We use a sample of Milky Way (MW) analogues for which we have stellar and disc gas mass measurements, published measurements of halo gas masses of the MW and of similar galaxies, and the well-established value of the cosmological baryon fraction to place a lower bound on the mass of the Galaxy of 7.7 x 10(11) M-circle dot and estimate that the mass is likely to be >= 1.2 x 10(12) M-circle dot. Although most dynamical analyses yield measurements consistent with these results, several recent studies have advocated for a total mass well below 10(12) M-circle dot. We reject such low-mass estimates because they imply a Galactic baryon matter fraction significantly above the universal value. Convergence between dynamical mass estimates and those based on the baryonic mass is an important milestone in our understanding of galaxies.

The Milky Way (MW) and M31 both harbour massive satellite galaxies, the Large Magellanic Cloud (LMC) and M33, which may comprise up to 10 per cent of their host's total mass. Massive satellites can change the orbital barycentre of the host-satellite system by tens of kiloparsec and are cosmologically expected to harbour dwarf satellite galaxies of their own. Assessing the impact of these effects crucially depends on the orbital histories of the LMC and M33. Here, we revisit the dynamics of theMW-LMC system and present the first detailed analysis of the M31-M33 system utilizing high-precision proper motions and statistics from the dark-matter-only Illustris cosmological simulation. With the latest Hubble Space Telescope proper motion measurements of M31, we reliably constrain M33' s interaction history with its host. In particular, like the LMC, M33 is either on its first passage (t(inf) < 2 Gyr ago) or if M31 is massive (>= 2 x 10(12) M-circle dot), it is on a long-period orbit of about 6 Gyr. Cosmological analogues of the LMC and M33 identified in Illustris support this picture and provide further insight about their host masses. We conclude that, cosmologically, massive satellites such as the LMC and M33 are likely completing their first orbits about their hosts. We also find that the orbital energies of such analogues prefer an MW halo mass similar to 1.5 x 10(12) M-circle dot and an M31 halo mass >= 1.5 x 10(12)M(circle dot). Despite conventional wisdom, we conclude it is highly improbable that M33 made a close (< 100 kpc) approach to M31 recently (t(peri) < 3 Gyr ago). Such orbits are rare (< 1 per cent) within the 4s error space allowed by observations. This conclusion cannot be explained by perturbative effects through four-body encounters amongst the MW, M31, M33, and the LMC. This surprising result implies that we must search for a new explanation for M33' s strongly warped gas and stellar discs.

In the era of high-precision astrometry, space observatories like the Hubble Space Telescope (HST) and Gaia are providing unprecedented 6D phase-space information of satellite galaxies. Such measurements can shed light on the structure and assembly history of the Local Group, but improved statistical methods are needed to use them efficiently. Here we illustrate such a method using analogues of the Local Group's two most massive satellite galaxies, the Large Magellanic Cloud (LMC) and Triangulum (M33), from the Illustris dark-matter-only cosmological simulation. We use a Bayesian inference scheme combining measurements of positions, velocities and specific orbital angular momenta (j) of the LMC/M33 with importance sampling of their simulated analogues to compute posterior estimates of the Milky Way (MW) and Andromeda's (M31) halo masses. We conclude that the resulting host halo mass is more susceptible to bias when using measurements of the current position and velocity of satellites, especially when satellites are at short-lived phases of their orbits (i.e. at pericentre). Instead, the j value of a satellite is well conserved over time and provides a more reliable constraint on host mass. The inferred virial mass of the MW(M31) using j of the LMC (M33) is M-vir,M- MW = 1.02(-0.55)(+0.77) x 10(12) M-circle dot (M-vir,M- M31 = 1.37(-0.75)(+1.39) x 10(12) M-circle dot). Choosing simulated analogues whose j values are consistent with the conventional picture of a previous (<3 Gyr ago), close encounter (<100 kpc) of M33 about M31 results in a very low virial mass for M31 (similar to 10(12) M-circle dot). This supports the new scenario put forth in Patel, Besla & Sohn, wherein M33 is on its first passage about M31 or on a long-period orbit. We conclude that this Bayesian inference scheme, utilizing satellite j, is a promising method to reduce the current factor of 2 spread in the mass range of the MW and M31. This method is easily adaptable to include additional satellites as new 6D phase-space information becomes available from HST, Gaia and the James Webb Space Telescope.

Fornecemos uma amostra de 170 Aglomerados Globulares Galácticos (GCs) e analisamos as propriedades de sua distribuição espacial. Utilizando um vasto catálogo de nuvens escuras identificadas, listamos os GCs que estão atrás de uma ou mais delas e que podem estar submetidos a uma extinção mais complexa do que a considerada por mapas de extinção. Valores de incerteza em distância são obtidos da literatura recente e comparados com valores derivados de uma fórmula de propagação de erro. GCs são agrupados de acordo com características inusitadas, tais como idades relativamente jovens ou possível conexão com núcleos de galáxias anãs, de forma que o efeito desses grupos pode ser isolado na distribuição espacial geral. Adicionalmente, computamos o centróide da distribuição de GCs e estudamos como esse se relaciona com a distância ao centro da Galáxia. Considerando que uma formação galáctica via colapso monolítico é supostamente simétrica, investigamos assimetrias e como os valores de incerteza das distâncias as modificam. Velocidades espaciais e um potencial Galáctico são empregados para verificar se quaisquer assimetrias na distribuição espacial são devidas a objetos em movimento coerente, ou se são somente efeitos transientes. / We provide a sample of 170 Galactic Globular Clusters (GCs) and analyse its spatial distribution properties. Using a comprehensive dust cloud catalogue, we list the GCs that are behind one or more identified dust clouds and could be subjected to a more complex extinction curve than extinction catalogues consider. Distance uncertainty values are gathered from recent literature and compared to values derived from an error propagation formula. GCs are grouped according to unusual characteristics, such as relatively young age or possible connection to dwarf galaxy nuclei, so that their effect on the general distribution can be isolated. Additionally, we compute the centroid of the GC distribution and study how it relates to the distance to the centre of the Galaxy. Considering that galactic formation via monolithic collapse is expected to be symmetrical, we probe asymmetries and how distance uncertainty values modify them. Spatial velocities and a Galactic potential are used to verify if any asymmetries in the spatial distribution are due to co-moving objects, or if they are merely transient effects.

Fornecemos uma amostra de 170 Aglomerados Globulares Galácticos (GCs) e analisamos as propriedades de sua distribuição espacial. Utilizando um vasto catálogo de nuvens escuras identificadas, listamos os GCs que estão atrás de uma ou mais delas e que podem estar submetidos a uma extinção mais complexa do que a considerada por mapas de extinção. Valores de incerteza em distância são obtidos da literatura recente e comparados com valores derivados de uma fórmula de propagação de erro. GCs são agrupados de acordo com características inusitadas, tais como idades relativamente jovens ou possível conexão com núcleos de galáxias anãs, de forma que o efeito desses grupos pode ser isolado na distribuição espacial geral. Adicionalmente, computamos o centróide da distribuição de GCs e estudamos como esse se relaciona com a distância ao centro da Galáxia. Considerando que uma formação galáctica via colapso monolítico é supostamente simétrica, investigamos assimetrias e como os valores de incerteza das distâncias as modificam. Velocidades espaciais e um potencial Galáctico são empregados para verificar se quaisquer assimetrias na distribuição espacial são devidas a objetos em movimento coerente, ou se são somente efeitos transientes. / We provide a sample of 170 Galactic Globular Clusters (GCs) and analyse its spatial distribution properties. Using a comprehensive dust cloud catalogue, we list the GCs that are behind one or more identified dust clouds and could be subjected to a more complex extinction curve than extinction catalogues consider. Distance uncertainty values are gathered from recent literature and compared to values derived from an error propagation formula. GCs are grouped according to unusual characteristics, such as relatively young age or possible connection to dwarf galaxy nuclei, so that their effect on the general distribution can be isolated. Additionally, we compute the centroid of the GC distribution and study how it relates to the distance to the centre of the Galaxy. Considering that galactic formation via monolithic collapse is expected to be symmetrical, we probe asymmetries and how distance uncertainty values modify them. Spatial velocities and a Galactic potential are used to verify if any asymmetries in the spatial distribution are due to co-moving objects, or if they are merely transient effects.

Fornecemos uma amostra de 170 Aglomerados Globulares Galácticos (GCs) e analisamos as propriedades de sua distribuição espacial. Utilizando um vasto catálogo de nuvens escuras identificadas, listamos os GCs que estão atrás de uma ou mais delas e que podem estar submetidos a uma extinção mais complexa do que a considerada por mapas de extinção. Valores de incerteza em distância são obtidos da literatura recente e comparados com valores derivados de uma fórmula de propagação de erro. GCs são agrupados de acordo com características inusitadas, tais como idades relativamente jovens ou possível conexão com núcleos de galáxias anãs, de forma que o efeito desses grupos pode ser isolado na distribuição espacial geral. Adicionalmente, computamos o centróide da distribuição de GCs e estudamos como esse se relaciona com a distância ao centro da Galáxia. Considerando que uma formação galáctica via colapso monolítico é supostamente simétrica, investigamos assimetrias e como os valores de incerteza das distâncias as modificam. Velocidades espaciais e um potencial Galáctico são empregados para verificar se quaisquer assimetrias na distribuição espacial são devidas a objetos em movimento coerente, ou se são somente efeitos transientes. / We provide a sample of 170 Galactic Globular Clusters (GCs) and analyse its spatial distribution properties. Using a comprehensive dust cloud catalogue, we list the GCs that are behind one or more identified dust clouds and could be subjected to a more complex extinction curve than extinction catalogues consider. Distance uncertainty values are gathered from recent literature and compared to values derived from an error propagation formula. GCs are grouped according to unusual characteristics, such as relatively young age or possible connection to dwarf galaxy nuclei, so that their effect on the general distribution can be isolated. Additionally, we compute the centroid of the GC distribution and study how it relates to the distance to the centre of the Galaxy. Considering that galactic formation via monolithic collapse is expected to be symmetrical, we probe asymmetries and how distance uncertainty values modify them. Spatial velocities and a Galactic potential are used to verify if any asymmetries in the spatial distribution are due to co-moving objects, or if they are merely transient effects.