Stable Galaxy

Question:

  1. What defines a stable Galaxy.
  2. Is it possible to simulate a flat galaxy rotation curve using Newton's Law
  3. What are the consequences relative to 2D versus 3D.
  4. In order to simulate a flat galaxy rotation curve is dark matter required?
  5. Is it possible to simulate a flat galaxy rotation curve using MOND

Purpose

The purpose of this question is to define a stable question and to see how much mass is required.
A stable Galaxy is a star configuration which maintains its global shape over a long period of time.
  1. it is the opinion of the author that galaxies can be simulated with almost any shape of rotation curve when the stars are configured in rings and when the # of stars in each ring is identical.
  2. for a good simulation the number of rings should be large and the number of stars (objects) in each ring should be large. Good values are 10 rings and 50 stars.
  3. outcome of the program is the mass of each objects of the simulation.
  4. The configuration of the stars is rather artificial. For a more realistic simulation each object can de divided into sub-objects each with their own speed. Care should be taken that the total mass of the sub-objects is the same as the original object. The same for the average speed of the sub-ojects. The resulting simulation will again be a stable galaxy in accordance with the rotation curve.
  5. for the consequences related to MOND see: MOND

Stable Galaxy in 2D

The proof that stable galaxies in 2D are easy to simulate is the program: GAL_2D.BAS. Select: Stable Galaxy

For a copy of gal_2d.exe select:gal_2d.zip. This zip file also contains the file gal_mond.exe.

The galaxy is represented by many objects (or stars). Each object has approximate the same mass. The actual mass is calculated in the program. Each object is a collection of many real stars.

In this simulation the central bulge of the galaxy is not represented by one object but by more. The speed of the objects that form the central bulge increases linear with distance.

Stable Galaxy in 3D

A 3D simulation is in essence the same as a 2D simulation.
  1. each "star" in the +z direction, you also need a star in the -z direction.
  2. the stars in the +z direction should be organised in rings. Again the distance between the stars in the same ring should be identical.
  3. the speed of each "star" should be linear to the distance of the center of rotation.
  4. the vz component of each "star" should be zero. However if this is not the case then all the star at +z in the same ring should have the same speed and the speed of all the stars at -z should be -vz.

Reflection part 1

In order to simulate a stable galaxy, which is in accordance with a rotation curve, no dark matter is required.

Reflection part 2

In order to simulate a stable galaxy is easy and difficult at the same time.
It is easy when you keep the speed of the stars linear as a function of distance. 8 rings and 8 stars per ring prove that.

It is "difficult"for a more realistic simulation when the speeds follows a rotation curve. In that case only the stars in the inner rings (bulge of the galaxy) have a speed linear to distance. For all the stars the initial starting configuration is stable. The stars in the outer rings leave this stable configuration. The only reason is lack of stars (accuracy). It has nothing to do with the simulation methode. The only solution is to include more stars.

Reflection part 3

It is possible that "stars" are ejected out of this simulation. This is not conflict with reality: Single stars can easily be ejected. That is no proof that your galaxy is not stable.

In this simulation the ejection of "stars" can be rather dramatically and can influence your whole Galaxy. The true problem is accuracy i.e. one "star" represents too many real stars. The solution for non linear speed simulations is: more stars. Improved simulation methodes will not help.

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Last modified: 8 November 1998

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