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To understand the history of the Magellanic System and the origin of the Magellanic Stream it is important to know the orbit of the Magellanic Clouds around the Milky Way. This requires for each Cloud knowledge of all three of the velocity components of the center of mass. Line-of-sight velocities can be accurately determined from the Doppler velocities of tracers. However, determination of the velocity in the plane of the sky through proper motions is much more difficult. This was the primary obstacle for a long time, but recent breakthroughs have now yielded considerable progress.

4.1. Proper Motions

Previous attempts at measuring the proper motions (PMs) of the LMC and SMC from the ground or with Hipparcos were reviewed in vdM02. However, this earlier work has now been largely superseded by the studies performed with the ACS/HRC on HST by Kallivayalil et al. (2006a, b; hereafter K06a,b). Two epochs of data were obtained with a ~ 2 year time baseline for 21 fields in the LMC and 5 fields in the SMC, all centered on background quasars identified from the MACHO database (Geha et al. 2003). PMs were obtained for each field by measuring the average shift of the stars with respect to the background quasar. Upon correction for the orientation and rotation of the LMC disk, each field yields an independent estimate of the center-of-mass PM. The average for the different fields yields the final estimate, while the RMS among the results from the N different fields yields the PM error RMS / N1/2.

K06a, b obtained for the PMs in the West and East directions that

Equation 6 (6)

The same data were reanalyzed more recently by P08. Using an independent analysis with different software and point spread function models they obtained that

Equation 7 (7)

P08 made magnitude-dependent corrections for small charge transfer inefficiency effects. By contrast, K06a, b assumed that these effects (always along the detector y axis) average to zero over all fields because of the random telescope orientations used for different fields. The fact the the results from these two studies are generally in good agreement for the LMC confirms the validity of this assumption. However, the explicit correction applied by P08 does yield better agreement between different fields, and therefore smaller errorbars. For the SMC, the results for the individual fields are in good agreement between the studies. However, the studies used different methods for weighted averaging of the fields, with K06a, b being more conservative and allowing for potential unknown systematic effects. This produces both larger errorbars than in P08, as well as a significant difference in µW.

Transformation of the PMs to a space velocity in km s-1 requires knowledge of the distance D0. For the LMC, D0 approx 50.1 kpc, so that 1 mas yr-1 corresponds to 238 km s-1. For the SMC, D0 approx 61.6 kpc, so that 1 mas yr-1 corresponds to 293 km s-1. After transformation of the PM to km s-1, it can be combined with the observed center-of-mass line-of-sight velocity to obtain the full three-dimensional velocity vector. For the LMC, vsys = 262.2 ± 3.4 km s-1 (vdM02); and for the SMC, vsys = 146 ± 0.6 km s-1 (Harris & Zaritsky 2006). The resulting vectors can be corrected for the solar reflex motion and transformed to the Galactocentric rest-frame as described in vdM02. For the LMC this yields that the motion has a radial component of Vrad = 89 ± 4 km s-1 pointing away from the Galactic center, and a tangential component of Vtan = 367 ± 18 km s-1. 2

4.2. Orbit around the Milky Way

The combination of a small but positive radial velocity and a tangential velocity that exceeds the circular velocity of the Milky Way halo implies that the Clouds must be just past pericenter. The calculation of an actual orbit requires detailed knowledge of the gravitational potential of the Milky Way dark halo. Past work had generally assumed that the dark halo can be approximated by a spherical logarithmic potential. Estimates of the transverse velocities of the Clouds based on models of the Magellanic Stream had suggested that for the LMC Vtan = 287 km s-1 (e.g., Gardiner, Sawa, & Fujimoto 1994; Gardiner & Noguchi 1996). This then yielded an orbit with an apocenter to pericenter ratio of ~ 2.6:1 and an orbital period of ~ 1.6 Gyr. This orbit was adopted by most subsequent modeling studies of the Magellanic System. However, the new HST PM measurements significantly revise this view. The observed Vtan is 80 ± 16 km s-1 larger than the Gardiner & Noguchi (1996) value, and therefore inconsistent with it at ~ 5sigma. The observed value implies a much larger apocenter distance (in excess of 200 kpc) at which the assumption of a logarithmic potential is not a good assumption.

Motivated by these considerations, Besla et al. (2007) performed a new study of the Magellanic Cloud orbits using an improved Milky Way model, combined with the K06a, b HST PMs. The Milky Way model was chosen similar to that proposed in Klypin et al. (2002). It consists of disk, bulge, hot gaseous halo, and dark halo components. The dark halo has a LambdaCDM-motivated NFW potential with adiabatic contraction. In the fixed Milky Way potential, the orbits of the LMC and SMC were integrated backwards in time, starting from the current observed positions and velocities. The extent of the galaxies was taken into account in the calculation of their mutual gravitational interaction, and a parameterized prescription was used to account for dynamical friction. The gravitational influence of M31 can be taken into account in this formalism as well, but this make little difference to the results (Kallivayalil 2007; Shattow & Loeb 2008).

The most favored Milky Way model presented by Klypin et al. (2002) has a total mass M = 1012 Modot. In this model, the escape velocity at 50 kpc is ~ 380 km s-1. This is very similar to the observed Vtan of the LMC, and as a result, the inferred orbit is approximately parabolic, with no previous pericenter passage. In other words, the Magellanic Clouds are passing by the Milky Way now for the first time. To obtain an orbit that is significantly bound, µW would have to be larger by ~ +0.3 mas yr-1 (4sigma with the K06a errorbar, or 7sigma with the P08 errorbar). Alternatively, it is possible that the Milky Way is more massive (Smith et al. 2007; Shattow & Loeb 2008). A mass of M = 2 × 1012 Modot is more or less the largest mass consistent with the available observational constraints (see also the discussion in van der Marel & Guhathakurta 2008). This would produce a bound orbit. However, with either the larger Milky Way mass or with the larger µW, the orbit would still be quite different than has been previously assumed in models of the Magellanic System. There would be only 1 previous pericenter passage, the apocenter distance would be 400 kpc or more, and the period would be 6-7 Gyr. 3 Therefore, the new PM results drastically alter our view of the history of the Magellanic System.

The view that the Magellanic Clouds may be passing by the Milky Way for the first time may seem revolutionary at first. However, there are arguments to consider this reasonable. Van den Bergh (2006) pointed out that the LMC and SMC are unusual in that they are the only satellites in the Local Group that are both gas rich and located close to their parent galaxy. He suggested based on this that the Magellanic Clouds are interlopers that were originally formed in the outer reaches of the Local Group. Moreover, cosmological simulations show that: (a) accretion of LMC-sized subhalos by Milky-Way sized halos is common since z ~ 1; and (b) finding long-term satellites with small pericenter distances around Milky-Way sized halos is rare (Kazantzidis et al. 2008). Therefore, a scenario in which the Magellanic Clouds are passing by the Milky Way now for the first time seems more likely from a purely cosmological perspective than a scenario in which they have been satellites for many orbital periods of 1-2 Gyr each.

4.3. LMC-SMC orbit

Although the Magellanic Clouds may not bound to the Milky Way, it would be much more unlikely for the Magellanic Clouds not to be bound to each other. The likelihood of two satellite galaxies running into each other by chance is quite low. Also, various properties of the Clouds (such as their common HI envelope) suggest that they have been associated with each other for a significant time. The K06a, b PMs imply a relative velocity between the SMC and LMC of 105 ± 42 km s-1. Orbit calculations (K06b; Besla et al. 2007) show that the error bar on this is too large to say with any confidence whether or not they are indeed bound. However, binary orbits do exist within the 1sigma error ellipse, so there seems little reason to depart from this null hypothesis. Indeed, there are allowed orbits that have close passages between the Clouds at ~ 0.3 Gyr and ~ 1.5 Gyr in the past (Besla et al., these proceedings). These are the time scales that have been previously associated with the formation of the Magellanic Bridge and Stream, respectively.

4.4. Magellanic Stream

The Magellanic Stream is discussed in detail in other contributions in this volume. One important thing to note though in the present context is that the new insights into the orbit of the Magellanic Clouds around the Milky Way drastically affect our understanding of the Magellanic Stream. The Stream does not lie along the projected path on the sky traced by the LMC and SMC orbits, and the HI velocity along the Stream is not as steep as that along the orbits (Besla et al. 2007). This is inconsistent with purely tidal models of the stream (e.g., Gardiner & Noguchi 1996; Connors, Kawata & Gibson 2006). Moreover, the more limited number of passages through the Milky Way disk, and the larger radius at which this occurs, imply that the ram pressure models that have been proposed (e.g., Moore & Davis 1994; Mastropietro et al. 2005) probably won't work either. It is therefore essential that models of the Magellanic Stream be revisited, with an eye towards inclusion of new physics and exploration of new scenarios (see Besla et al., these proceedings). The recent finding by Nidever, Majewski & Burton (2008) that one filament of the Magellanic Stream, containing more than half its gas mass, can be traced back to the 30 Doradus star forming region in the LMC is particularly interesting in this context. This indicates that an outflow may have created or contributed to the Stream, which has not been addressed in previous models.

2 These velocities are based on the K06a PM values. However, use of the P08 PM values would yield similar velocities that would not alter the arguments in the remainder of the text. Back.

3 if this were in fact the case, then the mass build-up of the Milky Way with time, as in e.g. Wechsler et al. (2002), would also have to be taken into account for calculation of an accurate orbit. Back.

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