Clustering and physical properties of the star-forming galaxies and AGN: does assembly bias have a role in AGN activity?

We compare the spatial clustering and physical properties of the active galactic nuclei (AGN) and star-forming galaxies (SFG) at fixed stellar mass using a volume limited sample from the Sloan Digital Sky Survey (SDSS). The analysis of the two-point correlation function shows that the AGN are more strongly clustered than the SFG. The closer proximity to the $5^{th}$ nearest neighbour for the AGN than that for the SFG indicates that AGN prefer the denser regions. We compare the distributions of the $(u-r)$ colour, star formation rate (SFR), D$4000$ and concentration index of the AGN and SFG after matching their stellar mass distributions. The null hypothesis can be rejected at $>99.99\%$ confidence level in each case. The comparisons are also carried out at different densities. The differences persist at the same significance level in both the high and low density regions, implying that such differences do not originate from the variations in the density. Alternatively stated, the AGN activity can be triggered in both the high and low density regions. An analysis of the correlations between the different physical properties at fixed stellar mass reveals that the anticorrelations of SFR with morphology, colour and recent star formation history are $2-3$ times stronger for the AGN than for the SFG. It suggests that the presence of a bulge and the availability of gas are the two most crucial requirements for AGN activity. We propose a picture where the galaxies at fixed stellar mass may have widely different assembly histories, leading to significant variations in bulge properties and cold gas content. Whether a galaxy of a given stellar mass can acquire the suitable conditions for AGN activity remains uncertain due to a broad diversity of assembly history. We conclude that AGN are stochastic phenomena owing to an underlying role of the assembly bias.