Formation of protostars and the launching of stellar core outflows with moving-mesh radiation non-ideal magnetohydrodynamics

TL;DR

This work develops a flux-limited diffusion (FLD) radiative transfer module for the moving-mesh AREPO code and couples it to non-ideal RMHD to model protostar formation across extreme density and temperature ranges. The authors implement an explicit–implicit splitting for diffusion and gas–radiation coupling, enable local timestepping with Dirichlet boundaries for non-active cells, and validate the approach with standard diffusion, coupling, and radiative-shock tests. Applied to the collapse of a $1\,M_\odot$ molecular cloud core, the method yields a magnetized first-core outflow and a fast second-core jet (with $v_{\rm rad} > 10$ km s$^{-1}$) while amplifying the magnetic field to $|\mathbf{B}|_{\max} > 10^5$ G, with a small inner disk forming around the second core. The results demonstrate robustness across scales on arbitrary meshes and enable high-resolution, physically realistic protostar simulations incorporating equation of state, opacities, and non-ideal MHD effects.

Abstract

We present an implementation of radiative transfer with flux-limited diffusion (FLD) for the moving-mesh code {\small AREPO} and use the method in a physical model for the formation of protostars with non-ideal radiation-magnetohydrodynamics (RMHD). We follow previous work in splitting the additional terms to the hydrodynamical equations arising from the inclusion of radiation into terms to be integrated explicitly and implicitly, as the diffusion and coupling terms would impose very restrictive timestep criteria. We validate the scheme with standard test problems for radiation diffusion, matter-gas coupling, and radiative shocks from the literature. Our implementation is compatible with local timestepping, which often presents problems for implicit schemes, and we found very good agreement with results obtained with global timesteps. We present an example application of the new implementation to the collapse of a $1\,{\rm M}_\odot$ molecular cloud core to a second Larson core modelled with radiation non-ideal magnetohydrodynamics. A high-velocity jet with v$_{\rm rad}> 10\, {\rm km\,s^{-1}}$ is self-consistently launched from the second core, nested within the first core, which produces a lower-velocity magnetorotational outflow. We observe magnetic field amplification up to more than $\vert \mathbf{B}\vert_{\rm max}>10^5$ G in the second core, which is surrounded by a small (<0.5 au) disk. This application demonstrates the robustness of our scheme in multi-scale and high-resolution simulations on arbitrary meshes and, as such, the model can be readily used for further simulations of protostar formation at high resolution.

Figures (12)

• Figure 1: Test of convergence order for the diffusion of a Gaussian. We use a reference timestep of $\Delta t = 1.5625\times 10^{-14}$ s at the lowest resolution and test the effect of different scalings of the timestep with resolution: Quadratic decrease, linear decrease, and keeping the timestep the same. Second-order convergence is achieved for the quadratic decrease, while the time integration error begins to dominate at higher resolution in the other cases, degrading the convergence order. See Subsection \ref{['subsec:test_diffusion']} for details.
• Figure 2: Radiation energy density as a function of position in the steady-state diffusion test, along with the analytical solution. We run both a simulation with a global timestep, where all cells are evolved with $\Delta t^{\rm ref} = 4.88281\times10^{-5}$, and one with local timesteps, where the timestep is set according to the values above the $x$-axis of the plot. Dashed grey lines denote boundaries between the timestepping regions. Both simulations show results very close to the analytical solution, and we do not observe any artifacts from local timesteps. See Subsection \ref{['subsec:test_diffusion']} for details.
• Figure 3: Propagation of a radiation pulse in an optically thin medium at time $t_{\rm end}=5\times10^{-12}$ s after the radiation is allowed to propagate out from the region with $R<1$ cm. Shown is the radiation energy density as a function of radius. The vertical line denotes the maximum propagation speed (as set by the speed of light). As required for physical consistency, the radiation front does not move away from the centre faster than $c$. See Subsection \ref{['subsec:test_streaming']} for details.
• Figure 4: Test of the coupling terms between gas internal energy and radiation energy. Shown are results for the internal energy density for the two different initial conditions; initially above- (circles, crosses) and below-equilibrium (squares) temperature. The standard runs (circles, squares) use a timestep of $\Delta t =10^{-11}$ s. The simulation shown as crosses starts with the same initial conditions as the circles, but instead uses a smaller timestep ($\Delta t = 6.10352 \times10^{-16}$ s) and is only run to $t = 10^{-11}$ s. The analytical solutions for the case of high and low initial internal energy are shown as lines. The cooling is underestimated in the run depicted as circles due to the use of a large timestep size as compared to the cooling time, which can be addressed by taking smaller timesteps (crosses). See Subsection \ref{['subsec:test_coupling']} for details.
• Figure 5: Gas and radiation temperature for the shocks with steady-state solution; subcritical case on the left, supercritical case on the right. We show the numerical results (points) along with the semi-analytical solutions (lines), the latter of which were extracted from Figure 7 of commercon2014adaptive and Figure 10 of zhang2011castro, respectively. The results are in good agreement with the expected solution. See Subsection \ref{['subsec:test_shocks']} for details.