Constrained simulations and excursion sets: understanding the risks and benefits of ‘genetically modified’ haloes

Abstract

Constrained realisations of Gaussian random fields are used in cosmology to design special initial conditions for numerical simulations. We review this approach and its application to density peaks providing several worked-out examples. We then critically discuss the recent proposal to use constrained realisations to modify the linear density field within and around the Lagrangian patches that form dark-matter haloes. The ambitious concept is to forge `genetically modified' haloes with some desired properties after the non-linear evolution. We demonstrate that the original implementation of this method is not exact but approximate because it tacitly assumes that protohaloes sample a set of random points with a fixed mean overdensity. We show that carrying out a full genetic modification is a formidable and daunting task requiring a mathematical understanding of what determines the biased locations of protohaloes in the linear density field. We discuss approximate solutions based on educated guesses regarding the nature of protohaloes. We illustrate how the excursion-set method can be adapted to predict the non-linear evolution of the modified patches and thus fine tune the constraints that are necessary to obtain preselected halo properties. This technique allows us to explore the freedom around the original algorithm for genetic modification. We find that the quantity which is most sensitive to changes is the halo mass-accretion rate at the mass scale on which the constraints are set. Finally we discuss constraints based on the protohalo angular momenta.