It is one of the objects with the most elongated stellar structure, with an ellipticity = 0.7.

A.21. Horologium I

Highly likely to have been part of the cohort of LMC satellites.

A.22. Horologium II

It is one of the objects with the most elongated stellar structure, with an ellipticity ∼0.7. Sparse distribution of members on the PM plane. All of them are outside the half-light radius. Compared to Fritz et al. (2019), the uncertainties are only slightly reduced and the value of the new systemic PM is between the two Gaia DR2-based options. This system remains tricky. There is also a relevant difference between our and McConnachie & Venn (2020b) systemic PM, which might be partly caused by their prior.

The bulk line of sight velocity of Horologium II is likely the most uncertain of all the systems in the sample, since its identification in Fritz et al. (2019) is based on only 3 potential members stars. In our analysis the faintest of these 3 stars is not used because of the quality cuts applied to the Gaia data. Without the use of spectroscopy, the faintest star, that closer to the cen- tre, has a probability of membership of 99.6%, and the brightest one, located further out, has 5.5%. Thus, one of the stars classified as spectroscopic members is clearly a certain member, which makes the use of its line-of-sight velocity trustworthy. The other star has a non-negligible likelihood despite its large distance from the centre, because it belongs to the now more visible PM peak of Horologium II. When we use also spectroscopy the probabilities of membership increase to 99.9% for the fainter star and 69.2% for the brighter one. Our PM changes by 0.57 and 0.15 σ in R.A. and DEC, respectively, when spectroscopy is used and the error decreases by 19%.

It is possible that this galaxy was linked to the LMC.

A.23. Hydrus I

Highly likely to have been part of the cohort of LMC satellites. There seems to be a secondary clump on the PM plane, around (1.7, -1) [mas yr−1].

A.24. IC1613

Our systemic motion, combined it to its small error bars, moves it away from the region of values that make a passage within 300kpc from M31 likely according to McConnachie et al. (2021). Thus IC1613 likely evolved in isolation.

A.25. Indus I/Kim 2

This system is likely a globular cluster (Kim et al. 2015). Our routine returns two members with P> 0.5, of a range of magnitudes, but quite offset from the centre. Double peaked PDF.

This is the system for which the uncertainty in the systemic PM increases the most compared McConnachie & Venn (2020b), independently on their 100 km s−1 prior. It is possible that we lose members with our conservative quality cuts.

A.26. Indus II

Only one P> 0.95 member, at very high PM. PDF with extended wings, but of low amplitude. According to Cantu et al. (2021), based on a deep photometric study, Indus II is a false-positive. Our analysis does not lead to a clean detection of the system either. The fact that our systemic PM leads to the object being clearly unbound from the MW does not increase our confidence in its existence.

A.27. Leo A

While our error bars are a factor 3-4 smaller than of McConnachie et al. (2021), they are still clearly too large to restrict its orbits relative to the MW or M31.

A.28. Leo I

It has experienced only one passage around the MW and its currently on its way out.

A.29. Leo V

Detections of over-densities, members at large radii and possibly a l.o.s. velocity gradient (e.g. Sand et al. 2012; Collins et al. 2017) have been interpreted as possible signs of tidal disturbance from the MW. Mutlu-Pakdil et al. (2019) do not confirm those signs, but do find members at large distances; Jenkins et al. (2021) find a weak velocity gradient, with only a 2 σ significance.

The member stars identified by our routine are at most within 3 half-light radii, or just beyond. While the pericentric distances in Tab. B.5 are rather well constrained and do not suggest Leo V coming close enough to the MW to experience tidal disruption, the error in the transverse velocity is about 130 km s−1 per dimension, hence the current determination of orbital parameters is likely to be biased and might have benefited from backward Monte-Carlo simulations.

A.30. Leo T

The routine returns 8 members with P> 0.5 and all very faint.

Our statistical PM errors improve compared to McConnachie et al. (2021), but they are still too large to exclude a backsplash origin for Leo T (see their Fig. 4). The error in the transverse velocity is extremely large, ∼660 km s−1, hence the current determination of orbital parameters cannot be considered robust. Nonetheless, it is unlikely that such a faint galaxy might have hold on to its gas if entering the MW halo.

A.31. M33

The systemic PM of M 33 seems to be somewhat sensitive to the spatial region used for the selection of the stars to be analysed. If we were to use a region within a semi-major axis radius of 0.2°, the μα, * component would remain practically unchanged, whilst the μδ component would decrease to ∼ − 0.009 ± 0.005 mas yr−1. However, it should be noticed that this change does not appear significant, since it is of the size of the systematic error related to a scale length of 0.6°, and this systematic error would increase when considering a smaller spatial region.

A.32. NGC3109

Despite the large distance of 1.46 Mpc, the transverse velocity error of ∼220 km s−1 is already of the size of the velocity dispersion between the isolated systems, thus possibly already useful for scientific applications and certainly will be so in the fourth Gaia data release.

A.33. NGC6822

Our statistical PM errors are about half of those by McConnachie et al. (2021).

According to our orbit integration, it is possible that NGC 6822 passed within the virial radius of the MW. If we compare our PMs to the predictions in McConnachie et al. (2021), we confirm that a passage within the virial radius of M31 is to be excluded.

A.34. Pegasus III

No stars with probability of membership larger than 0.5. Problematic PDF, with strong lopsidedness and/or very extended wings of high amplitude.

A.35. Phoenix

The spatial distribution of probable members has a cross-like shape. Wide-area photometric studies showed that a disc-like structure tilted of 90° with respect to the main body is visible in young (< 1 Gyr old) stars and absent in stars > 5 Gyr old (Battaglia et al. 2012b). We are probably seeing traces of this feature in our sample of members, which by construction should be RGB stars, unless of some young main-sequence stars scattered on the RGB by photometric errors.

The error in the transverse velocity of Phoenix is about 80 km s−1, hence the determination of the orbital parameters is likely to be biased. When comparing our systemic PM to the range of values that would allow a passage within the virial radius of the MW McConnachie et al. (2021), the uncertainties, while smaller than in that study, are still such that a backsplash origin cannot be excluded if the MW is more massive than 1.3×1012 M (with a MW DM halo mass of 1.3×1012 M there are no orbits that lead to a passage within the MW virial radius).

A.36. Phoenix II

The systemic PM of Fritz et al. (2019) is in excellent agreement with ours; in this work the statistical uncertainties are reduced of a factor of 2 with respect to that Gaia DR2 based analysis.

Highly likely to have been part of the cohort of LMC satellites.

A.37. PiscesII

No stars with probability of membership larger than 0.5 and flat PDF of the systemic PM if the spectroscopy is not taken into account. When the spectroscopic information is included, two stars with P> 0.95 are found and the PDF becomes clearly peaked.

A.38. Reticulum II

It is one of the objects with the most elongated stellar structure, with an ellipticity ∼0.6. Possibly lopsided spatial distribution of member stars.

Highly likely to have been part of the cohort of LMC satellites.

A.39. Reticulum III

The distribution of P > 0.5 stars on the sky, PM and CM-plane does not appear overly convincing. The different EDR3 estimates error bars overlap only partly, overall the error is still large in km s−1. The determination by Fritz et al. (2019) is just compatible with ours, given the large error-bars in both cases. While with Pace & Li (2019) systemic PM, Reticulum III would be unbound to the MW even for a massive (1.6×1012 M) MW DM halo, the other measurements in the literature, and ours, suggest it is bound (see Fig. C.5). See also the work by Li et al. (2021a) for the quantification of the probability to be bound in several MW potentials.

The determination of the l.o.s. velocity in Fritz et al. (2019) was uncertain, as based on 3 stars classified as probable spectroscopic members. Our analysis finds that without the inclusion of spectroscopic information, the star named ret3_2_70 in F19 has a probability of membership of only 0.2%. This only increases to 2.4% when including the spectroscopic information, thus star ret3_2_70 is likely not a member. The other two stars have probabilities of membership of 96% and 67% when not including spectroscopic information and therefore they are likely members. The brighter spectroscopic member star causes also a relatively large change between the PM determinations with and without spectroscopic information of 0.08/0.72 σ and an error reduction of 0.29 σ when spectroscopy is used.

A.40. Sagittarius II

Likely a globular cluster according to Longeard et al. (2021).

A.41. Segue 1

This system displays possible extra-tidal features, as summarised by Simon (2019).

A.42. Segue 2

Outlier in the mass-metallicity relation and argued to have become an ultra-faint through tidal stripping of a dwarf galaxy with a much larger stellar mass by Kirby et al. (2013a).

A.43. Sextans B

The uncertainty in the transverse velocity for this very distant galaxy exceeds 1000 km s−1. For a 10 years extended Gaia mission, we expect a much improved uncertainty, at least a factor 6.6 due to the scaling of PMs with time (Lindegren et al. 2021b).

A.44. Tucana III

Clearly embedded in a tidal stream (Drlica-Wagner et al. 2015), likely originating from a dwarf galaxy (Li et al. 2018a; Marshall et al. 2019).

A.45. Tucana IV

According to our analysis, it is possible that this galaxy was linked to the LMC.

A.46. Tucana V

Our routine returns three members with P> 0.5, of various magnitudes, but the brightest ones are quite offset from the centre. Problematic PDF, with strong lopsidedness and/or very extended wings of high amplitude when not including the spectroscopic information. The situation improves very significantly when including the spectroscopic information.

A.47. UGC 4879

Two of the handful of members have G-mag around 18.5. The absolute magnitude of these stars, if belonging to UGC 4879, would be about ∼ − 7, too bright even for OB stars (e.g. Wegner 2000). These might be contaminants, unresolved or partly resolved clusters, or H II regions.

A.48. Ursa Major I

It is one of the objects with the most elongated stellar structure, with an ellipticity ∼0.6.

A.49. Ursa Major II

There is a clear over-density in the PM plane, not associated with Ursa Major II, that seems to show up as a brighter HB in the CMD of non-member stars at G∼17. According to Muñoz et al. (2010, 2018), its radial surface density profile and morphology suggest that the object has been tidally destroyed.

A.50. Ursa Minor

The spatial distribution of members in the outskirts seems rounder than the assumed value of 0.55 for the global ellipticity of Ursa Minor’s stellar component. This can be a manifestation of Pace et al. (2020) finding that the metal-poor stars have a more extended and rounder spatial distribution than the metal-rich stars (with ellipticities of for the former and 0.75 ± 0.03 for the latter).

A.51. Virgo 1

No systemic PM determination. No stars with probability of membership larger than 0.5 and flat PDF. It is one of the objects with the most elongated stellar structure, with an ellipticity ∼0.6.

A.52. WLM

Our smaller error bars and slightly different systemic motion relatively to that in McConnachie et al. (2021) makes it less likely that in the past it reached within the virial radius of M31, although the errors are still too large to be certain.

Appendix B: Tables

Table B.1.

Sample of systems analysed in this work, together with their main global properties. These are the coordinates of the optical centre (cols.2 & 3), the distance modulus (4), half-light radius along the projected major axis (5), ellipticity, defined as 1 - b/a, with b and a being the projected minor and major axes of the stellar component (6), position angle, measured from north to east (7), heliocentric systemic l.o.s. velocity (8) and velocity dispersion (9), mean stellar metallicity (10), type (11), dispersion of the stars metallicity distribution function (12). Col. 13 lists the corresponding references, whose numeric code corresponds to: (1) Torrealba et al. (2019); (2) Torrealba et al. (2016b) ; (3) Okamoto et al. (2012); (4) Dall’Ora et al. (2006); (5) Roderick et al. (2016); (6) Koposov et al. (2011); (7) Norris et al. (2010); (8) Walsh et al. (2008); (9) Koch et al. (2009); (10) Ji et al. (2016); (11) Grillmair (2009); (12) Correnti et al. (2009); (13) Carlin et al. (2009); (14) Carlin & Sand (2018); (15) Homma et al. (2019); (16) Muñoz et al. (2018); (17) Kuehn et al. (2008); (18) Simon & Geha (2007); (19) Kirby et al. (2013b); (20) Greco et al. (2008); (21) Karczmarek et al. (2015); (22) Walker et al. (2009); (23) Fabrizio et al. (2012); (24) Torrealba et al. (2018); (25) Li et al. (2018b); (26) Ji et al. (2020); (27) Mau et al. (2020); (28) Drlica-Wagner et al. (2015); (29) Conn et al. (2018a); (30) Homma et al. (2018); (31) Carlin et al. (2017); (32) Fritz et al. (2019); (33) Musella et al. (2009); (34) Belokurov et al. (2014); (35) Weisz et al. (2016); (36) Kirby et al. (2015); (37) Vivas et al. (2020); (38) Torrealba et al. (2016a); (39) Caldwell et al. (2017); (40) Cerny et al. (2021); (41) Luque et al. (2017); (42) Muraveva et al. (2020); (43) Spencer et al. (2018); (44) Longeard et al. (2018); (45) Crnojević et al. (2016); (46) Li et al. (2017); (47) Conn et al. (2018b); (48) Battaglia et al. (2006); (49) Rizzi et al. (2007); (50) Cantu et al. (2021); (51) Martínez-Vázquez et al. (2019); (52) Walker et al. (2016); (53) Koposov et al. (2015a); (54) Koposov et al. (2015b); (55) Kim & Jerjen (2015); (56) Vivas et al. (2016); (57) Koposov et al. (2018); (58) Kim et al. (2015); (59) Stetson et al. (2014); (60) Mateo et al. (2008); (61) Gullieuszik et al. (2008); (62) Spencer et al. (2017); (63) Moretti et al. (2009); (64) Jenkins et al. (2021); (65) Mutlu-Pakdil et al. (2019); (66) Clementini et al. (2012); (67) Kim et al. (2016); (68) McConnachie (2012); (69) Holtzman et al. (2000); (70) Battaglia et al. (2012b); (71) Kacharov et al. (2017); (72) Mutlu-Pakdil et al. (2018); (73) Simon et al. (2020); (74) Garling et al. (2018); (75) Drlica-Wagner et al. (2016); (76) Belokurov et al. (2010); (77) Longeard et al. (2021); (78) Martínez-Vázquez et al. (2015); (79) Battaglia et al. (2008);(80) Belokurov et al. (2007); (81) Simon et al. (2011); (82) Frebel et al. (2014); (83) Boettcher et al. (2013); (84) Kirby et al. (2013a); (85) Cicuéndez et al. (2018); (86) Vivas et al. (2019); (87) Battaglia et al. (2011); (88) Kirby et al. (2017a); (89) Chiti et al. (2018); (90) Li et al. (2018a); (91) Garofalo et al. (2013); (92) Dall’Ora et al. (2012); (93) Bellazzini et al. (2002); (94) Homma et al. (2016); (95) Willman et al. (2006); (96) Willman et al. (2011); (97) Gerbrandt et al. (2015); (98) Kim et al. (2009); (99) Higgs et al. (2021); (100) Kirby et al. (2017b); (101) Bernard et al. (2010); (102) Taibi et al. in prep.; (103) Lee (1995); (104) Cook et al. (1999); (105) Clementini et al. (2003); (106) Kirby et al. (2014); (107) Gallagher et al. (1998); (108) Leaman et al. (2009); (109) Momany et al. (2002); (110) Bellazzini et al. (2011); (111) Bellazzini et al. (2014); (112) Dolphin et al. (2003); (113) Kim et al. (2002); (114) Kam et al. (2017); (115) Conn et al. (2012); (116) Crnojević et al. (2014); (117) Geha et al. (2010); (118) Ho et al. (2015); (119) McConnachie et al. (2005); (120) Geha et al. (2006); (121) Longeard et al. (2020). Notes a: According to Koposov et al. (2011), the losvd of Bootes I is best described by 2 Gaussians; the value of the velocity dispersion in this table corresponds to the colder Gaussian, which includes 70% of the stars. b: No half-light radius is given; the value of 30arcmin is taken from visual inspection of Fig. 10 of Grillmair (2009); c: No uncertainty given on the ellipticity; we assume 0.2; d: internal velocity dispersion is not completely resolved when they exclude binaries and dependent on the prior; e) updated online compilation.

Table B.2.

Systemic PMs (determined using the completeness correction for systems treated with the synthetic CMD, and without prior from spectroscopy). We highlight in red and orange the determinations we do not trust and those that might be particularly uncertainty, respectively (see main text). For Pisces II and Tucana V we list also the determination from the run that included the spectroscopic information. The columns are: (1) galaxy name; (2,3) systemic PM in the α, * and δ components, respectively; (4) fraction of stars in the galaxy under consideration; (5) the correlation coefficient; (6) Number of stellar objects analysed; (7,8,9) Number of stars with probability of membership to the galaxy > 0.5, 0.8 and 0.95, respectively. The zero-points and additional uncertainties from Gaia eDR3 systematics are kept separate from this table, and listed in B.4.

Table B.3.

Systemic proper motions obtained for the sub-set of systems analysed including the spectroscopic term for the likelihood.

Table B.4.

Zero-points and additional uncertainties from Gaia eDR3 systematics.

Table B.5.

Orbital parameters for the case of the 2 isolated MW potentials as described in Section 7): ’Light MW’ (light) and ’Heavy MW’ (heavy). For both of these models, are given: the pericentre (peri), apocentre (apo), eccentricity (ecc), period (T), time since last pericentre (Tlast, peri) and fraction of orbit reaching there apocentre in the last 8 Gyr (ℱapo). The values correspond to the median of these parameters calculated fro 100 Monte-Carlo realisations, and the uncertainties correspond to the 16th and 84th quantiles. When the majority of there orbits do not reach the apocentre, the uncertainties on the apocentre, eccentricity and period cannot be computed. Thus, for those galaxies, we rather give the values of the 16th quantile. These values are marked by a ⋆. Galaxies with name in italics indicate those for which the uncertainty on the total Galactocentric velocity is > 70 km s−1 (see Sect. 7). The systemic PM from the run with the spectroscopic information were used for Pisces II and Tucana V. Pegasus III is omitted due to the lack of a trustworthy systemic PM.

Table B.6.

Orbital parameters obtained in the perturbed potential.

Appendix C: Plots on tests and validation

Here we include plots showing the systemic PMs of the galaxies in the sample derived in different ways.

thumbnail Fig. C.1.

Comparison of systemic PMs determined with (blue) and without (red) the correction for the photometric completeness of Gaia eDR3 data, for the systems whose CMD probability distribution was calculated using a synthetic CMD (see Tab. 1), in the run not including spectroscopic information. The x-axis and y-axis show the μα, * and μδ component, respectively.

thumbnail Fig. C.2.

Comparison of systemic PMs determined with (red) and without (blue) the likelihood term for line-of-sight velocities. The x-axis and y-axis show the μα, * and μδ component, respectively. The sources of the spectroscopic works are those used in Fritz et al. (2018a, see references to the original studies therein), Kirby et al. (2013b), Kirby et al. (2015), Carlin & Sand (2018), Torrealba et al. (2019), Simon et al. (2020), Longeard et al. (2021).

thumbnail Fig. C.3.

As Figure 5, but for the galaxies specified in the labels.

thumbnail Fig. C.4.

As Figure 5, but for the galaxies specified in the labels.

thumbnail Fig. C.5.

As Figure 5, but for the galaxies specified in the labels.

thumbnail Fig. C.6.

As Figure 5, but for the galaxies specified in the labels.

Appendix D: Plots on orbital histories

Here we include plots showing the orbital evolution in the past 3 Gyr in the triaxial light MW potential with and without the inclusion of the LMC.

thumbnail Fig. D.1.

Distance from the MW centre as a function of time for the past 6 Gyr (at present time t = 0) for the ’perturbed’ and isolated ’Light MW’ potentials (cyan and orange lines, respectively), i.e. in the case with and without the infall of a massive LMC; the orbits are determined from the observed, error-free, bulk motions.

thumbnail Fig. D.2.

As D.1, but for the galaxies specified in the titles of the panels. For Pisces II the orbits shown are obtained using the systemic motion from the inclusion of the spectroscopic information.

thumbnail Fig. D.3.

As Fig. D.1, but for the galaxies specified in the titles of the panels. For Tucana V the orbits shown are obtained using the systemic motion from the inclusion of the spectroscopic information.

All Tables

Table 1.

Methodology used for the spatial and Colour-Magnitude (CM) of the likelihood for stars in the dwarf galaxy (Sect. 4.1).

Table 2.

Galaxies reaching within 60 kpc from the LMC centre and their relation to the LMC or to the MW.

Table B.1.

Sample of systems analysed in this work, together with their main global properties. These are the coordinates of the optical centre (cols.2 & 3), the distance modulus (4), half-light radius along the projected major axis (5), ellipticity, defined as 1 - b/a, with b and a being the projected minor and major axes of the stellar component (6), position angle, measured from north to east (7), heliocentric systemic l.o.s. velocity (8) and velocity dispersion (9), mean stellar metallicity (10), type (11), dispersion of the stars metallicity distribution function (12). Col. 13 lists the corresponding references, whose numeric code corresponds to: (1) Torrealba et al. (2019); (2) Torrealba et al. (2016b) ; (3) Okamoto et al. (2012); (4) Dall’Ora et al. (2006); (5) Roderick et al. (2016); (6) Koposov et al. (2011); (7) Norris et al. (2010); (8) Walsh et al. (2008); (9) Koch et al. (2009); (10) Ji et al. (2016); (11) Grillmair (2009); (12) Correnti et al. (2009); (13) Carlin et al. (2009); (14) Carlin & Sand (2018); (15) Homma et al. (2019); (16) Muñoz et al. (2018); (17) Kuehn et al. (2008); (18) Simon & Geha (2007); (19) Kirby et al. (2013b); (20) Greco et al. (2008); (21) Karczmarek et al. (2015); (22) Walker et al. (2009); (23) Fabrizio et al. (2012); (24) Torrealba et al. (2018); (25) Li et al. (2018b); (26) Ji et al. (2020); (27) Mau et al. (2020); (28) Drlica-Wagner et al. (2015); (29) Conn et al. (2018a); (30) Homma et al. (2018); (31) Carlin et al. (2017); (32) Fritz et al. (2019); (33) Musella et al. (2009); (34) Belokurov et al. (2014); (35) Weisz et al. (2016); (36) Kirby et al. (2015); (37) Vivas et al. (2020); (38) Torrealba et al. (2016a); (39) Caldwell et al. (2017); (40) Cerny et al. (2021); (41) Luque et al. (2017); (42) Muraveva et al. (2020); (43) Spencer et al. (2018); (44) Longeard et al. (2018); (45) Crnojević et al. (2016); (46) Li et al. (2017); (47) Conn et al. (2018b); (48) Battaglia et al. (2006); (49) Rizzi et al. (2007); (50) Cantu et al. (2021); (51) Martínez-Vázquez et al. (2019); (52) Walker et al. (2016); (53) Koposov et al. (2015a); (54) Koposov et al. (2015b); (55) Kim & Jerjen (2015); (56) Vivas et al. (2016); (57) Koposov et al. (2018); (58) Kim et al. (2015); (59) Stetson et al. (2014); (60) Mateo et al. (2008); (61) Gullieuszik et al. (2008); (62) Spencer et al. (2017); (63) Moretti et al. (2009); (64) Jenkins et al. (2021); (65) Mutlu-Pakdil et al. (2019); (66) Clementini et al. (2012); (67) Kim et al. (2016); (68) McConnachie (2012); (69) Holtzman et al. (2000); (70) Battaglia et al. (2012b); (71) Kacharov et al. (2017); (72) Mutlu-Pakdil et al. (2018); (73) Simon et al. (2020); (74) Garling et al. (2018); (75) Drlica-Wagner et al. (2016); (76) Belokurov et al. (2010); (77) Longeard et al. (2021); (78) Martínez-Vázquez et al. (2015); (79) Battaglia et al. (2008);(80) Belokurov et al. (2007); (81) Simon et al. (2011); (82) Frebel et al. (2014); (83) Boettcher et al. (2013); (84) Kirby et al. (2013a); (85) Cicuéndez et al. (2018); (86) Vivas et al. (2019); (87) Battaglia et al. (2011); (88) Kirby et al. (2017a); (89) Chiti et al. (2018); (90) Li et al. (2018a); (91) Garofalo et al. (2013); (92) Dall’Ora et al. (2012); (93) Bellazzini et al. (2002); (94) Homma et al. (2016); (95) Willman et al. (2006); (96) Willman et al. (2011); (97) Gerbrandt et al. (2015); (98) Kim et al. (2009); (99) Higgs et al. (2021); (100) Kirby et al. (2017b); (101) Bernard et al. (2010); (102) Taibi et al. in prep.; (103) Lee (1995); (104) Cook et al. (1999); (105) Clementini et al. (2003); (106) Kirby et al. (2014); (107) Gallagher et al. (1998); (108) Leaman et al. (2009); (109) Momany et al. (2002); (110) Bellazzini et al. (2011); (111) Bellazzini et al. (2014); (112) Dolphin et al. (2003); (113) Kim et al. (2002); (114) Kam et al. (2017); (115) Conn et al. (2012); (116) Crnojević et al. (2014); (117) Geha et al. (2010); (118) Ho et al. (2015); (119) McConnachie et al. (2005); (120) Geha et al. (2006); (121) Longeard et al. (2020). Notes a: According to Koposov et al. (2011), the losvd of Bootes I is best described by 2 Gaussians; the value of the velocity dispersion in this table corresponds to the colder Gaussian, which includes 70% of the stars. b: No half-light radius is given; the value of 30arcmin is taken from visual inspection of Fig. 10 of Grillmair (2009); c: No uncertainty given on the ellipticity; we assume 0.2; d: internal velocity dispersion is not completely resolved when they exclude binaries and dependent on the prior; e) updated online compilation.

Table B.2.

Systemic PMs (determined using the completeness correction for systems treated with the synthetic CMD, and without prior from spectroscopy). We highlight in red and orange the determinations we do not trust and those that might be particularly uncertainty, respectively (see main text). For Pisces II and Tucana V we list also the determination from the run that included the spectroscopic information. The columns are: (1) galaxy name; (2,3) systemic PM in the α, * and δ components, respectively; (4) fraction of stars in the galaxy under consideration; (5) the correlation coefficient; (6) Number of stellar objects analysed; (7,8,9) Number of stars with probability of membership to the galaxy > 0.5, 0.8 and 0.95, respectively. The zero-points and additional uncertainties from Gaia eDR3 systematics are kept separate from this table, and listed in B.4.

Table B.3.

Systemic proper motions obtained for the sub-set of systems analysed including the spectroscopic term for the likelihood.

Table B.4.

Zero-points and additional uncertainties from Gaia eDR3 systematics.

Table B.5.

Orbital parameters for the case of the 2 isolated MW potentials as described in Section 7): ’Light MW’ (light) and ’Heavy MW’ (heavy). For both of these models, are given: the pericentre (peri), apocentre (apo), eccentricity (ecc), period (T), time since last pericentre (Tlast, peri) and fraction of orbit reaching there apocentre in the last 8 Gyr (ℱapo). The values correspond to the median of these parameters calculated fro 100 Monte-Carlo realisations, and the uncertainties correspond to the 16th and 84th quantiles. When the majority of there orbits do not reach the apocentre, the uncertainties on the apocentre, eccentricity and period cannot be computed. Thus, for those galaxies, we rather give the values of the 16th quantile. These values are marked by a ⋆. Galaxies with name in italics indicate those for which the uncertainty on the total Galactocentric velocity is > 70 km s−1 (see Sect. 7). The systemic PM from the run with the spectroscopic information were used for Pisces II and Tucana V. Pegasus III is omitted due to the lack of a trustworthy systemic PM.

Table B.6.

Orbital parameters obtained in the perturbed potential.

All Figures

thumbnail Fig. 1.

Line-of-sight (l.o.s.) velocity of heliocentric distance for the galaxies in the sample (circles). The systems without a literature measurement of the l.o.s. velocity are assigned a null value, exclusively for the purpose of this figure, and are indicated as crosses. The colour-coding is based on the uncertainty in heliocentric transverse velocity, derived from the statistical uncertainties in the systemic proper motions and distance modulus (see Sect. 4).

In the text
thumbnail Fig. 2.

Distribution of member stars (large circles) projected on the tangent plane passing through the galaxy centre (left), and on the proper motion (middle) and colour-magnitude plane (right), for systems in the regime of > 500 stars with P > 0.95, in increasing order of distance from top to bottom. The galaxy names are indicated in the figure titles. The colour-coding indicates the probability of membership (only when above > 0.5; the stars with P < 0.5 are shown as grey dots. The ellipses in the left panel have semi-major axes equal to 1× and 3× the half-light radii in Table 1 (apart from M33, that is missing this quantity, for which we consider 0.5 deg), and ellipticity and position angle taken from the same table.

In the text
thumbnail Fig. 3.

As in Fig. 2, but for the regime of 50–200 stars with P > 0.95.

In the text
thumbnail Fig. 4.

As in Fig. 2, but for the regime of < 50 stars with P > 0.95. Cetus III and Bootes IV are two cases in which the uncertainties in McConnachie & Venn (2020b) are much smaller than in our determination.

In the text
thumbnail Fig. 5.

Comparison of our systemic PM measurements (labelled “This work”, shown as a black star) with literature measurements. The Gaia measurements are from Gaia Collaboration (2018b), Simon (2018), Simon et al. (2020), Fritz et al. (2018a, 2019), Carlin & Sand (2018), Massari & Helmi (2018), Kallivayalil et al. (2018), Pace & Li (2019), Pace et al. (2020), Fu et al. (2019), McConnachie & Venn (2020a,b), Longeard et al. (2018, 2020), Torrealba et al. (2019), Mau et al. (2020), Cerny et al. (2021), Chakrabarti et al. (2019), Gregory et al. (2020), Mutlu-Pakdil et al. (2019), Jenkins et al. (2021), Vasiliev & Baumgardt (2021), Martínez-García et al. (2021), Li et al. (2021a), Ji et al. (2021). Triangles indicate works that used only stars with additional information on membership, usually from spectroscopy, but also RR Lyrae variable stars in some cases, as Simon (2018). HST measurements are from Piatek et al. (2003, 2005, 2006, 2007), Pryor et al. (2015), Piatek et al. (2016), Sohn et al. (2013, 2017). Among them, those indicated by diamonds (pentagons) use background galaxies (QSOs) as references. The smaller error bars include only the random Gaia error, the larger one also the systematic error when they are given as separated in the source. We do not display the correlation between the PMs components here. The ellipses (when in the field of view of the plots) indicate the σ = 100 km s−1 prior (green) of McConnachie & Venn (2020a,b), and the escape velocity (grey) in the 1.6 × 1012M Milky Way of Fritz et al. (2018a) centred on the expected reflex motion for the system. For galaxies at a distance > 500 kpc, we only plot an ellipse (purple) corresponding to 200 km s−1.

In the text
thumbnail Fig. 6.

Apocentric (top) and pericentric (bottom) distance for the sample of likely MW satellite galaxies (excluding the high likely long-term LMC satellites of the LMC in Table 2) with error in 3D velocity less than 70 km s−1. The filled and open squares show the results for the “Light” and “Heavy” isolated MW potentials and the light blue asterisks for the perturbed potential. The arrows indicate those cases where either the median or the 84th percentiles were undefined. When not even the 16th percentile was defined, the symbols are placed at an apocentric distance = 900 kpc. We only consider cases where the galaxy has already experienced a pericentric passage. The horizontal lines that have a label indicate the virial radius of the DM halo in the corresponding gravitational potential; the line at a distance of 30 kpc is meant to indicate a region potentially dangerous in terms of tidal effects (see main text).

In the text
thumbnail Fig. 7.

Pericentric distance compared to the projected semi-major axis half light radius for the sample of likely MW satellite galaxies (excluding the highly likely long-term LMC satellites of the LMC in Table 2) with error in 3D velocity less than 70 km s−1. The filled and open squares show the results for the “Light” and “Heavy” isolated MW potentials and the asterisks for perturbed potential. The arrows indicate those cases where either the median or the 84th percentiles were undefined. We only consider cases where the galaxy has already experienced a pericentric passage.

In the text
thumbnail Fig. 8.

Distance from the LMC -as a function of look-back time for 100 Monte-Carlo realisations of the galaxies’s orbit. The horizontal solid and dashed lines, labelled rs and rt, correspond to the scale and truncation radius of the initial LMC potential, of 10.84 kpc and 108.4 kpc, respectively.

In the text
thumbnail Fig. 9.

Left panel: relative distance and velocity for the galaxies for which at least one of the 100 orbit realisations in the perturbed potential pass close to the LMC (< 60 kpc). The black line represents the escape velocity of the initial a 1.5 × 1011M LMC represented by a NFW profile with a scale radius rs = 10.84 kpc, while the dashed line shows the escape velocity of the current LMC. Each coloured line shows the evolution of the relative distance and velocity of the galaxies with each point marking 100 Myr of evolution. For the galaxies that are not currently at their closest approach, the triangles show their current position on this diagram. The vertical lines at the bottom of the panel show the location of the Jacobi radius at different epochs. Right panel: same as the left panel but assuming that the LMC follows the orbit of a point mass, and does not modify the MW potential. The black lines represent the escape velocity for a LMC with a mass of respectively 1, 5, 10, 15 and 20 × 1010M and a scale radius that respect the observational constraint following the requirement of Vasiliev et al. (2021).

In the text
thumbnail Fig. 10.

Distance from the LMC as a function of time for the last 3 Gyr. The thicker line gives the median of the 100 random realisations and the thinner lines the 16th and 84th percentiles. The first and second row from the top depict the likely long term satellites of the LMC; the third row the possible long term satellites of the LMC and the last row the recently captured satellites.

In the text
thumbnail Fig. C.1.

Comparison of systemic PMs determined with (blue) and without (red) the correction for the photometric completeness of Gaia eDR3 data, for the systems whose CMD probability distribution was calculated using a synthetic CMD (see Tab. 1), in the run not including spectroscopic information. The x-axis and y-axis show the μα, * and μδ component, respectively.

In the text
thumbnail Fig. C.2.

Comparison of systemic PMs determined with (red) and without (blue) the likelihood term for line-of-sight velocities. The x-axis and y-axis show the μα, * and μδ component, respectively. The sources of the spectroscopic works are those used in Fritz et al. (2018a, see references to the original studies therein), Kirby et al. (2013b), Kirby et al. (2015), Carlin & Sand (2018), Torrealba et al. (2019), Simon et al. (2020), Longeard et al. (2021).

In the text
thumbnail Fig. C.3.

As Figure 5, but for the galaxies specified in the labels.

In the text
thumbnail Fig. C.4.

As Figure 5, but for the galaxies specified in the labels.

In the text
thumbnail Fig. C.5.

As Figure 5, but for the galaxies specified in the labels.

In the text
thumbnail Fig. C.6.

As Figure 5, but for the galaxies specified in the labels.

In the text
thumbnail Fig. D.1.

Distance from the MW centre as a function of time for the past 6 Gyr (at present time t = 0) for the ’perturbed’ and isolated ’Light MW’ potentials (cyan and orange lines, respectively), i.e. in the case with and without the infall of a massive LMC; the orbits are determined from the observed, error-free, bulk motions.

In the text
thumbnail Fig. D.2.

As D.1, but for the galaxies specified in the titles of the panels. For Pisces II the orbits shown are obtained using the systemic motion from the inclusion of the spectroscopic information.

In the text
thumbnail Fig. D.3.

As Fig. D.1, but for the galaxies specified in the titles of the panels. For Tucana V the orbits shown are obtained using the systemic motion from the inclusion of the spectroscopic information.

In the text

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