A ‘head/tail’ plasmon model with a Hubble law velocity profile

Abstract

ABSTRACT We present a model of a hypersonic, collimated, ‘single pulse’ outflow, produced by an event with an ejection velocity that first grows, reaches a peak, and then decreases again to zero velocity in a finite time (simultaneously, the ejection density can have an arbitrary time-variability). We obtain a flow with a leading ‘head’ and a trailing ‘tail’ that for times greater than the width of the pulse develops a linear, ‘Hubble law’ velocity versus position. We present an analytical model for a simple pulse with a parabolic ejection velocity versus time and time-independent mass-loss rate, and compare it to an axisymmetric gasdynamic simulation with parameters appropriate for fast knots in planetary nebulae. This ‘head/tail plasmon’ flow might be applicable to other high-velocity clumps with ‘Hubble law’ tails.