Beyond single-stream with the Schr\"odinger method

TL;DR

This paper explores the Schr"odinger method for modeling collisionless dark matter, demonstrating its advantages over traditional fluid models by effectively handling multi-streaming and virialization in large-scale structure formation.

Contribution

It introduces the Schr"odinger method as an analytical tool for dark matter dynamics, surpassing the standard pressureless fluid model especially at shell crossing.

Findings

The Schr"odinger method handles multi-streaming effectively.

It avoids singularities present in the dust model.

It provides a superior analytical framework for structure formation.

Abstract

We investigate large scale structure formation of collisionless dark matter in the phase space description based on the Vlasov-Poisson equation. We present the Schr\"odinger method, originally proposed by Widrow and Kaiser (1993) as numerical technique based on the Schr\"odinger Poisson equation, as an analytical tool which is superior to the common standard pressureless fluid model. Whereas the dust model fails and develops singularities at shell crossing the Schr\"odinger method encompasses multi-streaming and even virialization.