Firehose instability

The firehose instability (or hose-pipe instability) is a dynamical instability of thin or elongated galaxies. The instability causes the galaxy to buckle or bend in a direction perpendicular to its long axis. After the instability has run its course, the galaxy is less elongated (i.e. rounder) than before. Any sufficiently thin stellar system, in which some component of the internal velocity is in the form of random or counter-streaming motions (as opposed to rotation), is subject to the instability. The firehose instability (or hose-pipe instability) is a dynamical instability of thin or elongated galaxies. The instability causes the galaxy to buckle or bend in a direction perpendicular to its long axis. After the instability has run its course, the galaxy is less elongated (i.e. rounder) than before. Any sufficiently thin stellar system, in which some component of the internal velocity is in the form of random or counter-streaming motions (as opposed to rotation), is subject to the instability. The firehose instability is probably responsible for the fact that elliptical galaxies and dark matter haloes never have axis ratios more extreme than about 3:1, since this is roughly the axis ratio at which the instability sets in. It may also play a role in the formation of barred spiral galaxies, by causing the bar to thicken in the direction perpendicular to the galaxy disk. The firehose instability derives its name from a similar instability in magnetized plasmas. However, from a dynamical point of view, a better analogy is with the Kelvin–Helmholtz instability, or with beads sliding along an oscillating string. The firehose instability can be analyzed exactly in the case of an infinitely thin, self-gravitating sheet of stars. If the sheet experiences a small displacement h ( x , t ) {displaystyle h(x,t)} in the z {displaystyle z} direction, the vertical acceleration for stars of x {displaystyle x} velocity u {displaystyle u} as they move around the bend is provided the bend is small enough that the horizontal velocity is unaffected. Averaged over all stars at x {displaystyle x} , this acceleration must equal the gravitational restoring force per unit mass F x {displaystyle F_{x}} . In a frame chosen such that the mean streaming motions are zero, this relation becomes where σ u {displaystyle sigma _{u}} is the horizontal velocity dispersion in that frame.