Question

Estimate how often stars collide in the Milky Way (using the model of a cylinder with radius = disc scale length and height = 2* disc scale height)

Answer 1

GIVEN:

Assuming the Milkyway galaxy to cylindrical, where

TO FIND:

Collision frequency between two stars in the Milkyway galaxy.

SOLUTION:

This problem can be treated in the same way as molecular dynamics, where the collision frequency is given by,

where is the collision frequency

is the relaxation time.

For a star moving with a velocity v past another star of mass M, for its velocity to be influenced, it must pass within a distance d of the star, where d is the radius of the circle of influence of the first star. The radius of the sphere of influence d is given by,

When the star moves through the galaxy let us imagine that it collides (influences the velocity) with various other stars and the distance travelled by the star between two successive collisions is called as mean free path represented by .

Thus we get the volume of influence as follows.

On the other hand, the mean volume per star in the galaxy is just the total volume of the galaxy divided by the number of stars in the galaxy.

Where is the radius of the galaxy

is the height of the galaxy

is the number of stars in the galaxy.

Since the radius of the galaxy=2*the height of the galaxy,

For a collision to take place, the two volumes must be equal.

Subsituting the value for d we get,

Now the relaxation time that is the time between encounters is just the mean free path over the velocity,

Therefore the collision frequency is given by,