Modelling supernova-driven turbulence

ABSTRACT

High Mach number shocks are ubiquitous in interstellar turbulence. The Pencil Code is particularly well suited to the study of magnetohydrodynamics in weakly compressible turbulence and the numerical investigation of dynamos because of its high-order advection and time evolution algorithms. However, the high-order algorithms and lack of Riemann solver to follow shocks make it less well suited to handling high Mach number shocks, such as those produced by supernovae (SNe). Here, we outline methods required to enable the code to efficiently and accurately model SNe, using parameters that allow stable simulation of SN-driven turbulence, in order to construct a physically realistic galactic dynamo model. These include the resolution of shocks with artificial viscosity, thermal conductivity and mass diffusion; the correction of the mass diffusion terms and a novel generalisation of the Courant condition to include all source terms in the momentum and energy equations. We test our methods with the numerical solution of the one-dimensional (1D) Riemann shock tube, also extended to a 1D adiabatic shock with parameters and Mach number relevant to SN shock evolution, including shocks with radiative losses. We extend our test with the three-dimensional (3D) numerical simulation of individual SN remnant evolution for a range of ambient gas densities typical of the interstellar medium and compare these to the analytical solutions of Sedov–Taylor (adiabatic) and the snowplough and Cioffi et al. results incorporating cooling and heating processes. We show that our new timestep algorithm leads to linear rather than quadratic resolution dependence as the strength of the artificial viscosity varies, because of the corresponding change in the strength of interzone gradients.

KEYWORDS:

• Numerical methods
• high Mach number shocks
• artificial diffusivity
• supernova-driven turbulence
• instabilities

Acknowledgments

We thank the anonymous referees for their constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

F. A. Gent http://orcid.org/0000-0002-1331-2260

M.-M. Mac Low http://orcid.org/0000-0003-0064-4060

M. J. Käpylä http://orcid.org/0000-0002-9614-2200

G. R. Sarson http://orcid.org/0000-0001-6774-9372

J. F. Hollins http://orcid.org/0000-0002-4435-4156

Notes

1 https://github.com/pencil-code.

2 http://pencil-code.nordita.org/doc/manual.

3 At sixth-order accuracy, we may apply a maximum from within one, two or three zones, with three yielding more stability at the expense of increased smoothing. Empirical trials of SN-driven turbulence as discussed in section 4.4 indicate two zones to be sufficient.

Additional information

Funding

The authors wish to acknowledge CSC – IT Center for Science, Finland, for computational resources and the financial support by the Academy of Finland to the ReSoLVE Centre of Excellence (Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta) (project no. 307411). M-MML was partly supported by US NSF (Division of Astronomical Sciences) grant AST18-15461.