Why does the clustering of haloes depend on their formation history

Abstract

We discuss in the framework of the excursion set formalism a recent discovery from N-body simulations that the clustering of haloes of given mass depends on their formation history. We review why the standard implementation of this formalism is unable to explain such dependencies, and we show that this can, in principle, be rectified by implementing in full an ellipsoidal collapse model where collapse depends not only on the overdensity but also on the shape of the initial density field. We also present an alternative remedy for this deficiency, namely the inclusion of collapse barriers for pancakes and filaments, together with the assumption that formation history depends on when these barriers are crossed. We implement both these extensions in a generalised excursion set method, and run large Monte Carlo realisations to quantify the effects. Our results suggest that effects as large as those found in simulations can only arise in the excursion set formalism if the formation history of a halo does indeed depend on the size of its progenitor filaments and pancakes. We also present conditional distributions of progenitor pancakes and filaments for low-mass haloes identified at present epoch, and discuss a recent claim by Mo et.al. that most low-mass haloes were embedded in massive pancakes at $z\sim 2$.