Comparison between axisymmetric numerical magnetohydrodynamical simulations and self-similar solutions of jet-emitting disks

Context . Turbulent accretion disks threaded by a large-scale vertical field near equipartition can drive tenuous and fast self-confined jets. Self-similar solutions of these jet-emitting disks (JEDs) have been known for a long time and provide the distributions of all physical quantities, from the turbulent disk to the asymptotic regime of ideal magnetohydrodynamic (MHD) jets. However, a thorough comparison with time-dependent numerical simulations has never been achieved, mostly because mass-loss rates found in simulations were always larger than those found analytically. This tension may have cast doubt on the analytical approach, the numerical one, or both. Aims . Our goal is to bridge the gap between these two complementary approaches and settle this long-standing issue. Methods . We performed 2.5D (axisymmetric) simulations of resistive and viscous accretion disks described by the same parameter sets as analytical JED solutions. The turbulent transport coefficients, as well as a turbulent magnetic pressure, have been included in the simulations. They follow the same α prescriptions as in the analytical work and are consistent with our current understanding of magnetic turbulence in accretion disks. Results . The numerical and the analytical solutions agree almost perfectly, and the previous tension now resolved. The JED solution thus appears to be structurally stable. Self-similarity is shown to bias the jet collimation properties only beyond the fast-magnetosonic point. Up to that point, the same set of disk parameters give rise to nearly indistinguishable numerical and analytical solutions, with magnetic surfaces displaying a near parabolic shape. The simulations also confirm that JEDs behave as dynamical attractors: starting from different initial conditions, the system consistently converges toward the expected steady-state solution. Conclusions . This work demonstrates that self-similar solutions provide valuable insights into accretion-ejection physics. However, as 2.5D numerical simulations which rely on α prescriptions, they strongly depend on the assumptions made for turbulent terms. In contrast, 3D simulations capture the turbulence, but become prohibitively expensive when modeling large-scale astrophysical systems. We advocate for the use of global 3D simulations to investigate turbulence and to derive physically motivated prescriptions for use in 2.5D studies.