Abstract
ABSTRACT A magnetohydrodynamic (MHD) shock front can be unstable to the corrugation instability, which causes a perturbed shock front to become increasingly corrugated with time. An ideal MHD parallel shock (where the velocity and magnetic fields are aligned) is unconditionally unstable to the corrugation instability, whereas the ideal hydrodynamic (HD) counterpart is unconditionally stable. For a partially ionized medium (for example, the solar chromosphere), both HD and MHD species coexist and the stability of the system has not been studied. In this paper, we perform numerical simulations of the corrugation instability in two-fluid partially ionized shock fronts to investigate the stability conditions, and compare the results to HD and MHD simulations. Our simulations consist of an initially steady two-dimensional parallel shock encountering a localized upstream density perturbation. In MHD, this perturbation results in an unstable shock front and the corrugation grows with time. We find that for the two-fluid simulation, the neutral species can act to stabilize the shock front. A parameter study is performed to analyse the conditions under which the shock front is stable and unstable. We find that for very weakly coupled or very strongly coupled partially ionized system the shock front is unstable, as the system tends towards MHD. However, for a finite coupling, we find that the neutrals can stabilize the shock front, and produce new features including shock channels in the neutral species. We derive an equation that relates the stable wavelength range to the ion-neutral and neutral-ion coupling frequencies and the Mach number. Applying this relation to umbral flashes gives an estimated range of stable wavelengths between 0.6 and 56 km.
Highlights
Magnetohydrodynamic (MHD) shock waves are a fundamental feature of astrophysical systems, occurring across a range of physical systems, for example, the solar atmosphere (Beckers & Tallant 1969; Hollweg 1982) and molecular clouds (Draine et al 1983)
2 CORRUGATION INSTABILITY SCHEMATIC In this paper, we focus on the parallel slow-mode shock, where the flow is aligned with the magnetic field either side of the shock
In this paper we have investigated the stability of slow-mode shocks in partially ionised plasma to the corrugation instability
Summary
Magnetohydrodynamic (MHD) shock waves are a fundamental feature of astrophysical systems, occurring across a range of physical systems, for example, the solar atmosphere (Beckers & Tallant 1969; Hollweg 1982) and molecular clouds (Draine et al 1983). The HD system has the opposite behaviour to an MHD system; vorticity can be exist across a HD contact discontinuity, but not a HD shock (since a transverse velocity is no longer supported by a magnetic field, Hayes 1957) This has consequences for instabilities such as the Richtmyer-Meshkov instability which results in a hydrodynamic contact discontinuity being unstable, the instability is suppressed in MHD (Wheatley et al 2009). We find that the shock-front can be stable or unstable depending on the wavelength of the perturbation relative to the finite width of the shock This may have consequences for observations by giving an expected range at which partially-ionised slow-mode shocks can be stable
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