THE ORIGIN OF THE MAGELLANIC STREAM

Ben Moore and Marc Davis

Department of Astronomy, University of California, Berkeley, CA 94720, USA

ABSTRACT

Recent measurements of the proper motion of the Large Magellanic Cloud (LMC) show it to be moving in a nearly circular orbit around the Milky Way and to be leading the Magellanic Stream which stretches in a well-confined arc 100 degrees behind it. We present numerical investigations designed to critically test models of the origin of the Magellanic Stream. The most developed model is the tidal model which fails to reproduce several of its characteristic properties: (i) High resolution numerical simulations of tidal stripping show that stripped material from the LMC would retain the internal velocities of the LMC and would define a thick plane surrounding the Milky Way, not the tightly confined wake actually observed. (ii) There is no leading stream as would be expected if it were tidally produced. (iii) The observed radial velocity along the Stream is inconsistent with the observed orbital parameters of the Magellanic Clouds. (iv) The uniform variation in column density along the Stream cannot be reproduced by tidal forces. (v) No stars have been observed within the Stream, but stars should be tidally stripped from the LMC as easily as gas. Recent refinements to the tidal model (Gardiner et al. 1994, Lin et al. 1994) address some, but not all of these problems.

We suggest an alternative model for the origin of the Magellanic Stream which can explain all of its observed features and dynamics, as well as provide a strong constraint on the distribution of gas within the halo of the Milky Way. We propose that the Stream consists of material which was ram-pressure stripped from the Magellanic System during its last passage through an extended ionized disk of the Galaxy. This collision took place some 500 million years ago at a galacto-centric distance of about 65 kpc, and swept % of the least bound HI into the Stream. The gas with the lowest column density lost the most orbital angular momentum. At the present time this material is at the tip of the Stream and has fallen to a distance of kpc from the Milky Way attaining a negative velocity of 200 . To prevent the stripped material from leading the Magellanic Clouds and attaining too large an infall velocity, we postulate the existence of an extended dilute halo of diffuse ionized gas surrounding the Milky Way. If the halo gas is at the virial temperature of the potential well of the Milky Way (K), its thermal emission would contribute 40% of the observed diffuse background radiation in the 0.5-1.0 keV (M) band which is consistent with recent ROSAT measurements as well as pulsar dispersion measures. Ram pressure stripping from this extended disk and gaseous halo would explain the absence of gas in globular clusters and dwarf spheroidal companions to the Milky Way. Some fraction of the observed high velocity clouds might be the infalling debris from previous orbits of the LMC through the extended disk.

Key words: ISM: general - Intergalactic medium - Galaxy: general - Galaxies: interactions - Magellanic Clouds - Dark matter

§1. INTRODUCTION

The Magellanic Stream (MS) is a thin tail of neutral hydrogen (HI) which stretches over across the sky and joins onto the Magellanic Clouds (MCs). The MS is essentially continuous throughout its length with width , although Mathewson et al. (1977,1984) identify six subclumps within the Stream which they name MSI - MSVI. The MS has several distinguishing features which allow a detailed comparison with models of its origin: The mean column density of gas decreases the further away from the MCs, from close to the MCs, to at the tip of the Stream. Furthermore, the radial velocity along the MS varies smoothly along its length, from at its tip to near the MCs. Table 1 summarises the main features of MSI - MSVI. Columns 2 to 4 list the mean column density of neutral hydrogen, the angular distance of each cloud behind the Small Magellanic Cloud (SMC), and the observed radial velocity calculated assuming a circular velocity at the sun of 220 . For continuity we have also shown the corresponding values for the SMC.

Several mechanisms for the origin of the MS have been proposed, although the only model to be developed in detail is the tidal model proposed by Lin & Lynden-Bell (1979, 1982) and Murai & Fujimoto (1980). These authors attempt to explain the variation of radial velocity along the MS by assuming that it is tidal debris torn from the MCs some 2 billion years ago when they were at pericenter one full orbit ago. In order to reproduce the high negative velocity at the tip of the MS, these models require a high transverse motion for the MCs and an extended massive halo surrounding the Milky Way. Dynamical evidence of large halos surrounding galaxies has been steadily accumulating. In particular, orbital analyses of the satellite galaxies of the Milky Way and our motion towards Andromeda suggest that our own halo extends to at least 100 kpc (Zaritsky et al. 1989, Kahn & Woltjer 1959).

The transverse motion of the Large Magellanic Cloud (LMC) has recently been measured by Jones et al. (1994) and Tucholke & Hiesgen (1991). These authors have compared the present day positions of stars with old photographic plate measurements to infer the proper motion of the LMC. Although the measurement errors are fairly large, the results confirm the assumptions of previous models that the MS is in fact trailing the MCs and lies close to the orbital plane. Furthermore, the orbit of the LMC is observed to be approximately circular, providing additional evidence for a massive halo extending beyond 50 kpc. The original tidal models were based on the results from fairly crude numerical simulations since the orbits of only a limited number of particles could be followed. It is therefore of interest to examine these models in more detail, taking advantage of the new orbital information and the ability to integrate the equations of motion of a large number of particles with high resolution.

In addition to the tidal scenario, several other models have been proposed for explaining the origin of the MS (see Wayte 1991 for a review). These models are not as well developed and all suffer from serious flaws. For example, Mathewson (1987) proposed that the Stream consists of material swept from the intra-cloud region of the MCs via ram pressure stripping by repeated collisions with high velocity clouds in the halo. This idea is motivated by the proximity of several such clouds to the MCs and MS, and the clumpy nature of the Stream. However, several direct encounters are needed, all of which must occur in the same direction and within the last half of a Gyr. This requires both a high level of coincidence and a high space density of gas clouds in the halo. Furthermore, this model would predict distinctly separated clumps of material within the Stream and no correlation of column density with distance from the MCs. Continuous ram-pressure stripping models (Meurer et al. 1985), which Liu (1992) combined with a gravitational wake scenario, require a high density of gas at large distances within the halo atoms . These models can be ruled out by the observed emission measure of low energy X-rays which is an order of magnitude lower than this model would predict. Futhermore, these models cannot explain the clumpy nature of the gas or the high infall velocity at the tip of the Stream.

In Section 2 we perform high resolution numerical simulations of satellite galaxies in order to investigate the dynamics of tidally produced features. We use the results from these simulations to discuss several fundamental flaws in the tidal model for the origin of the MS. In Section 3 we study possible orbits of the Magellanic Clouds in the light of the uncertain transverse velocities of the LMC and SMC. In Section 4 we propose and investigate a new model for the origin of the MS and in Section 5 we discuss some interesting observational consequences and predictions of this model. Our results are concluded in Section 6.

§2. TIDES AND TAILS

In this section we examine the processes by which tidal forces remove material from galaxies orbiting under the influence of an extended potential. In particular, we want to study the effects of the Galaxy's gravitational field on its satellite galaxies such as Fornax or the Magellanic Clouds. Our interest in this study is primarily in the stripped material and the formation of tidal features. (A complete analysis of the response of the internal structure of satellites orbiting within an extended potential is in preparation.)

The tidal radius, , specifies an approximate extent to a satellite galaxy beyond which material will become bound to the larger galaxy's deeper potential. For a bound system of stars of total mass orbiting within an extended massive halo, the tidal radius can be calculated approximately using

where is the mass within the pericentric distance and the gradient across the satellite has been ignored. Stars belonging to the satellite galaxy can gain energy via two body encounters causing a slow but constant mass loss as stars escape through the tidal radius. If the satellite is on an eccentric orbit then the rate of mass loss will increase during its passage through pericenter where the tidal radius is smallest.

Numerical simulations provide a convenient method of illustrating the forces at work. First we construct a model satellite galaxy using a self consistent density profile and stellar energy distribution. A King model provides a good approximation to most of the satellites in the halo (King 1966). Firstly, we shall model the Ursa Minor dwarf spheroidal which has mass , core radius pc and central velocity dispersion . For this simulation we will follow the evolution of 10,000 particles with the TREECODE described by Barnes (1986). We use a timestep of half a million years, and with a force resolution of 5 pc we conserve energy to better than 1% over 5 Gyrs.

We model the Galaxy's halo by a fixed isothermal sphere, specified by a constant circular velocity ; hence the total mass increases linearly with distance to beyond the orbit of the satellite. For a system of this mass the dynamical friction timescale is much longer than the orbital period and can be ignored. We set the satellite in an eccentric orbit with pericenter 20 kpc and apocenter 70 kpc, i.e. the eccentricity, . Figure 1a shows the system after 200,000 timesteps 10 Gyrs from a perspective looking down on the orbital plane. The solid line shows the orbital path taken by the satellite. Roughly 50% of the mass has been lost over this timescale and lies within two long tails which both contain similar amounts of material. The tail primarily below the satellite is leading the satellite and the tail above is trailing.

Figure 1. (a) A numerical simulation of the tidal effects of the Milky Way on a low mass satellite such as Ursa Minor. The solid curve shows the orbital path followed by the satellite which begins its 10 Gyr orbit at coordinates (70,0). The viewpoint is looking down upon the orbital plane and the present position of the satellite is about (15,65) kpc. Roughly half of the mass has been stripped and has formed two long tidal tails. (b) The same simulation viewed edge on shows that the stripped material occupies a very thin plane.

The origin of the material in each tail is distinct but counter-intuitive. The satellite becomes tidally extended along one axis which points towards the center of the deeper potential, and is compressed along the perpendicular axes. Material escapes primarily from both ends of the extended axis where the escape velocity is lowest. The stripped material has a velocity equal to that of the satellite's plus a residual velocity . In this simulation, is small since it is some fraction of the internal velocity dispersion of the satellite. Hence, material which was stripped Gyrs ago, presently lies at the end of the tails, a distance kpc away from the satellite where the units of are in . Material which escapes from the bottom of the satellite (the end of the extended axis pointing towards the center of the potential) has less angular momentum and will orbit with a slightly smaller major-axis. This implies that the orbital timescale will be shorter than for the satellite and the stripped material will form a leading tail. Similar reasoning applies to the formation of the trailing tail. The width of the tails reflects both and the eccentricity of the orbit. The velocity dispersion of stars within the tails is low, hence these tidal features are very narrow. Figure 1b shows the simulation viewed in the orbital plane. The stripped material lies in a very thin plane of comparable width to the satellite.

This simulation reveals several serious problems when using the tidal model to describe the origin of the Magellanic Stream. The 21cm surveys have not detected a leading Stream, whereas we expect a similar amount of material extending in front of the MCs. We also performed numerical simulations of satellites on circular and highly eccentric orbits and in each case both a leading and trailing tail formed. Furthermore, the stripped material lies within a highly uniform tail with very little variation in density along its length, in conflict with the 21cm observations which show that the density of material decreases by an order of magnitude along its length.

The above conclusions were drawn from a simulation of Ursa Minor. In order to mimic tidal stripping from the MCs we now perform a simulation of a more massive system. Our model galaxy is again constructed with a King profile with unit concentration, but with total mass . This model leads to a central velocity dispersion of , similar to the observed dispersion within the LMC. The halo is modelled by a fixed potential, hence the satellite in our model does not feel the effects of dynamical friction. We treat this effect analytically by calculating the effective braking force every 1000 timesteps. We take the mass of the satellite as the mass within the observed tidal radius after fitting the profile to a King model. The run is started with the satellite on an slightly eccentric orbit with and from an initial galactocentric distance of 150 kpc.

Figure 2. (a) A numerical simulation of the tidal effects of the Milky Way on the LMC. After 10 Gyrs the tidally stripped material fills most of the halo. The orbit of the satellite is discussed in the text. (b) The same simulation viewed edge on shows that the stripped material occupies a thick plane with most material concentrated inside the present orbit.

Figure 2a shows the results of this calculation after 10 Gyrs when the satellite reaches a distance of about 50 kpc. The perspective in this diagram is viewed from above the plane of the orbit, whereas Figure 2b is viewed from the orbital plane. It is clear from these plots that the stars are escaping from the model satellite with significant peculiar velocities which carry them well away from the orbital plane within a Hubble time. The large 's arise because of the large internal velocity dispersion. These pictures clearly bear little resemblance to the observed velocity and density structure of the Stream. It may be argued that these models are only simulating stars and not a gaseous component. However, the gravitational tides affect all material equally and we would expect to observe a significant number of stars within the MS. Several groups have systematically searched for a stellar component although no obvious enhancement of stars has been found in the vicinity of the MS (e.g. Irwin 1991). As Lin & Lynden-Bell originally noted, these null detections present a further problem for the tidal model.

Recent refinements to the tidal model (Gardiner et al. 1994), may be able to circumvent several of the problems we have raised with respect to the original Lin & Lynden-Bell scenario. Gardiner et al. discuss the possibility that the MS was formed after a close encounter between the SMC and LMC tore a cold, uniformly rotating ring of gas from the LMC. Although this scenario requires a carefully tuned interaction between the MCs, it is feasible that such an encounter could produce a narrow, single sided stream of tidal debris. The main objections to this model are that it is unable to reproduce the uniform variation of column density along the length of the MS, or the high radial velocities observed along the MS. Further objections are that is cannot reproduce the clumpy nature of the MS, and tidally stripped stars would also be visible within the MS. Lin et al. (1994) attempt to reconcile the observed radial velocities along the length of the MS by adopting a low mass model for the halo of the Galaxy which allows more eccentric orbits.

§3. THE ORBITS OF THE MAGELLANIC CLOUDS

Table 2 lists the observed orbital information of the MCs: and are the galactic longitude and latitude; is the distance from the center of the Galaxy; and are their radial and transverse velocities; the final two columns list the mass of gas in neutral hydrogen and their total mass. Once the transverse motions of the LMC and SMC are accurately measured, a model for the mass distribution in the outer halo will completely specify the past and future trajectories of these galaxies. The key unknown factor at present is the transverse motion of the SMC; we can however speculate on its value. The LMC and SMC lie kpc apart in the sky, close enough for this to be an unusual coincidence. They are within each other's tidal radii and hence appear marginally bound. Between the LMC and SMC lies of HI which has a smooth velocity gradient across its length. This bridge of gas also contains many stars and young star clusters which suggests that it was formed during a recent tidal encounter between the LMC and SMC. In order for material to be stripped from the SMC, the two galaxies must have passed by each other within a distance of about 5 kpc. Moreover, the encounter timescale must have been relatively long, hence we infer that these galaxies are most probably bound together, although this is not prerequisite for our model discussed in Section 4.

If we impose the constraint that the SMC is gravitationally bound to the LMC, or has been for several Gyrs, then we find that this provides a tight constraint on its transverse velocity . From their present positions, we can integrate the equations of motion backwards starting with various values of to find values which keep the two galaxies bound over a Hubble time. This calculation is straightforward once the mass distribution in the halo is specified, and as in Section 2, we assume an isothermal halo extending beyond the orbit of the MCs. Dynamical friction is again included analytically, although we ignore mass loss through the tidal radii of the satellites which would slowly decrease the rate of orbital decay.

Figure 3> shows two orbit calculations. In each plot the initial positions are the present day locations of the MCs, the solid line shows the LMC's orbit and the dashed line is that of the SMC. Figure 3a shows a bound orbit with and , close to the observed value. Figure 3b also shows a bound orbit but with the transverse velocity of the LMC equal to the upper limit from the observations and we adopt . In both orbits the initial velocity vectors are roughly parallel, and the MCs suffer two close collisions within the last 700 million years, at relative velocities and separations of order 7 kpc. Extensive investigation of parameter space shows that in order to maintain a stable bound orbit over at least half a Hubble time, the transverse velocity vector of the SMC must align closely to that of the LMC and have comparable magnitude. Differences in transverse velocity greater than 20% typically create unbound orbits within an orbital period. Orbits of higher eccentricity have more freedom than circular orbits since the tidal field of the Galaxy does not play as important a role in unbinding the orbits.

From Section 2 we have seen that the velocity structure along a tidal tail contains a great deal of information on the internal and orbital parameters of the satellite galaxy. Observations of the radial velocity along such a feature uniquely defines the orbit of the satellite. The tidal models for the MS as proposed by Lin & Lynden-Bell and Murai & Fujimoto both require that the transverse velocity of the LMC be significantly larger than the observed circular velocity, in order to reproduce the high negative infall velocity at the tip of the MS, a point several hundred million years and 100 kpc back along the orbital path taken by the MCs.

Table 1 lists the galacto-centric radial velocity of the LMC at a distance back along the orbital path at positions corresponding to the clouds MSI-MSVI. Columns 5 and 7 give velocities corresponding to the orbits in Figure 3a and Figure 3b respectively. These data should be compared to the observations in column 4. At the tip of the MS, some behind the LMC we expect an observed radial velocity of , substantially larger than value predicted by integrating the observed orbit back in time. At the same point in the orbit of Figure 3a we would expect to observe a radial velocity of only . Clearly, this cannot be the correct orbit for the LMC within the context of the tidal model. Adopting a larger transverse velocity for the LMC does not appear to alleviate this problem. In this case we do observe large negative radial velocities along the orbital path: at the tip of the Stream we expect a radial velocity of . However, this orbit predicts that observed radial velocity should increase to a maximum of between the location of MSIII and MSIV, clearly in conflict with the observational data. For comparison with our model proposed in the next section, in columns 6 and 8 we list the galactocentric distances of the LMC at the same positions back along the orbital path.

§4. A NEW MODEL FOR THE ORIGIN OF THE MAGELLANIC STREAM

4.1 Ram pressure stripping by an extended disk

Before proceeding with details, we shall outline the model we are proposing for the origin of the MS. We assume that beyond the extent of the observed thin HI disk of the Milky Way, hydrogen is still present at a column density of , but is mostly ionized by the extragalactic background radiation. The MCs collided with this extended disk of gas some 500 million years ago at a galactocentric distance of about kpc. Material was ram-pressure stripped, mainly from the intra-cloud region and the SMC, and began infalling towards the Galaxy. The HI with lower column density lost more orbital angular momentum than material of higher density, hence it has infallen the furthest into the galactic potential and is moving with the largest negative velocity. Material of column densities was barely perturbed and remains close to the MCs. A necessary component of the model is that the Milky Way has a hot gaseous halo with density falling as beyond a core radius kpc. This diffuse medium provides a braking effect on the infalling material and prevents it from attaining negative velocities larger than those observed and allows the stripped material to fall into the correct position in the sky.

In an attempt to determine how far the rotation curves of galaxies can be resolved by observing the 21cm emission, van Gorkom et al. (1993) spent 100 hours with the VLBA observing NGC 3198. This observation was capable of resolving column densities of ; however, at the observed column density of , the flux dropped below their detection limit in the interval of one beamwidth (2.7 kpc). This sharp drop was also noted by Corbelli et al. (1989) in their observation of M33. Motivated by these observations and the pioneering work of Bochkarev and Sunyaev (1977), several theoretical papers have subsequently argued that this sharp drop in column density can be naturally explained by ionization of the HI by the cosmic extragalactic UV radiation (Maloney 1992, 1993; Corbelli et al. 1993). Recent Hubble Space Telescope (HST) Faint Object Spectrograph observations toward 3C273 has shown that roughly half the observed Lyman alpha absorption clouds have redshifts coincident with spiral galaxies near the line of sight but with projected separations of up to 150 kpc, suggesting that disks extend in some form, presumably mostly ionized, to this radius (Lanzetta et al. 1993). In the context of standard models for galaxy formation (White and Rees 1978), we would expect the formation of disks to arise through the cooling of gas within an extended dark matter potential. Applying standard cooling arguments to primordial gas within a massive dark halo we find that to distances of about kpc, the gas would have had time to cool within a Hubble time.

At the solar distance, the column density of gas is . If the surface density falls as beyond the solar radius then we can expect a total column density, , of order at a galacto-centric distance of 60 kpc. The self gravity of the gas would be negligible and we can assume as did Maloney (1992) that the gas maintains a Gaussian vertical distribution:

with scale height at large . At the solar radius the vertical velocity dispersion of the stars is . Observations of face-on galaxies show that is constant over a large range of radii, hence the midplane density at large distances can be estimated from

Note that the resulting stripping is expected to be dependent on the total column density, but not on or the details of the vertical density distribution in the disk. (We obtain almost indistinguishable results if we approximate the disk as a very thin, uniform density slab.)

We can apply conservation of momentum to gain an insight into the origin of the MS. As a first approximation consider the evolution of a gas cloud within the SMC of column density . If we approximate the disk as a very thin slab, the velocity of the gas cloud after passing through the disk will be simply , where is the impact velocity. >From the orbit in Figure 3a, , hence the orbital velocity of a gas cloud of column density will suddenly be reduced to 130 . This is significantly larger than the escape velocity of material within the SMC which is . A gas cloud of column density , will end up with a change in velocity of 24 . Clouds of this density in the MS must originate either from the outer edges of the SMC and LMC or from within the intra-cloud region where the escape velocity is very low.

There is an additional impulse which must be considered since the ionized disk is rotating with circular velocity . This impulse will be roughly perpendicular to that previously described since the orbit of the MCs passes close to the Galactic poles, and again we can apply conservation of momentum to calculate the resulting velocity change. The net effects are to increase the amount of stripped material and to force the gas to infall along a spiral orbit which offsets the final distribution of MS gas from a great circle. This provides an additional constraint on at the impact distance.

From this simple picture we can see how the main features of the MS arise. Namely, the most dense clouds receive the smallest change in momentum and hence will remain in orbit closest to the MCs. Likewise, the least dense clouds will lose the most energy and fall furthest into the potential well of the Galaxy and will achieve the highest radial velocity. In this model we would expect a smooth transition of both density and velocity along the MS. The orbit in Figure 3a results in an interaction between the MCs immediately before and after they pass through the disk. Therefore gas of the same column density might be stripped from the LMC, SMC and the intra-cloud region, but with varying amounts of momentum loss, hence the final distribution of material would be both continuous and clumpy.

To test this model in greater detail we follow numerically the orbits of gas clouds of different mean column densities chosen to match clouds MSI-MSVI. As well as the gravitational force we include an extra term to describe the ram-pressure force, , where is the density of the medium and is the velocity of the cloud. The key constraint on the model is the position of the gas clouds in the sky and their radial velocity components. We adopt the orbit shown in Figure 3a and place test particles of different column densities at the position of the SMC 500 million years ago, the time when the MCs were about to pass through the extended disk. As expected, we find the resulting momentum loss from the disk crossing to be sensitive only to the total column density in the disk and not to the actual vertical density profile.

Figure 4a shows the subsequent evolution of these six clouds superimposed on the orbits of the MCs from Figure 3a. By the present time the clouds are actually in front of the LMC and SMC. This is obvious when one realises that because the clouds lose energy, the apogalactic distance of their orbit decreases; correspondingly, their orbital period decreases so they must overtake their predecessor as projected on the sky. Clearly an additional force must play an important role in the subsequent orbits of the stripped material.

Figure 4. The simulated orbits of six gas clouds which represent MSI - MSVI superimposed on top of our adopted orbits of the Magellanic Clouds (see Figure 3a). (a) Gravity and ram pressure from the extended ionized disk are considered. (b) as (a) and including the braking force from an extended spherical halo of ionized gas.

4.2 An extended gaseous halo for our Galaxy?

We now consider the ram-pressure which could be provided by a large halo of hot gas surrounding the Galaxy. Such a gaseous component is naturally expected as material left over from the process of galaxy formation, as well as intragalactic material which is continually accreting into the halo of the Milky Way. The gas is collisionally heated to the virial temperature of the dark halo, K, thus allowing an extended spherical distribution about the center of the halo. This halo of HII should not be confused with the hot component of ionized gas which is localised within a few kpc of the plane of the Galaxy as in the standard 3 phase model of the ISM (McKee & Ostriker 1977).

The orbit of the MS is sensitive only to the mass density of this halo, not its temperature. Rather than a diffuse halo, the constraint below would equally well be satisfied by a multiphase medium of lower pressure. Direct evidence for the existence of such a diffuse halo is the existence of a bow wave along the leading edge of the LMC where the HI gradients are very steep (Mathewson et al. 1977). In this case the ram pressure of the dilute gas is far too weak to expel the gas from the LMC, but it does drive a shock into the interstellar medium of the LMC.

We model the gaseous halo with a core radius and an power law:

It is important to note that the orbits of the gas within the MS provides no constraint on the shape of the gaseous halo within kpc; we use the parameterisation of equation (4) for convenience.

Figure 4b shows the orbits of the same six clouds after including the braking effect of the above gaseous halo with atoms cm and kpc. At a distance of 65 kpc this yields a gaseous halo of atoms cm, and atoms cm at the solar radius. The halo gas plays a crucial role in the subsequent evolution of the stripped material and at the present time the six test particles have fallen into roughly the same position as observed in MSI-MSVI. The final radial velocities and galactocentric distances of the Clouds are tabulated in columns 9 and 10 respectively of Table 1. The agreement with the observations is very good given the crude treatment of the dynamical and hydro-dynamical processes involved. The only observation we have difficulty in reproducing are the separations of the most dense clouds MSI-MSIII, which the model predicts to lie closer to the MCs. A more detailed simulation should provide tighter constraints on the structure of the gaseous disk and halo.

We have a fair amount of freedom in our orbital parameters for the MCs, disk column density and halo gas distribution. However, the above model provides interesting constraints on all of these quantities. The final radial velocities and galactic latitudes of the clouds are sensitive primarily to the halo gas density and the mass of the dark halo within 65 kpc. If we increase by more than 30%, we find that the clouds can never attain the high infall velocity of 200 . If we decrease by more than 30%, then both the radial velocities and the positions in the sky become incompatible with the data. Of course our models are not really sensitive to the density of gas near the distance of the sun, since the MS lies outside this distance. Thus and can be freely adjusted so long as the density at kpc is held nearly constant. The galactic longitude of the clouds are sensitive to both the total column density and the rotational velocity of the disk. Figure 5 shows the orbits of the test clouds from a perspective looking down upon the orbital plane. Clearly the angular momentum provided by the rotation of the disk has not significantly perturbed the most dense clouds from their orbits on a great circle. The least dense clouds follow a curved orbital path which brings them back close to the great circle by the present time. In the next section we discuss the constraints provided by the geometry of the MS.

Figure 5.

The orbits of six gas clouds as described in Figure 4b, but viewed from a perspective looking edge on to the orbital plane.

5.1 Magellanic Geometry

The orbits of the satellite galaxies lie on great circles about the Galactic center. In the case of the MS there are two effects which would spoil the expected great circle: (i) The orbital plane is not being viewed from the center of the Galaxy, but from a position kpc away. (ii) The gas in the MS receives a transverse velocity impulse due to the rotation of the disk. Figure 5 shows that this deviation is not large so long as the column density of disk material is . (This column density could be higher, but the circular velocity at the impact distance would have to be reduced by the same factor.) Here we assumed the circular velocity at 65 kpc is 220 .

Lower density material stripped from the MCs might be expected to receive a larger transverse kick from the rotation of the galactic plane, and thus be offset relative to the denser clouds in the MS. The Galactic plane rotates clockwise around the North Galactic pole which would cause less dense material to lie at longitudes less than . Material of column densities would remain bound to the higher density gas in MS clouds MSI - MSIII, however less dense material would receive transverse velocities large enough to carry them away from the Stream. We expect that this material, at column densities , is likely to have been completely photoionised by the present day (see Section 5.3 below). Towards the tip of the MS the gravitating mass is much lower and less dense material would free-fall through the halo on a different great circle. In fact, of order a dozen low density clouds are visible close to MSIV - MSVI, and offset in the expected direction.

If the tip of the MS had fallen close to the center of the galaxy then the MS would appear curved in the sky due to our offset location. Figure 6 shows the geometry: the large dashed circle is centered on the sun's position, S, and extends 60 kpc to the position of the SMC at in the sun's frame. The solid circle shows the perspective of an observer at the center of the Galaxy, G, who would place the SMC at . If material in the tip of the Stream originated in the SMC, then it would form a great circle about G represented by the dot-dash line, and would have an observed longitude in the Galaxy's frame at point T where . Converting this to the sun's frame would place the tip of the Stream along the dotted line at .

Figure 6.

A sketch of the geometry of the Magellanic Stream. The viewpoint is looking down from the North Galactic Pole. The large dashed circle shows the sun's frame of reference for galactic coordinates centered on the small open circle, whereas the solid circle shows the frame as viewed from the center of the galaxy 8.5 kpc, away centered on the small filled circle. The dash-dot line shows the great circle in which the SMC would orbit. Within the plot we list the expected galactic longitude of the tip of the MS for different values of its galacto-centric distance.

In our model, the tip of the Stream has actually fallen towards the Galaxy and now lies at about kpc. The tip therefore appears to lie along the dashed line at T which corresponds to a longitude of , agreeing well with the observed coordinates which are centered on . If the tip had fallen to within 20 kpc, then we would begin to observe a strong curvature in the MS. The tidal model predicts that the tip of the stream originated in the LMC and presently lies at a distance kpc. Performing the same geometrical exercise, we find that in this model, the tip of the Stream should appear to lie at , 10 degrees away from its observed position.

Radio maps of the neutral hydrogen distribution place of HI within the Stream where a mean distance of 50 kpc has typically been adopted (Wakker & Schwarz 1991). In our model, the bulk of the MS is closer to the Galaxy, and the corresponding mass estimate is reduced, but only by about 25% since most of the high column density material is still at a distance of about 50 kpc. The material in the MCs has mean metallicity somewhat below the Galaxy's. During previous disk crossings, a similar mass of material may have been swept from the MCs and has since accreted onto the Milky Way enriching the disk and bulge material. It is possible that some of this material constitutes a large fraction of the high velocity clouds (HVCs) observed in 21cm radio surveys. The highest density material stripped about a Gyr ago would presently lie mainly in the Southern hemisphere and have negative velocities of order 200-300 . In addition, this picture would account for the below solar abundances within the HVC's and their proximity to the sun. (Note that dynamical friction decreases the distance to the LMC by about 10 kpc/Gyr, therefore significant stripping can occur within the last couple of orbits.) Wang (1993) discusses the possibility that tidally stripped material from the MCs and dwarf galaxies could produce the bulk of the observed high velocity clouds. A more detailed comparison between these models is in preparation.

5.2 The absence of gas in nearby satellites and globular clusters

Many globular clusters and several other less massive satellite galaxies orbit within the halo of the Milky Way. It is something of a paradox that none of these systems contain any neutral hydrogen. The absence of significant amounts of gas in the globular clusters at galacto-centric distances less than 10 kpc has been explained by ram pressure stripping as the clusters cross the observed neutral hydrogen disk. However, continual stellar mass loss is expected to deposit up to of gas over a period of about 100 million years (Tayler & Wood 1975). Observational searches have not detected this material and have placed upper limits of a few solar masses of HI (i.e. Smith et al. 1990).

The absence of gas within the clusters and satellites beyond the solar radius provides an additional paradox since the disk is thought to extend to about 15 kpc. The most massive clusters e.g. -Cen, have escape velocities of the order of 40 . The satellite galaxies in our halo are larger and more massive, yet are less centrally concentrated and have escape velocities of order 20 . It is possible that an initial burst of supernovae could inject enough energy into the ISM to clear the system of any gas left over from the formation epoch. However, the satellites orbiting beyond the solar radius will have time to form several thousand solar masses of hydrogen via stellar mass loss. A natural consequence of our model is that the bulk of material left over from star formation will be ram-pressure stripped after a single crossing of either the neutral or ionized hydrogen disk. Any satellite crossing the disk at distances less than 100 kpc will encounter a column density of hydrogen of at least a few times , sufficient to strip all material of column density . Furthermore, the diffuse halo provides a density of at the solar radius, sufficient pressure to continually strip new material from the globular clusters as they orbit through the halo. One prediction of this model is that we do not expect to observe low mass gas rich satellite galaxies or globular clusters within a distance of about 100 kpc from the center of spiral galaxies.

5.3 The ionizing background

The UV background responsible for ionizing the outer disk of the Milky Way will also ionize the HI in the Magellanic Stream. For a uniform column density of absorbing material, the timescale for ionization is , where is the incident ionizing photon flux at the Lyman limit. Detailed modelling of the HI cutoff in the disk of NGC 3198 requires photons cm s. Observations of the proximity effect at low redshift using the HST yield background intensities consistent with this range (Kulkarni & Fall 1993).

The column ionization timescale for gas at would be at most 0.13 Gyrs, a timescale shorter than the half billion year lifetime of the MS, therefore the ionization rate must be balanced by the recombination rate which is . The width of the tip of the MS is about 5 kpc assuming a distance of 25 kpc, giving a central density of atoms of about . The Hydrogen recombination coefficient for gas at K, , therefore the column recombination timescale is Gyrs. The similarity between these timescales suggests that the recombination rate could balance the ionization rate. A more detailed calculation would take into account the density structure of the absorbing material, a diffuse component of radiation due to recombination within the gas etc. It is interesting to note that if the material in the tip of the Stream was at a distance of kpc as the tidal model would predict, then the recombination timescale would be four times as long and the neutral fraction of the Stream would be small.

5.4 Emission and dispersion measures

Observations of soft X-rays by ROSAT provide a constraint on the amount of hot gas in the halo. Burrows & Mendenhall (1991) observed the shadowing effect of the Draco cold interstellar gas cloud and conclude that a large fraction of the low energy X-ray background arises from sources beyond 300 pc. Snowden et al. (1993) used the shadowing effect to determine that essentially all of the M (0.5-1.0 keV) band radiation originates from distances beyond 60 pc. At least 40% of the observed background is due to discrete sources, such as distant QSO's, however, the origin of a large fraction is still unaccounted for. Gas at the virial temperature of the halo, K, would primarily emit X-rays in the C band keV, although a substantial component will also fall into the M-band. Wang & McCray (1993) analysed two deep ROSAT images and concluded that up to 60% of the M band radiation can be fit by discrete sources, however, 40% of the radiation in the M band arises in a diffuse thermal component with a temperature of K.

In our model we require an extended halo of HII, rather than localised hot gas close to the disk as in the standard three phase model of the ISM. The integrated electron density along the line of sight quantifies the emission measure, , of hot gas which could lie within the halo. We can estimate for our adopted halo parameters by integrating the electron density over the correct geometry. Wang & McCray determine that the hard diffuse component has an emission measure of pc, in the direction and . Integrating over the electron density in our model halo, in the same direction and using the parameters adopted in equation (4), we find an identical emission measure as observed by Wang & McCray.

The emission measure toward any line of sight is obviously dominated by the inner edge of our postulated halo, which is not constrained by the MS. Furthermore, the cooling timescale for gas of temperature K and primordial abundance is years, where is the density in units of . One expects the inner edge of this postulated halo to have cooled off and to form a modest cooling flow, unless reheating by cosmic rays or supernovae winds counteract the cooling. Ignoring the contribution to from all the gas which could cool within 10 Gyrs () would reduce the emission measure by a factor of two in the direction probed by Wang & McCray. Note that the total mass of ionized gas within the orbit of the LMC is about , roughly 0.5% of the total mass within this radius. Of this amount, only lies within the core radius.

The dispersion measure of pulsars within the halo globular clusters provides another measurement of the total column density of free electrons along the line of sight to the pulsar. Nordgren et al. (1992) show that the electron cloud of the disk of the Milky Way extends to a scale height of between 500 kpc and 800 kpc, hence contributing a minimum dispersion measure, 16 pc. Within the Magellanic Clouds, the four observed pulsars yield 100 pc, with 40 pc arising from our disk. Presumably, material in the MCs contributes a similar , leaving an excess of about 20 pc, which can be well explained by the contribution from the diffuse halo in this direction which is 14 pc. Another constraint arises from a pulsar within the globular cluster NGC 5024 which lies at high galactic latitude, 18.6 kpc above the disk and 18.9 kpc from the sun, with pc (Kulkarni et al. 1991). The from the halo gas towards this pulsar is pc, hence the total disk plus halo agrees well with the observations. The uniform slab model for the galactic disk is a simple approximation to a complex medium which is filled with bubbles and holes from supernovae winds. For example, the Galaxy is located within a local void, relatively empty of ionized gas and with a scale of several hundred pc (Phillips & Clegg 1992). For this reason we consider the X-ray measurements to provide the strongest constraint to our model at present.

5.5 Confining the Magellanic Stream

High resolution velocity maps of individual components of the stream show relative motions on small scales of the order 20 - 30 . Several authors have claimed that such motions would effectively double the width of the Stream in a timescale of order a hundred million years. However, this material is moving on epicyclic orbits and the observed internal dispersion is of the correct magnitude to produce the observed thickness of the MS. Furthermore, gas within the MS of column density is likely to be gravitationally bound. We must also consider the pressure, , provided by the diffuse halo. At the distance where the stripping occurred, the pressure exerted by the halo is five times greater than the internal pressure of the MS, where we adopted as the temperature of the MS. This pressure imbalance is at least an order of magnitude higher at the present distance of the tip of the MS. However, it is likely that the components of the MS are in rough pressure equilibrium with the diffuse halo gas; if they were not, the pressure of a hot diffuse halo gas would crush them in a timescale of years. The total pressures we are considering are very small and could easily be supplemented by the pressure of a weak magnetic field of order , which provides an internal pressure . Fields of this strength are typical within the interstellar medium, and would naturally remain trapped within the stripped material which forms the MS.

§6. CONCLUSIONS

The unusual velocity and density structure of the Magellanic Stream provide strong constraints on models for its origin. We have investigated in some detail the tidal model and find several disparities between the predictions and the observations. This leads us to suggest a new formation scenario for the MS in which material is stripped from the Magellanic Clouds as it passes through an extended ionized disk of the Milky Way. The subsequent orbits of this material suggest that an additional ram pressure exerted by a diffuse halo gas, is braking the infalling components of the MS. A simple investigation of this model suggests that it can account for all the observed features and dynamics of the MS.

Observational and theoretical evidence is accumulating that the disks of spiral galaxies do not end abruptly, as does the HI distribution, but rather continue in a photoionized form beyond kpc. Hubble Space Telescope observations of the nearby quasar 3C273 show numerous Lyman alpha absorption lines at coincident redshifts with spiral galaxies along the line of sight (Lanzetta et al. 1993). This observation supports the notion that most spiral galaxies have extended disks of mostly ionized gas extending to scales of kpc. If the Milky Way has such an extended disk, it partially strips gas out the Magellanic clouds each time they pass through the galactic plane.

We find that reasonable parameters for the column density of the extended disk and density structure of the diffuse halo results in a stream of stripped gas which closely matches the observables of the Magellanic Stream, which stretches in an arc for 100 degrees behind the Magellanic clouds. We are able to match the velocity structure of the MS, the correlation of column density with angular proximity to the MCs, the fact that the MS is neutral, and the apparent trajectory of the MS on the sky. Most importantly, our model is fully consistent with the observed transverse motion of the LMC.

A necessary component of our model is that a diffuse halo of gas surrounds the Milky Way. This material provides an effective braking force on the stripped material which plays a crucial role in determining the orbits of the gas. The predicted X-ray emission from this ionized halo gas naturally accounts for % of the background radiation in the 0.5-1.0 keV band. The halo material contributes to the dispersion measure of pulsars in globular clusters and the MCs, however, the contribution from the disk is somewhat uncertain due to the frothy nature of the local interstellar medium, hence does not provide as useful a constraint as the ROSAT measurements.

There are several observations which could directly measure the amount and distribution of gas in the outer halos of spiral galaxies. HST observations of nearby quasars, especially quasar-galaxy pairs, will provide the best constraint on the extent and distribution of hydrogen associated with spiral galaxies at large galactocentric distances. X-ray observations of the halos of spiral galaxies may be able to directly constrain hot ionized gas at the low expected temperatures keV. High resolution neutral hydrogen observations of gas rich satellite galaxies close to other massive spiral galaxies may be able to detect stripped material. The velocity and density structure of these features will enable tidal models to be distinguished from disk stripping models. Finally high resolution ultraviolet spectroscopy toward extragalactic sources using the Hubble Space Telescope will probe the physical conditions of the diffuse halo gas of the Milky Way.

Acknowledgments

We would like to thank Chris McKee for valuable comments and suggestions. This research was supported by a NSF grant AST-9321540.

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