Supernovae-induced accretion and star formation in the inner kiloparsec of a gaseous disc

We consider the effects of supernovae (SNe) on accretion and star formation in a massive gaseous disc in a large primeval galaxy. The gaseous disc we envisage, roughly 1 kpc in size with >~10⁸M_solar of gas, could have formed as a result of galaxy mergers where tidal interactions removed angular momentum from gas at larger radius and thereby concentrated it within the central ~1 kpc region. We find that SNe lead to accretion in the disc at a rate of roughly 0.1-1M_solar yr^-1 and induce star formation at a rate of ~10-100M_solar per year which contributes to the formation of a bulge; a part of the stellar velocity dispersion is due to SN shell speed from which stars are formed and a part due to the repeated action of stochastic gravitational field of SNe remnant network on stars. The rate of SN in the inner kpc is shown to be self-regulating, and it cycles through phases of low and high activity. The SN-assisted accretion transports gas from about 1 kpc to within a few pc of the centre. If this accretion were to continue down to the central black hole then the resulting ratio of black hole mass to the stellar mass in the bulge would be of the order of ~ 10^-2-10^-3, in line with the observed Magorrian relation.