Erratum for: A&A, 596, A74 (2016), https://doi.org/10.1051/0004-6361/201628955

In the last paragraph of Sect. 2.5 of the original paper, the treatment of the boundary condition was incorrectly described. In the original paper, we stated that $\frac{\partial }{\partial r}\left({\displaystyle \sum r^{\frac{3}{2}}}\right)=0$ was imposed at the inner and outer boundaries, r = r_in = 0.01 au and = r_out = 10⁴ au, and that this condition corresponds to the zero-torque boundary condition. However, this statement and explanation were incorrect. The actual boundary condition implemented in our calculations was to impose $\frac{\partial }{\partial r}\left({\displaystyle \sum r}\right)=0$ at r = r_in and = r_out.

This is consistent with the zero-torque boundary condition, $r^2{\displaystyle \sum \overline{{\alpha }_{r\varphi }}{c}_{\text{s}}^2}$ ($\propto {\displaystyle \sum r^{\frac{3}{2}}}$ for a constant $\overline{{\alpha }_{r\varphi }}$ and $T\propto r^{-\frac{1}{2}}$; see Eqs. (10) and (A.5)) → 0 at the centre, r → 0. The physical meaning of $\frac{\partial }{\partial r}\left({\displaystyle \sum r}\right)=0$ at r = r_in and = r_out is to impose a constant mass accretion rate induced by the rϕ stress for a constant $\overline{{\alpha }_{r\varphi }}$ and $T\propto r^{-\frac{1}{2}}$ (Eq. (33)) across the boundary. All of the results presented in the original paper remain unchanged.

© T. K. Suzuki et al. 2022