The stress-pressure lag in MRI turbulence and its implications for thermal instability in accretion discs

TL;DR

This study investigates the lag between turbulent stress and pressure in MRI turbulence within accretion disks, revealing a significant lag that impacts thermal stability models.

Contribution

The paper provides the first direct measurement of the stress-pressure lag in MRI turbulence through 3D simulations, challenging the instantaneous response assumption in classical models.

Findings

Stress lags behind pressure by about 5 orbits.

Lag increases with longer oscillation periods.

Implications for thermal and viscous overstability in accretion disks.

Abstract

The classical alpha-disc model assumes that the turbulent stress scales linearly with -- and responds instantaneously to -- the pressure. It is likely, however, that the stress possesses a non-negligible relaxation time and will lag behind the pressure on some timescale. To measure the size of this lag we carry out unstratified 3D magnetohydrodynamic shearing box simulations with zero-net-magnetic-flux using the finite-volume code PLUTO. We impose thermal oscillations of varying periods via a cooling term, which in turn drives oscillations in the turbulent stress. Our simulations reveal that the stress oscillations lag behind the pressure by $\sim 5$ orbits in cases where the oscillation period is several tens of orbits or more. We discuss the implication of our results for thermal and viscous overstability in discs around compact objects.