Motivation and challenge to capture both large-scale and local transport in next generation accretion theory

Abstract

Accretion disc theory is less developed than stellar evolution theory although a similarly mature phenomenological picture is ultimately desired. While the interplay of theory and numerical simulations has amplified community awareness of the role of magnetic fields in angular momentum transport, there remains a long term challenge to incorporate the insights gained from simulations into improving practical models for comparison with observations. What has been learned from simulations that can lead to improvements beyond SS73 in practical models? Here, we emphasize the need to incorporate the role of non-local transport more precisely. To show where large-scale transport would fit into the theoretical framework and how it is currently missing, we review why the wonderfully practical approach of Shakura & Sunyaev (Astron. Astrophys., vol. 24, 1973, pp. 337-355, SS73) is necessarily a mean field theory, and one which does not include large-scale transport. Observations of coronae and jets, combined with the interpretation of results from shearing box simulations, of the magnetorotational instability (MRI) suggest that a significant fraction of disc transport is indeed non-local. We show that the Maxwell stresses in saturation are dominated by large-scale contributions and that the physics of MRI transport is not fully captured by a viscosity. We also clarify the standard physical interpretation of the MRI as it applies to shearing boxes. Computational limitations have so far focused most attention toward local simulations, but the next generation of global simulations should help to inform improved mean field theories. Mean field accretion theory and mean field dynamo theory should in fact be unified into a single theory that predicts the time evolution of spectra and luminosity from separate disc, corona and outflow contributions. Finally, we note that any mean field theory, including that of SS73, has a finite predictive precision that needs to be quantified when comparing the predictions to observations.

Synthesizing Observations and Theory to Understand Galactic Magnetic Fields: Progress and Challenges

“…This is why mean-field pitch angles are expected to be smaller than anisotropic fluctuating field pitch angles. The same argument was used to make a similar prediction for accretion disks [192].…”

Radially dependent large-scale dynamos in global cylindrical shear flows and the local cartesian limit

“…For a single MRI mode, large-scale magnetic fields generated via an EMF can cause MRI saturation (Ebrahimi et al 2009). In short, the large-scale dynamos of MRI-unstable systems are of interest both as phenomena on their own, and because they may be closely connected to angular momentum transport in accretion disks by local and nonlocal Maxwell stresses (Blackman & Nauman 2015). In addition to numerical simulations, flow-dominated laboratory experiments are also investigating the MRI MHD unstable systems in Taylor-Couette flow geometry (Goodman & Ji 2002;Rüdiger et al 2003;Kageyama et al 2004;Noguchi et al 2002;Sisan et al 2004;Stefani et al 2007).…”

“…But choices must always be made both due to limited computational resources and for isolating key physical processes that contribute to the global dynamics. The shearing box model has been the workhorse for simulating MRI turbulence for this purpose-but it is a local model and has limitations associated with boundary conditions, box size and so is a limited model for real astrophysical disks (Regev & Umurhan 2008;Bodo et al 2008;Blackman & Nauman 2015). The cylindrical model used here also has some complementary limitations due to its boundary conditions, but on the other hand provides solutions in a real global domain.…”

Experimental confirmation of the standard magnetorotational instability mechanism with a spring-mass analogue

“…The minimalist MHD version of the equations depends only on the displacement of the field lines in the plane perpendicular to the initial magnetic field. Two masses tethered by a weak spring orbiting in a central potential [15] then provide an analogue of this local instability, although the minimalist MHD MRI equations most directly correspond to the motion of a single mass tethered to a fixed point in a co-rotating frame [16] ( Fig. 1a vs. Fig.…”

“…The spring represents the magnetic field and the mass represents a parcel of MHD fluid. It has been speculated [16] that this analogue might be experimentally testable in the laboratory, distinct from multi-tethered configurations that have been previously theoretically explored [45][46][47].…”