Non-conservation and time non-locality of biased tracers

Abstract

We study the effect of ongoing formation and merger on the assumed number conservation of biased tracers. Using a Lagrangian approach we present a model of the number density which accounts for such effects. The model is nonlocal in time, reflecting the gradual assembly of tracers from the underlying matter. The loss of tracers through merger is modelled by an environmentally-dependent sink, such that the merger rate is proportional to the local number density (higher probability of an event in higher density regions). We derive from our model a formula for the linear bias of non-conserved tracers, showing that such tracers debias more rapidly than conserved ones. Over time the large-scale power becomes increasingly suppressed relative to the conserved prediction, behaviour which has been observed in simulations elsewhere. Implications for current modelling approaches are discussed.