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I am putting together a toy program which shows how stars move around in the galaxy.

To run the simulation I need to know strength of the Milky Way's gravitational field at any location in it. I'm looking for a model (e.g. a collection of uniformly dense planes/rods) rather than a database of potentials.

Where can I get such a model?

I could simply construct an infinite plane of uniform density, but is that good enough? This is only a toy so I'm looking for something which preserves integrity of the overall shape and statistics of the galaxy, rather than worrying about the specific location of any particular star.

Qmechanic
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spraff
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2 Answers2

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Note first that there are three different sources of gravitational potential: the disk, the bulge, and the dark halo.

There are a few different models of the gravitational field of the disk, two of the more common potentials are:

  • Kuzmin model:
    $$\Phi(r,z)=-\frac{GM}{\sqrt{r^2+(a+|z|)^2}}$$
  • Miyamoto-Nagai model:
    $$\Phi(r,z)=-\frac{GM}{\sqrt{r^2+(a+\sqrt{z^2+b^2})^2}}$$ where $a$ and $b$ are scale lengths.

For the bulge, you can use spherically symmetric potentials such as

  • Plummer model:
    $$\Phi(r)=−\frac{GM}{\sqrt{r^2+a^2}}$$
  • Jaffe model: $$\Phi(r)=\frac{GM}{a}\ln\left(\frac{r}{r+a}\right)$$ where $a$ also is a scale length and not necessarily the same as those for the disk.

The dark halo takes a spherical form, $$ \Phi(r)=\frac12V_h^2\ln\left(r^2+a^2\right) $$ where $V_h$ is the radial velocity of the galaxy at far distances ($\sim200$ km/s) and $a$ another scale length that isn't necessarily the same as above.

See also

Kyle Kanos
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1

Deriving the galactic mass from rotation has the following chart (on the right) for the enclosed mass as a function of radius

pic

John Alexiou
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