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MHD-conditions in the explosive shock wave from the last supernova prior to formation of the Solar system

Isotopic anomalies of xenon in the nanodiamonds of chondrites testify to the rigid radiation and magneto hydrodynamic conditions at the last supernova explosion prior to formation of the Solar system.

generated inductive electric fields; i.e., the longer particles are held in the wave front region, the more they are accelerated. In other words, the larger the particle velocity and, therefore, its path before the scattering, the more often and from larger distances the particle can return to the front region and get the velocity increment. As a result, the particle power-law energy spectrum forms: F(E) ~ E -γ with the index γ = (σ + 2)/(σ -1), where σ is the degree of matter compression at the shock front [4]. Obviously, in strong shock waves (at σ >> 1), a very hard spectrum of accelerated particles (with γ → 1) can be formed. Similarly, heavy ions with a large path will have a priority of acceleration; this leads to the enrichment of the spectrum with heavy ions proportionate to A/Z, where A is the mass number and Z is the ion charge.
In fact, the process of the diffusive acceleration of particles by shock waves is the knocking-out of new particles from the background plasma by the shock wave and the transferring of particles from the low-energy region of the spectrum to its high-energy part. This leads to the increase of fluxes of nuclear-active particles above the threshold energy of nuclear reactions and, accordingly, to the increase of the rate of isotope production in spallation reactions (see [5] and references therein). In addition, the change of the energy spectrum of nuclear-active particles leads to the change of the weighted spectrum-averaged cross sections for the production of many isotopes, excitation functions of which are sensitive to the particle spectrum shape. As a result, in reservoirs reprocessed by shock waves, for example, in expanding shells of supernovas, absolutely different isotopic and elemental ratios than those in matter not affected by such reprocessing are formed. Indeed, in samples of extraterrestrial matter, numerous isotopic anomalies that could have been caused by such violations of isotopic ratios are observed [5][6][7].

Isotopic anomalies of xenon in relic nanodiamond grains
Such anomalies identified in carbonaceous and nonequilibrium ordinary chondrites [8], are of particular interest. For meteoritic nanodiamonds, a bimodal character of xenon release is observed: mainly as the Xe-P 3 component with the almost-solar isotopic composition and as the anomalous Xe-HL component with the exotic isotopic composition (enriched about twice with light 124 Xe, 126 Xe isotopes and heavy 134 Xe, 136 Xe isotopes). Besides the processes of nucleosynthesis, all xenon isotopes could be produced in reactions of spallation of neighboring Ba, Cs, Ce, and La nuclei by high-energy particles [5,7]. The anomalous Xe-HL in meteoritic nanodiamonds was formed simultaneously with nanodiamonds themselves during the shock wave propagation at the last supernova explosion before the formation of the Solar System [7]. Indeed, since the conversion of the protosolar nebula into the protostar was accompanied by huge changes in the physical state of the matter, all of the previously synthesized nanodiamond grains, even if preserved, should have lost all their noble gases. But the last supernova was not the SnII [5]. The absence of excesses of heavy extinct radionuclides (products of the r-process) in CAI of carbonaceous chondrites with a formation interval of ~1 million years indicates that the last supernova during the formation of the Solar System was the carbon-detonation supernova SnIa which was devoid of both a heavy core and a hydrogen shell [5]. During its explosion, all of the rock-forming elements up to the iron peak are synthesized, but products of the r-process are absent. This fact puts spallation reactions in the key role of the generation of isotopes of xenon captured by nanodiamonds.
The modeling of rates of xenon isotope production in spallation reactions of neighboring Ba, Cs, Ce, and La nuclei by high-energy protons with different spectrum hardness (at variations of γ from 1.1 to 6) shows [7] (see rows 3 and 6 of the table 1) that the isotopic ratios observed in chondrites in the Xe-HL component are higher than the corresponding isotopic ratios in the Xe-P 3 component [8] almost as much as isotopic ratios of xenon generated under hard radiation conditions of the matter reprocessing by shock waves (γ = 1.1, for example, in expanding shells of supernovas) are higher than those in the matter not affected by such reprocessing (γ = 3, for example, in the main volume of the protosolar cloud). This reveals the spallogenic nature of both anomalous and normal components of xenon and points to the different hardness of the energy spectrum of nuclear-active particles as the major cause of the difference in their isotopic systems. The table 1 implies that spallation reactions are insufficient only for the generation of the heaviest 134 Xe and 136 Xe isotopes, and an additional nucleogenetic source is required. However, the most favorable for the synthesis of the nanodiamond front of the explosion shock wave was enriched with these isotopes because of the preferential acceleration of just heavy isotopes of the medium [4], in particular, of products of the r-process from previous explosions of SnII, at the shock front. Thus, during the nanodiamond synthesis in the shock wave from the SnIa explosion, the xenon produced in spallation reactions by protons which were accelerated by the shock wave was captured, and heavy isotopes of xenon from preceding explosions of supernovas, with which the wave front was enriched, were captured. This is what formed the anomalous Xe-HL component. The Xe-P 3 , could be captured simultaneously, but most likely, this component was implanted later during the uniform mixing of the matter of the supernova and the protosolar cloud by supersonic turbulence.
The table 1 also allows comparing the observed isotopic ratios of the xenon in the Xe-HL component with theoretical ones at γ = 1.1 (row 7) and the observed isotopic ratios of the xenon in the Xe-P 3 component with theoretical ones at γ = 3 (row 8). It is seen well that the xenon preserved in the nanodiamond is significantly heavier than the originally generated xenon, and almost to the same extent for both components. The latter suggests that processes that led to such weighting occurred after the formation of these components, most likely, during the accretion. Indeed, the multiple acts of partial recrystallization of nanodiamond grains at the stage of the young Sun were accompanied by the diffusion and escaping of xenon from destroyed traps, cracks, and other disturbances of the crystal lattice and, consequently, led to the gradual enrichment of the isotopic system of the preserved xenon with heavy isotopes in comparison with its original isotopic system during the generation. Table 1. Isotopic ratios of Xe in the observed Xe-HL a and Xe-P 3 a components in nanodiamonds of chondrites and the similar ratios, generated by the shock wave accelerated nuclear-active particles with various hardness of the energy spectrum F( >E 0 ) ~ E - : at γ = 1.1 and γ = 3.

Magneto hydrodynamic conditions in the early Solar system
The obtained results demonstrate the quantitative estimations of isotope anomalies in the primordial matter due to the diffusive acceleration of cosmic rays by shock waves; these estimations represent a subtle tool for studying processes in the early Solar System [7]. The magneto hydrodynamic conditions of particle acceleration at the stage of the free expansion of the shock wave during the SnIa explosion are concretized for the first time. The experimental evidence for the formation of the power law spectrum of particles with the index γ = 1.1 indicates that the degree of matter compression at the front of the explosion shock wave from the SnIa explosion was σ = 31, which corresponds to the Mach number M ~ 97 at σ ~ M 3/4 [9]. This implies that the interstellar magnetic field (B ~ 10 -5 G), which is proportionate to the degree of compression, increased by a factor of 31 at the shock wave front, and the maximum energy of accelerated particles, which is proportionate to the magnetic field, increased by the same factor. Since the mean interstellar magnetic field is sufficient to accelerate protons to ~ 10 14 eV [1], the energies of ~ 3 · 10 15 eV were reached at the acceleration by the explosion shock wave. Further investigations should show how these energies were modified during the further evolution of the shock wave in accompanying processes, what fraction they contributed to the total PCR spectrum from different sources, and for what part of the spectrum they turned out to be the most operative. Indeed, the effects of high radiation conditions (γ ~ 1) are observed in the production of extinct radionuclides in some refractory grains of the Ca and Al rich inclusions (CAI) of carbonaceous chondrites (see figures 1 and 2 for 26 Al and 53 Mn, respectively), as well as they follow from the production of abundances of isotopes of the light elements Li, Be and B (figure 3) [6]. Since the interval of CAI formation is ~ 1 My [10], the stage of free expansion of explosive shock wave was long enough and should make noticeable contribution to the formation of the highest energy part of integral spectrum of the primary cosmic rays.