Numerical Methods for Simulating Star Formation

Abstract

We review the numerical techniques for ideal and non-ideal magneto-hydrodynamics (MHD) used in the context of star formation simulations. We outline the specific challenges offered by modeling star forming environments, which are dominated by supersonic and super-Alfvenic turbulence in a radiative, self-gravitating fluid. These conditions are rather unique in physics and engineering and pose particularly severe restrictions on the robustness and accuracy of numerical codes. One striking aspect is the formation of collapsing fluid elements leading to the formation of singularities that represent point-like objects, namely the proto-stars. Although a few studies have attempted to resolve the formation of the first and second Larson cores, resolution limitations force us to use sink particle techniques, with sub-grid models to compute the accretion rates of mass, momentum and energy, as well as their ejection rate due to radiation and jets from the proto-stars. We discuss the most popular discretisation techniques used in the community, namely smoothed particle hydrodynamics, finite difference and finite volume methods, stressing the importance to maintain a divergence-free magnetic field. We discuss how to estimate the truncation error of a given numerical scheme, and its importance in setting the magnitude of the numerical diffusion. This can have a strong impact on the outcome of these MHD simulations, where both viscosity and resistivity are implemented at the grid scale. We then present various numerical techniques to model non-ideal MHD effects, such as Ohmic and ambipolar diffusion, as well as the Hall effect. These important physical ingredients are posing strong challenges in term of resolution and time stepping. For the latter, several strategies are discussed to overcome the limitations due to prohibitively small time steps (abridged).

62 pages, 5 figures, accepted for publication in Frontiers in Astronomy and Space Science

References in corpus (46)

• Athena: A New Code for Astrophysical MHD
• A High Order Godunov Scheme with Constrained Transport and Adaptive Mesh Refinement for Astrophysical MHD
• Radiation-Hydrodynamic Simulations of Collapse and Fragmentation in Massive Protostellar Cores
• Turbulent Structure of a Stratified Supernova-Driven Interstellar Medium
• Circumventing the radiation pressure barrier in the formation of massive stars via disk accretion
• Magnetic Braking and Protostellar Disk Formation: The Ideal MHD Limit
• Inefficient star formation through turbulence, magnetic fields and feedback
• Three-dimensional simulation of massive star formation in the disk accretion scenario
• A scheme for radiation pressure and photon diffusion with the M1 closure in RAMSES-RT
• The Fragmentation of Magnetized, Massive Star-Forming Cores with Radiative Feedback
• Modeling jet and outflow feedback during star cluster formation
• Fragmentation of gravitationally unstable gaseous protoplanetary disks with radiative transfer
• Equations and Algorithms for Mixed Frame Flux-Limited Diffusion Radiation Hydrodynamics
• Magnetic field amplification in turbulent astrophysical plasmas
• A radiative transfer scheme for cosmological reionization based on a local Eddington tensor
• Towards a more realistic sink particle algorithm for the RAMSES code
• Effects of Ohmic and ambipolar diffusion on the formation and evolution of the first cores, protostars and circumstellar discs
• An Unstable Truth: How Massive Stars get their Mass
• Kinematic Dynamos using Constrained Transport with High Order Godunov Schemes and Adaptive Mesh Refinement
• Magnetically self-regulated formation of early protoplanetary discs
• Simulations of magnetized multiphase galactic disk regulated by supernovae explosions
• Formation of Magnetized Prestellar Cores with Ambipolar Diffusion and Turbulence
• Constrained Hyperbolic Divergence Cleaning for Smoothed Particle Magnetohydrodynamics
• Second Core Formation and High Speed Jets: Resistive MHD Nested Grid Simulations
• Grand Design Spiral Arms in A Young Forming Circumstellar Disk
• Episodic accretion: the interplay of infall and disc instabilities
• Radiation Magnetohydrodynamics Simulation of Proto-Stellar Collapse: Two-Component Molecular Outflow
• Feedback in Clouds II: UV Photoionisation and the first supernova in a massive cloud
• Introducing a Hybrid Method of Radiative Transfer for Smoothed Particle Hydrodynamics
• Protostellar Outflows and Radiative Feedback from Massive Stars. II. Feedback, Star Formation Efficiency, and Outflow Broadening
• Monte Carlo Radiation Hydrodynamics with Implicit Methods
• SPHRAY: A Smoothed Particle Hydrodynamics Ray Tracer for Radiative Transfer
• Is the dust-to-gas ratio constant in molecular clouds?
• Nascent bipolar outflows associated with the first hydrostatic core candidates Barnard 1b-N and 1b-S
• Radiation-hydrodynamical simulations of massive star formation using Monte Carlo radiative transfer: I. Algorithms and numerical methods
• On the dynamics of dust during protostellar collapse
• Ambipolar diffusion in smoothed particle magnetohydrodynamics
• Simulating hydromagnetic processes in star formation: introducing ambipolar diffusion into an adaptive mesh refinement code
• An Explicit Scheme for Incorporating Ambipolar Diffusion in a Magnetohydrodynamics Code
• Hybrid Adaptive Ray-Moment Method (HARM${}^2$): A Highly Parallel Method for Radiation Hydrodynamics on Adaptive Grids
• Kiloparsec-Scale Simulations of Star Formation in Disk Galaxies III. Structure and Dynamics of Filaments and Clumps in Giant Molecular Clouds
• Particle splitting in smoothed particle hydrodynamics based on Voronoi diagram
• The Effects of Protostellar Jet Feedback on Turbulent Collapse
• A Two-Fluid Method for Ambipolar Diffusion
• A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR
• Magnetohydrodynamics of Protostellar Disks