The paper ‘Magnetic fields during the early stages of massive star formation – I. Accretion and disc evolution’ was published in Mon. Not. R. Astron. Soc. 417, 1054–1073 (2011). In this erratum we present the corrected analysis of the Toomre parameter as originally done in section 3.5 of the paper. Because of an error in the numerical calculation, the Toomre parameter was calculated wrongly, resulting in a factor of ∼10 lower values. The main conclusions, however, do not change significantly. The magnetic field still contributes significantly – although the effect is not as pronounced as originally proposed – to stabilizing the discs.
The pure hydro and magnetic Toomre parameters, Q and QM, are now calculated as correctly defined in the original paper (Seifried et al. 2011). With the newly evaluated Q-values we re-analyse the stability of the mid-plane for the runs 26-20, 10-20, 5.2-20 and 26-0.4. From Fig. 1 it can be seen that in all cases the Toomre parameters are higher than the values erroneously calculated before. For the disc in run 26-20 (top left) the hydrodynamical Toomre parameter Q drops below 1 around 200 and 400 au. However, only around 200 au is a fragmented ring observed in the column density plot of the disc, which agrees with the magnetic Toomre parameter QM dropping to ∼1 only at this position.
In run 10-20 (top right) no fragmentation has occurred, in agreement with a value for Q of ∼1 except around 500 au where it is lower. Here QM is above 1, indicating that the magnetic pressure contributes to the stability of the disc just as in run 26-20 at r = 400 au.
For the sub-Keplerian discs found in runs 5.2-20 and 26-0.4 (bottom panel of Fig. 1) the hydrodynamical Toomre parameter is below 1 over a wide range, indicating instability. This is not the case, as can be seen in the column density plots. In contrast to Q, the magnetic Toomre parameter QM is in general above 1 which fits better to the actually observed behaviour in the column density plots. This indicates that the magnetic field is responsible for stabilizing the disc. However, it is not clear to what extent the Toomre analysis, originally derived for linear instabilities of rotationally supported discs without infall motions, is applicable for strongly sub-Keplerian discs with significant infall motions as presented here.
To summarize, in parts the Keplerian discs, and also those in the other runs not shown here, are reasonably well described by the hydrodynamical Toomre parameter Q. However, there is some indication that the magnetic pressure is required to stabilize the disc against fragmentation as already concluded in Seifried et al. (2011). For sub-Keplerian discs the magnetic field seems to contribute even more to the stability of the discs which is in agreement with the conclusion drawn in Seifried et al. (2011). However, in this case the Toomre analysis might be misleading because of the sub-Keplerian nature of the discs not accounted for in the derivation of the Toomre criterion.