The emergence of the M_D − Ṁ_* correlation in the magnetohydrodynamic wind scenario

¹ Dipartimento di Fisica ‘Aldo Pontremoli’, Università degli Studi di Milano, via G. Celoria 16, 20133 Milano, Italy
² European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching bei München, Germany
³ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
⁴ Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405 Orsay, France
⁵ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40122 Bologna, Italy
⁶ Fakultat für Physik, Ludwig-Maximilians-Universität München, Scheinersts. 1, 81679 München, Germany

^★ Corresponding author; luigi.zallio@unimi.it

Received: 8 May 2024
Accepted: 30 October 2024

Abstract

Context. There is still much uncertainty around the mechanism that rules the accretion of proto-planetary disks. In recent years, magnetohydrondynamic (MHD) wind-driven accretion has been proposed as a valid alternative to the more conventional viscous accretion. In particular, winds have been shown to reproduce the observed correlation between the mass of the disk M_D and the mass accretion rate onto the central star Ṁ_*, but this has been done only for specific conditions. It is not clear whether this implies fine tuning or if it is a general result.

Aims. We investigated under which conditions the observed correlation between the mass of the disk M_D and the mass accretion rate onto the central star Ṁ_*, can be obtained.

Methods. We present mainly analytical calculations, supported by Monte Carlo simulations. We also perform a comparison with the observed data to test our predictions.

Results. In the absence of a correlation between the initial mass M₀ and the initial accretion timescale t_acc,0 , we find that the slope of the M_D − Ṁ_* correlation depends on the value of the spread of the initial conditions of masses and lifetimes of disks. Then we clarify the conditions under which a disk population can be fitted with a single power law. Moreover, we derive an analytical expression for the spread of log(M_D/Ṁ_*) valid when the spread of t_acc is taken to be constant. In the presence of a correlation between M₀ and t_acc,0, we derive an analytical expression for the slope of the M_D−Ṁ_* correlation in the initial conditions of disks and at late times. In this new scenario, we clarify under which conditions the disk population can be fitted by a single power law, and we provide empirical constraints on the parameters ruling the evolution of disks in our models.

Conclusions. We conclude that MHD winds can predict the observed values of the slope and the spread of the M_D−Ṁ_* correlation under a broad range of initial conditions. This is a fundamental expansion of previous works on the MHD paradigm, exploring the establishment of this fundamental correlation beyond specific initial conditions.