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  • Technical Reviews
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Cosmological simulations of galaxy formation

Nature Reviews Physics volume 2, pages 42–66 (2020)Cite this article

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Abstract

Over recent decades, cosmological simulations of galaxy formation have been instrumental in advancing our understanding of structure and galaxy formation in the Universe. These simulations follow the nonlinear evolution of galaxies, modelling a variety of physical processes over an enormous range of time and length scales. A better understanding of the relevant physical processes, improved numerical methods and increased computing power have led to simulations that can reproduce a large number of the observed galaxy properties. Modern simulations model dark matter, dark energy and ordinary matter in an expanding space-time starting from well-defined initial conditions. The modelling of ordinary matter is most challenging due to the large array of physical processes affecting this component. Cosmological simulations have also proven useful to study alternative cosmological models and their impact on the galaxy population. This Technical Review presents a concise overview of the methodology of cosmological simulations of galaxy formation and their different applications.

Key points

  • The formation of structures and galaxies in the Universe, which consists of ordinary matter, dark energy and dark matter, involves various physical processes such as gravity, gas cooling, star formation, supernova feedback, supermassive black hole feedback, stellar evolution, radiation, magnetic fields, cosmic rays and more.

  • Cosmological simulations allow detailed studies of the formation and evolution of structures and galaxies in the cosmos, starting from smooth initial conditions constrained through observations of the cosmic microwave background, yielding detailed predictions of the galaxy population at different epochs of the Universe.

  • The dark matter component is typically numerically modelled through the N-body approach. Here, the dark matter phase-space distribution is sampled by an ensemble of phase-space sampling points, resulting in a Monte Carlo scheme, to follow its dynamics, which are governed by the collisionless Boltzmann equation.

  • The gas content of the baryonic matter component is, in its simplest form, described through the Euler equations, discretized with Eulerian, Lagrangian or arbitrary Lagrangian–Eulerian schemes, coupled to other physical processes such as gravity, cooling processes, feedback processes and star formation.

  • Alternative forms of dark matter, dark energy and gravity can also be explored through suitable modified simulation methods to test and constrain such theories in the context of structure and galaxy formation, by comparing to observational data such as galaxy surveys, leading to important insights into the overall cosmological framework of structure formation and cosmological parameters.

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Fig. 1: Visual representations of some selected structure and galaxy formation simulations.
Fig. 2: Overview of the key ingredients of cosmological simulations.

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Acknowledgements

The authors thank D. Barnes, M. Boylan-Kolchin, L. Hernquist, R. Kannan, H. Li, S. O’Neil, R. Pakmor, C. Pfrommer, L. Sales, A. Smith, V. Springel and R. Weinberger for useful comments. The authors also thank the reviewers for helpful feedback. M.V. acknowledges support through a Massachusetts Institute of Technology (MIT) RSC award, a Kavli Research Investment Fund, NASA ATP grant NNX17AG29G and National Science Foundation (NSF) grants AST-1814053 and AST-1814259. F.M. acknowledges support through the programme ‘Rita Levi Montalcini’ of the Italian Ministry of Education, University and Research.

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Authors and Affiliations

  1. Department of Physics, Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA

    Mark Vogelsberger

  2. Department of Physics and Astronomy, University of Bologna, Bologna, Italy

    Federico Marinacci

  3. Department of Astronomy, University of Florida, Gainesville, FL, USA

    Paul Torrey

  4. Leibniz-Institut fur Astrophysik Potsdam, Potsdam, Germany

    Ewald Puchwein

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  1. Mark Vogelsberger
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  4. Ewald Puchwein
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Glossary

Friedmann–Lemaître–Robertson–Walker space-time

A metric that is an exact solution of Einstein’s field equations of general relativity describing a homogeneous, isotropic, expanding universe.

Comoving coordinates

Spatial coordinates within an isotropic and uniformly expanding universe, where the overall expansion is divided out.

Method of characteristics

A technique for solving partial differential equations based on finding curves along which the original partial differential equation becomes an ordinary differential equation.

Octree

A tree data structure in which each internal node has exactly eight children. Octrees are often used to partition a 3D space by recursively subdividing it into eight octants.

Virial mass

The virial mass is the mass of a gravitationally bound astrophysical system within a spherical region, bounded by the so-called virial radius, where the system obeys the virial theorem.

Riemann problem

A specific partial differential equation initial value problem composed of a conservation equation together with piecewise constant initial data, which has a single discontinuity in the domain of interest.

Voronoi tessellation

A subdivision of space into convex cells.

Jeans mass

Threshold mass above which a self-gravitating system becomes unstable and begins to collapse.

r-process

The abbreviation of ‘rapid neutron-capture nuclear process’, whereby a nucleus rapidly increases its atomic number by repeatedly capturing neutrons.

Biermann battery

A process by which a weak seed magnetic field can be generated from zero initial conditions.

Galactic dynamo

A theory describing how a conducting and rotating fluid can build and sustain a magnetic field over galactic scales.

Eddington tensor

A tensor relating the radiation pressure to radiative energy for radiative transfer calculations.

Sunyaev–Zeldovich scaling relations

Scaling relations connecting galaxy cluster properties, such as mass and luminosity, to the Sunyaev–Zeldovich Compton parameter.

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Vogelsberger, M., Marinacci, F., Torrey, P. et al. Cosmological simulations of galaxy formation. Nat Rev Phys 2, 42–66 (2020). https://doi.org/10.1038/s42254-019-0127-2

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