Disk fragmentation around a massive protostar: Comparison of two 3D codes

Abstract

Context. Most massive stars are located in multiple stellar systems. The modeling of disk fragmentation, a mechanism that may plausibly lead to stellar multiplicity, relies on parallel 3D simulation codes whose agreement remains to be evaluated. Aims. Cartesian adaptive-mesh refinement (AMR) and spherical codes have frequently been used in the past decade to study massive star formation. We aim to study how the details of collapse and disk fragmentation depend on these codes. Methods. Using the Cartesian AMR code RAMSES within its self-gravity radiation-hydrodynamical framework, we compared disk fragmentation in a centrally condensed protostellar system to the findings of earlier studies performed on a grid in spherical coordinates using PLUTO. Results. To perform the code comparison, two RAMSES runs were considered, effectively giving qualitatively distinct pictures. On the one hand, when allowing for unlimited sink particle creation with no initial sink, Toomre instability and subsequent gas fragmentation leads to a multiple stellar system whose multiplicity is affected by the grid when triggering fragmentation and via numerically assisted mergers. On the other hand, using a unique, central, fixed-sink particle, a centrally-condensed system forms that is similar to that reported by PLUTO. Hence, the RAMSES-PLUTO comparison was performed with the latter and an agreement between the two codes is found as to the first rotationally supported disk formation, the presence of an accretion shock onto it, and the first fragmentation phase. Gaseous fragments form. The properties of the fragments (i.e., number, mass, and temperature) are dictated by local thermodynamics and are in agreement between the two codes given that the system has entered a highly nonlinear phase. Over the simulations, the stellar accretion rate is made of accretion bursts and continuous accretion on the same order of magnitude. As a minor difference between both codes, the dynamics of the fragments causes the disk structure to be sub-Keplerian in RAMSES, whereas it is found to be Keplerian, thus reaching quiescence, in PLUTO. We attribute this discrepancy to the central star being twice less massive in RAMSES because of the different stellar accretion subgrid models in use - rather than the potential grid effects. Conclusions. In a centrally condensed system, the agreement between RAMSES and PLUTO regarding many of the collapse properties and fragmentation process is good. In contrast, fragmentation occurring in the innermost region and given specific numerical choices (use of sink particles, grid, etc.) have a crucial impact when similar but smooth initial conditions are employed. These aspects prove more crucial than the choice of code, with regard to the system being multiple or centrally condensed.