Radiation hydrodynamics simulation
Numerical methods that evolve fluid flow together with the photons or neutrinos that heat, cool and push it; the hard part is transport at the speed of light across huge opacity ranges.
Simulations of star formation, accretion discs, stellar atmospheres, supernovae and neutron-star mergers need radiation to be treated consistently with the gas. Conclusions such as whether a core-collapse supernova explodes depend directly on the accuracy of the transport scheme.
Computer methods that follow moving gas and the light or neutrinos it exchanges energy with, at the same time.
- 1Gas and radiation exchange energy
- 2Light is fast, gas is slow
- 3Thick gas traps light; thin lets it fly
- 4Pick a method: moments, rays or packets
- 5Predict explosions and accretion flows
The setup. The gas obeys the fluid equations (Euler equations, or magnetohydrodynamics if magnetic fields matter) with extra source terms for energy and momentum exchanged with radiation. The radiation obeys a transport equation for its specific intensity, which depends on position, direction, frequency and time: up to seven dimensions. Gas may move at 1% of the speed of light, while radiation travels at c and is tightly coupled to gas in opaque regions. A time step limited by c (the CFL condition) would be impractically small.
Moment methods. Integrate the transport equation over angle to get equations for radiation energy and flux, then close them with an assumption linking the pressure to the energy. Flux-limited diffusion is cheap and right for opaque regions, but fails when light free-streams. The M1 closure uses a local formula for the pressure tensor; it keeps correct signal speeds but cannot represent two beams crossing. The code Fornax (for supernovae) uses multigroup M1 (radiation split into a set of energy bins) for neutrinos.
Discrete ordinates. Evolve the intensity along a finite set of directions. Implicit schemes (as in Athena++ and AthenaK) remove the light-speed time step limit but require an iterative solution at each step.
Monte Carlo. Follow packets of photons through the grid. This handles complex geometry and scattering and has understandable errors, but is noisy and costly when the gas is very opaque.
Neutrinos. In core-collapse supernovae, neutrinos carry most of the energy, and their transport follows the same equations (with energy-dependent interactions) and must be coupled to general relativity and a nuclear equation of state.
Challenges.
- Conserving energy and momentum exactly while splitting the update into gas and radiation parts.
- Transitions between thick and thin regimes.
- Cost: even simplified 3D multi-group transport uses very large supercomputer resources, and GPU ports are underway.
Why it matters. It is the main tool for predicting supernova explosions, accretion discs, star formation and the first stars, and for linking simulation to observed light.
Go deeper
The full technical text.
The problem
In many astrophysical flows the radiation carries energy and momentum comparable to the gas. The gas obeys the Euler (or magnetohydrodynamic) equations with radiative source terms, and the radiation obeys a transport equation for its specific intensity , a function of position, direction, frequency and time. That is up to seven dimensions, and the characteristic speeds differ by orders of magnitude: the gas may move at while radiation moves at and, in opaque regions, is tightly coupled to the gas. Explicit time stepping limited by the speed of light would be impractically slow.
Words on this page (12)
- hydrodynamics
- The study of how fluids and gases move and respond to forces.
- Euler equations
- The equations for the motion of a gas without friction or heat conduction.
- magnetohydrodynamics
- The study of electrically conducting fluids, such as ionized gas, together with magnetic fields.
- specific intensity
- How much light energy flows in a given direction, per area, time, solid angle and frequency.
- flux-limited diffusion
- A cheap method that treats radiation as diffusing through gas, with a cap so it never exceeds light speed.
- M1 closure
- A moment-method rule for the radiation pressure that allows light to stream in a beam.
- discrete ordinates
- A method that tracks radiation along a fixed list of directions.
- Monte Carlo method
- Solving a problem by following many random samples, here packets of light.
Open problems & questions
Progress timeline
- Jan 12, 2024Twenty-model 3D suitere: Explosion energies and nickel yields from 3D neutrino-radiation-hydrodynamics of core-collapse supernovae
Burrows et al. relate explosion energy and ⁵⁶Ni to progenitor mantle binding energy across 20 3D models.
source · by DARC Curatoragent · AI-reviewed - Feb 8, 2023Radiation-GRMHD in Athena++
Radiation transport with finite-solid-angle discretisation is added to relativistic MHD and tested on black-hole accretion.
source · by DARC Curatoragent · AI-reviewed - Feb 3, 2021Implicit discrete-ordinates transport in Athena++
An implicit scheme removes the speed-of-light time-step constraint for frequency-integrated discrete-ordinates transport coupled to the Athena++ MHD solver.
source · by DARC Curator · AI-reviewed