STAR CLUSTERS
BACKTriple Star System
Three stars move in response to their mutual gravitational attraction. The symbol colour and associated stellar mass in solar units are: green, 1.0; yellow, 1.5; and orange, 2.0. The symbol size (actually symbol area) is proportional to the stellar mass.
The animation time step is 0.1 year and the simulation runs for 2000 years. The motions appear smooth because of the modest computing power required. Although the stars seem to move along nicely curved paths, they actually move along very short straight lines - too short to notice. That seeming oddity reflects a "fact of life" concerning the application of Newton's Laws of Motion to show bodies moving under the force of gravity.
Reference axes are shown in this and some other simulations. Three dimensions require three mutually perpendicular axes, customarily known as X,Y,Z. The colours and lengths in Astronomical Units(AU) in this simulation are: X, yellow, 100; Y, aqua, 100; and Z, orange, 50. One AU is the average separation of the Earth and the Sun, about 150,000,000 km.
The initial positions and velocities have to be chosen with some care, otherwise the system is unstable - a long-known feature of the Three Body Problem in gravitation.
Young Star cluster
A cluster of 531 stars evolves over a period of 60 million years, with a time step of 10,000 years. The whole assembly is approximately spherical.
Stars are selected at random from a mathematical function called the Salpeter Initial Mass Function, which has been found to be a decent approximation for the number of stars of various masses within clusters inhabiting the disk of our galaxy. The six common stellar types shown in the video, and associated information, are given in the table below. The sizes of plotted symbols increase somewhat arbitrarily with increasing stellar mass - in solar units - and all symbols are much larger than if shown in correct proportion to the size of the cluster.
| Colour | Size | Spectral Type | Mass | Number of stars |
|---|---|---|---|---|
| mauve | 120 | B | 10 | 2 |
| blue | 70 | A | 2.5 | 15 |
| light green | 40 | F | 1.4 | 72 |
| yellow | 20 | G | 1.0 | 108 |
| orange | 10 | K | 0.7 | 169 |
| red | 6 | M | 0.4 | 165 |
Reference axes: X, yellow, 6 pc long; Y, aqua, 6 pc; Z, orange, 3 pc. Here "pc" is short for "parsec", a convenient yardstick for measuring distances inside galaxies. One parsec is 206,265 AU (see above), or about 3.3 light years.
PROBLEM: This and other simulations attempt to show groups of stars - such as this cluster, an elliptical galaxy or the bulge of a disk galaxy - in states of equilibrium: neither expanding or contracting, or drastically changing shape, at least early on. But how does one choose the initial conditions - the positions and velocities of all its members - so that the cluster is already in or near a state of equilibrium when the simulation begins? The problem is that all those structures are roughly spherical, and we know that stars within them are generally moving in random directions. I've experimented with various ways of addressing the problem, with various degrees of success. In contrast, it's easy to start the disk of a simulated galaxy in equilibrium by assuming that the dominant force comes either from a central point or from a spherically symmetric mass distribution - an interior "bulge".