Shock Waves in ISM Collisions

This project explores the characterization of shock waves in interstellar-medium collisions, combining analytical shock-jump conditions with numerical diagnostics in magnetohydrodynamic simulations. Using the Orszag–Tang vortex as a benchmark problem, we analyze compression, pressure jumps, and local Mach-number structure to identify shock regions in a consistent way.

ISYA 2025 project: This work was developed as part of the International School for Young Astronomers (ISYA) 2025 in Ecuador, as a collaborative project on shock-wave characterization in magnetohydrodynamic simulations of the interstellar medium.
2-D MHDOrszag–Tang vortex benchmark
256 × 256Periodic box domain [0, 2π]
γ = 5/3Ideal MHD setup with PLUTO
Mach mapsShock-region identification

PLUTO code Rankine–Hugoniot conditions ∇·v < 0 |∇P| thresholding Cell-wise Mach number

Why it matters

Shock waves are a common feature of astrophysical systems, from supernova remnants and gamma-ray bursts to solar-wind shocks, galaxy clusters, and ISM/cloud collisions. Characterizing them in numerical experiments helps connect discontinuities in fluid variables with the physical processes that drive compression, heating, and turbulent energy dissipation.

Physical framework: the analysis is grounded in the Rankine–Hugoniot jump conditions, relating density, pressure, and velocity jumps across shocks and linking them to the Mach number of the flow.

Methodology

The workflow starts from an idealized MHD simulation of the Orszag–Tang vortex and builds a shock-detection pipeline based on local flow diagnostics. Compression regions are identified through the velocity divergence, pressure gradients are used to isolate discontinuities, and the sound speed is computed to derive Mach numbers for individual cells.

  • Velocity divergence: selects compressive regions through ∇·v < 0.
  • Pressure gradient: highlights candidate discontinuities through a threshold on |∇P|.
  • Sound speed and Mach number: used to distinguish subsonic, transonic, and shock-dominated regions.
  • Binary shock mask: combines compression and pressure-jump criteria into a single detection map.

What this project produces

  • Pressure, density, and velocity maps: to visualize the evolving fluid structure.
  • Pressure-gradient and divergence maps: to isolate candidate shock fronts.
  • Binary detection masks: combining multiple shock indicators.
  • Mach-number maps and histograms: to characterize the strength of detected shock regions.

Simulation setup

The setup follows the standard Orszag–Tang vortex configuration in a doubly periodic domain, widely used as a controlled testbed for two-dimensional supersonic MHD turbulence.

Collaborators

  • Wladimir E. Banda-Barragán Universidad Yachay Tech (Urcuquí, Ecuador)
  • Esteban F. Cárdenas-Andino Escuela Politécnica Nacional (Quito, Ecuador)
  • José D. Salles-Lozano Universidad Nacional Mayor de San Marcos (Lima, Perú)