A cellular automaton model for the magnetic activity in accretion discs

In this paper we attempt, for the first time, to simulate the magnetic activity of an accretion disc using a probabilistic cellular automaton model. Our model is based on three free parameters, the probabilities of spontaneous and stimulated generation of magnetic flux above the surface of the disc (S0, and, respectively, P ), and the probability of diffusive disappearance of flux below the surface (D). The model describes a changing collection of flux tubes which stick out of the disc and are anchored inside the disc at their foot-points. Magnetic flux tubes transfer angular momentum outwards at a rate which is analytically estimated for each single loop. Our model monitors the dynamic evolution of both the distribution of magnetic loops and the mass transfer which results from angular momentum transport due to this distribution. The energy release due to magnetic flaring is also recorded as a function of time and exhibits temporal fluctuations with power spectra that depend on the assumed emission-profile of single flaring loops: (i) for instantaneous emission, the power-spectra are flat at low frequencies and turn over at high frequencies to a power-law with index −0.3; (ii) for emission-profiles in the form of one-sided exponentials, the power-spectra exhibit clear power-law behaviour with index −1.7. Fluctuations with a power law index between −1 and −1.7 are observed in many systems undergoing accretion. We found that our approach allows steady accretion in a disc by the action of coronal magnetic flux tubes alone. If we express the effective viscosity caused by coronal loops in the usual Shakura-Sunyaev α parameter of viscosity, we find values which are in good agreement with observed values.