Shock Propagation in Inhomogeneous Gases. V

Ishizuka, Toshihisa; Hashimoto, Yoshiaki; Ôno, Y.

doi:10.1143/ptp.32.207

Cited by 6 publications

(7 citation statements)

References 5 publications

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“…It is well known in nonrelativistic fluid dynamics that oblique shocks produce or alter the vorticity of a fluid (Ishizuka et al 1964). In this paper we show that the same is true for an ultrarelativistic shock passing over density inhomogeneities in the preshock circumburst medium.…”

Section: Introductionsupporting

confidence: 58%

Production of Magnetic Energy by Macroscopic Turbulence in GRB Afterglows

Sironi

Goodman

2007

ApJ

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Afterglows of gamma-ray bursts are believed to require magnetic fields much stronger than that of the compressed preshock medium. As an alternative to microscopic plasma instabilities, we propose amplification of the field by macroscopic turbulence excited by the interaction of the shock with a clumpy preshock medium, for example, a stellar wind. Using a recently developed formalism for localized perturbations to an ultrarelativistic shock, we derive constraints on the length scale, amplitude, and volume filling factor of density clumps required to produce a given magnetic energy fraction within the expansion time of the shock, assuming that the energy in the field achieves equipartion with the turbulence. Stronger and smaller scale inhomogeneities are required for larger shock Lorentz factors. Hence, it is likely that the magnetic energy fraction evolves as the shock slows. This could be detected by monitoring the synchrotron cooling frequency if the radial density profile ahead of the shock, smoothed over clumps, is known.

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Section: Introductionsupporting

confidence: 58%

Production of Magnetic Energy by Macroscopic Turbulence in GRB Afterglows

Sironi

Goodman

2007

ApJ

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“…Two approximate forms are shown for the shape of the shock front: an extrapolation of the self-similar shock acceleration law (eq. ( 7) with x 0s = 0.61ℓϕ, blue dashed line), which is valid in the limit y ≪ −ℓϕ, and the Ishizuka et al (1964) approximation (eq. ( 11) with D n = 0.80, green dash-dot line).…”

Section: Two-dimensional Model and An Asymptotic Solution For Non-rel...mentioning

confidence: 99%

“…Shock structure A full description of the oblique breakout flow on the scale of ℓ ϕ requires two-dimensional numerical simulations like the ones we shall present in Paper 2. However, we can gain some insight by considering the approximate theory for oblique shocks in inhomogeneous media developed by Ishizuka et al (1964). These authors first solve for the flow induced by a shock front as it runs at some angle over a contact discontinuity between two uniform regions.…”

Section: Two-dimensional Model and An Asymptotic Solution For Non-rel...mentioning

confidence: 99%

Oblique Shock Breakout in Supernovae and Gamma-Ray Bursts. I. Dynamics and Observational Implications

Matzner

Levin

2013

ApJ

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In a non-spherical stellar explosion, non-radial motions become important near the stellar surface. For realistic deviations from spherical symmetry, non-radial flow dramatically alters the dynamics and emission of shock emergence on a significant fraction of the surface. The breakout flash is stifled, ejecta speeds are limited, and matter is cast sideways. Non-radial ejection allows for collisions outside the star, which may engender a new type of transient. Strongly oblique breakouts are most easily produced in compact stellar progenitors, such as white dwarfs and stripped-envelope core collapse supernovae. We study the shock structure and post-shock acceleration using conservation laws, a similarity analysis, and an approximate theory for oblique shocks. The shock is likely to extend vertically from the stellar surface, then kink before joining a deep asymptotic solution. Outflow from the region crossed by an oblique shock is probably unsteady and may affect the surface ahead of the main shock. We comment on the implications for several notable explosions in which the nonspherical dynamics described in this paper are likely to play an important role. We also briefly consider relativistic and superluminal pattern speeds.

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“…A couple weak shocks are also launched from the curving primary shock, where there is no clear interaction with the stellar surface, and these may also depend on the simulation volume. As for the geometrical shape of the primary shock, the approximate theory of Ishizuka et al (1964) would suggest that this is quite insensitive, in a power-law atmosphere, to the details of the simulationat least, up to an overall scaling (the value of ℓ ϕ ) and the absolute location of shock breakout (x s for y s = 0).…”

Section: Finite Volumementioning

confidence: 99%

Oblique Shock Breakout in Supernovae and Gamma-Ray Bursts. Ii. Numerical Solutions for Non-Relativistic Pattern Speeds

Salbi

Matzner

et al. 2014

ApJ

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Non-spherical explosions develop non-radial flows as the pattern of shock emergence progresses across the stellar surface. In supernovae these flows can limit ejecta speeds, stifle shock breakout emission, and cause collisions outside the star. Similar phenomena occur in stellar and planetary collisions, tidal disruption events, accretion-induced collapses, and propagating detonations. We present two-dimensional, nested-grid Athena simulations of non-radial shock emergence in a frame comoving with the breakout pattern, focusing on the adiabatic, non-relativistic limit in a plane stratified envelope. We set boundary conditions using a known self-similar solution and explore the role of box size and resolution on the result. The shock front curves toward the stellar surface, and exhibits a kink from which weak discontinuities originate. Flow around the point of shock emergence is neither perfectly steady nor self-similar. Waves and vortices, which are not predominantly due to grid effects, emanate from this region. The post-shock flow is deflected along the stellar surface, and its pressure disturbs the stellar atmosphere upstream of the emerging shock. We use the numerical results and their analytical limits to predict the effects of radiation transfer and gravity, which are not included in our simulations.

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Shock Propagation in Inhomogeneous Gases. V

Cited by 6 publications

References 5 publications

Production of Magnetic Energy by Macroscopic Turbulence in GRB Afterglows

Production of Magnetic Energy by Macroscopic Turbulence in GRB Afterglows

Oblique Shock Breakout in Supernovae and Gamma-Ray Bursts. I. Dynamics and Observational Implications

Oblique Shock Breakout in Supernovae and Gamma-Ray Bursts. Ii. Numerical Solutions for Non-Relativistic Pattern Speeds

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