§3.1 宇宙学流体动力学模拟

Being gravity the force that drives structure formation, the building block of the majority of cosmological simulations is an N-body code (see e.g. ^[1] for a discussion on alternative approaches). The goal of an N-body code is to investigate the non-linear dynamical evolution of a self-gravitating, collisionless system (see ^[2] ,^[3] , for reviews).

A collisionless fluid is a system whose constituent elements move under the effect of the collective gravity field generated by the total mass distribution: in a collisionless system, gravitational collisions and interactions between fluid elements are negligible and do not influence the motion and general properties of the constituent elements themselves. In order to establish quantitatively whether a system can be considered collisionless or not, the relaxation timescale has to be contrasted to the timescale over which the system evolves. A system featuring N elements moving with typical velocity $v$ across its size $L$ is characterised by the crossing time $t_{\rm cross} = L/v$ ^[4] . Possible collisions with nearby particles result in a quadratic velocity perturbation $(\Delta v)^2$ of each particle's velocity, since each encounter contributes with a randomly oriented $\Delta v$. The relaxation time is the timescale over which the quadratic velocity perturbation amounts to roughly the squared velocity itself $t_{\rm relax} = v^2/(\Delta v)^2 \times t_{\rm cross}$. Here, $v^2/(\Delta v)^2$ quantifies the number of crossings required to have a velocity change of the same order as $v^2$ and depends on the number N of particles ^[4] . Therefore, the relaxation time can be cast as $t_{\rm relax} = N/(8 \ln N) \times t_{\rm cross}$. A system can be deemed as collisionless if its relaxation time exceeds by far the age of the Universe $\sim 1/H_0$ ($H_0$ being the present-day value of the Hubble constant). After the timescale $t_{\rm relax}$, deflections in a particle motion by interactions with other particles are expected, and the system cannot be considered collisionless anymore. DM and stars in galaxies can be represented as a collisionless, non-relativistic fluid made of particles, while gas is a collisional component.

To a first approximation, the formation of cosmic structures can be studied using N-body simulations, which only follow the evolution of collisionless particles under gravity. Such simulations have been performed with high resolution for individual objects, like galaxies and galaxy clusters, as well as for very large-scale structures. The numerical methods and different possible approaches used to tackle the problem of integrating the equations of motion of the N particles in the cumulative gravity field are described in N体章节.

However, with the possible exception of gravitational lensing, observations mainly reflect the state of the ordinary (baryonic) matter. Therefore, their interpretation in the framework of cosmic structure evolution requires that we understand the complex, non-gravitational physical processes which determine the evolution of the cosmic baryons. How DM, gas and stars co-evolve – with baryons falling into the potential well of the underlying DM distribution, cooling, and finally condensing to form stars (see Video 1, page xiii) – within the hierarchical formation scenario contributes to the state and composition of the intergalactic and intracluster media (IGM and ICM, respectively), and is responsible for feedback in energy and metals, magnetic fields, and high-energy particles. Depending on their origin, these components will be blown out by jets, winds or ram pressure effects and finally mix with the surrounding IGM/ICM. While some of these effects will be naturally followed within hydrodynamic simulations (like ram pressure effects), others have to be included in simulations via effective models (like star formation and ensuing feedback, and chemical pollution of the ISM, IGM and ICM by SNe).

Thanks to the improved computing power and advancements in numerical methods, the number of resolution elements¹ which can be used in such simulations has increased dramatically over the last decades, as shown in Fig. 1. Note that the largest, hydrodynamical simulations up to date (e.g. Magneticum² Box0/mr^[5] and FLAMINGO³ L2p8_m9^[6] ) followed a total number of more than 2×10¹¹ particles (e.g., DM, gas, stars and BH particles) across the entire evolution of the Universe.

In this chapter, we will review the basic numerical methods which are used to describe the hydrodynamics, and discuss the main approaches adopted to incorporate the fundamental astrophysical processes in the context of cosmological hydrodynamical simulations (see Video 3, page xiii). Further components like magnetic fields and high-energy particles need additional modelling of their injection processes and evolution. Therefore, they must be self-consistently coupled with hydrodynamics and are described in more detail in 星系团章节.