--- title: "Astronomy and cosmology · Simulations · Simulation Hypothesis" url: https://simulation-hypothesis.com/simulations/astronomy-cosmology description: "The universe from its first minutes to the cosmic web, and the stars, planets and black holes within it." license: https://creativecommons.org/licenses/by/4.0/ credit: "Ross Allan Dahl, Simulation Hypothesis (simulation-hypothesis.com)" --- [Simulations](https://simulation-hypothesis.com/simulations)domain 2 of 18 # Astronomy and cosmology The universe from its first minutes to the cosmic web, and the stars, planets and black holes within it. We can't rerun the universe, so astronomers build models of it. Cosmological simulations are the nearest real thing to the Sandbox's "whole universe" scale. They stay tractable because a single particle stands in for roughly a million suns. ## The universe as a whole ### Cosmological N-body Dark matter as billions of particles, grown under gravity from an almost uniform early universe into the cosmic web of filaments, walls and voids. Question it answers: Does our model of the universe grow the same large-scale structure telescopes see? Leaves out: One particle stands for a million suns, so nothing smaller than a galaxy is really there. Runs on: about 10^17.5 FLOPS rough a large fraction of a national supercomputer, for weeks. Since: 1970 Peebles’s 300-point model of the formation of a galaxy cluster, among the earliest; N-body runs of star clusters began with von Hoerner in 1960 [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Bodies ### Galaxy formation Gas cooling, star formation and supernova explosions, and black-hole accretion driving outflows, all layered on top of the dark-matter web. Question it answers: Why do galaxies come in the shapes and sizes they do? Leaves out: Star formation and black-hole feedback are represented by tunable sub-grid prescriptions, not derived from first principles. Runs on: about 10^17 FLOPS rough a large slice of a national supercomputer, weeks of runtime. Since: 1992 early combined gravity-plus-gas simulations of forming galaxies. [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Big Bang nucleosynthesis The first twenty minutes, when the universe was a nuclear reactor making hydrogen, helium and a trace of lithium. Question it answers: Do the predicted element ratios match the oldest gas we can measure? Leaves out: Assumes the early universe was perfectly homogeneous, although it contained small inhomogeneities. Runs on: about 10^12 FLOPS rough a laptop; the whole calculation takes seconds. Since: 1967 Wagoner, Fowler and Hoyle's first computed light-element abundances. [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Subatomic ### Cosmic microwave background Ripples in the hot plasma of the young universe, evolved until the light was released 380,000 years after the Big Bang. Question it answers: Which cosmological parameters produce the pattern of hot and cold spots we observe? Leaves out: Assumes the standard cosmological model is correct and fits only its small set of parameters. Runs on: about 10^13 FLOPS rough a desktop workstation; minutes per parameter set. Since: 1996 Seljak and Zaldarriaga's fast Boltzmann code for the microwave sky. [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Fields ### Cosmic reionization Ultraviolet light from the first stars and galaxies spreading through and ionising the neutral hydrogen filling the early universe. Question it answers: What reionised the universe after the cosmic dark ages? Leaves out: The faint, faraway sources doing most of the ionising are still below what any telescope can see directly, so their numbers are extrapolated. Runs on: about 10^17 FLOPS rough a large share of a national supercomputer, for weeks. Since: 1999 early radiative-transfer simulations of the first ionised bubbles. [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Intergalactic medium and the Lyman-alpha forest The thin gas strung between galaxies, evolved under gravity and heating until its absorption pattern matches the flickering forest of lines in a distant quasar's spectrum. Question it answers: How much ordinary matter is out there in the gas between galaxies, and how hot is it? Leaves out: Depends on assumptions about how ultraviolet light from galaxies heats the gas, which is not directly observed. Runs on: about 10^16 FLOPS rough a university or national cluster, weeks per simulated volume. Since: 1994 early hydrodynamic simulations reproducing the Lyman-alpha forest. [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Wave dark matter simulations The universe is evolved with dark matter treated as a coherent quantum wave obeying the Schrodinger and Poisson equations instead of as classical particles. Question it answers: What would cosmic structure look like if dark matter were an ultralight wave? Leaves out: The wave resolution requirement makes large volumes hard, and baryons are mostly left out. Runs on: about 10^19 FLOPS rough Large adaptive-mesh wave simulations Since: 2014 Cosmic structure as the quantum interference of a coherent dark wave (2014) [source](https://arxiv.org/abs/1406.6586) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Constrained simulations of the local universe Cosmological runs whose initial conditions are tuned so that the evolved volume reproduces the observed neighbours of our galaxy, including nearby clusters. Question it answers: Can we simulate the actual structures around the Milky Way rather than a typical patch of universe? Leaves out: Constraints come from noisy distance data, so the match is statistical rather than exact. Runs on: about 10^19 FLOPS rough Large N-body or hydrodynamic runs from constrained initial conditions Since: 2010 Constrained Local UniversE Simulations (CLUES) (2010) [source](https://arxiv.org/abs/1005.2687) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Cosmological emulators A modest set of expensive cosmological simulations is used to train a fast interpolator that predicts statistics such as the matter power spectrum for nearby parameter values. Question it answers: Can we predict structure for thousands of parameter choices from only a few dozen simulations? Leaves out: It only covers the parameter range and statistics it was trained on. Runs on: about 10^18 FLOPS rough Design of dozens of N-body runs, then near-free predictions Since: 2010 The Coyote Universe III: simulation suite and precision emulator (2010) [source](https://doi.org/10.1088/0004-637X/713/2/1322) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Fields ### Stellar population synthesis The combined light of many generations of stars added up from stellar evolution tracks and spectra, to read ages, masses and star-formation history from a galaxy's colours. Question it answers: What mixture of stars gives a galaxy its colour? Leaves out: Stellar tracks and spectral libraries carry their own uncertainties, such as for late stages of evolution. Runs on: about 10^9 FLOPS rough inexpensive spectra synthesis, repeated across a grid of ages and metallicities. Since: 1983 Bruzual's spectral evolution of galaxies, early-type systems. [source](https://doi.org/10.1086/161352) [Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Rules ### Galactic chemical evolution The build-up of heavy elements in a galaxy over time, from gas inflow, star formation, stellar death and gas outflow, written as a set of coupled rate equations. Question it answers: How did a galaxy accumulate its iron and oxygen? Leaves out: Mixing and gas flows are lumped into a few free parameters, so the model fits but does not predict. Runs on: about 10^8 FLOPS rough cheap rate-equation integration, scanned across parameters. Since: 1968 Tinsley's model of the evolution of the stars and gas in galaxies. [source](https://doi.org/10.1086/149455) [System dynamics](https://simulation-hypothesis.com/simulations/methods#m-system-dynamics)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Rules ### Semi-analytic galaxy formation Galaxies painted onto the merging halos of a dark-matter simulation with simple rules for cooling, star formation and feedback, tracing every galaxy at low cost. Question it answers: How many galaxies of each size do dark-matter halos host? Leaves out: The recipes for star formation and feedback are tuned rather than derived. Runs on: about 10^13 FLOPS rough rules applied to millions of merger trees, far cheaper than hydrodynamics. Since: 1993 Kauffmann, White and Guiderdoni's galaxy formation within merging dark-matter haloes. [source](https://doi.org/10.1093/mnras/264.1.201) [Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Self-interacting dark matter simulation Dark-matter particles allowed to scatter off each other, so halo cores flatten and satellites change shape, tested against galaxy observations. Question it answers: Do dark-matter particles collide, and does it soften galaxy cores? Leaves out: The cross-section is a free number, and baryonic feedback can mimic or hide the same core. Runs on: about 10^16 FLOPS rough N-body runs with a scattering step added. Since: 2000 Yoshida, Springel, White and Tormen's weakly self-interacting dark matter and the structure of dark halos. [source](https://doi.org/10.1086/317306) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Fields ### Massive-neutrino cosmological simulation Neutrinos with a small mass added to a structure-formation run as particles or a grid fluid, so the effect on the growth of the cosmic web can be measured. Question it answers: How much does the mass of the neutrino slow cosmic structure growth? Leaves out: Thermal noise from the neutrinos makes particle schemes noisy, and their mass is itself unknown. Runs on: about 10^17 FLOPS rough large-volume N-body runs with an added neutrino component. Since: 2008 Brandbyge, Hannestad, Haugboelle and Thomsen's effect of thermal neutrino motion on the non-linear matter power spectrum. [source](https://doi.org/10.1088/1475-7516/2008/08/020) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Modified-gravity structure formation N-body runs in which gravity departs from general relativity on large scales, with a screening mechanism that restores it nearby, so the cosmos can be tested for new forces. Question it answers: Would a change to gravity leave a signature in cosmic structure? Leaves out: Each theory needs its own tailored solver, and screening is expensive to follow accurately. Runs on: about 10^17 FLOPS rough N-body runs solving an extra nonlinear field equation at every step. Since: 2008 Oyaizu's nonlinear evolution of f(R) cosmologies, methodology. [source](https://doi.org/10.1103/physrevd.78.123524) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Weak-lensing ray tracing through simulated universes Light rays traced through the matter of a large simulation to forecast how galaxy shapes are slightly distorted, so surveys can be calibrated. Question it answers: How much are distant galaxy shapes sheared by the intervening matter? Leaves out: Multiple-plane approximations and finite resolution blur the smallest lensing structures. Runs on: about 10^16 FLOPS rough ray tracing through hundreds of N-body snapshots. Since: 2000 Jain, Seljak and White's ray-tracing simulations of weak lensing by large-scale structure. [source](https://doi.org/10.1086/308384) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Cosmic string network evolution A network of thin, stretched defects left over from an early phase transition, evolved to see how many loops and long strings survive and how they would gravitate. Question it answers: Do cosmic strings, if they exist, settle into a pattern that stays scale-free? Leaves out: Field-theory runs cannot reach realistic string widths, and the scaling regime is only approached by extrapolation. Runs on: about 10^14 FLOPS rough Nambu-Goto or field-theory simulations in an expanding box. Since: 1985 Albrecht and Turok's computed evolution of cosmic strings. [source](https://doi.org/10.1103/physrevlett.54.1868) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Early-universe lattice field dynamics Scalar fields on a lattice evolved through the end of inflation to see how the energy of the inflaton is passed into particles in a violent resonant burst. Question it answers: How did the universe heat up after inflation? Leaves out: Classical fields stand in for quantum fluctuations, which is valid only while occupation numbers are large. Runs on: about 10^13 FLOPS rough classical lattice field runs of up to a few thousand points per side. Since: 1996 Khlebnikov and Tkachev's classical decay of the inflaton. [source](https://doi.org/10.1103/physrevlett.77.219) [Lattice field theory](https://simulation-hypothesis.com/simulations/methods#m-lattice)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Subatomic ### Galactic cosmic-ray propagation Charged particles from supernovae wandering through the Galaxy under diffusion, energy loss and nuclear reactions, to predict what reaches Earth and the gamma rays they emit. Question it answers: How do cosmic rays diffuse through the Galaxy, and what do they leave behind? Leaves out: The Galaxy's magnetic field and gas distribution are smoothed, so diffusion coefficients are fitted. Runs on: about 10^12 FLOPS rough numerical solution of a transport equation across a grid of parameters. Since: 1998 Strong and Moskalenko's propagation of cosmic-ray nucleons in the Galaxy. [source](https://doi.org/10.1086/306470) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Differentiable cosmological simulation A particle-mesh simulation of structure growth written so that gradients flow through it, letting the initial conditions or parameters be adjusted to fit observed galaxies directly. Question it answers: Which starting density field and cosmology reproduce the galaxies we actually see? Leaves out: The fast particle-mesh scheme is coarse on small scales, so it fits large structures but not the inside of galaxies. Runs on: about 10^16 FLOPS rough hundreds of GPU hours per fitted volume. Since: 2020 Modi and colleagues' FlowPM, a distributed TensorFlow particle-mesh cosmological solver. [source](https://arxiv.org/abs/2010.11847) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Synthetic sky survey catalogues and images A mock universe of galaxies, stars and transients is drawn from simulations, then turned into the pixel images a survey telescope and its pipeline would record, with noise, blending and instrument effects. Question it answers: Would the survey's software recover the true cosmology from a sky whose truth we know? Leaves out: The mock sky contains only the physics and instrument effects its authors thought to include, so unforeseen systematics stay unforeseen. Runs on: about 10^17 FLOPS rough months on a few supercomputer allocations for catalogue and image generation. Since: 2021 The LSST Dark Energy Science Collaboration's DC2 simulated sky survey. [source](https://doi.org/10.3847/1538-4365/abd62c) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)floor: Fields ### Galaxy collision and merger simulation Two galaxies treated as discs of test stars passing each other under gravity, to show how tidal tails, bridges and mergers form. Question it answers: Do the long streams of stars seen around some galaxies come from a past close encounter? Leaves out: Early versions ignore the gravity of the stars on each other and on the gas, and any one match to a real pair is only one possible history. Runs on: about 10^12 FLOPS rough hours to days on a workstation for a modern high-resolution merger. Since: 1972 Toomre and Toomre's restricted three-body calculations of galactic bridges and tails. [source](https://doi.org/10.1086/151823) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ## Stars ### Stellar evolution A star as nested shells of gas, burning through its fuel from birth to white dwarf, neutron star or black hole. Question it answers: How long does a star of this mass live, and how does it die? Leaves out: Treats convection and rotation with parametrised prescriptions rather than solving the turbulence directly. Runs on: about 10^12 FLOPS rough a laptop; a full evolutionary track takes minutes. Since: 1955 Hoyle and Schwarzschild's early computed models of red giant stars. [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Core-collapse supernovae The last second of a massive star: the core collapsing, neutrinos flooding out, and a shock wave that either blows the star apart or stalls. Question it answers: What mechanism drives the explosion of a massive star? Leaves out: The mechanism that revives the stalled shock is not yet settled, and models differ from star to star. Runs on: about 10^17 FLOPS rough a large share of a national supercomputer, for months. Since: 1966 Colgate and White's first computer models of core collapse. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Fields ### Star formation Cold gas clouds collapsing under gravity into clusters of stars, with turbulence and magnetic fields pushing back. Question it answers: Why do stars form with the spread of masses they do? Leaves out: Cannot yet resolve both a whole cloud and the tiny scales where a single star actually forms. Runs on: about 10^16 FLOPS rough a university or national cluster, weeks for one cloud. Since: 1969 Larson's first computed collapse of a protostellar cloud. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Fields ### Stellar oscillations Sound and gravity waves ringing through a star's interior, computed to predict the pattern of brightness flickers a telescope would see. Question it answers: What does a star's wobble tell us about what is inside it? Leaves out: Only the outer layers are well constrained. The very core is still a matter of inference, not direct measurement. Runs on: about 10^12 FLOPS rough a laptop; a full oscillation spectrum takes minutes. Since: 1975 early computed oscillation models compared against the Sun's observed five-minute pulsations. [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Binary star evolution Two stars orbiting close enough to pull gas from one another, swap mass, merge or end as a bound pair of compact remnants. Question it answers: Will this pair of stars end as a merger, a surviving pair, or a source of gravitational waves? Leaves out: Mass transfer between two stars is still represented by a small set of tunable prescriptions rather than derived from first principles. Runs on: about 10^12 FLOPS rough a laptop; a population of binaries evolves in minutes. Since: 1967 early computed models of mass transfer between close binary stars. [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Stellar atmospheres and spectra Light escaping through the outer layers of a star, computed against temperature and composition to predict the spectrum a telescope would record. Question it answers: What is this star made of, and how hot is its surface? Leaves out: Assumes a smooth, calm atmosphere, when starspots and convection cells actually roughen the real surface. Runs on: about 10^13 FLOPS rough a workstation; hours per star modelled. Since: 1967 early computed model atmospheres compared against measured stellar spectra. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Supernova neutrino flavour evolution The dense stream of neutrinos leaving a collapsing star, followed as they scatter off one another and change flavour, which affects the explosion and the elements forged. Question it answers: How do neutrinos swap flavour in the crowd inside a supernova? Leaves out: The full problem is too large to solve alongside the explosion, so flavour physics is treated in small, simplified boxes. Runs on: about 10^15 FLOPS rough coupled quantum kinetic equations in a few dimensions. Since: 2006 Duan, Fuller, Carlson and Qian's simulation of coherent nonlinear neutrino flavour transformation in the supernova environment. [source](https://doi.org/10.1103/physrevd.74.105014) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Subatomic ### Stellar surface convection simulation The boiling surface layers of a star computed in three dimensions with radiation, to reproduce granulation and the shapes of spectral lines. Question it answers: What does the surface of a star look like, and how do its lines form? Leaves out: Only a thin patch is modelled, and the deep layers beneath are imposed from one-dimensional stellar models. Runs on: about 10^15 FLOPS rough three-dimensional radiation hydrodynamics of a surface patch. Since: 1998 Stein and Nordlund's simulations of solar granulation. [source](https://doi.org/10.1086/305678) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Common-envelope evolution A compact star spiralling inside the swollen outer layers of its companion, expelling the gas or merging, followed with hydrodynamics to see which close binaries survive. Question it answers: Does the spiralling star eject the envelope or merge with the core? Leaves out: Runs last far less than the real event and cannot cool the gas, so final separations remain uncertain. Runs on: about 10^16 FLOPS rough three-dimensional hydrodynamic runs of a few orbits. Since: 1996 Rasio and Livio's hydrodynamic simulations of common-envelope systems. [source](https://doi.org/10.1086/177975) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Binary population synthesis Millions of binary stars evolved with fast rules for mass transfer, tides and supernova kicks, to predict how many mergers, novae and gravitational-wave sources a galaxy holds. Question it answers: How many black-hole and neutron-star binaries does a galaxy make? Leaves out: Fast fitting formulae replace detailed stellar models, so rare outcomes hinge on the assumed rules. Runs on: about 10^12 FLOPS rough millions of binaries evolved using analytic fits. Since: 2002 Hurley, Tout and Pols's rapid evolution of binary stars including tides, for population studies. [source](https://doi.org/10.1046/j.1365-8711.2002.05038.x) [Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)floor: Fields ### Collapsar and gamma-ray burst jets A massive star collapsing into a black hole and driving a jet through the stellar envelope, followed with relativistic hydrodynamics to see whether a burst can escape. Question it answers: Can a jet from a collapsing star break out to make a gamma-ray burst? Leaves out: Jet launching is imposed by hand, because the central engine is too small and fast to follow with the envelope. Runs on: about 10^16 FLOPS rough axisymmetric to three-dimensional relativistic hydrodynamics. Since: 1999 MacFadyen and Woosley's collapsars simulations of gamma-ray bursts and explosions in failed supernovae. [source](https://doi.org/10.1086/307790) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Astrochemical reaction networks Hundreds of gas-phase and grain-surface reactions integrated in a cold interstellar cloud to predict which molecules form and how they deplete as stars begin to condense. Question it answers: Which molecules form in a cold cloud, and how fast? Leaves out: Many rate coefficients are measured only at room temperature or are guessed. Runs on: about 10^8 FLOPS rough stiff rate equations for thousands of species, cheap per cloud. Since: 1973 Herbst and Klemperer's model of the formation and depletion of molecules in dense interstellar clouds. [source](https://doi.org/10.1086/152436) [System dynamics](https://simulation-hypothesis.com/simulations/methods#m-system-dynamics)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Molecules ### Interstellar magnetised turbulence A compressible, magnetised gas stirred in a periodic box to find how quickly turbulence loses energy, which sets how fast clouds collapse into stars. Question it answers: How fast does turbulence in interstellar gas die away? Leaves out: Numerical dissipation stands in for the real small-scale physics, and the box has no walls or gravity. Runs on: about 10^15 FLOPS rough three-dimensional MHD runs at high resolution. Since: 1998 Stone, Ostriker and Gammie's dissipation in compressible magnetohydrodynamic turbulence. [source](https://doi.org/10.1086/311718) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ## Planets and orbits ### Planet formation Dust in a disc around a young star sticking into pebbles, planetesimals and eventually planets. Question it answers: How does a disc of dust end up as a solar system? Leaves out: The step from pebble to planetesimal, kilometres across, is still more assumed than derived. Runs on: about 10^15 FLOPS rough a university cluster, days to weeks for one disc. Since: 1978 Greenberg and colleagues' first numerical planetesimal accretion runs. [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Bodies ### Orbital dynamics The planets pulling on each other over billions of years, and asteroids and comets threading between them. Question it answers: Is the solar system stable, and will this asteroid hit anything? Leaves out: Chaos means a tiny rounding error can flip the answer after long enough. Runs on: about 10^13 FLOPS rough a desktop computer; billions of years fit in days. Since: 1988 Sussman and Wisdom's digital orrery found chaos in Pluto's orbit. [Run the interactive model](https://simulation-hypothesis.com/simulations/run#toy-threebody) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Bodies ### Planetary and exoplanet atmospheres Climate models adapted to other worlds: different gases, gravity, rotation and starlight. Question it answers: Could liquid water survive on the surface of this planet? Leaves out: Applies Earth-calibrated cloud and chemistry parametrisations to atmospheres that may behave very differently. Runs on: about 10^15 FLOPS rough a university cluster, days per simulated planet-year. Since: 1969 Leovy and Mintz's first general-circulation model of Mars. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Planetary interiors and dynamos Hot, convecting rock or metal deep inside a planet, modelled to see whether it generates a magnetic field and how heat escapes to the surface. Question it answers: Why does this planet have a magnetic field, and why does another one, similar in size, not? Leaves out: Runs at a viscosity and rotation rate far gentler than a real planetary core, then scaled up by assumption. Runs on: about 10^16 FLOPS rough a national cluster, weeks for one interior model. Since: 1995 early three-dimensional computer models of the geodynamo generating Earth's field. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Impact cratering An asteroid or comet striking a planet, modelled from the shockwave through the ground to the crater, debris and climate effects left behind. Question it answers: How big a crater, and how much damage, would this impactor cause? Leaves out: The strength and internal structure of the impactor are usually inferred from its size and speed alone. Runs on: about 10^14 FLOPS rough a workstation or small cluster, hours per impact scenario. Since: 1980 early hydrocode simulations of impact craters, spurred by the dinosaur-extinction hypothesis. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Bodies ### Exoplanet detection and characterisation The dimming or wobble a planet would cause in its star's light, computed to compare against real telescope data and pull out its size and orbit. Question it answers: Is that dip in brightness really a planet, and if so, how big is it? Leaves out: Starspots and stellar jitter can mimic a planet's signal closely enough to fool an automated search. Runs on: about 10^13 FLOPS rough a workstation; minutes to hours per candidate signal. Since: 1984 early computed light-curve models used to plan the first exoplanet searches. [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Bodies ### Giant-impact simulations Smoothed-particle hydrodynamics of two planet-sized bodies colliding, tracking the melt and debris that may assemble into a moon. Question it answers: Could a collision between young planets have produced the Moon? Leaves out: Outcomes depend on equation of state and on the assumed initial spin and angle. Runs on: about 10^17 FLOPS rough Millions of SPH particles with realistic equations of state Since: 2001 Origin of the Moon in a giant impact near the end of Earth's formation (2001) [source](https://doi.org/10.1038/35089010) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Planet population synthesis Fast semi-analytic planet-formation models are run for thousands of simulated systems to produce a statistical population that is compared with exoplanet surveys. Question it answers: What mix of planet masses and orbits does a given formation theory predict? Leaves out: Each system is a simplified one-dimensional model, not a full hydrodynamic run. Runs on: about 10^14 FLOPS rough Thousands of cheap one-dimensional disc runs Since: 2004 Toward a deterministic model of planetary formation I (2004) [source](https://doi.org/10.1086/381724) [Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Exoplanet atmosphere retrieval A model atmosphere run thousands of times against a transmission or emission spectrum to infer temperature and molecular abundances. Question it answers: What is the air of a distant planet made of? Leaves out: One-dimensional models are fitted to data of limited quality, so degenerate solutions are common. Runs on: about 10^12 FLOPS rough millions of spectrum evaluations in a Bayesian sampler. Since: 2009 Madhusudhan and Seager's temperature and abundance retrieval method for exoplanet atmospheres. [source](https://doi.org/10.1088/0004-637x/707/1/24) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Molecules ### Habitable-zone climate modelling A one-dimensional climate model of a rocky planet at different distances from its star, balancing starlight, greenhouse gases and clouds to find where liquid water can last. Question it answers: How far from its star can a planet be and keep liquid water? Leaves out: One column cannot represent clouds or day-night contrast, so edges of the zone move with three-dimensional models. Runs on: about 10^6 FLOPS rough a one-dimensional radiative-convective column, light enough for a laptop. Since: 1993 Kasting, Whitmire and Reynolds's habitable zones around main-sequence stars. [source](https://doi.org/10.1006/icar.1993.1010) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Planetesimal formation by streaming instability Dust grains in a gas disk clumping into the first kilometre-sized bodies, simulated with particles and gas to see whether turbulence can concentrate them enough to collapse. Question it answers: How do pebbles clump into the first planetary building blocks? Leaves out: Small boxes cover a patch of the disk, and the particle sizes are a narrow range. Runs on: about 10^16 FLOPS rough three-dimensional local box runs with hundreds of millions of particles. Since: 2007 Johansen and colleagues' rapid planetesimal formation in turbulent circumstellar disks. [source](https://doi.org/10.1038/nature06086) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Planet-disk interaction and migration A planet embedded in the gas disk it formed from, which pulls a spiral wake that drags it inward or outward. Question it answers: Why do planets move from where they formed? Leaves out: Migration rate is sensitive to disk thermodynamics and viscosity, which are poorly known. Runs on: about 10^14 FLOPS rough hydrodynamic disk runs for thousands of orbits. Since: 2000 Kley's hydrodynamic simulations of the migration of a system of protoplanets. [source](https://doi.org/10.1046/j.1365-8711.2000.03495.x) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ## Extreme gravity and space plasma ### Black hole mergers Einstein’s equations solved directly as two black holes spiral together, producing the gravitational-wave signal detectors listen for. Question it answers: What waveform should we see from two black holes of these masses? Leaves out: The last fraction of a second before merger still needs approximations no computer fully resolves. Runs on: about 10^16.5 FLOPS rough a large cluster, weeks for one waveform. Since: 1964 Hahn and Lindquist's first computed head-on collision of two black holes. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Accretion discs and jets Magnetised gas spiralling into a black hole, heating up and launching jets that run for thousands of light years. Question it answers: How does a black hole shine brighter than the galaxy around it? Leaves out: Cannot track the disc down to the black hole's own scale and the wider galaxy at once. Runs on: about 10^16 FLOPS rough a large cluster, weeks for a global disc run. Since: 1991 Balbus and Hawley's simulations revealing the magnetorotational instability. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Space weather The solar wind and eruptions from the Sun striking Earth’s magnetic field. Question it answers: Will this solar storm damage satellites or power grids, and when does it arrive? Leaves out: Predicts the arrival time of an eruption with moderate accuracy and its strength with considerably less. Runs on: about 10^15 FLOPS rough a national forecasting centre's cluster, run several times a day. Since: 1978 early global MHD simulations of the solar wind hitting Earth's field. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Fields ### Neutron star mergers Two neutron stars spiralling together and colliding, tracked through Einstein's equations and nuclear physics at once to see what debris and light are flung out. Question it answers: Does this merger make a black hole, and does it forge the heavy elements found on Earth? Leaves out: The nuclear physics of matter this dense is still not fully known, so the debris composition carries real uncertainty. Runs on: about 10^17 FLOPS rough a large share of a national supercomputer, for weeks. Since: 1990 early relativistic hydrodynamics simulations of colliding neutron stars. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Pulsar magnetospheres The whirling magnetic field and plasma around a spinning neutron star, computed to see how it beams radio waves and high-energy particles into space. Question it answers: Why does a pulsar's beam sweep periodically across the line of sight, and what determines its shape? Leaves out: The plasma right at the star's surface, where the beam actually forms, is still poorly understood physically. Runs on: about 10^15 FLOPS rough a university cluster, days per magnetosphere model. Since: 1999 early global simulations of a pulsar's rotating magnetic field. [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Solar interior and dynamo Hot plasma convecting and rotating inside the Sun, modelled to see how it winds up magnetic field into the eleven-year sunspot cycle. Question it answers: Why does the Sun's magnetic activity rise and fall on an eleven-year cycle? Leaves out: Cannot yet reproduce the cycle's period and amplitude reliably without tuning the model towards the observed values. Runs on: about 10^16 FLOPS rough a national cluster, weeks for one simulated cycle. Since: 1983 early three-dimensional convection simulations of the solar interior. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Gravitational-wave template banks from numerical relativity Hundreds to thousands of simulated black-hole mergers spanning mass ratios and spins, calibrated into waveform models that detectors match against data. Question it answers: What does the signal of any given black-hole merger look like? Leaves out: Catalogues are sparse in the parameter space, so the waveform models between them are fits, not simulations. Runs on: about 10^17 FLOPS rough thousands of merger runs, each weeks on a cluster. Since: 2013 Mroue and colleagues' catalogue of 174 binary black hole simulations for gravitational-wave astronomy. [source](https://doi.org/10.1103/physrevlett.111.241104) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Gravitational-wave mock data challenges Simulated detector data with many injected sources and realistic noise, used to test whether analysis pipelines can recover the astrophysical signals hidden inside. Question it answers: Can an analysis pipeline find and measure every source buried in the noise? Leaves out: Noise is idealised and the injected source population is assumed, so real-data complications are missing. Runs on: about 10^14 FLOPS rough many long data streams with thousands of overlapping sources. Since: 2006 The Mock LISA Data Challenges, the first community blind tests of space-based gravitational-wave analysis. [source](https://doi.org/10.1063/1.2405108) [Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Rules ### Magnetar magnetosphere and flare simulation The twisted magnetic field outside a magnetar, the neutron star with the strongest known fields, followed as it builds up stress, reconnects and releases flares. Question it answers: How does a neutron star's twisted field blow off energy in a flare? Leaves out: Force-free physics forgets the plasma's inertia and the pair-production that drives real flares. Runs on: about 10^16 FLOPS rough relativistic force-free runs on a cluster. Since: 2012 Parfrey, Beloborodov and Hui's simulation of twisting, reconnecting magnetar magnetospheres. [source](https://doi.org/10.1088/2041-8205/754/1/l12) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Black-hole shadow and image rendering Light rays traced through the curved spacetime around a black hole and its hot gas to predict the ring-shaped image a telescope would see. Question it answers: What does the glowing gas around a black hole look like from Earth? Leaves out: The gas model is a post-processing guess, so the image depends on assumed electron temperatures and magnetic field. Runs on: about 10^15 FLOPS rough ray tracing through thousands of accretion simulation snapshots. Since: 2000 Falcke, Melia and Agol's simulated image of the shadow of the black hole at the Galactic centre. [source](https://doi.org/10.1086/312423) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Tidal disruption of stars by black holes A star pulled apart by a massive black hole, its debris stretched into a stream that falls back and lights up, followed with hydrodynamics. Question it answers: How much of a shredded star falls into the black hole, and how bright is the flare? Leaves out: The radiation that makes the flare visible is only approximated, so the light curve is inferred, not simulated end to end. Runs on: about 10^16 FLOPS rough smoothed-particle or grid runs with a general-relativistic treatment. Since: 1989 Evans and Kochanek's hydrodynamic simulation of the tidal disruption of a star by a massive black hole. [source](https://doi.org/10.1086/185567) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Kilonova radiative transfer The glowing cloud of heavy-element debris from a neutron-star merger, modelled with radioactive heating and radiation transport to predict its light and colour. Question it answers: How bright and how red is the afterglow of a neutron-star merger? Leaves out: Opacities of the heaviest elements rest on incomplete atomic data and dominate the uncertainty in predicted colour. Runs on: about 10^14 FLOPS rough multi-dimensional Monte Carlo radiation transport with atomic opacity data. Since: 2010 Metzger and colleagues' model of electromagnetic counterparts powered by r-process radioactive decay. [source](https://doi.org/10.1111/j.1365-2966.2010.16864.x) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### Radiation belt modelling High-energy electrons and protons trapped in the magnetic field around a planet, moved by diffusion, injection and loss to predict hazards for satellites. Question it answers: Why do belts of trapped radiation swell and drain during magnetic storms? Leaves out: Wave-particle diffusion rates are parametrised from limited measurements, a main source of error. Runs on: about 10^13 FLOPS rough three-dimensional diffusion runs over storm intervals. Since: 1995 Beutier and Boscher's three-dimensional model of the electron radiation belt. [source](https://doi.org/10.1029/94ja03066) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### Neural inference for gravitational waves A neural network is trained on millions of simulated merger signals in synthetic detector noise so that it can output the likely masses, spins and distance of a new event almost instantly. Question it answers: Can the properties of a black-hole merger be inferred in seconds, early enough to point telescopes at it? Leaves out: It is only as good as the waveform model and noise it was trained on, and unusual signals can fall outside what it learned. Runs on: about 10^17 FLOPS rough weeks of GPU training on simulated waveforms. Since: 2021 Dax and colleagues' neural posterior estimation for gravitational-wave events. [source](https://arxiv.org/abs/2106.12594) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Fields [◂ Fundamental physics](https://simulation-hypothesis.com/simulations/fundamental-physics)[Earth and climate ▸](https://simulation-hypothesis.com/simulations/earth-climate)