Modified viscosity in accretion disks

Aims. Black holes (BHs) surrounded by accretion disks are present in the Universe at different scales of masses, from microquasars up to the active galactic nuclei (AGNs). Since the work of Shakura & Sunyaev (1973, A&A, 24, 337) and their α-disk model, various prescriptions for the heat-production rate are used to describe the accretion process. The current picture remains ad hoc due the complexity of the magnetic field action. In addition, accretion disks at high Eddington rates can be radiation-pressure dominated and, according to some of the heating prescriptions, thermally unstable. The observational verification of their resulting variability patterns may shed light on both the role of radiation pressure and magnetic fields in the accretion process. Methods. We compute the structure and time evolution of an accretion disk, using the code GLADIS (which models the global accretion disk instability). We supplement this model with a modified viscosity prescription, which can to some extent describe the magnetisation of the disk. We study the results for a large grid of models, to cover the whole parameter space, and we derive conclusions separately for different scales of black hole masses, which are characteristic for various types of cosmic sources. We show the dependencies between the flare or outburst duration, its amplitude, and period, on the accretion rate and viscosity scaling. Results. We present the results for the three grids of models, designed for different black hole systems (X-ray binaries, intermediate mass black holes, and galaxy centres). We show that if the heating rate in the accretion disk grows more rapidly with the total pressure and temperature, the instability results in longer and sharper flares. In general, we confirm that the disks around the supermassive black holes are more radiation-pressure dominated and present relatively brighter bursts. Our method can also be used as an independent tool for the black hole mass determination, which we confront now for the intermediate black hole in the source HLX-1. We reproduce the light curve of the HLX-1 source. We also compare the duration times of the model flares with the ages and bolometric luminosities of AGNs. Conclusions. With our modelling, we justify the modified μ-prescription for the stress tensor τrφ in the accretion flow in microquasars. The discovery of the Ultraluminous X-ray source HLX-1, claimed to be an intermediate black hole, gives further support to this result. The exact value of the μ parameter, as fitted to the observed light curves, may be treated as a proxy for the magnetic field strength in the accretion flow in particular sources, or their states