Evolution of Hubble wedges in episodic protostellar outflows
  Young low-mass protostars undergo short phases of high accretion and outburst
activity leading to lumpy outflows. Recent observations have shown that the
position-velocity and mass-velocity diagrams of such outflows exhibit
individual bullet-like features; some of these bullets subscribe to a `Hubble
Law' velocity relation, and others are manifest as `Hubble wedges'. In order to
explore the origin of these features, we have developed a new episodic outflow
model for the SPH code {\sc gandalf}, which mimics the accretion and ejection
behaviour of FU Ori type stars. We apply this model to simulations of star
formation, invoking two types of initial conditions: spherically symmetric
cores in solid-body rotation with $\rho\propto r^{-2}$, and spherically
symmetric turbulent cores with density proportional to the density of a
Bonnor-Ebert sphere. For a wide range of model parameters, we find that
episodic outflows lead to self-regulation of the ejected mass and momentum, and
we achieve acceptable results, even with relatively low resolution. Using this
model, we find that recently ejected outflow bullets produce a `Hubble wedge'
in the position-velocity relation. However, once such a bullet hits the leading
shock front, it decelerates and aligns with older bullets to form a
`Hubble-law'. Bullets can be identified as bumps in the mass-velocity relation,
which can be fit with a power-law, $dM/d\upsilon_{_{\rm
RAD}}\propto\upsilon_{_{\rm RAD}}^{-1.5}$.
