Magellanic Clouds: Model A
The orbit of ModelA was generated with a single test particle in an
axisymmetric fixed potential generated by a distribution similar to
the one plotted below. The calculated orbit is plotted against the
background distribution of disk, bulge, and halo. This orbit neglects
the effect of dynamical friction.
Orbital Parameters
The initial orbital parameters of the test particle were:
R = 52 kpc, Vt = -213 km/s, Inc = -76 degrees. In XYZ space:
| X | Y | Z | VX | VY | VZ |
|---|
| Time 0 | 3.14497 | -0.048409 | -12.6138 |
-0.000699985 | -0.968175 | 0.00282693 |
|---|
| Time -500 | 3.30491 | -12.0344 | -12.8554 |
-0.101248 | -0.552651 | 0.425855 |
|---|
The radius varies between a maximum of 72.3 kpc and a minimum of 52 kpc.
Velocity varies between 213.4 km/s and 153.3 km/s. This orbit is probally
too circular to be a good representation of the Magellanic Clouds; their
last apogalacticon is thought to be a little over 100 kpc. This model's
eccentricity is ~0.17.
Orbital Period
Assuming a circular orbit of R = 62 kpc, circumference is ~391 kpc. The
average circular velocity is 185 km/s or ~6.0 x 10^-15 kpc/s. That gives
an orbital time of ~6.5 x 10^16 seconds or ~2.1 x 10^9 yr.
In 250 time steps we complete ~2.5 orbits, which estimates ~2.1 x 10^7 years
per timestep. Therefore we computed orbits for ~5.3 x 10^9 years into
the past.
Discussion
The orbit computed here is a bit slower than the orbits considered by
Gardiner et al. (MNRAS 266,567 1994); they found a period of roughly
1.5 Gyr. Their calculations also predict a apogalacticon of close to
150 kpc at t = -5 Gyr. If dynamical friction decays less than 10% of
the orbital radius per orbit, then the orbit of modelA should only fall
to ~40 kpc at worst. Gardiner et al. estimate the last perigalacticon
to be ~45 kpc. More eccentric orbits may be required in order to
better represent the Magellanic Clouds.
Plots
Coordinate axes are in green. Luminous stars are in yellow, non-luminous
dark matter is in grey-blue. The stellar disk is very flat, with a
small bulge in its center. The satellite galaxy is the yellow
association of stars away from the disk; its calculated orbit is
also shown in yellow. The satellite is 10K particles, as is the bulge,
the halo is 100K particles. The ring system is 1000 rings * 32 particles
per ring.
XY Plane.
With a positive velocity, the test particle would start at time = -500 at
the satellite endpoint, heading under the disk and out the far side. The
t = 0 endpoint is beneath the disk.
XZ Plane.
The satellite orbit is the inclined line; the disk is horizontal and mostly
invisible in this perspective.
YZ Plane.
With a positive velocity, the test particle would start at time = -500 at
the endpoint at 7-oclock. Its orbit is counter-clockwise and ends
at time = 0 at the bare endpoint.
Non-planar Views.
Graphics generated using Tipsy-2.1.7, xv3.10a, and xpaint-2.1.1.
Thesis Work