Adaptive smoothing lengths in SPH

Abstract

Context: There is a need to improve the fidelity of SPH simulations of self-gravitating gas dynamics. Aims: We remind users of SPH that, if smoothing lengths are adjusted so as to keep the number of neighbours, $\mathcal{N}$, in the range ${\mathcal{N}}_{{}_{\mathrm{NEIB}}}\pm \Delta {\mathcal{N}}_{{}_{\mathrm{NEIB}}}$, the tolerance, $\Delta {\mathcal{N}}_{{}_{\mathrm{NEIB}}}$, should be set to zero, as first noted by Nelson & Papaloizou. We point out that this is a very straightforward and computationally inexpensive constraint to implement. Methods: We demonstrate this by simulating acoustic oscillations of a self-gravitating isentropic monatomic gas-sphere (cf. Lucy), using ${\mathcal{N}}_{{}_{\mathrm{TOT}}}\sim 6,000$ particles and ${\mathcal{N}}_{{}_{\mathrm{NEIB}}}=50$. Results: We show that there is a marked reduction in the rates of numerical dissipation and diffusion as $\Delta {\mathcal{N}}_{{}_{\mathrm{NEIB}}}$ is reduced from 10 to zero. Moreover this reduction incurs a very small computational overhead. Conclusions: We propose that this should become a standard test for codes used in simulating star formation. It is a highly relevant test, because pressure waves generated by the switch from approximate isothermality to approximate adiabaticity play a critical role in the fragmentation of collapsing prestellar cores. Since many SPH simulations in the literature use ${\mathcal{N}}_{{}_{\mathrm{NEIB}}}=50$ and $\Delta {\mathcal{N}}_{{}_{\mathrm{NEIB}}}\ge 10$, their results must be viewed with caution.

5 pages, 2 figures, accepted for publication in A&A

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