Forming the Moon
This animation shows a (log10) density slice through the collision midplane of a 3D numerical simulation of a magnetized, Moon-forming giant impact using Athena++. Upon initial contact, a shock propagates through the proto-Earth and the impactor. At ~1 hr post-impact, the impactor and target are stretched/distorted; a wave of material is launched around the surface of the proto-Earth with a ~4 hr period. Ejected debris forms a tidal arm. The debris either escapes the system or falls back towards the proto-Earth, contributing mass to a debris disk. At ~48 hr, we see an early picture of the “protolunar disk”–that is, the birthplace of our Moon.
Who says that all numerical simulations must be physically motivated? This animation shows off the capabilities of Athena++ AMR. The problem advects a single passive scalar (i.e., a color dye) across a 2D mesh. The passive scalar is set to a random value between 0 and 1 inside the boundaries of randomly sized, positioned, and oriented autumn leaves. The shapes of the leaf boundaries are intricate. To maintain these sharp features, we employ adapative mesh refinment (AMR) at leaf boundaries. As my Ph.D. advisor frequently says,
“The solution to diffusion is resolution.”–C. F. Gammie
This is a classic test in numerical magnetohydrodynamics. The problem sets up a set of MHD shocks that ultimately form a central current sheet. The current sheet breaks up into plasmoids, or “magnetic islands”. The animation below runs the Orszag-Tang Vortex in 2D and 3D using Athena++. Both runs are seeded with white noise in the pressure profile. We plot the current density squared in a slice through the simulation (z=0). Does the evolution look identical? If so, check again! Seemingly, 3D instabilities break apart the plasmoids rapidly, i.e., magnetic islands are more long-lived in 2D evolution. Credit to Matt Coleman (@msbc) for the wonderful colormap!
This animation shows the onset of the convective instability in a 2D polytropic disk. Typically, you might think that the convective instability is set up by heating the disk at the midplane and cooling it at the surface, but that is not the case here! Instead, we set up an unstable disk “equilibrium”, where the adiabatic index is less than the polytropic index. The Brunt-Väisälä frequency squared is negative in the bulk of the disk; convection ensues!
Sometimes, the assumption of ideal magnetohydrodynamics just doesn’t quite cut it. In many astrophysical environments, we must also consider diffusive physics. The numerical time-step for diffusive physics is proportional to the numerical linear resolution squared. This can make the integration of diffusive physics quite expensive. However, we can obtain significant speed-ups when applying super-time-stepping (STS) algorithms. This animation shows the diffusion of a Gaussian magnetic field distribution due to Ohmic resistivity using an STS module that I contributed to the Athena++ framework. To show off, we use a 2D cylindrical mesh with adaptive mesh refinement (AMR), where the origin of the Gaussian is offset from the mesh origin.
The Magnetorotational Instability
Differentially rotating, magnetized flows may be unstable to the magnetorotational instability (MRI). The MRI promotes vigorous magnetized turbulence and is capable of growing magnetic field strengths exponentially in time. This animation shows the onset of the MRI in a a shearing box simulation. The shearing box follows a patch of disk material in a Cartesian reference frame co-rotating with the disk. Color denotes density; black lines represent magnetic field lines.