# NUMERICAL STUDY OF THE VISHNIAC INSTABILITY IN SUPERNOVA REMNANTS

## Abstract

The Vishniac instability is thought to explain the complex structure of radiative supernova remnants in their Pressure-Driven Thin Shell (PDTS) phase after a blast wave (BW) has propagated from a central explosion. In this paper, the propagation of the BW and the evolution of the PDTS stage are studied numerically with the two-dimensional (2D) code HYDRO-MUSCL for a finite-thickness shell expanding in the interstellar medium (ISM). Special attention is paid to the adiabatic index, {gamma}, and three distinct values are taken for the cavity ({gamma}{sub 1}), the shell ({gamma}{sub 2}), and the ISM ({gamma}{sub 3}) with the condition {gamma}{sub 2} < {gamma}{sub 1}, {gamma}{sub 3}. This low value of {gamma}{sub 2} accounts for the high density in the shell achieved by a strong radiative cooling. Once the spherical background flow is obtained, the evolution of a 2D-axisymmetric perturbation is computed from the linear to the nonlinear regime. The overstable mechanism, previously demonstrated theoretically by E. T. Vishniac in 1983, is recovered numerically in the linear stage and is expected to produce and enhance anisotropies and clumps on the shock front, leading to the disruption of the shell in the nonlinear phase. The period of the increasing oscillations and the growthmore »

- Authors:

- LUTH, Observatoire de Paris, CNRS, Universite Paris-Diderot, F-92190 Meudon (France)

- Publication Date:

- OSTI Identifier:
- 22086430

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 759; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTRONOMY; ASTROPHYSICS; AXIAL SYMMETRY; DENSITY; DISTURBANCES; H CODES; HYDRODYNAMICS; INDEXES; INSTABILITY; MACH NUMBER; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; OSCILLATIONS; RADIATIVE COOLING; SHOCK WAVES; STAR EVOLUTION; SUPERNOVA REMNANTS; SUPERNOVAE

### Citation Formats

```
Michaut, C., Cavet, C., Bouquet, S. E., Roy, F., and Nguyen, H. C., E-mail: claire.michaut@obspm.fr.
```*NUMERICAL STUDY OF THE VISHNIAC INSTABILITY IN SUPERNOVA REMNANTS*. United States: N. p., 2012.
Web. doi:10.1088/0004-637X/759/2/78.

```
Michaut, C., Cavet, C., Bouquet, S. E., Roy, F., & Nguyen, H. C., E-mail: claire.michaut@obspm.fr.
```*NUMERICAL STUDY OF THE VISHNIAC INSTABILITY IN SUPERNOVA REMNANTS*. United States. doi:10.1088/0004-637X/759/2/78.

```
Michaut, C., Cavet, C., Bouquet, S. E., Roy, F., and Nguyen, H. C., E-mail: claire.michaut@obspm.fr. Sat .
"NUMERICAL STUDY OF THE VISHNIAC INSTABILITY IN SUPERNOVA REMNANTS". United States. doi:10.1088/0004-637X/759/2/78.
```

```
@article{osti_22086430,
```

title = {NUMERICAL STUDY OF THE VISHNIAC INSTABILITY IN SUPERNOVA REMNANTS},

author = {Michaut, C. and Cavet, C. and Bouquet, S. E. and Roy, F. and Nguyen, H. C., E-mail: claire.michaut@obspm.fr},

abstractNote = {The Vishniac instability is thought to explain the complex structure of radiative supernova remnants in their Pressure-Driven Thin Shell (PDTS) phase after a blast wave (BW) has propagated from a central explosion. In this paper, the propagation of the BW and the evolution of the PDTS stage are studied numerically with the two-dimensional (2D) code HYDRO-MUSCL for a finite-thickness shell expanding in the interstellar medium (ISM). Special attention is paid to the adiabatic index, {gamma}, and three distinct values are taken for the cavity ({gamma}{sub 1}), the shell ({gamma}{sub 2}), and the ISM ({gamma}{sub 3}) with the condition {gamma}{sub 2} < {gamma}{sub 1}, {gamma}{sub 3}. This low value of {gamma}{sub 2} accounts for the high density in the shell achieved by a strong radiative cooling. Once the spherical background flow is obtained, the evolution of a 2D-axisymmetric perturbation is computed from the linear to the nonlinear regime. The overstable mechanism, previously demonstrated theoretically by E. T. Vishniac in 1983, is recovered numerically in the linear stage and is expected to produce and enhance anisotropies and clumps on the shock front, leading to the disruption of the shell in the nonlinear phase. The period of the increasing oscillations and the growth rate of the instability are derived from several points of view (the position of the perturbed shock front, mass fluxes along the shell, and density maps), and the most unstable mode differing from the value given by Vishniac is computed. In addition, the influence of several parameters (the Mach number, amplitude and wavelength of the perturbation, and adiabatic index) is examined and for wavelengths that are large enough compared to the shell thickness, the same conclusion arises: in the late stage of the evolution of the radiative supernova remnant, the instability is dampened and the angular initial deformation of the shock front is smoothed while the mass density becomes uniform with the angle. As a result, our model shows that the supernova remnant returns to a stable evolution and the Vishniac instability does not lead to the fragmentation of the shock as predicted by the theory.},

doi = {10.1088/0004-637X/759/2/78},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 2,

volume = 759,

place = {United States},

year = {2012},

month = {11}

}