Numerical simulations of galaxies

The spectacular advances in the field of numerical simulations now allow for an in-depth exploration of the complexity of galaxies and their evolution within the universe. The computational models developed by international teams, utilizing cutting-edge supercomputers, offer a unique window into star formation, galactic dynamics, and the gravitational effects of dark matter. This computer modeling opens fascinating prospects for contemporary cosmology by reproducing cosmic environments over billions of years.

In the era of big data, the creation of the largest virtual galaxy catalog by the European Space Agency (ESA) marks a major milestone. Titled “Flagship 2 Galaxy Mock,” this catalog simulates over 3.4 billion galaxies over a spatial volume of about 10 billion light-years around Earth. This technical feat is not only a computational breakthrough: it allows for testing theories about the nature of dark matter, studying the cosmic web, and refining models of the cosmos as a whole, while paving the way to analyze real data collected by the Euclid space telescope.

In this context, numerical simulations in cosmology continue to improve, now integrating complex criteria from both fundamental physics, including the hydrodynamics of space plasmas, and advances in artificial intelligence. This digital holography of the universe grants them unprecedented power to model the formation and transformation of galaxies over the ages, simulating as accurately as possible their global behavior and the underlying physical phenomena.

Recent approaches based on adaptive spacetime partitioning, as well as multi-scale simulations, provide unambiguous insights into the combined impacts of gravity, galactic fluids, and interactions with dark matter. Throughout this article, readers will undoubtedly discover the methods, challenges, and results obtained in these gigantic modeling efforts that push the boundaries of human knowledge about cosmic vastness.

In short:

• The creation of the Euclid virtual catalog simulates over 3.4 billion galaxies, covering 10 billion light-years.
• Supercomputers are essential for solving complex equations of gravity and hydrodynamics through adaptive mesh.
• Simulations allow for the study of dark matter and testing the standard cosmological model with unprecedented precision.
• The integration of artificial intelligence revolutionizes astrophysical data analysis and computer modeling.
• The simulated data serves as a training base for space telescopes like Euclid, to anticipate and interpret real observations.

The technical foundations of numerical simulations of galaxies in cosmology

Numerical simulations play a central role in understanding phenomena at galactic and cosmic scales. Computational modeling requires the simultaneous integration of gravitational equations, hydrodynamics, and plasma physics, which govern the evolution of galaxies.

These simulations rely on accurate data from observations, including imagery provided by space missions such as Euclid. The process begins with a primordial universe often modeled around an initial distribution solely composed of non-baryonic dark matter, which is invisible but influential through its gravity. Each simulation thus calculates the dynamic behavior of trillions of particles, reproducing the formation of cosmic structures over a spatial volume of several billion light-years.

To handle such a volume of information and ensure sufficient detail quality, astrophysicists use advanced numerical methods such as adaptive meshing. This technique adjusts the mesh resolution according to the local complexity of the system being studied: regions of nearly homogeneous void benefit from a coarse mesh, whereas areas of star formation and interactions between galaxies are modeled with a fine mesh to capture complex phenomena.

This approach is made possible thanks to high-performance computing infrastructures available in centers like CEA Bruyères-le-Châtel. The concerted use of skills in applied mathematics and computational physics serves as a fundamental lever to reliably reproduce galactic dynamics. The use of supercomputers such as Piz Daint in Switzerland has enabled simulations of unprecedented complexity and scale, simulating in particular four trillion particles to construct the cosmic web.

At the core of these models, accurate representation of gravitational fields, dark matter, and plasmatic environments is essential. The interaction between these components determines the formation and evolution of galaxies, their morphology, and the dynamics of galactic clusters. The computing power allows experimenting with different cosmological scenarios and comparing the results obtained with real observations, thus enhancing the understanding of the underlying physical processes.

Multi-scale approach and modeling of gravitational interactions

Numerical simulations in cosmology are based on sophisticated multi-scale modeling. Gravity, which regulates the organization and dynamics of galaxies, acts simultaneously over vast distances, but also on the scale of clusters and galactic substructures. Resolving this complexity requires algorithms capable of integrating both global effects and fine, often non-linear interactions.

The challenge lies particularly in representing haloes of dark matter with sufficient detail, these dense regions that serve as the “skeleton” for galaxy formation. From these haloes, simulations inject stellar populations while respecting observed properties such as brightness, color, or intrinsic motion.

Thanks to these models, astrophysicists can reproduce certain observed phenomena, such as the merger of two spiral galaxies resulting in an elliptical galaxy, or the distribution of satellite galaxies around a massive halo. This computer modeling provides a robust theoretical framework for studying galactic dynamics, and opens the way for the discovery of previously unknown phenomena.

Euclid Virtual Catalog: A Leap Forward for Digital Astronomy

One of the major recent developments in the field of numerical simulations of galaxies is undoubtedly the creation of the “Flagship 2 Galaxy Mock” virtual catalog by ESA. This simulation reproduces what the Euclid space telescope will observe in space, in a region extending over more than 10 billion light-years around our planet. This virtual catalog contains about 3.4 billion galaxies, each described by about 400 different properties.

This colossal work required collaboration from eight institutions, with the University of Zurich playing a crucial role with its innovative computational models. The calculations, performed on the Piz Daint supercomputer, utilized nearly the entire capacity of the machine to meet the challenge.

This vast inventory is not only intended for modeling. It represents an essential “training universe” for preparing researchers to manage the significant amount of data that Euclid will provide during its mission. With this, they can test analysis algorithms, identify potential flaws, and optimize the quality of future scientific interpretations.

The catalog also provides a valuable opportunity to compare observed data with simulated models, dark energy and dark matter being key components studied. This experimental and theoretical convergence is crucial for verifying the validity of the standard cosmological model, and for potential discoveries of unanticipated physical phenomena.

Choice of parameters and assignment of properties to simulated galaxies

A fundamental aspect in carrying out this type of simulation lies in the precise calibration of the physical properties inserted into the models. Researchers rely on numerous observational data from previous astronomical surveys to associate to each virtual galaxy parameters such as size, color, brightness, as well as dynamic characteristics related to speed or chemical composition.

By filtering approximately 16 billion dark matter haloes, they selected the most relevant ones to invite galactic populations. This process relies on solid foundations from fundamental physics, but also due to advances in numerical simulations in cosmology, where the juxtaposition of multiple disciplines allows for a rendering close to the observed reality.

The results illustrate not only the large-scale mass distribution, revealing the natural formation of clusters, filaments, and quasi-empty areas, but can also be explored to analyze star formation and the internal dynamics of galaxies in various temporal and environmental contexts.

Physical parameters and equations solved in galactic computational modeling

The solution of the equations integrated into these models is based on fundamental principles of physics.

• Gravity: represented by Newtonian and relativistic physics, it governs the formation of large-scale structures such as dark matter haloes and galaxy clusters.
• Hydrodynamics: it models the behavior of gases in space, including thermal interactions and the complex movements of the interstellar medium.
• Star formation: procedures integrated into the models to simulate the emergence and evolution of stars within galaxies.
• Plasma dynamics: a key factor influencing dispersion and fusion phenomena in galactic environments.

Moreover, the equations are integrated according to a discrete division of space and time known as meshing. The size of these meshes adapts to ensure a good balance between precision and computation time. This technique allows simulating very fine interactions in dense areas while maintaining an overview of the cosmic structure.

Physical Parameter	Role in the Simulation	Modeling Technique
Gravity	Formation of clusters and galactic haloes	Newtonian and relativistic models
Hydrodynamics	Behavior of interstellar gases	Navier-Stokes equations
Star formation	Birth and evolution of stars in galaxies	Integrated sub-grid models
Plasma dynamics	Electromagnetic interactions in galactic environments	Magnetohydrodynamic (MHD) models

Each component is essential for building a coherent system capable of reproducing the complex movements observed in galaxies, in particular rotation, mergers, or interactions with dark matter. The close integration of these parameters into a robust numerical framework places galactic simulations at the forefront of modern astrophysics.

The impact of numerical simulations on the understanding of dark matter and cosmic megastructures

Numerical simulations have led to major advances in the presentation and analysis of the large structures of the universe. In particular, they have established the detailed mapping of superclusters of galaxies and accurately revealed the distribution of cosmic filaments, key elements of the cosmic web.

It is particularly thanks to these tools that the very nature of dark matter has been studied from a new perspective. The standard cosmological model states that it represents 27% of the matter-energy of the universe, strongly influencing galactic dynamics but remaining undetectable by light. Simulations have modeled how this dark matter shapes the formation and arrangement of galaxies, providing researchers with a framework to test hypotheses about its physical properties.

The megastructures formed by the accumulation of visible and dark matter are made visible thanks to these digital reconstructions, illustrating the complexity and diversity of scales in the universe. These numerical models allow for the exploration of interactions at various scales, from the movement of satellite galaxies to the organization into superclusters.

• Precise identification of massive dark matter haloes
• Modeling of galactic mergers and their impact on morphology
• Study of cosmic filaments and voids between clusters
• Testing of alternative models of dark energy and modified gravity

This capability to visually and quantitatively grasp universal structure is a decisive advance for fundamental research in astrophysics. To deepen the understanding of the nature and issues related to these megastructures, superclusters of galaxies and cosmic megastructures represent a privileged field of study thanks to simulations.

What is a numerical simulation in astrophysics?

It is a computational model that uses physical equations to replicate the behavior of galactic and cosmic systems over very large time and space scales.

What is the importance of dark matter in these simulations?

Dark matter constitutes the majority of the mass in the universe, influencing the dynamics of galaxies and is essential to model the distribution of large-scale structures.

How do numerical simulations help in understanding star formation?

They allow for the replication of physical processes on the scale of gas clouds and formation regions, integrating hydrodynamic and gravitational laws to predict the birth and evolution of stars.

Why are supercomputers used for these simulations?

The calculations needed are extremely complex and require a very high computing power, often distributed across thousands of processors, to process billions of interacting particles.

What is the role of the virtual catalog created for the Euclid mission?

It serves as a training universe to prepare for the analysis of real data, to test algorithms, and to better understand galactic dynamics before receiving observations.