Fluid dynamic mathematical aspects of supernova remnants

Abstract

Supernovae - explosions of stars - are a central problem in astrophysics since they encapsulate the entire process of stellar evolution and nucleosynthesis. Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities, developing during the supernova blast, lead to intense interfacial RT/RM mixing of the star's materials and couple astrophysical to atomic scales. This work analyzes some fluid dynamic mathematical aspects of the titanic task of supernova's blast. We handle mathematical challenges of RT/RM dynamics in supernova relevant conditions by directly linking the conservation laws governing RT/RM dynamics to symmetry-based momentum model, by exactly deriving the model parameters in the scale-dependent and scale-invariant regimes, and by exploring the special self-similar class for RT/RM interfacial mixing with variable accelerations. We reveal that RT/RM dynamics is strongly influenced by deterministic (the initial and the flow) conditions in the scale-dependent linear and nonlinear regimes and in the self-similar mixing regime. The theory outcomes are consistent with the observations of supernova remnants, explain the results of the scaled laboratory experiments in high energy density plasmas, and yield the design of future experiments for accurate quantification of RT/RM dynamics in supernova relevant conditions. We find that from fluid dynamic mathematical perspectives supernovae can be regarded as an astrophysical initial value problem. Along with the guidance of what explodes at microscopic scales, supernova remnants encapsulate information on the explosion hydrodynamics and the associated deterministic conditions at macroscopic scales. We urge such effects be considered in interpretations of the observational data.

Velocity Fluctuations Spectra in Experimental Data on Rayleigh–Taylor Mixing

“…Success in solving the problem is achieved with the group theory approach, including accurate analytical solutions for the scale-dependent early-time and late-time nonlinear dynamics, as well as for the self-similar Rayleigh-Taylor mixing in a broad range of conditions. Particularly, the dynamics of Rayleigh-Taylor mixing can be captured within the framework of the momentum model that has the same symmetries and scaling transformations as, and is directly linked to, the governing equation [9,24,26,29,[43][44][45][46].…”

“…In the regime of self-similar mixing, the length scale is L ∼ |h|, where h is the amplitude in the acceleration direction increasing quadratic with time |h| ∼ gt 2 . The rates of loss and gain of momentum relate as µ ∼ μ ∼ g, whereas the rates of energy dissipation and gain are time-dependent with ∼ ˜ ∼ g 2 t [9, 24,26,29,[43][44][45][46].…”

“…Quantification of power-laws is a key objective of experimental diagnostics of canonical turbulence and RT mixing. Reliable identification of an exponent and a prefactor of a power-law requires a substantial span of resolved scales; it is a challenge to achieve this in experiments and simulations [10,15,26,41,42,45,46].…”

“…These outcomes are consistent with group theory foundations and with other experiments. See Tables 1 and 2, Figures 2-7, Equations ( 1)-( 4) [9,15,17,23,24,29,30,37,39,[44][45][46]51].…”

Laser and Astrophysical Plasmas and Analogy between Similar Instabilities

“…This shock wave expands into the surrounding interstellar medium, sweeping up an expanding shell of gas and dust. The ejected debris mixes with the interstellar medium and forms a nebulas a supernova remnant [76,77], such as the Crab Nebula.…”