Spectral retrieval is a key computational tool for interpreting spectroscopic observations of exoplanets. As data quality has dramatically improved with the launch of JWST, so the complexity of retrieval models has also increased. Due to the lack of ground truth and prior knowledge for exoplanets, retrievals adopt algorithms capable of exploring a wide parameter space, such as MCMC or Nested Sampling, which become increasingly inefficient for higher dimensionality problems. Tuning retrieval complexity for these scenarios requires a delicate compromise between sufficient physical accuracy and pragmatic approximations. Retrievals can be applied to many different types of observation, with specific challenges associated with each. In the current environment, as we begin characterize smaller, temperate planets that may potentially be habitable, interpretation of retrievals and calculation of detection significance must be approached with special care. In this review, we summarize the current computational challenges in all aspects of the retrieval process: atmospheric modelling; data preparation; inversion and likelihood calculation; and interpretation, for a range of observational strategies. We conclude with a series of recommendations for scientists approaching retrievals for the first time in this new data-rich era for exoplanet science.
Today, more than 6000 exoplanets are known after the first detection of an extrasolar planet around a main sequence star in 1995. Among them are representatives of new planetary classes such as Super-Earths and Mini-Neptunes, in addition to those already known from the solar system: rocky planets (Mercury, Earth, Venus, Mars), gas giants (Jupiter, Saturn), and ice giants (Uranus, Neptune). In order to understand the formation of planets, their interior structure and composition, thermal evolution and magnetic field, precise data on the equation of state, the transport coefficients, and the optical properties of the most abundant planetary materials are necessary. Relevant temperatures and densities cover a wide range from cold and dilute molecular clouds or planetary atmospheres up to warm and dense planetary cores. Ab initio simulations allow to determine thermophysical properties of warm dense matter with high precision. In this review we give an introduction into the ab initio methods and demonstrate their capacity for planetary physics by showing exemplary results for the thermophysical properties of key materials such as H-He (gas giants) and H-C-N-O mixtures (ice giants). Based on these results, advanced models for the interior structure of planets, their thermal evolution, and their magnetic field can be developed.
Stars are born with a surrounding disk made up of gas entrained by dusty and icy particles, which are the building material for planetary systems. The evolution from small grains towards planetesimals and embryos is regulated by turbulence-driven transport and collisions. Likewise, the migration and growth of planets depends on the gas turbulence. In order to make interpretations of disk observations, one needs to model the turbulent state and the dynamic evolution in these disks. Typical observations of molecular lines provide us with information about the velocity deviation from laminar rotation, and continuum observations of emitted and scattered light helps us determine the spatial and size distribution of dust. The purpose of this review is to provide a guide book on how to set up hydrodynamic and radiation hydrodynamic simulations of a disk around a young star reflecting the current state of code development. These models can then be used to study the effect of turbulence on the distribution and evolution of dust up to planetesimals and planetary embryos, as well as to study the interaction of planets with the disk gas. We will focus on the effects of radiation transport on dynamic stability in global three-dimensional simulations and, therefore, neglect the effects of self-gravity, particle feedback and magnetic fields to some later iteration of the topic.
Multiphase gas-ranging from cold molecular clouds ( ≲ 100 K) to hot, diffuse plasma ( ≳ 10^6 K) is a defining feature of the interstellar, circumgalactic, intracluster, and intergalactic media. Accurately simulating its dynamics is critical to improving our understanding of galaxy formation and evolution, however, due to their multi-scale and multi-physics nature, multiphase systems are highly challenging to model. In this review, we provide a comprehensive overview of numerical simulations of multiphase gas in and around galaxies. We begin by outlining the environments where multiphase gas arises and the physical and computational challenges associated with its modeling. Key quantities that characterize multiphase gas dynamics are discussed, followed by an in-depth look at idealized setups such as turbulent mixing layers, cloud-wind interactions, thermal instability, and turbulent boxes. The review then transitions to less idealized and/or larger-scale simulations, covering radiative supernovae bubbles, tall box simulations, isolated galaxy models including dwarf and Milky Way-mass systems, and cosmological zoom-in simulations, with a particular focus on simulations that enhance resolution in the halo. Throughout, we emphasize the importance of connecting scales, extracting robust diagnostics, and comparing simulations to observations. We conclude by outlining persistent challenges and promising directions for future work in simulating the multiphase Universe.
Most of the physical information about astrophysical objects is obtained via the analysis of their electromagnetic spectra. Observed data coupled with radiation transfer models in physical conditions representative of stars, planets, kilonovae, and ISM, yield constrains on their physical structure, gas flow dynamics at the surface, mass loss, and detailed chemical composition of the systems. All these core astrophysical parameters are only as reliable as the physical quality of the models that are employed for simulations of radiation transfer. Recent advances in multi-dimensional transfer modelling with Non-Local Thermodynamic Equilibrium (NLTE) in inhomogeneous time-dependent systems revealed systematic shortcomings of canonical models. Owing to major complexities of solving coupled multi-frequency RT equations in 3D geometry, a number of approximations have been introduced. This review presents an overview of the physical problem, standard solutions, and recent methodological advances. We also provide an overview of main results in the area of 3D NLTE radiation transfer and its applications to modelling diverse astrophysical environments, including FGKM type- and OBA-type stars, multi-epoch spectra of kilonovae, and atmospheres of rocky and gaseous exoplanets.
The strong magnetic fields of neutron stars are closely linked to their observed thermal, spectral, and timing properties, such as the distribution of spin periods and their derivatives. To understand the evolution of astrophysical observables over time, it is essential to develop robust theoretical frameworks and numerical models that solve the coupled thermal and magnetic field evolution equations, incorporating detailed microphysics such as thermal and electrical conductivities and neutrino emission rates. These efforts are key to uncovering how the strength and geometry of magnetic fields change with age, ultimately shedding light on the diverse phenomenology of neutron stars. In this review, we outline the fundamental theory underlying magneto-thermal evolution models, with an emphasis on numerical methods and a comprehensive set of benchmark tests intended to guide current and future code development. We revisit established results from axisymmetric simulations, highlight recent progress in fully three-dimensional models, and offer a perspective on the anticipated developments in this rapidly evolving field.
Fuzzy dark matter (FDM), composed of ultralight bosons, exhibits intricate wave phenomena on galactic scales. Compared to cold dark matter, FDM simulations are significantly more computationally demanding due to the need to resolve the de Broglie wavelength and its rapid oscillations. In this review, we first outline the governing equations and distinctive features of FDM. We then present a range of numerical algorithms for both wave- and fluid-based simulations, discuss their respective advantages and limitations, and highlight representative test problems. To facilitate code comparison, we also provide publicly available initial condition files for both isolated-halo and cosmological simulations.
This paper reviews Vlasov-based numerical methods used to model plasma in space physics and astrophysics. Plasma consists of collectively behaving charged particles that form the major part of baryonic matter in the Universe. Many physical concepts ranging from our own planetary environment to the Solar system and beyond can be understood in terms of kinetic plasma physics, represented by the Vlasov equation. We introduce the physical basis for the Vlasov systems, and then outline the associated numerical methods that are typically used. A particular application of the Vlasov system is Vlasiator, the world’s first global hybrid-Vlasov simulation for the Earth’s magnetic domain, the magnetosphere. We introduce the design strategies for Vlasiator and outline its numerical concepts ranging from solvers to coupling schemes. We review Vlasiator’s parallelisation methods and introduce the used high-performance computing (HPC) techniques. A short review of verification, validation, and physical results is included. The purpose of the paper is to present the Vlasov equation and its use in numerical modelling, introduce an example implementation, and to illustrate that even with massive computational challenges, an accurate description of physics is highly rewarding as it allows to significantly advance our understanding of complex plasma systems. As an update to the previous paper in this series, we especially highlight latest trends in HPC including graphics processing units (GPUs) and emerging applications in astrophysical plasmas.
Supernovae (SNe) and kilonovae (KNe) are the most violent explosions in cosmos, signalling the destruction of a massive star (core-collapse SN), a white dwarf (thermonuclear SN) and a neutron star (KN), respectively. The ejected debris in these explosions is believed to be the main cosmic source of most elements in the periodic table. However, decoding the spectra of these transients is a challenging task requiring sophisticated spectral synthesis modelling. Here, the techniques for such modelling is reviewed, with particular focus on the computational aspects. We build from a historical review of how methodologies evolved from modelling of stellar winds, to supernovae, to kilonovae, studying various approximations in use for the central physical processes. Similarities and differences in the numeric schemes employed by current codes are discussed, and the path towards improved models is laid out.
In this review, the methodology of large eddy simulations (LES) is introduced and applications in astrophysics are discussed. As theoretical framework, the scale decomposition of the dynamical equations for neutral fluids by means of spatial filtering is explained. For cosmological applications, the filtered equations in comoving coordinates are also presented. To obtain a closed set of equations that can be evolved in LES, several subgrid scale models for the interactions between numerically resolved and unresolved scales are discussed, in particular the subgrid scale turbulence energy equation model. It is then shown how model coefficients can be calculated, either by dynamical procedures or, a priori, from high-resolution data. For astrophysical applications, adaptive mesh refinement is often indispensable. It is shown that the subgrid scale turbulence energy model allows for a particularly elegant and physically well motivated way of preserving momentum and energy conservation in AMR simulations. Moreover, the notion of shear-improved models for inhomogeneous and non-stationary turbulence is introduced. Finally, applications of LES to turbulent combustion in thermonuclear supernovae, star formation and feedback in galaxies, and cosmological structure formation are reviewed.
Galaxies are observed to host magnetic fields with a typical total strength of around 15microgauss. A coherent large-scale field constitutes up to a few microgauss of the total, while the rest is built from strong magnetic fluctuations over a wide range of spatial scales. This represents sufficient magnetic energy for it to be dynamically significant. Several questions immediately arise: What is the physical mechanism that gives rise to such magnetic fields? How do these magnetic fields affect the formation and evolution of galaxies? In which physical processes do magnetic fields play a role, and how can that role be characterized? Numerical modelling of magnetized flows in galaxies is playing an ever-increasing role in finding those answers. We review major techniques used for these models. Current results strongly support the conclusion that field growth occurs during the formation of the first galaxies on timescales shorter than their accretion timescales due to small-scale turbulent dynamos. The saturated small-scale dynamo maintains field strengths at a few percent of equipartition with turbulence. The subsequent action of large-scale dynamos in differentially rotating discs produces observed modern field strengths in equipartition with the turbulence and having power at large scales. The field structure resulting appears consistent with observations including Faraday rotation and polarisation from synchrotron and dust thermal emission. Major remaining challenges include scaling numerical models toward realistic scale separations and Prandtl and Reynolds numbers.
Evolved cool stars of various masses are major cosmic engines, delivering substantial mechanical and radiative feedback to the interstellar medium through strong stellar winds and supernova ejecta. These stars play a pivotal role in enriching the interstellar medium with vital chemical elements that constitute the essential building blocks for the formation of subsequent generations of stars, planets, and potentially even life. Within the complex tapestry of processes occurring in the atmospheres of these cool and luminous stars, convection takes center stage. Convection is a non-local, complex phenomenon marked by non-linear interactions across diverse length scales within a multi-dimensional framework. For these particular stars, characterized by their considerable luminosities and extensive scale heights, convection transitions to a global scale. This transition is facilitated by the transmission of radiative energy through the non-uniform outer layers of their atmospheres. To have a full understanding of this phenomenon, the application of global comprehensive 3D radiation-hydrodynamics simulations of stellar convection is of paramount importance. We present two state-of-the-art numerical codes: CO5BOLD and Athena++. Furthermore, we provide a view on their applications as: pivotal roles in enabling a comprehensive investigation into the dynamic processes linked to convection; and critical tools for accurately modeling the emissions produced during shock breakouts in Type II-P supernovae.
Observations of neutron star mergers have the potential to unveil detailed physics of matter and gravity in regimes inaccessible by other experiments. Quantitative comparisons to theory and parameter estimation require nonlinear numerical simulations. However, the detailed physics of energy and momentum transfer between different scales, and the formation and interaction of small scale structures, which can be probed by detectors, are not captured by current simulations. This is where turbulence enters neutron star modelling. This review will outline the theory and current status of turbulence modelling for relativistic neutron star merger simulations.
Numerical simulations of neutron star–neutron star and neutron star–black hole binaries play an important role in our ability to model gravitational-wave and electromagnetic signals powered by these systems. These simulations have to take into account a wide range of physical processes including general relativity, magnetohydrodynamics, and neutrino radiation transport. The latter is particularly important in order to understand the properties of the matter ejected by many mergers, the optical/infrared signals powered by nuclear reactions in the ejecta, and the contribution of that ejecta to astrophysical nucleosynthesis. However, accurate evolutions of the neutrino transport equations that include all relevant physical processes remain beyond our current reach. In this review, I will discuss the current state of neutrino modeling in general relativistic simulations of neutron star mergers and of their post-merger remnants. I will focus on the three main types of algorithms used in simulations so far: leakage, moments, and Monte-Carlo scheme. I will review the advantages and limitations of each scheme, as well as the various neutrino–matter interactions that should be included in simulations. We will see that the quality of the treatment of neutrinos in merger simulations has greatly increased over the last decade, but also that many potentially important interactions remain difficult to take into account in simulations (pair annihilation, oscillations, inelastic scattering).
Dense star clusters are spectacular self-gravitating stellar systems in our Galaxy and across the Universe - in many respects. They populate disks and spheroids of galaxies as well as almost every galactic center. In massive elliptical galaxies nuclear clusters harbor supermassive black holes, which might influence the evolution of their host galaxies as a whole. The evolution of dense star clusters is not only governed by the aging of their stellar populations and simple Newtonian dynamics. For increasing particle number, unique gravitational effects of collisional many-body systems begin to dominate the early cluster evolution. As a result, stellar densities become so high that stars can interact and collide, stellar evolution and binary stars change the dynamical evolution, black holes can accumulate in their centers and merge with relativistic effects becoming important. Recent high-resolution imaging has revealed even more complex structural properties with respect to stellar populations, binary fractions and compact objects as well as - the still controversial - existence of intermediate mass black holes in clusters of intermediate mass. Dense star clusters therefore are the ideal laboratory for the concomitant study of stellar evolution and Newtonian as well as relativistic dynamics. Not only the formation and disruption of dense star clusters has to be considered but also their galactic environments in terms of initial conditions as well as their impact on galactic evolution. This review deals with the specific computational challenges for modelling dense, gravothermal star clusters.
When the primary star in a close binary system evolves into a giant and engulfs its companion, its core and the companion temporarily orbit each other inside a common envelope. Drag forces transfer orbital energy and angular momentum to the envelope material. Depending on the efficiency of this process, the envelope may be ejected leaving behind a tight remnant binary system of two stellar cores, or the cores merge retaining part of the envelope material. The exact outcome of common-envelope evolution is critical for in the formation of X-ray binaries, supernova progenitors, the progenitors of compact-object mergers that emit detectable gravitational waves, and many other objects of fundamental astrophysical relevance. The wide ranges of spatial and temporal timescales that characterize common-envelope interactions and the lack of spatial symmetries present a substantial challenge to generating consistent models. Therefore, these critical phases are one of the largest sources for uncertainty in classical treatments of binary stellar evolution. Three-dimensional hydrodynamic simulations of at least part of the common-envelope interaction are the key to gain predictive power in modeling common-envelope evolution. We review the development of theoretical concepts and numerical approaches for such three-dimensional hydrodynamic simulations. The inherent multi-physics, multi-scale challenges have resulted in a wide variety of approximations and numerical techniques to be exercised on the problem. We summarize the simulations published to date and their main results. Given the recent rapid progress, a sound understanding of the physics of common-envelope interactions is within reach and thus there is hope that one of the remaining fundamental problems of stellar astrophysics may be solved before long.
We review well-balanced methods for the faithful approximation of solutions of systems of hyperbolic balance laws that are of interest to computational astrophysics. Well-balanced methods are specialized numerical techniques that guarantee the accurate resolution of non-trivial steady-state solutions, that balance laws prominently feature, and perturbations thereof. We discuss versatile frameworks and techniques for generic systems of balance laws for finite volume and finite difference methods. The principal emphasis of the presentation is on the algorithms and their implementation. Subsequently, we specialize in hydrodynamics' Euler equations to exemplify the techniques and give an overview of the available well-balanced methods in the literature, including the classic hydrostatic equilibrium and steady adiabatic flows. The performance of the schemes is evaluated on a selection of test problems.
The transformation of cold neutral intergalactic hydrogen into a highly ionized warm plasma marks the end of the cosmic dark ages and the beginning of the age of galaxies. The details of this process reflect the nature of the early sources of radiation and heat, the statistical characteristics of the large-scale structure of the Universe, the thermodynamics and chemistry of cosmic baryons, and the histories of star formation and black hole accretion. A number of massive data sets from new ground- and space-based instruments and facilities over the next decade are poised to revolutionize our understanding of primeval galaxies, the reionization photon budget, the physics of the intergalactic medium (IGM), and the fine-grained properties of hydrogen gas in the "cosmic web". In this review we survey the physics and key aspects of reionization-era modeling and describe the diverse range of computational techniques and tools currently available in this field.
We review the field of collisionless numerical simulations for the large-scale structure of the Universe. We start by providing the main set of equations solved by these simulations and their connection with General Relativity. We then recap the relevant numerical approaches: discretization of the phase-space distribution (focusing on N -body but including alternatives, e.g., Lagrangian submanifold and Schrödinger–Poisson) and the respective techniques for their time evolution and force calculation (direct summation, mesh techniques, and hierarchical tree methods). We pay attention to the creation of initial conditions and the connection with Lagrangian Perturbation Theory. We then discuss the possible alternatives in terms of the micro-physical properties of dark matter (e.g., neutralinos, warm dark matter, QCD axions, Bose–Einstein condensates, and primordial black holes), and extensions to account for multiple fluids (baryons and neutrinos), primordial non-Gaussianity and modified gravity. We continue by discussing challenges involved in achieving highly accurate predictions. A key aspect of cosmological simulations is the connection to cosmological observables, we discuss various techniques in this regard: structure finding, galaxy formation and baryonic modelling, the creation of emulators and light-cones, and the role of machine learning. We finalise with a recount of state-of-the-art large-scale simulations and conclude with an outlook for the next decade.
We review numerical methods for simulations of cosmic ray (CR) propagation on galactic and larger scales. We present the development of algorithms designed for phenomenological and self-consistent models of CR propagation in kinetic description based on numerical solutions of the Fokker–Planck equation. The phenomenological models assume a stationary structure of the galactic interstellar medium and incorporate diffusion of particles in physical and momentum space together with advection, spallation, production of secondaries and various radiation mechanisms. The self-consistent propagation models of CRs include the dynamical coupling of the CR population to the thermal plasma. The CR transport equation is discretized and solved numerically together with the set of MHD equations in various approaches treating the CR population as a separate relativistic fluid within the two-fluid approach or as a spectrally resolved population of particles evolving in physical and momentum space. The relevant processes incorporated in self-consistent models include advection, diffusion and streaming propagation as well as adiabatic compression and several radiative loss mechanisms. We discuss, applications of the numerical models for the interpretation of CR data collected by various instruments. We present example models of astrophysical processes influencing galactic evolution such as galactic winds, the amplification of large-scale magnetic fields and instabilities of the interstellar medium.
