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).

The treatment of radiative transfer with multiple radiation sources is a critical challenge in simulations of star formation and the interstellar medium. In this paper we present the novel TreeRay method for solving general radiative transfer problems, based on reverse ray tracing combined with tree-based accelerated integration. We implement TreeRay in the adaptive mesh refinement code flash, as a module of the tree solver developed by Wünsch et al. However, the method itself is independent of the host code and can be implemented in any grid based or particle based hydrodynamics code. A key advantage of TreeRay is that its computational cost is independent of the number of sources, making it suitable for simulations with many point sources (e.g. massive star clusters) as well as simulations where diffuse emission is important. A very efficient communication and tree-walk strategy enables TreeRay to achieve almost ideal parallel scalings. TreeRay can easily be extended with sub-modules to treat radiative transfer at different wavelengths and to implement related physical processes. Here, we focus on ionising radiation and use the On-the-Spot approximation to test the method and its parameters. The ability to set the tree solver time step independently enables the speedy calculation of radiative transfer in a multi-phase interstellar medium, where the hydrodynamic time step is typically limited by the sound speed of the hot gas produced in stellar wind bubbles or supernova remnants. We show that complicated simulations of star clusters with feedback from multiple massive stars become feasible with TreeRay.

Radiation is an important contributor to the energetics of the interstellar medium, yet its transport is difficult to solve numerically. We present a novel approach towards solving radiative transfer of diffuse sources via backwards ray tracing. Here we focus on the radiative transfer of infrared radiation and the radiation pressure on dust. The new module, TreeRay/RadPressure, is an extension to the novel radiative transfer method TreeRay implemented in the grid-based MHD code Flash. In TreeRay/RadPressure, every cell and every star particle is a source of infrared radiation. We also describe how gas, dust and radiation are coupled via a chemical network. This allows us to compute the local dust temperature in thermal equilibrium, leading to a significantly improvement over the classical grey approximation. In several tests, we demonstrate that the scheme produces the correct radiative intensities as well as the correct momentum input by radiation pressure. Subsequently, we apply our new scheme to model massive star formation from a collapsing, turbulent core of 150 M⊙. We include the effects of both, ionizing and infrared radiation on the dynamics of the core. We find that the newborn massive star prevents fragmentation in its proximity due to radiative heating. Over time, dust and radiation temperature equalize, while the gas temperature can be either warmer due to shock heating or colder due to insufficient dust-gas coupling. Compared to gravity, the effects of radiation pressure are insignificant for the stellar mass on the simulated time scale in this work.