Evolution of Hubble wedges in episodic protostellar outflows

During the early phase of star formation, protostars undergo short phases of high accretion rates. Such outbursts are observed in FU Orionis type stars (FUors), which experience a rapid increase in accretion rate, from $ \sim 10 ^{-7}\,{\rm M}_\odot\,{\rm yr}^{-1}$ to $\sim10 ^{-4}\,{\rm M_\odot\,yr}^{-1}$, for a period of order 10 years.
Most, possibly all forming protostars launch fast bipolar outflows. The inference is that, during the collapse of the dense core, gravitational energy is converted into kinetic and magnetic energy, which then drives and collimates the outflow. Changes in the ejection rate, caused by sudden accretion events, lead to the formation of bullets and internal working surfaces, which are shocked layers between the fast ejecta and the gas in the outflow cavity. More evolved outflows break out of their parental core or cloud and form parsec-scale outflows, traced by chains of Herbig--Haro objects. In some cases these chains extend to over $10\,{\rm pc}$, e.g. HH 131 with an extent of $17\,{\rm pc}$.
We have developed a new episodic outflow model for the SPH code GANDALF, which mimics the accretion and ejection behaviour of FU Ori type stars (Stamatellos et al. 2012; Hubber et al. 2018; Rohde et al. 2019). We apply this model to simulations of star formation, invoking two types of initial conditions: spherically symmetric cores of $ 1.0 \, \mathrm{M}_{\odot}$ in solid-body rotation with $\rho\propto r^{-2}$ density profile, and spherically symmetric turbulent cores of $ 2.7 \, \mathrm{M}_{\odot}$ 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 reducing the star formation efficiency by a factor of $\sim \, 0.6$.
A common relation observed in protostellar outflows is a linear position-velocity (PV) relation, i.e. a `Hubble Law', in which the velocity of the outflowing gas increases linearly with distance from the source. Recent observations show that the PV diagram also exhibits so-called `Hubble Wedges' of high-velocity emission, caused by the bow shocks of individual outflow bullets. In our model, we are able to reproduce the `Hubble Wedges' as recently ejected outflow bullets. The outflow bullets then decelerate and align with the older bullets forming the well known `Hubble-Law' relation when they hit the leading shock front.
Figure: Position-velocity (PV) diagram for a turbulent core simulation at $t = 117 \, \mathrm{kyr}$ (top) and $t = 120 \, \mathrm{kyr}$ (bottom). Labels A to F show the individual outflow bullets in order of their ejection history. The high-velocity bullets E and F have been ejected recently, they are moving through the low-density cavity. Bullets A, B and C are older bullets that have already decelerated and moved downwards onto the linear Hubble-Law relation. The time evolution from top to bottom panel shows that bullet D is in the process of hitting the leading shock front and aligning with the former bullets.