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Cosmological Simulation

General Introduction

Including history, methods, and theory === will emphasize on hydrodynamics simulation

Hydrodynamics Simulation

Dark energy and dark matter account for most of the Universe's energy, so it is valid to ignore baryons(N-body simulation) when simulating large-scale structure formation. However, since the visible components of galaxies consist of baryons, it is crucial to include baryons in the simulation to study the detailed structures of galaxies. At first, the baryon component consists of mostly hydrogen and helium gas, which later transforms into stars during the formation of structures.

Euler equations

In cosmological simulations, astrophysical gases are typically modeled as inviscid ideal gases that follow the Euler equations, which can be expressed mainly in three different ways: Lagrangian, Eulerian, or arbitrary Lagrange-Eulerian methods. Different methods give specific forms of hydrodynamical equations . When using the Lagrangian approach to specify the field, it is assumed that the observer tracks a specific fluid parcel with its unique characteristics during its movement through space and time. In contrast, the Eulerian approach emphasizes particular locations in space that the fluid passes through as time progresses.

Baryonic Physics

To shape the population of galaxies, the hydrodynamical equations must be supplemented by a variety of astrophysical processes mainly governed by baryonic physics.

Gas cooling

Processes, such as collisional excitation, ionization, and inverse Compton scattering, can cause the internal energy of the gas to be dissipated. In the simulation, cooling processes are realized by coupling cooling functions to energy equations. Besides the primordial cooling, at high temperature,$\ 10^{5}K<T<10^{7}K\,$, heavy elements (metals) cooling dominates . When $\ T<10^{4}K\,$, the fine structure and molecular cooling also need to be considered to simulate the cold phase of the interstellar medium.

Interstellar medium

Complex multi-phase structure, including relativistic particles and magnetic field, makes simulation of interstellar medium difficult. In particular, modeling the cold phase of the interstellar medium poses technical difficulties due to the short timescales associated with the dense gas. In the early simulations, the dense gas phase is frequently not modeled directly but rather characterized by an effective polytropic equation of state. More recent simulations use a multimodal distribution to describe the gas density and temperature distributions, which directly model the multi-phase structure. However, more detailed physics processes needed to be considered in future simulations, since the structure of the interstellar medium directly affects star formation.

Star formation

As cold and dense gas accumulates, it undergoes gravitational collapse and eventually forms stars. To simulate this process, a portion of the gas is transformed into collisionless star particles, which represent coeval, single-metallicity stellar populations and are described by an initial underlying mass function. Observations suggest that star formation efficiency in molecular gas is almost universal, with around 1% of the gas being converted into stars per free fall time. In simulations, the gas is typically converted into star particles using a probabilistic sampling scheme based on the calculated star formation rate. Some simulations seek an alternative to the probabilistic sampling scheme and aim to better capture the clustered nature of star formation by treating star clusters as the fundamental unit of star formation. This approach permits the growth of star particles by accreting material from the surrounding medium. In addition to this, modern models of galaxy formation track the evolution of these stars and the mass they return to the gas component, leading to an enrichment of the gas with metals.

Stellar feedback

Stars have an influence on their surrounding gas by injecting energy and momentum. This creates a feedback loop that regulates the process of star formation. To effectively control star formation, stellar feedback must generate galactic-scale outflows that expel gas from galaxies. Various methods are utilized to couple energy and momentum, particularly through supernova explosions, to the surrounding gas. These methods differ in how the energy is deposited, either thermally or kinetically. However, excessive radiative gas cooling must be avoided in the former case. Cooling is expected in dense and cold gas, but it cannot be reliably modeled in cosmological simulations due to low resolution. This leads to artificial and excessive cooling of the gas, causing the supernova feedback energy to be lost via radiation and significantly reducing its effectiveness. In the latter case, kinetic energy cannot be radiated away until it thermalizes. However, using hydrodynamically-decoupled wind particles to inject momentum non-locally into the gas surrounding active star-forming regions may still be necessary to achieve large-scale galactic outflows. Recent models explicitly model stellar feedback. These models not only incorporate supernova feedback but also consider other feedback channels such as energy and momentum injection from stellar winds, photoionization, and radiation pressure resulting from radiation emitted by young, massive stars.

Supermassive black holes

Simulation of supermassive black holes is also considered, numerically seeding them in dark matter haloes, due to their observation in many galaxies and the impact of their mass on the mass density distribution. Their mass accretion rate is frequently modeled by the Bondi-Hoyle model.

Active galactic nuclei

Active galactic nuclei (AGN) have an impact on the observational phenomena of supermassive black holes, and further have a regulation of black hole growth and star formation. In simulations, AGN feedback is usually classified into two modes, namely quasar and radio mode. Quasar mode feedback is linked to the radiatively efficient mode of black hole growth and is frequently incorporated through energy or momentum injection. The regulation of star formation in massive galaxies is believed to be significantly influenced by radio mode feedback, which occurs due to the presence of highly-collimated jets of relativistic particles. These jets are typically linked to X-ray bubbles that possess enough energy to counterbalance cooling losses.

Magnetic fields

The ideal magnetohydrodynamics approach is commonly utilized in cosmological simulations since it provides a good approximation for cosmological magnetic fields. The effect of magnetic fields on the dynamics of gas is generally negligible on large cosmological scales. Nevertheless, magnetic fields are a critical component of the interstellar medium since they provide pressure support against gravity and affect the propagation of cosmic rays .

Cosmic rays

Cosmic rays play a significant role in the interstellar medium by contributing to its pressure , serving as a crucial heating channel , and potentially driving galactic gas outflows . The propagation of cosmic rays is highly affected by magnetic fields. So in the simulation, equations describing the cosmic ray energy and flux are coupled to magnetohydrodynamics equations .

Radiation Hydrodynamics

Radiation hydrodynamics simulations are computational methods used to study the interaction of radiation with matter. In astrophysical contexts, radiation hydrodynamics is used to study the epoch of reionization when the Universe had high redshift. There are several numerical methods used for radiation hydrodynamics simulations, including ray-tracing, Monte Carlo, and moment-based methods. Ray-tracing involves tracing the paths of individual photons through the simulation and computing their interactions with matter at each step. This method is computationally expensive but can produce very accurate results.

Results of Hydrodynamical Simulations

The simulation results can be compared with observations to test models used in simulations.