The nature of assembly bias – III. Observational properties
We analyse galaxies in groups in the Sloan Digital Sky Survey (SDSS) and find a weak but significant assembly-type bias, where old central galaxies have a higher clustering amplitude (61 $\pm$ 9 per cent) at scales > 1 Mpc than young central galaxies of equal host halo mass ($M_{h} \sim 10^{11.8} h^{-1}$ $M_{\odot}$). The observational sample is volume-limited out to z=0.1 with $M_r -$ 5 log$(h) \le -19.6$. We construct a mock catalogue of galaxies that shows a similar signal of assembly bias (46 $\pm$ 9 per cent) at the same halo mass. We then adapt the model presented by Lacerna & Padilla (Paper I) to redefine the overdensity peak height, which traces the assembly bias such that galaxies in equal density peaks show the same clustering regardless of their stellar age, but this time using observational features such as a flux limit. The proxy for peak height, which is proposed as a better alternative than the virial mass, consists in the total mass given by the mass of neighbour host haloes in cylinders centred at each central galaxy. The radius of the cylinder is parametrized as a function of stellar age and virial mass. The best-fitting set of parameters that make the assembly bias signal lower than 5$-$15 per cent for both SDSS and mock central galaxies are similar. The idea behind the parametrization is not to minimize the bias, but it is to use this method to understand the physical features that produce the assembly bias effect. Even though the tracers of the density field used here differ significantly from those used in paper I, our analysis of the simulated catalogue indicates that the different tracers produce correlated proxies, and therefore the reason behind this assembly bias is the crowding of peaks in both simulations and the SDSS.