tokens: disc. Fig. 7 confirms that the time lag increases with increasing R acc and with increasing ξ, and does not change significantly with τ r and τ w . Observations show time lags of about 50–250 Myr which are reproduced by most of our simulations, but a few of our simulations produce time lags that have values of up to 550 Myr. Such large time lags have not been directly observed yet. However, Wild et al. ( 2010 ) only measure the average time lag of a sample of about 400 galaxies with a result of 250 Myr, thus some of the galaxies involved will have time lags that exceed this average value. Fig. 8 shows SFR, BHAR and AGNAR versus time for different levels of resolution. We increase the number of particles by a factor of 2 and a factor of 4, respectively. For the former resolution level the gravitational softening length for the halo particles is 0.64 kpc and 0.4 kpc for all other particles, for the latter resolution level the gravitational softening length for the halo particles is 0.5 kpc and 0.32 kpc for all other particles. Figure 7. Time lag between starburst and AGN activity with the values of R acc , ξ, τ r and τ w from our parameter study (Table 2 ) and our reference model. Figure 8. SFR, AGNAR and BHAR as functions of time for different resolution levels. Left: particle number increased by a factor of 2, right: particle number increased by a factor of 4. The vertical lines mark the peak of the SFR and the peak of the BHAR, respectively. Both resolution levels show the same features as our reference model: the simulations produce a starburst and a peak in the BHAR, and a time lag between these phenomena of about 200 Myr. However, there are still small differences between these simulations, to further reduce these deviations additional adjustments to the respective resolution levels would be necessary. For instance, Hopkins, Narayanan Murray ( 2013 ) argue that the critical density for the onset of star formation ρ crit has to be adjusted for resolution. But as the above mentioned key features are already reproduced we refrain from such a fine tuning of our simulation parameters. 5 SUMMARY With only one model setup we were able to reproduce three observational findings that have been identified in galaxies. The observed time lag between starburst and AGN activity is, in our work, principally caused by a viscous time lag the gas needs to flow through the AGN's accretion disc until it reaches the central black hole. Our results match the observed M BH -σ correlation, but additionally include the aforementioned time lags. As, e.g. Di Matteo et al. ( 2005 ) or Debuhr et al. ( 2011 ) have already shown, AGN feedback is responsible for this relation. The large scatter of the M BH -σ correlation is, in our work, caused by the continuing evolution of the black hole mass after the merging event. The time lag does not only occur between starburst and AGN activity, but also between the peak in the AGNAR and the peak in the BHAR. Thus it is
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