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

TL;DR

This paper introduces an analytic model of a hypersonic outflow with a head and tail structure, exhibiting a Hubble law velocity profile, supported by simulation results relevant to planetary nebulae.

Contribution

It presents a novel analytic model of a pulsed outflow with a head/tail structure and compares it with gasdynamic simulations, applicable to high-velocity astrophysical clumps.

Findings

Analytic model matches simulation results for head/tail velocity profiles.

Flow develops a linear Hubble law velocity vs. position at late times.

Model applicable to high-velocity clumps in planetary nebulae.

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 vs. position. We present an analytic model for a simple pulse with a parabolic ejection velocity vs. 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.