Nov 19, 2010 - It is shown that at the stage of free expansion of the explosive shock wave, the degree ..... V. N. Zirakashvili, V. S. Ptuskin, and E. S. Seo, Report.
ISSN 10283358, Doklady Physics, 2011, Vol. 56, No. 4, pp. 219–223. © Pleiades Publishing, Ltd., 2011. Original Russian Text © G.K. Ustinova, 2011, published in Doklady Akademii Nauk, 2011, Vol. 437, No. 4, pp. 472–476.
ASTRONOMY, ASTROPHYSICS, COSMOLOGY
Effects of the Diffusive Acceleration of Particles by Shock Waves in the Primordial Matter of the Solar System G. K. Ustinova Presented by Academician M.Ya. Marov November 19, 2010 Received November 24, 2010
Abstract—The effects of the shock wave diffusive acceleration of particles are considered in the case of for mation of isotopic relations of the anomalous XeHL component of xenon in relic grains of nanodiamonds in chondrites. It is shown that this component could be formed and captured simultaneously with the nano diamond synthesis in the conditions of the explosive shock wave propagation from supernova outbursts. The specificity of isotopic composition of XeHL is due to the high hardness of the spectrum of nuclearactive particles at the shock wave front and its enrichment with heavy isotopes. The spallogenic nature of both the anomalous and normal components of xenon is ascertained, and the role of the subsequent evolutionary pro cesses in the change of their isotopic systems is shown. Experimental evidence of the formation of the power law spectrum of particles with the spectral index γ ~ 1 by the supersonic turbulence during the carbondeto nation supernova SnIa explosion is obtained; this perhaps opens new perspectives in studying the problem of the origin of cosmic rays. It is shown that at the stage of free expansion of the explosive shock wave, the degree of compression of the matter at the wave front was σ = 31 (the corresponding Mach number M ~ 97); this led to a 31fold increase of the magnetic field as well as of the maximum energy of accelerated particles, so that even the energy of protons reached ~3 × 1015 eV, i.e., the “knee” region. DOI: 10.1134/S1028335811040057
On the threshold of the centenary of the discovery of cosmic rays in 2012, their origin is still one of the key presentday problems. Due to the rapid develop ment of wave astronomy, in particular of gammaray astronomy, in the past century, it was ascertained that potential sources of cosmic rays can be both in the Galaxy (e.g., supernova outbursts, pulsars, explosions in the nucleus of the Galaxy), and in the Metagalaxy (e.g., close superclusters of galaxies, quasars) [1]. Numerous models considering different astrophysical objects, combinations of them, and accompanying processes as possible sources of cosmic rays are devel oped [2]. An adequacy criterion of models is their abil ity to reproduce the observed spectrum and composi tion of primary cosmic rays (PCRs), the energy range of which extends up to ~1021 eV to date [3]. Character istic features of the PCR spectrum are changes of the spectral index, i.e., kinks of the spectrum at ~1015– 1017 eV (the famous “knee”), at ~1016–1018 eV (the second knee?), and at the highest energies ≥1019 eV (the ankle), as well as the gradual enrichment of the spectrum with heavy ions: above the knee the spec
Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Moscow, Russia
trum consists almost entirely of iron. There are two approaches to the interpretation of experimental data: nuclear physical and astrophysical (see reviews [4, 5]). In the nuclear physical interpretation, observed fea tures of the PCR spectrum are connected with the possible formation of new particles, new interactions, or new states of matter (e.g., quarkgluon plasma) at energies ≥1015 eV, which could influence the spectrum character and PCR composition. However, recent experiments at the Large Hadron Collider (LHC) at the total energy of colliding beams of 7 TeV (in the lab oratory system, it corresponds to the energy of the incident particle of ≥1016 eV) did not show any devia tions from the standard model of particles and interac tions [6], so this fact allows giving preference to the astrophysical aspect. At present, it is considered to be universally recog nized that the main sources of PCR in our Galaxy are supernova outbursts providing the necessary energy inflow into the interstellar medium [2]. A reliable jus tification of this hypothesis was the discovery of the universal mechanism of cosmic ray acceleration in shock waves accompanying supernova outbursts (see [7] and references in [8]). While the ejected matter of the supernova moves in the turbulent interstellar medium, a shock wave forms; it represents a magneto hydrodynamic discontinuity, at the front of which in
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the matter compression region, the regular magnetic field undergoes a jump, and in addition, the stochastic magnetic field of the plasma turbulence develops; this creates scattering centers for the diffusive scattering of charged particles. The physical meaning of the accel eration mechanism is the following: as a result of the diffusive scattering, charged particles can repeatedly cross the compression region at the wave front, getting an energy increment in 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. For example, the Bohm diffusion, when the path before the scatter ing is equal to the particle gyroradius, is particularly effective. As a result, the particle powerlaw spectrum in momentum forms; in the relativistic case, this is equivalent to the powerlaw energy spectrum F(E) ~ E–γ with the index γ = (σ + 2)/(σ – 1), where σ is the degree of matter compression at the shock front [7, 8]. Obviously, in strong shock waves (at σ Ⰷ 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 propor tionate to A/Z, where A is the mass number and Z is the ion charge. While expanding, the shock wave passes the stage of free expansion in which the maximum field amplifica tion and the highest energies of particles are reached immediately after the explosion, which forms the cos mic ray source spectrum. However, it is assumed that as times goes by, the field becomes weaker, and the fastest particles are lost early from the total spectrum which is formed mainly in the next adiabatic (Sedov) stage of the shock wave, when the total mass of the supernova ejecta is dynamically balanced by the mass of the interstellar medium gas compressed in front of the shock wave [9]. The final spectrum of particles at the Sedov stage corresponds to the spectral index γ~2. The stage of supernova remnants is well studied and considered to be the most effective PCR source in the Galaxy. Indeed, calculated for this stage spectra of protons, helium nuclei and iron are adequate to obser vations at energies up to ~1018 eV, and the shape of the knee in the spectrum of all particles at the energy of 3 × 1015 eV is reproduced sufficiently clearly [9]. Nev ertheless, the problem on the origin of the highest energy particles, with E > 1019 eV, is still unsolved; however, there are hypotheses of the possible positive role of extragalactic sources [2]. Nonetheless, we would like to draw attention to the fact that the stage of free expansion of a shock wave deserves more in
depth study, especially in view of new concrete infor mation offered in this paper and provided by effects of the particle acceleration by shock waves in the primor dial matter of the Solar System. In fact, the process of the diffusive acceleration of particles by shock waves is the knockingout 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 highenergy part. This leads to the increase of fluxes of nuclearactive particles above the threshold energy of nuclear reac tions and, accordingly, to the increase of the rate of isotope production in spallation reactions (see [10] and references therein). In addition, the change of the energy spectrum of nuclearactive particles leads to the change of the weighted spectrumaveraged cross sections for the production of many isotopes, excita tion 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 elemen tal ratios than those in matter not affected by such reprocessing are formed. Indeed, in samples of extra terrestrial matter, numerous isotopic anomalies that could have been caused by such violations of isotopic ratios are observed [10–12]. Isotopic anomalies of xenon in relic nanodiamond grains identified in carbonaceous and nonequilibrium ordinary chondrites [13] are of particular interest. Experimentally artificial nanodiamonds were obtained in processes of the detonation synthesis at high pressures and temperatures, by the method of chemical vapor deposition of carbon atoms (CVD process) at low pressures and moderate temperatures, as well as under the irradiation of carbonaceous mate rials by laser, ultraviolet radiation, and fluxes of high energy particles [14]. Thus, a very wide range of phys ical–chemical conditions (possible combinations of temperatures, pressures, and the initial substance) for nanodiamond synthesis is demonstrated; this fact allows expecting its ubiquitous distribution in space, in particular due to the universal possibility to generate it in shock waves: both in extreme PTconditions at the wave front, and by nucleation in the rarefaction region behind the wave front, as well as under the bombard ment of carbonic grains by highenergy particles accelerated in shock waves. For meteoritic nanodiamonds, a bimodal character of xenon release is observed: mainly as the XeP3 com ponent with the almostsolar isotopic composition at the temperature of 200–900°C and as the anomalous XeHL component with the exotic isotopic composi tion at 1100–1600°C [13]. In comparison with solar xenon, the XeHL component is enriched about twice with light 124Xe, 126Xe isotopes and heavy 134Xe, 136Xe DOKLADY PHYSICS
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EFFECTS OF THE DIFFUSIVE ACCELERATION OF PARTICLES BY SHOCK WAVES
isotopes. In the nineisotope system of xenon, heavy neutronexcess 131,132,134,136Xe isotopes are products of the rprocess of nucleosynthesis and, in addition, they could be formed at the 244Pu and 238U fission. 128–130Xe isotopes are products of the sprocess of nucleosyn thesis, but 129Xe can also be radiogenic due to the decay of the extinct 129I radionuclide. Finally, light neutrondeficient 124,126Xe isotopes are most likely products of pprocess of nucleosynthesis (reactions involving protons). At the same time, all xenon iso topes could be produced in reactions of spallation of neighboring Ba, Cs, Ce, and La nuclei by highenergy particles. The nanodiamond population observed in meteor ites is most often connected with the synthesis during the supernova SnII explosion; it allows explaining the anomalous XeHL component by enrichment with products of p and rprocesses [15]. Indeed, over ~10 million years of its existence before the collapse into the protosun, the protosolar nebula had uni formly mixed with products of nucleosynthesis and of nanodiamond populations of about ten SnII, by supersonic turbulence. However, the conversion of a gasdust cloud into a star is accompanied by huge changes in the physical state of the matter, right up to the relativistic plasma state. Therefore, it is natural to expect that the nanodiamond population with the anomalous XeHL component observed in meteorites was synthesized during the explosion of only the last supernova during the formation of the Solar System: 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. The absence of excesses of heavy extinct radionuclides (products of the rprocess) in refractory, Ca and Alrich inclusions 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 car bondetonation SnIa supernova which was devoid of both a heavy core and a hydrogen shell [10]. During its explosion, all of the rockforming elements up to the iron peak are synthesized, but products of the rpro cess are absent. This fact puts spallation reactions in the key role of the generation of isotopes of xenon cap tured by nanodiamonds. Since the XeHL component is observed only in the nanodiamond of meteorites and is absent in other presolar relics, it is natural to suppose that it was formed under the same conditions under which the nanodiamond was synthesized, in particular under conditions of the reprocessing of the matter by shock waves during explosions of supernovas. This log ically implies that the abovedescribed peculiarities of the change of isotopic ratios and of the law of the frac tionation of noble gases during the passage of strong DOKLADY PHYSICS
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shock waves [10] could cause the exotic isotopic com position of the XeHL. The modeling of rates of xenon isotope production in spallation reactions of neighboring Ba, Cs, Ce, and La nuclei by highenergy protons with different spec trum hardness (at variations of γ from 1.1 to 6) shows [10] that the increase in rates of the Xe isotope produc tion with an increase in the spectrum hardness of the initiating particles (with a decrease of γ) is a general rule; however, the rate of the increase differs for differ ent isotopes, and so isotopic ratios change. It is obtained (see rows 3 and 6 of the table) that the isoto pic ratios observed in chondrites in the XeHL compo nent are higher than the corresponding isotopic ratios in the XeP3 component almost as much as isotopic ratios of xenon generated under hard radiation condi tions 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 nuclearactive particles as the major cause of the difference in their isotopic systems. The table implies that spallation reactions are insufficient only for the generation of the heaviest 134Xe and 136Xe isotopes, and an additional nucleoge netic 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 [8], in particular of products of the rprocess 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 XeP3, could be captured simul taneously, but most likely, this component was implanted later during the uniform mixing of the mat ter of the supernova and the protosolar cloud by super sonic turbulence. It should not be expected that nanodiamonds had not undergone any changes since the time of their for mation, and that the xenon was preserved with the same isotopic ratios with which it had been generated. The table allows comparing the observed isotopic ratios of the xenon in the XeHL component with the oretical ones at γ = 1.1 (row 7) and the observed isoto pic ratios of the xenon in the XeP3 component with theoretical ones at γ = 3 (row 8). It is seen well that the
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Isotopic ratios of xenon in observed XeHL and XeP3 components in the nanodiamond of chondrites and during its gen eration by nuclearactive particles accelerated in shock waves with different spectrum hardness F(>E0) ~ E–γ: at γ = 1.1 and γ = 3 Xe components
124
Xe 132 Xe
136
XeHL* XeP3*
0.0084
0.0057
0.091
0.844
0.636
0.7
0.0045
0.004
0.159
0.823
0.377
0.31
Xe HL* Xe P3*
1.86
1.02
0.97
1.03
1.85
2.26
Xe (γ = 1.1)
3.16
4.16
1.29
9.61
0.036
0.0065
0.90
2.69
4.44
1.18
10.44
0.026
0.0045
1.87
1.53
1.17
0.94
1.09
0.92
1.38
1.44
Xe (γ = 1.1) Xe HL*
69.05
242.11
34.73
3.92
8.38
11.39
0.057
0.0093
Xe (γ = 3) Xe P3*
68.89
225.00
33.21
4.27
7.42
12.69
0.069
0.0145
Xe 132 Xe
126
Xe 132 Xe
128
Xe 132 Xe
129
Xe 132 Xe
130
131
Xe 132 Xe
Xe 132 Xe
1.06
0.154
0.081
1.04
1.43
1.12
0.58
1.38
Xe (γ = 3)
0.31
Xe (γ = 1.1) Xe (γ = 3)
134
132
Xe Xe
* According to the data of [13].
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, powerful nonstationary processes at the stage of the young Sun led to multiple acts of partial recrystallization of nan odiamond grains. This was accompanied by the diffu sion and escaping of xenon from destroyed traps, cracks, and other disturbances of the crystal lattice which were removed by the recrystallization and, con sequently, led to the gradual enrichment of the isoto pic system of the preserved xenon with heavy isotopes in comparison with its original isotopic system during the generation.
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 ~1014 eV [9], knee energies of ~3 × 1015 eV were reached at the accelera tion by the explosion shock wave. Further investiga tions should show how these energies were modified during the further evolution of the shock wave in accompanying processes, what fraction they contrib uted to the total PCR spectrum from different sources, and for what part of the spectrum they turned out to be the most operative.
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 [10]. The magnetohydrodynamic conditions of parti cle acceleration at the stage of the free expansion of the shock wave during the SnIa explosion are concret ized 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 mat ter compression at the front of the explosion shock wave from the SnIa explosion was σ = 31, which cor responds to the Mach number M ~ 97 at σ ~ M3/4. This
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Translated by O. Merkulova
