Chandrasekhar Dynamical Friction Formula
The full Chandrasekhar dynamical friction formula for the change in velocity of the object involves integrating over the phase space density of the field of matter and is far from transparent.
A commonly used special case is where there is a uniform density in the field of matter, with matter particles significantly lighter than the major particle under consideration and with a Maxwellian distribution for the velocity of matter particles. In this case, the dynamical friction force is as follows:
where
- G is the gravitational constant.
- M is the mass under consideration.
- is the velocity of the object under consideration, in a frame where the center of gravity of the matter field is initially at rest.
- is the ratio of the velocity of the object under consideration to the modal velocity of the Maxwellian distribution. ( is the velocity dispersion).
- is the "error function" obtained by integrating the normal distribution.
- is the density of the matter field.
- is the "Coulomb logarithm".
In general, a simplified equation for the force from dynamical friction has the form
where the dimensionless numerical factor depends on how compares to the velocity dispersion of the surrounding matter.
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