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

¹ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
² INAF – Osservatorio Astrofisico di Torino, Strada Osservatorio 20, Pino Torinese 10025, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 18 October 2025
Accepted: 7 February 2026

Abstract

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.