Non-conservation and time non-locality of biased tracers

TL;DR

This paper presents a nonlocal-in-time model for biased tracers that accounts for ongoing formation and mergers, showing that such tracers lose bias and power more rapidly than conserved tracers.

Contribution

It introduces a novel Lagrangian, nonlocal-in-time model for biased tracers that incorporates environmental effects and merger-driven loss, advancing current understanding.

Findings

Biased tracers debias more rapidly than conserved tracers.

Large-scale power is suppressed over time relative to conserved predictions.

The model aligns with simulation observations of non-conservation effects.

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.