Our knowledge of the dynamics and masses of galaxies in the Local Group has long been limited by the fact that only line-of-sight velocities were observationally accessible. This introduces significant degeneracies in dynamical models, which can only
be resolved by measuring also the velocity components perpendicular to the line of sight. However, beyond the solar neighborhood, the corresponding proper motions have generally been too small to measure. This has changed dramatically over the past decade, especially due to the angular resolution and stability available on the Hubble Space Telescope. Proper motions can now be reliably measured throughout the Local Group, as illustrated by, e.g., the work of the HSTPROMO collaboration. In this review, I summarize the importance of proper motions for Local Group science, and I describe the current and future observational approaches and facilities available to measure proper motions. I highlight recent results on various Milky Way populations (globular clusters, the bulge, the metal-poor halo, hypervelocity stars, and tidal streams), dwarf satellite galaxies, the Magellanic Clouds and the Andromeda System.
We present a multi-epoch Hubble Space Telescope (HST) study of stellar proper motions (PMs) for four fields spanning 200 degrees along the Sagittarius (Sgr) stream: one trailing arm field, one field near the Sgr dwarf spheroidal tidal radius, and two
leading arm fields. We determine absolute PMs of dozens of individual stars per field, using established techniques that use distant background galaxies as stationary reference frame. Stream stars are identified based on combined color-magnitude diagram and PM information. The results are broadly consistent with the few existing PM measurements for the Sgr galaxy and the trailing arm. However, our new results provide the highest PM accuracy for the stream to date, the first PM measurements for the leading arm, and the first PM measurements for individual stream stars; we also serendipitously determine the PM of the globular cluster NGC~6652. In the trailing-arm field, the individual PMs allow us to kinematically separate trailing-arm stars from leading-arm stars that are 360 degrees further ahead in their orbit. Also, in three of our fields we find indications that two distinct kinematical components may exist within the same arm and wrap of the stream. Qualitative comparison of the HST data to the predictions of the Law & Majewski and Penarrubia et al. N-body models show that the PM measurements closely follow the predicted trend with Sgr longitude. This provides a successful consistency check on the PM measurements, as well as on these N-body approaches (which were not tailored to fit any PM data).
The Hubble Space Telescope (HST) has proven to be uniquely suited for the measurement of proper motions (PMs) of stars and galaxies in the nearby Universe. Here we summarize the main results and ongoing studies of the HSTPROMO collaboration, which ov
er the past decade has executed some two dozen observational and theoretical HST projects on this topic. This is continuing to revolutionize our dynamical understanding of many objects, including: globular clusters; young star clusters; stars and stellar streams in the Milky Way halo; Local Group galaxies, including dwarf satellite galaxies, the Magellanic Clouds, and the Andromeda galaxy; and AGN Black Hole Jets.
We present the first detailed assessment of the large-scale rotation of any galaxy based on full three-dimensional velocity measurements. We do this for the LMC by combining our HST average proper motion (PM) measurements for stars in 22 fields, with
existing line-of-sight (LOS) velocity measurements for 6790 individual stars. We interpret these data with a model of circular rotation in a flat disk. The PM and LOS data paint a consistent picture of the LMC rotation and their combination yields several new insights. The PM data imply a stellar dynamical center that coincides with the HI dynamical center, and a rotation curve amplitude consistent with that inferred from LOS velocity studies. The implied disk viewing angles agree with the range of values found in the literature, but continue to indicate variations with stellar population and/or radius. Young (RSG) stars rotate faster than old (RGB/AGB) stars due to asymmetric drift. Outside the central region, the circular velocity is approximately flat at Vcirc = 91.7 +/- 18.8 km/s. This is consistent with the baryonic Tully-Fisher relation, and implies an enclosed mass M(8.7 kpc) = (1.7 +/- 0.7) x 10^10 solar masses. The virial mass is larger and depends on the full extent of the dark halo. The tidal radius is 22.3 +/- 5.2 kpc (24.0 +/- 5.6 degrees). Combination of the PM and LOS data yields kinematic distance estimates for the LMC, but these are not yet competitive with other methods.
We present proper motions for the Large & Small Magellanic Clouds (LMC & SMC) based on three epochs of textit{Hubble Space Telescope} data, spanning a $sim 7$ yr baseline, and centered on fields with background QSOs. The first two epochs, the subject
of past analyses, were obtained with ACS/HRC, and have been reanalyzed here. The new third epoch with WFC3/UVIS increases the time baseline and provides better control of systematics. The three-epoch data yield proper motion random errors of only 1-2% per field. For the LMC this is sufficient to constrain the internal proper motion dynamics, as will be discussed in a separate paper. Here we focus on the implied center-of-mass proper motions: mu_W(LMC) = -1.910 +/- 0.020 mas/yr, mu_N(LMC) = 0.229 +/- 0.047 mas/yr, and mu_W(SMC) = -0.772 +/- 0.063 mas/yr, mu_N(SMC) = -1.117 +/- 0.061 mas/yr. We combine the results with a revised understanding of the solar motion in the Milky Way to derive Galactocentric velocities: v_{tot,LMC} = 321 +/- 24 km/s and v_{tot,SMC} = 217 +/- 26 km/s. Our proper motion uncertainties are now dominated by limitations in our understanding of the internal kinematics and geometry of the Clouds, and our velocity uncertainties are dominated by distance errors. Orbit calculations for the Clouds around the Milky Way allow a range of orbital periods, depending on the uncertain masses of the Milky Way and LMC. Periods $lesssim 4$ Gyr are ruled out, which poses a challenge for traditional Magellanic Stream models. First-infall orbits are preferred (as supported by other arguments as well) if one imposes the requirement that the LMC and SMC must have been a bound pair for at least several Gyr.
We present the first absolute proper motion measurement of Leo I, based on two epochs of HST ACS/WFC images separated by ~5 years. The average shift of Leo I stars with respect to ~100 background galaxies implies a proper motion of (mu_W, mu_N) = (0.
1140 +/- 0.0295, -0.1256 +/- 0.0293) mas/yr. The implied Galactocentric velocity vector, corrected for the reflex motion of the Sun, has radial and tangential components V_rad = 167.9 +/- 2.8 km/s and V_tan = 101.0 +/- 34.4 km/s, respectively. We study the detailed orbital history of Leo I by solving its equations of motion backward in time for a range of plausible mass models for the Milky Way and its surrounding galaxies. Leo I entered the Milky Way virial radius 2.33 +/- 0.21 Gyr ago, most likely on its first infall. It had a pericentric approach 1.05 +/- 0.09 Gyr ago at a Galactocentric distance of 91 +/- 36 kpc. We associate these time scales with characteristic time scales in Leo Is star formation history, which shows an enhanced star formation activity ~2 Gyr ago and quenching ~1 Gyr ago. There is no indication from our calculations that other galaxies have significantly influenced Leo Is orbit, although there is a small probability that it may have interacted with either Ursa Minor or Leo II within the last ~1 Gyr. For most plausible Milky Way masses, the observed velocity implies that Leo I is bound to the Milky Way. However, it may not be appropriate to include it in models of the Milky Way satellite population that assume dynamical equilibrium, given its recent infall. Solution of the complete (non-radial) timing equations for the Leo I orbit implies a Milky Way mass M_MW,vir = 3.15 (-1.36, +1.58) x 10^12 Msun, with the large uncertainty dominated by cosmic scatter. In a companion paper, we compare the new observations to the properties of Leo I subhalo analogs extracted from cosmological simulations.
We study the future orbital evolution and merging of the MW-M31-M33 system, using a combination of collisionless N-body simulations and semi-analytic orbit integrations. Monte-Carlo simulations are used to explore the consequences of varying the init
ial phase-space and mass parameters within their observational uncertainties. The observed M31 transverse velocity implies that the MW and M31 will merge t = 5.86 (+1.61-0.72) Gyr from now, after a first pericenter at t = 3.87 (+0.42-0.32) Gyr. M31 may (probability p=41%) make a direct hit with the MW (defined here as a first-pericenter distance less than 25 kpc). Most likely, the MW and M31 will merge first, with M33 settling onto an orbit around them. Alternatively, M33 may make a direct hit with the MW first (p=9%), or M33 may get ejected from the Local Group (p=7%). The MW-M31 merger remnant will resemble an elliptical galaxy. The Sun will most likely (p=85%) end up at larger radius from the center of the MW-M31 merger remnant than its current distance from the MW center, possibly further than 50 kpc (p=10%). The Sun may (p=20%) at some time in the next 10 Gyr find itself moving through M33 (within 10 kpc), but while dynamically still bound to the MW-M31 merger remnant. The arrival and possible collision of M31 (and possibly M33) with the MW is the next major cosmic event affecting the environment of our Sun and solar system that can be predicted with some certainty. (Abridged)
We determine the velocity vector of M31 with respect to the Milky Way and use this to constrain the mass of the Local Group, based on HST proper-motion measurements presented in Paper I. We construct N-body models for M31 to correct the measurements
for the contributions from stellar motions internal to M31. We also estimate the center-of-mass motion independently, using the kinematics of satellite galaxies of M31 and the Local Group. All estimates are mutually consistent, and imply a weighted average M31 heliocentric transverse velocity of (v_W,v_N) = (-125.2+/-30.8, -73.8+/-28.4) km/s. We correct for the reflex motion of the Sun using the most recent insights into the solar motion within the Milky Way. This implies a radial velocity of M31 with respect to the Milky Way of V_rad = -109.3+/-4.4 km/s, and a tangential velocity V_tan = 17.0 km/s (<34.3 km/s at 1-sigma confidence). Hence, the velocity vector of M31 is statistically consistent with a radial (head-on collision) orbit towards the Milky Way. We revise prior estimates for the Local Group timing mass, including corrections for cosmic bias and scatter. Bayesian combination with other mass estimates yields M_LG = M_MW(vir) + M_M31(vir) = (3.17 +/- 0.57) x 10^12 solar masses. The velocity and mass results imply at 95% confidence that M33 is bound to M31, consistent with expectation from observed tidal deformations. (Abridged)
We present the first proper motion measurements for the galaxy M31. We obtained new V-band imaging data with the HST ACS/WFC and WFC3/UVIS of a spheroid field near the minor axis, an outer disk field along the major axis, and a field on the Giant Sou
thern Stream. The data provide 5-7 year time baselines with respect to pre-existing deep first-epoch observations. We measure the positions of thousands of M31 stars and hundreds of compact background galaxies in each field. High accuracy and robustness is achieved by building and fitting a unique template for each individual object. The average proper motion for each field is obtained from the average motion of the M31 stars between the epochs with respect to the background galaxies. For the three fields, the observed proper motions (mu_W,mu_N) are (-0.0458, -0.0376), (-0.0533, -0.0104), and (-0.0179,-0.0357) mas/yr, respectively. The ability to average over large numbers of objects and over the three fields yields a final accuracy of 0.012 mas/yr. The robustness of the proper-motion measurements and uncertainties are supported by the fact that data from different instruments, taken at different times and with different telescope orientations, as well as measurements of different fields, all yield statistically consistent results. Papers II and III explore the implications for our understanding of the history, future, and mass of the Local Group. (Abridged)
We review our understanding of the kinematics of the LMC and the SMC, and their orbit around the Milky Way. The line-of-sight velocity fields of both the LMC and SMC have been mapped with high accuracy using thousands of discrete traces, as well as H
I gas. The LMC is a rotating disk for which the viewing angles have been well-established using various methods. The disk is elliptical in its disk plane. The disk thickness varies depending on the tracer population, with V/sigma ranging from 2-10 from the oldest to the youngest population. For the SMC, the old stellar population resides in a spheroidal distribution with considerable line-of-sight depth and low V/sigma. Young stars and HI gas reside in a more irregular rotating disk. Mass estimates based on the kinematics indicate that each Cloud is embedded in a dark halo. Proper motion measurements with HST show that both galaxies move significantly more rapidly around the Milky Way than previously believed. This indicates that for a canonical 10^12 solar mass Milky Way the Clouds are only passing by us for the first time. Although a higher Milky Way mass yields a bound orbit, this orbit is still very different from what has been previously assumed in models of the Magellanic Stream. Hence, much of our understanding of the history of the Magellanic System and the formation of the Magellanic Stream may need to be revised. The accuracy of the proper motion data is insufficient to say whether or not the LMC and SMC are bound to each other, but bound orbits do exist within the proper motion error ellipse.
