Turbulent gas accretion between supermassive black holes and star-forming rings in the circumnuclear disk

While supermassive black holes are known to co-evolve with their host galaxy, the precise nature and origin of this co-evolution is not clear. We here explore the possible connection between star formation and black hole growth in the circumnuclear disk (CND) to probe this connection in the vicinity close to the black hole. We adopt here the circumnuclear disk model developed by Kawakatu & Wada (2008) and Wutschik et al. (2013), and explore both the dependence on the star formation recipe as well as the role of the gravitational field, which can be dominated by the central black hole, the CND itself or the host galaxy. A specific emphasis is put on the turbulence regulated star formation model by Krumholz et al. (2005) to explore the impact of a realistic star formation recipe. It is shown that this model helps to introduce realistic fluctuations in the black hole and star formation rate, without overestimating them. Consistent with previous works, we show that the final black hole masses are rather insensitive to the masses of the initial seeds, even for seed masses of up to 10^6 M_sol. In addition, we apply our model to the formation of high-redshift quasars, as well as to the nearby system NGC 6951, where a tentative comparison is made in spite of the presence of a bar in the galaxy. We show that our model can reproduce the high black hole masses of the high-redshift quasars within a sufficiently short time, provided a high mass supply rate from the host galaxy. In addition, it reproduces several of the properties observed in NGC 6951. With respect to the latter system, our analysis suggests that supernova feedback may be important to create the observed fluctuations in the star formation history as a result of negative feedback effects.