Erratum and Addendum: Smoothed particle magnetohydrodynamic simulations of protostellar outflows with misaligned magnetic field and rotation axes [MNRAS, 464, (2017) (2499-2501)]

Abstract

The paper 'Smoothed particle magnetohydrodynamic simulations of protostellar outflows with misaligned magnetic field and rotation axes' was published inMNRAS 451, 288 (2015) (hereafter 'the Original Paper'). The calculations presented in that work were performed using a smoothed particle magnetohydrodynamics (SPMHD) code known as SPHNG. Unfortunately, a bug was present in the integrator that was used to evolve the magnetic field. The bug caused an 'instability' in some SPMHD calculations, whereby poor energy conservation could produce an explosion. In the Original Paper, the cause of the poor energy conservation was incorrectly ascribed to a deficiency in our SPMHD scheme (discussed in section 2.2 of the Original Paper), and we are grateful to Dobbs (private communication) for discovery of the underlying cause. In the Original Paper, we proposed a modified SPMHD method - the average h method - that employed an average smoothing length term in some of the MHD equations to correct the spurious 'instability' (see Section 2.2). In this addendum, we compare results from calculations using that method with the integrator bug (i.e. calculations as published in the Original Paper) with otherwise identical calculations that use the standard SPMHD equations (without the average h method) and a correct integrator. We show that the results of the calculations using each method exhibit some differences, particularly on small scales. These differences do not affect the conclusions in the Original Paper on the evolution of outflows and jets, and how they depend on the alignment between the field and the rotation axis. However, they do eliminate some of the fine structures that were seen at scales of ≲100 au. We note that as a result of the correction of the integrator bug, the 'average h' formalism is redundant and we no longer recommend it be used. Nonetheless, our observations in Lewis et al. (2015a) that the choice of averages used for smoothed particle hydrodynamics (SPH) equations are fairly flexible are still correct and this may still be of some interest for SPH schemes, which use an averaged smoothing length as opposed to a Price&Monaghan (2004) scheme. Section 1 of this addendum discusses the integrator bug in detail and then in Section 2, we provide a side-by-side comparison of calculations from the Original Paper with those using a corrected integrator and without the average h equations.