# Gravitationally aligned orbits

Ellipses can be aligned at the focus to generate a logarithmic spiral.

Stars in a spiral galaxy move in certain orbits under the influence of the gravitational field associated with the totality of stars in that galaxy. The patterns of these orbits have been studied observationally and using simulation methods.

From observations of the motions of over 20,000 local stars (within 300 parsecs), and using numerical simulation, Charles Francis and Erik Anderson have shown that, contrary to conventional wisdom, stars tend to move along a spiral arm during the inward part of their orbits, leaving the arm shortly after pericentre crossing the other arm on the outward part of the orbit and rejoining the original arm shortly before apocentre.[1]

## Potential in a spiral galaxy

The gravitational potential of a bisymmetric spiral galaxy, showing the alignment of elliptical orbits with troughs in the potential.

The gravitational potential of a spiral galaxy can be described as a giant, spiral-grooved funnel. The grooves represent the gravitational field of the galaxy's spiral arms. As a star nears apocentre, the slowest part of its orbit, it will tend to fall into a groove. It will then tend to follow the groove, picking up momentum as it goes, on a path closely aligned with an elliptical orbit. Near the innermost part of the orbit, the alignment between the orbital path and the arm comes to an end, and the star gains enough momentum to jump free of its groove. It crosses over the next-highest groove, then falls back to a higher point in its original groove. At the same time, the funnel may rotate slowly, so that orbits form rosettes rather than ovals.

Numerical simulation establishes that orbits can precess either prograde or retrograde due to the spiral potential, and that they tend to align with the arms such that the star follows the arm during the inward part of the orbit. The mass of the star contributes to the mass of the arm during this part of the orbit, increasing the potential. Thus, as stars are drawn into an arm, the gravitational field of the arm grows stronger, drawing greater number of stars into the arm, and reinforcing spiral structure.

## Star formation in spiral arms

Gas motions in a bisymmetric spiral galaxy.

Under gravity, gas clouds follow similar motion to stars. Gas in the arm is in turbulent motion, as gas clouds seek to cross in the arm and gain velocity as they approach pericentre. Whereas stars rarely collide because of their small size compared to space between them, when outgoing gas from one arm meets ingoing gas in another arm, collisions between gas clouds create regions of higher pressure, and greater turbulence. Pockets of extreme pressure due to turbulence generate the molecular clouds in which new stars form.

## Bisymmetric spirals

In a multi-arm spiral, outgoing gas meeting an arm would outweigh ingoing gas in the arm. This would tend to remove gas from the arm. In a two armed spiral, the gas in the arm has greater mass. Thus, a two-armed gaseous spiral can be stable, whereas multiarmed gaseous spirals cannot. Outgoing gas applies pressure to the trailing edge of a spiral arm with an inverse proportionality to radius. If one gaseous arm advances compared to the bisymmetric position, the pressure due to gas from the other arm will be reduced. At the same time, pressure on the retarded arm due to outgoing gas from the advanced arm will be increased. Thus gas motions preserve the symmetry of two-armed spirals.

## References

1. ^ Francis, Charles; Anderson, Erik (8 November 2009). "Galactic spiral structure". Proc. R. Soc. A. 465 (2111): 3425–3446. doi:10.1098/rspa.2009.0036.