Galaxy dynamics

Galaxy dynamics studies the gravitational motions and evolution of stars, gas, dark matter, and satellite systems in galaxies.

Chandrasekhar dynamical friction is the drag on a massive body produced by its gravitational wake in a background of lighter particles. Its magnitude is proportional to the body's mass and the background density.

The tidal radius bounds material that remains gravitationally attached to a satellite in the differential gravitational field of its host.

Tidal stripping removes satellite material outside the tidal radius. The resulting mass loss weakens dynamical friction and can greatly delay or prevent a merger.

Dynamical-friction stalling by tidal stripping occurs when inward motion shrinks a satellite's tidal radius so rapidly that its remaining mass and frictional drag tend to zero before it reaches the host center.

Stellar dynamics studies the collective gravitational motion of stars in galaxies and star clusters.

Two-body relaxation is the cumulative randomization of stellar velocities by many weak gravitational encounters. Its timescale in a system of $N$ comparable stars is of order $N/\log N$ crossing times.

The Coulomb logarithm $\log \Lambda =\log (b_{\max }/b_{\min })$ collects the logarithmically equal contributions of gravitational encounters over a wide range of impact parameters. For a self-gravitating system of $N$ comparable stars, $\Lambda$ is of order $N$.

A stellar system is collisional on a timescale of interest when its two-body relaxation time is shorter than that timescale, so discrete encounters materially alter its distribution function.

A singular isothermal sphere with one-dimensional velocity dispersion $\sigma$ has $\rho (r)={\sigma }^2/(2\pi G{r}^2)$, enclosed mass $M(<r)=2{\sigma }^{2}r/G$, and constant circular speed $\sqrt{2}\sigma$.