Sagittarius Stream Research Articles

Mapping the Milky Way in 5D with 170 Million Stars

We present Augustus, a catalog of distance, extinction, and stellar parameter estimates for 170 million stars from 14 mag < r < 20 mag and with ∣b∣ > 10° drawing on a combination of optical to near-infrared photometry from Pan-STARRS, 2MASS, UKIDSS, and unWISE along with parallax measurements from Gaia DR2 and 3D dust extinction maps. After applying quality cuts, we find 125 million objects have “high-quality” posteriors with statistical distance uncertainties of ≲10% for objects with well-constrained stellar types. This is a substantial improvement over the distance estimates derived from Gaia parallaxes alone and in line with the recent results from Anders et al. We find the fits are able to reproduce the dereddened Gaia color–magnitude diagram accurately, which serves as a useful consistency check of our results. We show that we are able to detect large, kinematically coherent substructures in our data clearly relative to the input priors, including the Monoceros Ring and the Sagittarius Stream, attesting to the quality of the catalog. Our results are publicly available at doi:10.7910/DVN/WYMSXV. An accompanying interactive visualization can be found at http://allsky.s3-website.us-east-2.amazonaws.com.

Mapping the Milky Way with LAMOST – IV. The large Galactic disc extending to 35 kpc

ABSTRACT We investigate extent of the disc in both vertical and radial directions by separately analysing the density and azimuthal velocity distributions using 31116 M giant stars selected from LAMOST DR5. We first measure the metallicities, radial velocities, and the distances with precision of 0.26 dex, 5.01 km s−1, and 20.8 per cent, respectively. Then, a Bayesian method is applied to model the distributions of the outer Galaxy including components of the thin, thick discs and the halo, to obtain the scale height and azimuthal velocity distributions for the thin and thick discs as a function of galactocentric distance R. The density profile of the thin disc shows that it extends out to R ∼ 35 kpc, beyond which there are no M giant stars in the halo except for Sagittarius Stream members. By using azimuthal velocity to trace the thin disc out to 26 kpc from the Galactic Centre, we show that both the density profile and azimuthal velocity decrease with Galactocentric distance R. In both the density and azimuthal velocity distributions, there is a significant breakpoint at a galactocentric distance of R ∼ 14 kpc. The scale height distribution shows that the thin disc is significantly flared, consistent with previous works. We also find that there is no significant thick disc (as traced by M giant stars) in the outer region beyond R ∼ 15.5 kpc.

The GALAH survey: tracing the Milky Way’s formation and evolution through RR Lyrae stars

ABSTRACT Stellar mergers and accretion events have been crucial in shaping the evolution of the Milky Way (MW). These events have been dynamically identified and chemically characterized using red giants and main-sequence stars. RR Lyrae (RRL) variables can play a crucial role in tracing the early formation of the MW since they are ubiquitous, old (t ≥ 10 Gyr) low-mass stars and accurate distance indicators. We exploited Data Release 3 of the GALAH survey to identify 78 field RRLs suitable for chemical analysis. Using synthetic spectra calculations, we determined atmospheric parameters and abundances of Fe, Mg, Ca, Y, and Ba. Most of our stars exhibit halo-like chemical compositions, with an iron peak around [Fe/H] ≈ −1.40, and enhanced Ca and Mg content. Notably, we discovered a metal-rich tail, with [Fe/H] values ranging from −1 to approximately solar metallicity. This sub-group includes almost 1/4 of the sample, it is characterized by thin disc kinematics and displays sub-solar α-element abundances, marginally consistent with the majority of the MW stars. Surprisingly, they differ distinctly from typical MW disc stars in terms of the s-process elements Y and Ba. We took advantage of similar data available in the literature and built a total sample of 535 field RRLs for which we estimated kinematical and dynamical properties. We found that metal-rich RRLs (1/3 of the sample) likely represent an old component of the MW thin disc. We also detected RRLs with retrograde orbits and provided preliminary associations with the Gaia–Sausage–Enceladus, Helmi, Sequoia, Sagittarius, and Thamnos stellar streams.

Chemical Cartography of the Sagittarius Stream with Gaia

The stellar stream connected to the Sagittarius (Sgr) dwarf galaxy is the most massive tidal stream that has been mapped in the Galaxy, and is the dominant contributor to the outer stellar halo of the Milky Way (MW). We present metallicity maps of the Sgr stream, using 34,240 red giant branch stars with inferred metallicities from Gaia BP/RP spectra. This sample is larger than previous samples of Sgr stream members with chemical abundances by an order of magnitude. We measure metallicity gradients with respect to Sgr stream coordinates (Λ, B), and highlight the gradient in metallicity with respect to stream latitude coordinate B, which has not been observed before. Including the core, we find ∇[M/H] = −2.48 ± 0.08 × 10−2 dex deg−1 above the stream track (B > B 0, where B 0 = 1.5° is the latitude of the Sgr remnant) and ∇[M/H] = −2.02 ± 0.08 × 10−2 dex deg−1 below the stream track (B < B 0). By painting metallicity gradients onto a tailored N-body simulation of the Sgr stream, we find that the observed metallicities in the stream are consistent with an initial radial metallicity gradient in the Sgr dwarf galaxy of ∼−0.1 to −0.2 dex kpc−1, well within the range of observed metallicity gradients in Local Group dwarf galaxies. Our results provide novel observational constraints for the internal structure of the dwarf galaxy progenitor of the Sgr stream. Leveraging new large data sets in conjunction with tailored simulations, we can connect the present-day properties of disrupted dwarfs in the MW to their initial conditions.

Hints of a disrupted binary dwarf galaxy in the Sagittarius stream

ABSTRACT In this work, we look for evidence of a non-unity mass ratio binary dwarf galaxy merger in the Sagittarius stream. Simulations of such a merger show that, upon merging with a host, particles from the less massive galaxy will often mostly be found in the extended stream and less so in the central remnant. Motivated by these simulations, we use the Apache Point Observatory Galactic Evolution Experiment Data Release 17 chemical data from approximately 1100 stars in both the Sagittarius remnant and stream to look for evidence of contamination from a second dwarf galaxy. We separate the Sagittarius data into its remnant and stream and compare the [Mg/Fe] content of the two populations. In particular, we select [Mg/Fe] to search for hints of unique star formation histories among our sample stars. Comparing the stream and remnant populations, we find regions that have distinct [Mg/Fe] distributions for fixed [Fe/H], in addition to distinct chemical tracks in [Mg/Fe]–[Fe/H] abundance space. We show that there are large regions of the tracks for which the probability of the two samples being drawn from the same distribution is very low (p &amp;lt; 0.05). Furthermore, we show that the two tracks can be fit with unique star formation histories using simple, one-zone galactic chemical evolution models. While more work must be done to discern whether the hypothesis presented here is true, our work hints at the possibility that Sagittarius may consist of two dwarf galaxy progenitors.

Extended Stellar Populations in Ultrafaint Dwarf Galaxies

The possible existence of stellar halos in low-mass galaxies is being intensely discussed nowadays after some recent discoveries of stars located in the outskirts of dwarf galaxies of the Local Group. RR Lyrae stars can be used to identify the extent of these structures, taking advantage of the minimization of foreground contamination they provide. In this work we use RR Lyrae stars obtained from Gaia DR3, the Dark Energy Survey, the Zwicky Transient Facility, and Pan-STARRS1 to explore the outskirts of 45 ultrafaint dwarf galaxies. We associate the stars with a host galaxy based on their angular separations, magnitudes, and proper motions. We find a total of 120 RR Lyrae stars that belong to 21 different galaxies in our sample. We report seven new RR Lyrae stars in six ultrafaint dwarf galaxies (Hydrus I, Ursa Major I, Ursa Major II, Grus II, Eridanus II, and Tucana II). We found a large number of new possible members in Bootes I and Bootes III as well, but some of them may actually belong to the nearby Sagittarius stream. Adding to our list of 120 RR Lyrae stars the observations of other ultrafaint dwarf galaxies that were beyond the reach of our search, we find that at least 10 of these galaxies have RR Lyrae stars located at distances greater than four times their respective half-light radius, which implies that at least 33% of the 30 ultrafaint dwarfs with a population of RR Lyrae stars have extended stellar populations.

A Dynamically Distinct Stellar Population in the Leading Arm of the Sagittarius Stream

We present a chemical and dynamical analysis of the leading arm (LA) and trailing arm (TA) of the Sagittarius (Sgr) stream, as well as for the Sgr dwarf galaxy core (SC), using red giant branch, main-sequence, and RR Lyrae stars from large spectroscopic survey data. The different chemical properties among the LA, TA, and SC generally agree with recent studies and can be understood by a radial metallicity gradient established in the progenitor of the Sgr dwarf, followed by preferential stellar stripping from the outer part of the Sgr progenitor. One striking finding is a relatively larger fraction of low-eccentricity stars (e < 0.4) in the LA than in the TA and SC. The TA and SC exhibit very similar distributions. Considering that a tidal tail stripped off from a dwarf galaxy maintains the orbital properties of its progenitor, we expect that the e-distribution of the LA should be similar to that of the TA and SC. Thus, the disparate behavior of the e-distribution of the LA is of particular interest. Following the analysis of Vasiliev et al., we attempt to explain the different e-distribution by introducing a time-dependent perturbation of the Milky Way by the Large Magellanic Cloud's (LMC) gravitational pull, resulting in substantial evolution of the angular momentum of the LA stars to produce the low-e stars. In addition, we confirm from RR Lyrae stars with high eccentricity (e > 0.6) that the TA stars farther away from the SC are also affected by disturbances from the LMC.

Discovery of the shell structure via break radii in the outer halo of the Milky Way

ABSTRACT Based on the Gaia DR3 RR Lyrae catalogue, we use two methods to fit the density profiles with an improved broken power law, and find that there are two break radii coinciding with the two apocentre pile-ups of high-eccentricity Gaia-Sausage-Enceladus (GSE) merger. Also, there is a break caused by the Sagittarius (Sgr) stream. Combining the positions of all breaks, we briefly analyse the metallicity and its dispersion as a function of r as well as its distribution in cylindrical coordinates. For the clean sample, the z−x ellipsoid axial ratio q in $36\, {\rm kpc}\, \lt \, r\, \lt \, 96\, {\rm kpc}$ becomes much smaller than that of the inner halo $(r\, \lt \, 36\, {\rm kpc})$, while the major axis has a large uncertainty in the region of $36-66\, {\rm kpc}$ and the one in the region of $66-96\, {\rm kpc}$ is obviously different from that dominated by the Hercules–Aquila Cloud (HAC) and the Virgo Overdensity (VOD) in the inner halo, which indicates that there is an over-density structure distributed at low-zenithal angles. Finally, we found that the over-density structure in the outer halo ($r\, \gt \, 50\, {\rm kpc}$) is shell-shaped and relatively metal-rich compared to the outer background halo. We conclude that the shells could be the apocentre pile-ups of the high-eccentricity GSE merger, which is supported by previous numerical simulations.

Distant Echoes of the Milky Way’s Last Major Merger

The majority of the Milky Way’s stellar halo consists of debris from our galaxy’s last major merger, the Gaia-Sausage-Enceladus (GSE). In the past few years, stars from the GSE have been kinematically and chemically studied in the inner 30 kpc of our galaxy. However, simulations predict that accreted debris could lie at greater distances, forming substructures in the outer halo. Here we derive metallicities and distances using Gaia DR3 XP spectra for an all-sky sample of luminous red giant stars, and map the outer halo with kinematics and metallicities out to 100 kpc. We obtain follow-up spectra of stars in two strong overdensities—including the previously identified outer Virgo Overdensity—and find them to be relatively metal rich and on predominantly retrograde orbits, matching predictions from simulations of the GSE merger. We argue that these are apocentric shells of GSE debris, forming 60–90 kpc counterparts to the 15–20 kpc shells that are known to dominate the inner stellar halo. Extending our search across the sky with literature radial velocities, we find evidence for a coherent stream of retrograde stars encircling the Milky Way from 50 to 100 kpc, in the same plane as the Sagittarius Stream but moving in the opposite direction. These are the first discoveries of distant and structured imprints from the GSE merger, cementing the picture of an inclined and retrograde collision that built up our galaxy’s stellar halo.

Atmospheric Parameters and Kinematic Information for the M Giant Stars from LAMOST DR9

A catalog of more than 43,000 M giant stars has been selected by Li et al. from the ninth data release of LAMOST. Using the data-driven method SLAM, we obtain the stellar parameters (T eff, , [M/H], [α/M]) for all the M giant stars with uncertainties of 57 K, 0.25 dex, 0.16 dex and 0.06 dex at SNR > 100, respectively. With those stellar parameters, we constrain the absolute magnitude in the K − band, which brings distance with relative uncertainties around 25% statistically. Radial velocities are also calculated by applying cross correlation on the spectra between 8000 and 8950 Å with synthetic spectra from ATLAS9, which covers the Ca ii triplet. Comparison between our radial velocities and those from APOGEE DR17 and Gaia DR3 shows that our radial velocities have a system offset and dispersion around 1 and 4.6 km s−1, respectively. With the distances and radial velocities combining with the astrometric data from Gaia DR3, we calculate the full 6D position and velocity information, which are able to be used for further chemo-dynamic studies on the disk and substructures in the halo, especially the Sagittarius Stream.

Phase-space Properties and Chemistry of the Sagittarius Stellar Stream Down to the Extremely Metal-poor ([Fe/H] ≲ −3) Regime

In this work, we study the phase-space and chemical properties of the Sagittarius (Sgr) stream, the tidal tails produced by the ongoing destruction of the Sgr dwarf spheroidal (dSph) galaxy, focusing on its very metal-poor (VMP; [Fe/H] < −2) content. We combine spectroscopic and astrometric information from SEGUE and Gaia EDR3, respectively, with data products from a new large-scale run of the StarHorse spectrophotometric code. Our selection criteria yield ∼1600 stream members, including >200 VMP stars. We find the leading arm (b > 0°) of the Sgr stream to be more metal-poor, by ∼0.2 dex, than the trailing one (b < 0°). With a subsample of turnoff and subgiant stars, we estimate this substructure’s stellar population to be ∼1 Gyr older than the thick disk’s. With the aid of an N-body model of the Sgr system, we verify that simulated particles stripped earlier (>2 Gyr ago) have present-day phase-space properties similar to lower metallicity stream stars. Conversely, those stripped more recently (<2 Gyr) are preferentially akin to metal-rich ([Fe/H] > −1) members of the stream. Such correlation between kinematics and chemistry can be explained by the existence of a dynamically hotter, less centrally concentrated, and more metal-poor population in Sgr dSph prior to its disruption, implying that this galaxy was able to develop a metallicity gradient before its accretion. Finally, we identified several carbon-enhanced metal-poor ([C/Fe] > +0.7 and [Fe/H] ≤ −1.5) stars in the Sgr stream, which might be in tension with current observations of its remaining core where such objects are not found.

The Sagittarius stream inGaiaEarly Data Release 3 and the origin of the bifurcations

Context.The Sagittarius dwarf spheroidal (Sgr) is a dissolving galaxy being tidally disrupted by the Milky Way (MW). Its stellar stream still poses serious modelling challenges, which hinders our ability to use it effectively as a prospective probe of the MW gravitational potential at large radii.Aims.Our goal is to construct the largest and most stringent sample of stars in the stream with which we can advance our understanding of the Sgr-MW interaction, focusing on the characterisation of the bifurcations.Methods.We improved on previous methods based on the use of the wavelet transform to systematically search for the kinematic signature of the Sgr stream throughout the whole sky in theGaiadata. We then refined our selection via the use of a clustering algorithm on the statistical properties of the colour-magnitude diagrams.Results.Our final sample contains more than 700 000 candidate stars and is three times larger than previousGaiasamples. With it, we have been able to detect the bifurcation of the stream in both the northern and southern hemispheres, which requires four branches (two bright and two faint) to fully describe the system. We present the detailed proper motion distribution of the trailing arm as a function of the angular coordinate along the stream, showing, for the first time, the presence of a sharp edge (on the side of the small proper motions) beyond which there are no Sgr stars. We also characterise the correlation between kinematics and distance. Finally, the chemical analysis of our sample shows that the faint branch of the bifurcation is more metal poor than the bright. We provide analytical descriptions for the proper motion trends as well as for the sky distribution of the four branches of the stream.Conclusions.Based on our analysis, we interpret the bifurcations as a misaligned overlap of the material stripped at the antepenultimate pericentre (faint branches) with the stars ejected at the penultimate pericentre (bright branch), given that Sgr just went through its perigalacticon. The source of this misalignment is still unknown, but we argue that models with some internal rotation in the progenitor – at least during the time of stripping of the stars that are now in the faint branches – are worth exploring.

Probing the Galactic halo with RR Lyrae stars – II. The substructures of the Milky Way

ABSTRACT We identify substructures of the Galactic halo using 3003 type ab RR Lyrae stars with six-dimensional position–velocity information from the Sloan Digital Sky Survey, the Large Sky Area Multi-Object Fiber Spectroscopic Telescope and the Gaia Early Data Release 3. Based on this information, we define the separation of any two of the stars in the integrals of motion space and we identify substructures by utilizing the friends-of-friends algorithm. We identify members belonging to several known substructures: the Sagittarius stream, the Gaia-Enceladus-Sausage (GES), the Sequoia and the Helmi streams. In addition to these known substructures, there are three other substructures possibly associated with globular clusters NGC 5272, 6656 and 5024, respectively. Finally, we also find three remaining unknown substructures, one of which has large angular momentum and a mean metallicity −2.13 dex, which may be a new substructure. As for the GES, we find that it accounts for a large part of substructures in the inner halo and the apocentre distance is in the range 10–34 kpc, which suggests that the GES is mainly distributed in the inner halo. The near one-third proportion of the GES and the peak value of 20 kpc of the apocentre distance suggest that the GES could account for the break in the density profile of the Galactic halo at the Galactocentric distance ~20–25 kpc. The similarity when comparing the kinematic properties of the GES with the Hercules–Aquila Cloud and Virgo Overdensity suggests that the three substructures may have similar origins.

The chemo-dynamical groups of Galactic globular clusters

ABSTRACT We introduce a multicomponent chemo-dynamical method for splitting the Galactic population of globular clusters (GCs) into three distinct constituents: bulge, disc, and stellar halo. The latter is further decomposed into the individual large accretion events that built up the Galactic stellar halo: the Gaia–Enceladus–Sausage, Kraken and Sequoia structures, and the Sagittarius and Helmi streams. Our modelling is extensively tested using mock GC samples constructed from the auriga suite of hydrodynamical simulations of Milky Way (MW)-like galaxies. We find that, on average, a proportion of the accreted GCs cannot be associated with their true infall group and are left ungrouped, biasing our recovered population numbers to $\sim 80{{\ \rm per\ cent}}$ of their true value. Furthermore, the identified groups have a completeness and a purity of only $\sim 65{{\ \rm per\ cent}}$. This reflects the difficulty of the problem, a result of the large degree of overlap in energy-action space of the debris from past accretion events. We apply the method to the Galactic data to infer, in a statistically robust and easily quantifiable way, the GCs associated with each MW accretion event. The resulting groups’ population numbers of GCs, corrected for biases, are then used to infer the halo and stellar masses of the now defunct satellites that built up the halo of the MW.

A search for stellar structures around nine outer halo globular clusters in the Milky Way

ABSTRACT We use deep imaging from the Dark Energy Camera to explore the peripheral regions of nine globular clusters in the outer halo of the Milky Way. Apart from Whiting 1 and NGC 7492, which are projected against the Sagittarius stream, we see no evidence for adjacent stellar populations to indicate any of these clusters is associated with coherent tidal debris from a destroyed host dwarf. We also find no evidence for tidal tails around any of the clusters in our sample; however, both NGC 1904 and 6981 appear to possess outer envelopes. Motivated by a slew of recent Gaia-based discoveries, we compile a sample of clusters with robust detections of extra-tidal structure, and search for correlations with orbital properties. While we observe that clusters with tidal tails are typically on moderately or very eccentric orbits that are highly inclined to the Galactic plane and often retrograde, these are neither necessary nor sufficient conditions for the formation of extra-tidal structure. That many objects with tidal tails appear to be accreted leads us to speculate that this lack of consistency may stem from the inhomogeneous dynamical history of the Milky Way globular cluster system. Finally, we note that clusters with prominent stellar envelopes detected in ground-based imaging (such as NGC 1851 and 7089) are now all known from Gaia to possess long tidal tails – experimental confirmation that the presence of an extended envelope is indicative of tidal erosion.

The Galaxy Progenitors of Stellar Streams around Milky Way–mass Galaxies in the FIRE Cosmological Simulations

Abstract Stellar streams record the accretion history of their host galaxy. We present a set of simulated streams from disrupted dwarf galaxies in 13 cosmological simulations of Milky Way (MW)–mass galaxies from the FIRE-2 suite at z = 0, including seven isolated MW-mass systems and six hosts resembling the MW–M31 pair. In total, we identify 106 simulated stellar streams, with no significant differences in the number of streams and the masses of their progenitors between the isolated and paired environments. We resolve simulated streams with stellar masses ranging from ∼5 × 105 up to ∼109 M ⊙, similar to the mass range between the Orphan and Sagittarius streams in the MW. We confirm that present-day simulated satellite galaxies are good proxies for stellar stream progenitors, with similar properties including their stellar mass function, velocity dispersion, [Fe/H] and [α/H] evolution tracks, and orbital distribution with respect to the galactic disk plane. Each progenitor’s lifetime is marked by several important timescales: its infall, star formation quenching, and stream formation times. We show that the ordering of these timescales is different between progenitors with stellar masses higher and lower than ∼2 × 106 M ⊙. Finally, we show that the main factor controlling the rate of phase mixing, and therefore the rate of fading, of tidal streams from satellite galaxies in MW-mass hosts is the nonadiabatic evolution of the host potential. Other factors commonly used to predict phase-mixing timescales, such as progenitor mass and orbital circularity, show virtually no correlation with the number of dynamical times required for a stream to become phase-mixed.

Identification of Sagittarius stream members in angular momentum space with gaussian mixture techniques

ABSTRACT This paper uses Gaussian mixture techniques to dissect the Milky Way (MW) stellar halo in angular momentum space. Application to a catalogue of 5389 stars near the plane of the Sagittarius (Sgr) stream with full 6D phase-space coordinates supplied by Gaia EDR3 and SEGUE returns four independent dynamical components. The broadest and most populated corresponds to the smooth MW halo. The narrowest and faintest contains 40 stars of the Orphan stream. We find a component with little or no angular momentum likely associated with the Gaia-Sausage-Enceladus substructure. We also identify 925 stars and 7 globular clusters with probabilities $\gt 90{{\ \rm per\ cent}}$ to be members of the Sgr stream. Comparison against N-body models shows that some of these members trace the continuation of the leading/trailing tails in the Southern/Northern hemispheres. The new detections span ∼800° on the sky, thus wrapping the Galaxy twice.

The outer disc in shambles: Blind detection of Monoceros and the ACS with Gaia’s astrometric sample

Context. The Gaia astrometric sample allows us to study the outermost Galactic disc, the halo, and their interface. It is precisely at the very edge of the disc where the effects of external perturbations are expected to be the most noticeable. Aims. Our goal is to detect the kinematic substructure present in the halo and at the edge of the Milky Way (MW) disc and provide observational constraints on their phase-space distribution. Methods. We download, one HEALpix at a time, the proper motion histogram of distant stars, to which we apply a wavelet transformation to reveal the significant overdensities. We then analyse the large coherent structures that appear in the sky. Results. We reveal a sharp yet complex anticentre dominated by Monoceros (MNC) and the Anticentre Stream (ACS) in the north – which we find have intensities comparable to the Magellanic Clouds and the Sagittarius stream – and by MNC South and TriAnd at negative latitudes. Our method allows us to perform a morphological analysis of MNC and the ACS, both of which span more than 100° in longitude, and to provide a high purity sample of giants with which we track MNC down to latitudes as low as ∼5°. Their colour-magnitude diagram is consistent with extended structures at a distance of ∼10−11 kpc that originated in the disc, with a very low ratio of RR Lyrae over M giants, and with kinematics compatible with the rotation curve at those distances or slightly slower. Conclusions. We present a precise characterisation of MNC and the ACS, two previously known structures that our method reveals naturally, allowing us to detect them without limiting ourselves to a particular stellar type and, for the first time, using only kinematics. Our results will allow future studies to model their chemo-dynamics and evolution, thus constraining some of the most influential processes that shaped the MW.

Proper motion measurements for stars up to 100 kpc with Subaru HSC and SDSS Stripe 82

ABSTRACT We present proper motion measurements for more than 0.55 million main-sequence stars, by comparing astrometric positions of matched stars between the multiband imaging data sets from the Hyper Suprime-Cam (HSC) Survey and the Sloan Digital Sky Survey (SDSS) Stripe 82. In doing this, we use 3 million galaxies to recalibrate the astrometry and set up a common reference frame between the two catalogues. The exquisite depth and the nearly 12 yr of time baseline between HSC and SDSS enable high-precision measurements of statistical proper motions for stars down to i ≃ 24. A validation of our method is demonstrated by the agreement with the Gaia proper motions, to the precision better than 0.1 mas yr−1. To retain the precision, we make a correction of the subtle effects due to the differential chromatic refraction in the SDSS images based on the comparison with the Gaia proper motions against colour of stars, which is validated using the SDSS spectroscopic quasars. Combining with the photometric distance estimates for individual stars based on the precise HSC photometry, we show a significant detection of the net proper motions for stars in each bin of distance out to 100 kpc. The two-component tangential velocities after subtracting the apparent motions due to our own motion display rich phase-space structures including a clear signature of the Sagittarius stream in the halo region of distance range [10, 35] kpc. We also measure the tangential velocity dispersion in the distance range 5–20 kpc and find that the data are consistent with a constant isotropic dispersion of 80 ± 10 km s−1. More distant stars appear to have random motions with respect to the Galactic Centre on average.

The mass of the Milky Way out to 100 kpc using halo stars

ABSTRACT We use a distribution function analysis to estimate the mass of the Milky Way (MW) out to 100 kpc using a large sample of halo stars. These stars are compiled from the literature, and the vast majority (${\sim } 98{{\ \rm per\ cent}}$) have 6D phase-space information. We pay particular attention to systematic effects, such as the dynamical influence of the Large Magellanic Cloud (LMC), and the effect of unrelaxed substructure. The LMC biases the (pre-LMC infall) halo mass estimates towards higher values, while realistic stellar haloes from cosmological simulations tend to underestimate the true halo mass. After applying our method to the MW data, we find a mass within 100 kpc of M (&amp;lt;100 kpc) = 6.07 ± 0.29 (stat.) ± 1.21 (sys.) × 1011 M⊙. For this estimate, we have approximately corrected for the reflex motion induced by the LMC using the Erkal et al. model, which assumes a rigid potential for the LMC and MW. Furthermore, stars that likely belong to the Sagittarius stream are removed, and we include a 5 per cent systematic bias, and a 20 per cent systematic uncertainty based on our tests with cosmological simulations. Assuming the mass–concentration relation for Navarro–Frenk–White haloes, our mass estimate favours a total (pre-LMC infall) MW mass of M200c = 1.01 ± 0.24 × 1012 M⊙, or (post-LMC infall) mass of M200c = 1.16 ± 0.24 × 1012 M⊙ when a 1.5 × 1011 M⊙ mass of a rigid LMC is included.