Young low-mass protostars undergo short phases of high accretion and outburst activity leading to lumpy outflows. Recent observations have shown that the positionvelocity 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 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 ρ ∝ 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/dυ RAD ∝ υ −1.5 RAD .

The accretion of material onto young protostars is accompanied by the launching of outflows. Observations show that accretion, and therefore also outflows, are episodic. However, the effects of episodic outflow feedback on the core-scale are not well understood. We have performed 88 Smoothed Particle Hydrodynamic simulations of turbulent dense $1 \, \rm {M}_{\odot }$ cores, to study the influence of episodic outflow feedback on the stellar multiplicity and the star formation efficiency (SFE). Protostars are represented by sink particles, which use a sub-grid model to capture stellar evolution, inner-disc evolution, episodic accretion and the launching of outflows. By comparing simulations with and without episodic outflow feedback, we show that simulations with outflow feedback reproduce the binary statistics of young stellar populations, including the relative proportions of singles, binaries, triples, etc. and the high incidence of twin binaries with q ≥ 0.95; simulations without outflow feedback do not. Entrainment factors (the ratio between total outflowing mass and initially ejected mass) are typically ∼7 ± 2, but can be much higher if the total mass of stars formed in a core is low and/or outflow episodes are infrequent. By decreasing both the mean mass of the stars formed and the number of stars formed, outflow feedback reduces the SFE by about a factor of 2 (as compared with simulations that do not include outflow feedback).

During the early phases of low-mass star formation, episodic accretion causes the ejection of high-velocity outflow bullets, which carry a fossil record of the driving protostar’s accretion history. We present 44 SPH simulations of 1 M⊙ cores, covering a wide range of initial conditions, and follow the cores for five free-fall times. Individual protostars are represented by sink particles, and the sink particles launch episodic outflows using a subgrid model. The Optics algorithm is used to identify individual episodic bullets within the outflows. The parameters of the overall outflow and the individual bullets are then used to estimate the age and energetics of the outflow, and the accretion events that triggered it; and to evaluate how reliable these estimates are, if observational uncertainties and selection effects (like inclination) are neglected. Of the commonly used methods for estimating outflow ages, it appears that those based on the length and speed of advance of the lobe are the most reliable in the early phases of evolution, and those based on the width of the outflow cavity and the speed of advance are most reliable during the later phases. We describe a new method that is almost as accurate as these methods, and reliable throughout the evolution. In addition we show how the accretion history of the protostar can be accurately reconstructed from the dynamics of the bullets if each lobe contains at least two bullets. The outflows entrain about ten times more mass than originally ejected by the protostar.