The dynamical evolution of the Large Magellanic Cloud

The Large Magellanic Cloud (LMC) and its apparent neighbour, the Small Magellanic Cloud (SMC), are dwarf irregular galaxies on the southern hemisphere. Both galaxies are visible to the naked eye, appearing as nebulae in the constellations Dorado (LMC) and Tucana (SMC). They are therefore known since ancient times, but adopt their name from Ferdinand Magellan who discovered them on his expedition in 1517-1521.

The Magellanic Clouds and the Milky Way form the nearest ensemble of interacting galaxies (Figure 1). The distance to the LMC/SMC is only 50/60 kpc (Westerlund 1997). This proximity and the fact that the clouds are lying outside the Galactic plane allow to perform detailed studies of these galaxies. Furthermore the radial velocities are quite high - 266 km/s (LMC) and 150 km/s (SMC) - so that its gas and stars can be kinematically distinguished from those of the Milky Way.


Figure 1: A sketch of all forces acting upon the LMC. The Magellanic Clouds and the Milky Way are projected to the y-z plane. The red arrows represent the space velocity vectors of LMC and SMC. The black arrows indicate the different forces acting upon the LMC: tidal forces of the Milky Way and the SMC and ram pressure forces of the ambient medium.
The Magellanic Clouds have been studied in great detail covering the entire spectral range. The interaction becomes most evident in neutral, atomic hydrogen (HI). Huge gaseous arms have been detected covering a large fraction of the southern sky. Figure 2 shows the HI column density distribution of the Magellanic Clouds and their environment and a mean velocity map obtained from Brüns et al. (2004). The LMC and the SMC are not isolated galaxies but embedded in a common HI envelope called the Magellanic Bridge (Hindman 1961). Moreover, the two galaxies possess prominent gaseous arms, the Magellanic Stream (Mathewson et al. 1974) and the Leading Arm (Putman et al. 1998), with an extension of about 180° on the sky. The Magellanic Stream shows a huge velocity gradient of ΔvLSR = 650 km/s over its extent of about 100° that is still considerable in the Galactic-standard-of-rest frame, ΔvGSR = 390 km/s, while the Leading Arm shows no clear velocity gradient.

Figure 2: Single-dish observations of HI gas (Brüns et al. 2004).
Left: HI column density map of the entire Magellanic System. Right: Mean velocity v(LSR), map of the entire Magellanic System.


Observations can determine some parameters of a galaxy with high accuracy. The big problem is that we can only observe a two-dimensional projection on the sky at the present time, where the three-dimensional distribution of positions and velocities are partly unknown. While the space position of the Magellanic Clouds is well known, the space velocities are less well constrained. It is therefore very difficult to construct a three-dimensional orbit that matches all observations. Realistic simulations of the Magellanic Clouds would require the knowledge of the exact three-dimensional orbits of the LMC and SMC. As this is not possible, I could only investigate the effects of the interactions on the LMC for a chosen set of orbital parameters. In my diploma thesis I performed n-body simulations on the dynamical evolution of the Large Magellanic Cloud taking into account tidal and ram pressure forces.
In order to get suitable starting parameters for the n-body simulations of the LMC-SMC-Galaxy triple system in the past, I traced back two-particle trajectories from the present position of the LMC and SMC. The two clouds were represented by Plummer models moving in an analytically given gravitational potential of our Galaxy (Wolfire et al. 1995).

The current position of the Magellanic Clouds is well determined: the position on the sky is easily observable and the distance was derived in numerous studies.
Unfortunately the space velocities of the Magellanic Clouds are less well known: the radial velocities are easy to measure, whereas the tangent velocity is very difficult to observe. Table 1 shows the recent determination of the velocity vectors by Kroupa & Bastian (1997) and van der Marel et al. (2002). The two velocity vectors for the LMC agree within the uncertainties but show a considerable discrepancy in the x-component vx. Setting the velocity in x-direction equal to zero places the LMC on a polar orbit, in agreement with observations. I have also set the x-component of the velocity of the SMC to zero as the set of parameters yields suitable orbits for both galaxies including an interesting interaction scenario.

Coordinates

LMC orbit

SMC orbit

x, y, z [kpc]

-1.0, -40.7, -26.3

14.8, -36.1, -41.9

vx, vy, vz [km/s]

41±44, -200±31, 169±37

60±172, -174±172, 173±128

Kroupa & Bastian

vx, vy, vz [km/s]

-56±39, -219±23, 186±35

 

van der Marel

vx, vy, vz [km/s]

0, -219, 186

0, -174, 173

my choice
Table 1: Current position of the LMC and SMC with different choices of the velocity vectors. All three sets of coordinates use the current position of the LMC and SMC to derive the orbits. The two measured velocity vectors are from Kroupa & Bastian 1997 and van der Marel 2002. The observational uncertainties show that there is a considerable range of velocity vectors that are consistent with observations.

For my orbit I have set the velocity components in x-direction for both, LMC and SMC equal to zero. The other velocity components were taken from van der Marel (LMC) and Kroupa (SMC). Figure 3 shows the two-particle orbits of the LMC and SMC projected onto the xy-, the xz-, and the yz-plane within a time period from t = -3.5 Gyr to t = 2 Gyr. With my choice of the velocity vector the LMC has a polar orbit.

Figure 3: The orbit of the Magellanic Clouds between t = -3.5 Gyr and t = +2 Gyr projected to the xy-, the xz-, and the yz-plane with my choice of the velocity vectors for the LMC and SMC. The red and blue star indicate the current positions of the LMC and SMC. The red and blue lines indicate the past orbit and the dash-dotted lines illustrate the future evolution.

My choice of the velocity vector yields an interaction history that lies in between the two scenarios suggested by Kroupa & Bastian and van der Marel with respect to Galactocentric distances. The Magellanic Clouds will interact over a significant amount of time without catastrophic encounters (see Figure 4). My orbit has three close encounters. The first approach occurred 2.5 Gyr ago with a relative distance of 16 kpc. Afterwards they have larger distances up to about 50 kpc and come close again near t = -0.5 Gyr for a longer period of time. The relative distance at this time is 15 kpc. In the near future, 410 Myr from now, the two galaxies will have their closest encounter of about 10 kpc. The Galactic distance of the LMC has a minimum and maximum value of 45 kpc and 129 kpc and the orbital period is about 2.2 Gyr.

Figure 4:
Left: The distance of the Magellanic Clouds to the Galactic center.
Right: The distance between the LMC and the SMC as a function of time with my choice of the velocity vectors for the LMC and SMC.

For my simulations I have used an initial mass of 18.4 ⋅ 109 MSun for the LMC and 2.5 ⋅ 109 MSun for the SMC. The LMC mass is estimated using the observed disk mass, MDisk = 2.7 ⋅ 109 MSun, and a halo-to-disk ratio of 5.8 that is commonly used for simulations (see Vollmer et al. 2001 and references therein).

n-body simulations of the Large Magellanic Cloud

A typical spiral galaxy consists of a stellar disk, a more extended disk of gas and a thick spheriod of stars with little gas known as bulge embedded in a Dark Matter Halo. Therefore the n-body code has to treat four different kinds of particles: disk-, bulge-, halo- and gascloudparticles. Disk-, bulge- and haloparticles are assumed to be collisionless, because stars are point-like objects where a direct collision is extremely unlikely. On the other hand clouds can collide as they are extended objects. Due to this fact the particles are classified into non-collisional and collisional particles. The collisional particles evolve similarly to the non-collisional particles, but can encounter inelastic collisions and, by this, dissipate kinetic energy.

I have performed three different non-collisional n-body simulations using different orbital parameters:
  1. The realistic LMC orbit with the observed orientation of the LMC disk.
  2. The realistic LMC orbit with the observed orientation of the LMC disk including the SMC as a perturber.
  3. An exemplary orbit with the observed orientation of the LMC disk, which brings the LMC much closer to the Milky Way. For this scenario the interaction with the Milky Way is severe, amplifying the feedback of the galaxy. The chosen velocity vector is not consistent with the observed velocity vector of the LMC.
N-body simulations need to make a trade-off between the number of particles and computing time. Consequently, the individual particles of an n-body simulation do not represent single stars, but rather large associations of matter. The initial conditions for the non-collisional component of the LMC were derived using the program BUILDGAL developed by Hernquist (1993). My n-body model of the LMC consists of 65 536 particles, which form an exponential disk and an isothermal DM halo.
The LMC does not show a bulge, consequently no bulge component was added. The characteristics of the different components are presented in Table 2. The SMC is simulated by 30 340 particles forming a Plummer sphere with a core radius of 2 kpc and a mass of MSMC=2.5 ⋅ 109 MSun, i.e. 8.2 ⋅ 104 MSunper particle. The softening parameter is the same as for the disk, i.e. b = 80 pc.

 

N

m [104 MSun]

M [109 MSun]

b [pc]

Halo

32 768

47.8

15.7

400

Disk

32 768

8.2

2.7

80

SMC

30 340

8.2

2.5

80
Table 2: Number of particles N, particle mass m, total mass M, and softening parameter b for the different components of the LMC and the companion galaxy representing the SMC.

Gassimulations are far more complicated as cloudparticles are additionally exposed to collision forces and rampressure. I have performed six different collisional n-body simulations:
  1. The LMC in the potential of the Milky Way.
  2. The LMC in the potential of the Milky Way with the SMC as a perturber.
  3. The LMC in the gaseous halo of the Milky Way (nH = 10-5 cm-3).
  4. The LMC as in 3, but with the SMC as a perturber.
  5. The LMC in the gaseous halo of the Milky Way (nH = 10-4 cm-3).
  6. The LMC as in 5, but with the SMC as a perturber.
The collisional n-body simulations use the same stellar disk and DM halo as the non-collisional simulations. The gaseous disk is added by creating an initial distribution of 10 000 cloud particles that uniformly fills a cylindrical volume defined by 0.5 kpc < R < 9.5 kpc and |z| < 500 pc. The central hole is introduced to minimize the computational efforts. Especially the central part of a gaseous disk needs a significant amount of computing time

The initial HI mass is roughly estimated: The current HI mass of the LMC is MHI ≈ 4.5 ⋅ 108 MSun (Brüns et al. 2004). The total gas mass is larger, as for instance helium or molecular hydrogen are not traced by the 21-cm line of neutral hydrogen. The usual amount of helium (10% by number) adds 40% to the total gas mass, hence Mgas ≈ 6.3 ⋅ 108 MSun. The total HI mass of the gaseous arms, the Magellanic Bridge, the Interface Region, the Magellanic Stream, and the Leading Arm, is MHI ≈ 4.8 ⋅ 108 MSun, or Mgas ≈ 6.7 ⋅ 108 MSun including helium. Assuming that about half of this gas originates from the LMC, while the rest was torn out of the SMC, the total initial gas mass of the LMC is estimated to have been about Mgas ≈ 1 ⋅ 109 MSun. Swaters et al. (2002) observed a large sample of dwarf irregular galaxies and found a relation between the total HI-mass and the diameter of a galaxy. Their result suggests an initial radius for the gaseous LMC disk of Rgas≈10 kpc. For comparison, the current radius of the HI disk of the LMC is approximately 6.5 kpc.

In contrast to the star and halo particles, where all particles have the same mass, I use a power law (M-1.5) for the cloud mass spectrum covering five orders of magnitude from 10 to 106 solar masses.

The velocity of a cloud particle is calculated as a circular velocity, determined by the total acceleration due to all other particles (stars, DM, and gas) at the individual cloud position. Moreover, a Gaussian velocity dispersion with sigma = 5 km/s is added to each component of the cloud velocities.

This initial distribution of cloud particles is certainly not in equilibrium. Therefore, the initial disk is inserted together with the stellar disk and halo to an n-body code without external forces. This simulation is integrated over 1.4 Gyr to allow for relaxation. The relaxed disk is used as the initial disk for all following simulations.

The N-body LMC on the Sky

To compare the results of the n-body simulations to observations I have projected my data onto the sky using the HI map from Brüns et al. (2004, see Figure 2) as a reference map. For each individual pixel of the HI map (at coordinate l,b) I have calculated the number of particles within ± 15' of this position. Accordingly, I have also calculated the mean radial velocity within ± 15' of this position. The resulting maps for stars and clouds are presented in Figure 5.

Figure 5: Results of the gas simulation (upper row) and the observed HI distribution (lower row). The area between the LMC and the Galactic Plane is not covered by the Parkes HI survey of the Magellanic System (Brüns et al. 2004).

The simulation shown in Figure 5 includes the influence of the Milky Way, the SMC, and ram pressure. The upper left map displays the cloud distribution of the simulation, and the upper right map the modeled velocity field. The lower left map shows the observed HI column density distribution and the lower right map the observed mean velocity of the HI gas. The simulated gas disk appears to be slightly larger than the observed HI disk. However, the outer parts are made up by very few particles. Figure 6 demonstrates that the general orientation and the axis ratio of the simulated and the observed HI disk are comparable. My simulations do not reproduce the HI gas of the Magellanic Stream and the Leading Arm, suggesting that they were torn out of the SMC as indicated by previous simulations of the SMC (see Connors et al. 2004 and references therein).

Figure 6:This figure compares the observed HI disk (colors) with the simulations (contours). The contours indicate 5 and 10 particles per pixel further increasing in steps of 10. The extent and the orientation of the observed and the modeled LMC agree well.

My simulations reveal that clouds pile up between the LMC and the SMC demonstrating that at least some of the gas in the Magellanic Bridge was stripped from the LMC. The modeled clouds near (l,b) = (295°, -35°) are consistent with an observed cloud complex in this region. Moreover, the southern gaseous arm of the simulation corresponds to an observed HI feature near (l,b) = (315°, -52°). While the simulated arm is greatly unresolved due to a low number of particles, the observed and the simulated arm agree well, both in position and in velocity. This feature was not reproduced by any previous simulation considering solely the gaseous disk of the SMC.

The HI data do not cover the entire map: the region between the LMC and the Galactic Plane contains no data. A direct comparison of the gas stream predicted by my simulations and HI observations is therefore not possible. Putman et al. (2002) detected, however, compact HI clouds in this region that show radial velocities consistent with my simulations. The HI map shows numerous HI clouds north of the Galactic Plane where my northern gaseous arm is located. These HI clouds show significantly lower radial velocities than the modeled gas stream. This discrepancy could be explained by higher densities of the medium in the outer Galactic disk where the modeled gas stream crosses the line of sight of the Galactic Plane. The higher density would result in higher ram pressure forces decelerating the clouds while passing the Galactic Plane. The implementation of a realistic density distribution of the gaseous Galactic halo medium, as well as the implementation of a realistic SMC model, are important next steps for the simulations to allow for a reasonable comparison with HI data.

Last update: 2.Juni 2004
E-Mail: rcbruens@astro.uni-bonn.de