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Cutoff of primary cosmic ray energy spectrum without the knee and the ankle
Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223 www.elsevierphysics.com
Cutoff of primary cosmic ray energy spectrum without the knee and the ankle A.A.Petrukhin Moscow Engineering Physics Institute, Kashirskoe shosse, 31, Moscow 115409, Russia Experimental and theoretical situation in investigations of cosmic rays with energies higher than the knee is considered. The evidences of new state of matter production in interactions of PeV cosmic rays are analysed. Theoretical model of cosmic ray acceleration in cosmic plasma pinches with constant slope of energy spectrum γ = 3 is described. Consequences for future experiments and for interpretation of their results around the cutoff are discussed. 1. INTRODUCTION
Usually cutoff problem in considered in relation with cosmic ray acceleration and propagation. In this case, the cutoff shape and position strongly depend on the distance to the source of the production of cosmic rays or/and their propagation time. Considerably less attention is paid to the problem of correctness of primary particle energy evaluation. Since no direct measurements of EHE particles exist, the results of EAS investigations can be used only. At that, theoretical models of EAS development are used to evaluate primary particle energy. And if to suppose that the model of interaction is changed with the increase of energy, our knowledge about primary spectrum behavior at EHE energies may be very far from the reality. As it is known, the measured EAS energy spectrum has two peculiarities: the knee at about 3 − 5 PeV and the ankle near 5 EeV. At present, most part of cosmic ray investigators believe that these peculiarities has the primary spectrum. In papers [1], a possibility of explanation of the knee and the ankle appearance as a result of a drastic change of hadron interaction at energies 0920-5632/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2004.10.065
around the knee and the ankle was analysed on the basis of the hypothesis [2] about the production of a new heavy short-lived particle (state of matter) with mass about 1 TeV. To the present, many evidences in support of this hypothesis have been found. The situation in theoretical description of cosmic ray acceleration and propagation has been also changed. Practically all well-known theoretical models cannot describe energy spectrum in the whole energy range and cannot predict unambiguously the value of the integral spectrum slope γ ≈ 1.7. To obtain the necessary value, it is usually supposed that the energy spectrum is steepening with ∆γ ~ 0.5 during propagation of cosmic rays in the Galaxy. But very long life time of cosmic rays in Galaxy is required for that. In these models, the knee position is the maximal energy of cosmic rays which can be kept by magnetic fields in the Galaxy. Correspondingly, the ankle is the energy at which the flux of extragalactic particles will prevail galactic cosmic rays. Meanwhile, the model of acceleration of particles in cosmic
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
plasma pinches exists, which predicts unambiguous value of γ = 3 and does not require separation of cosmic rays on galactic and extragalactic ones [3]. Unfortunately, this very interesting model was practically unknown among cosmic ray physicists. Therefore the purpose of this paper is the consideration of these new circumstances and the analysis of possible consequences for primary spectrum behavior near cutoff. 2. EXPERIMENTAL SITUATION To the present, a wide set of experimental data which evidence for the inclusion of new physical processes in PeV energy region has been accumulated. Of course as a rule it is impossible to evaluate the energy of primary particles in cosmic ray experiments with a good accuracy. But certainly all unusual experimental data have the energy threshold in PeV interval. These phenomena cannot be explained in frame of existing theories of particle interactions or have negligibly small probability. Unusual experimental data can be separated in three groups: unusual events detected in hadron experiments, unexpected behavior of EAS characteristics, and evidences of the excess of VHE muons. Most important unusual events in hadron interactions were observed in experiments "Pamir" and "Chacaltaya" [4] and in Tien-Shan hadron calorimeter [5]. Among them: Halos, Alignment, Centauros, Anti-Centauros, Penetraiting cascades and Long-flying particles. More detailed description of these events may be found elsewhere [4, 5]. The attempts to describe these phenomena in frame of existing theoretical models were unsuccessful, and for their explanation different new approaches were suggested. But too large number of new ideas
219
has lead to a skeptical attitude of most part of physicists to them. Measured EAS characteristics at knee energies and higher did not give direct indications on new physical process inclusion but many obtained results appeared unexpected in comparison with lower energies. And since the EAS development depends not only on hadron interaction model but also on primary cosmic ray composition, changes of observed EAS characteristics were interpreted as a consequence of the change in composition of primary cosmic rays. Among them: Nµ/Ne-ratio, dependence of Xmax on Ne, fraction of young showers, various anomalies in lateral distribution. In the last years, the phenomenon of copious production of delayed neutrons near the EAS core was observed [6]. Study of VHE muons (i.e. muons with energy > 100 TeV) is a very hard problem because of a very steep muon energy spectrum with γ ∼ 2.7, and there are only two experiments which touch this energy region [7, 8], and two observations of individual VHE muons [9, 10]. These results indicate some excess of VHE muons and can evidence for new physics inclusion since for their explanation the flux of muons from the known sources of muon generation is not sufficient [11]. To explain all listed unusual (unexpected) results from a single point of view the production of new heavy particle (state of matter) is most applicable. Large mass explains the threshold of its appearance and the absence of any serious evidences of its existence in accelerator experiments. Particle with such large mass has to decay into W±, Z0-bosons, which in their turn can decay into both leptons (eνe), (µνµ), (τντ) and hadrons (on average, about 20 secondary particles, mainly pions). This circumstance can explain big fluctuations in detected events and in EAS development.
220
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
Generation of neutrinos with large energies, which are not detected in EAS experiments, leads to a missing energy and allows to explain the knee appearance and a big spread in results of different experiments in conditions of limited statistics. Calculations show that in decays of heavy particles with PeV energies, muons with energies more 100 TeV are generated [2]. The appearance of additional flux of VHE muons allows to explain many unusual results obtained in hadron experiments, f.e. production of penetrating cascades, generation of AntiCentauros, long-flying component etc, since any hadron detector should register muon interactions. Of course, this additional flux explains all evidences of VHE muon excess observation. And finally, new proposed physical object can be considered as a resonance state. In this case, according to Chew-Frautschi diagram, it must have spin about 106. Of course, this value is unusual and unaccustomed, but there are no principal limitations for Chew-Frautschi diagram application. The resonance state with such large momentum may be considered as a quasiclassical object, and Fig.1 illustrates some possible consequences of such object decays. More detailed consideration of possible explanation of various unusual experimental data in frame of the discussed hypotheses is given elsewhere [12]. The main conclusion for the present paper is the following: the inclusion of new physics with production of massive shortlived particles allows to explain the knee as the result of change of interaction but not as the result of primary spectrum changes. As it was shown in [1], within the frame of the considered hypothesis it is possible to explain the ankle also, if to suppose that the ankle energy (∼ 5 EeV) is the critical energy for new particles in the atmosphere (as, f.e., 100 GeV is the critical energy for pions and 700 GeV
is that for kaons). At critical energy, the probabilities of decay and interaction in the atmosphere become equal. For higher energies new particles mostly interact, the fraction of missing energy is decreasing, and the measured integral spectrum slope returns to initial value γ ∼ 1.7.
Figure 1. Halo and alignment production in decays of a resonance state with a large spin.
3. THEORETICAL DESCRIPTION OF PRIMARY ENERGY SPECTRUM The theoretical models of cosmic ray production and acceleration can be divided in
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
two basic groups: explosion type, f.e. Supernova, and multiple interaction type, f.e. Fermi mechanism. The main problem for models of the first type is the absence the point sources of cosmic rays. The main problem for models of the second type is relatively low limit of maximal energy of accelerated particles. In a whole, there is no model, which describes primary spectrum in the full energy range. And finally, though in all models the spectrum is assumed in the form N ∼ E-γ, there is no model, which unambiguously predicts the value of γ. Practically all these problems were solved 15 years ago [3]. Since the results of [3] were obtained by plasma physicists, reported at conferences and published in magazines and books on plasma physics, these results are almost unknown among cosmic ray community. Therefore the basic ideas and results of this model are given below. In this model, charged particles of cosmic rays are produced and accelerated in cosmic plasma, and mechanism of their production and acceleration is the following. In cosmic plasma (of any origin) the electrical discharges – "cosmic lightnings" − can occur, at which cylindrical pinches are formed, similar to laboratory ones. Two basic instabilities of plasma pinches are known: snaky and neck (Fig.2). In the latter case plasma jets are squeezed out of pinch neck. These jets are the accelerated particle beams. For description of this process the well-known equations of plasma physics are used only. This model has no free parameters except for absolute intensity. The main results of this model: − Integral energy spectrum slope has unambiguous value γ = 3 ≈ 1.73, which does not depend on pinch sizes, currents in pinches and other parameters. These parameters determine coefficient of proportionality only. − Accelerated particle energy has no limitation since density in plasma pinch neck goes to infinity when its radius tends to zero.
221
Of course, the considered model cannot close other models of cosmic ray production and acceleration, but if to suppose that generation of cosmic rays in plasma pinches is the main source of cosmic rays in Universe, in this case some problems of cosmic ray physics will be solved and answers to many questions will be obtained.
Figure 2. Acceleration of particles in pinches of cosmic plasma. For example, this model does not require additional change of γ during long time propagation of cosmic rays in the Galaxy. Apparently, it is not necessary to divide cosmic rays in galactic and extragalactic ones, since the contribution of various sources of cosmic plasma (stars, Supernovae, Galaxy, black holes, etc.) can be summed, and it explains the absence of point sources of cosmic rays, since even near Supernova the plasma pinches can be oriented in any direction. At the same time, generation of cosmic rays in narrow jets can explain the appearance of correlated particles in cosmic rays. Very simple solution for cosmic ray composition
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
problem is obtained also. The composition of cosmic rays must be the same as composition of cosmic plasma, which consists mainly of hydrogen and must not depend on particle energy, since all equations for plasma pinches are solved for the variable E/m = 1/ 1 - β2 . Naturally, near the Earth, the Sun, Galaxy nuclei, etc. energy spectrum and composition of cosmic rays may be changed due to the influence of local magnetic field, additional sources of accelerated particles, etc. If to combine constant energy spectrum slope of primary cosmic rays and the hypothesis about the origin of the knee and the ankle as a result of changes in the interaction, then new approach to cutoff problem will be necessary.
curve 4 shows the same spectrum but without cutoff. Of course, the appearance of "bump" is possible in traditional model also if the extragalactic spectrum has the slope less than 1.7. 10
E2.7 dN/dE (cm-2 sr-1 s-1 GeV1.7)
222
5 4
2 1
3
0.5
2
0.2 0.1
1
1014
4. CUTOFF PROBLEM New approach to cutoff problem has to take into account the following circumstances. Firstly, a possibility of generation of particles in the Galaxy (in plasma pinches) without limitation of energy, which will have no cutoff due to a short distance between points of production and observation. Secondly, if the knee and the ankle are results of particle interaction change, the behavior of energy spectrum above the ankle will be changed. Fig.3 illustrates the difference of existing model and proposed behavior of the energy spectrum. Curve 1 in the figure shows the cutoff for the case when the energy spectrum above the ankle is represented by the extragalactic component with the same slope (γ ~ 1.7). Curve 2 shows energy spectrum for the case of a single primary spectrum with constant γ = 1.7. Cutoff will have the same place in energy scale, but the famous "bump" appears. If cosmic rays from our Galaxy and other nearest galaxies give considerable part of primary particles at these energies cutoff appears at larger energy (curve 3). And at last
1016
1018 E (eV/nucleus)
1020
1022
Figure 3. Cutoff in various models of primary spectrum: 1 − with the knee and the ankle; 2, 3, 4 − without them (2 − uniform spectrum; 3 − spectrum from Galaxy; 4 − without cutoff). The choice between two approaches is very difficult but some ideas can be suggested. Firstly, it is necessary to confirm or to reject the change of interaction in PeV energy region. For that, investigation of VHE muons in EAS below and higher the knee is the best way. The absence of VHE muons in EAS below the knee and their appearance above the knee will be irrefutable proof of new physics existence. In the opposite case, it is necessary to wait for LHC results. Secondly, it is desirable to conduct EAS investigations in maximal wide intervals of energies. This will allow to match more correctly experimental data obtained for different energy intervals. And, at last, it is very important to measure energy-lateral distribution of HE muons in EAS with energies more than 1017 eV. These energies correspond to energies more than 14 TeV in the center-of-mass system and will not be
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
investigated at accelerators in the visible future. Of course, the development of theoretical evaluations for description of EAS in the atmosphere for various suppositions about primary spectrum and interaction models is required. Let us mark one more interesting opportunity. If the idea of generation of cosmic rays in plasma pinches is correct and particles are accelerated in jets, then attempts of correlated EHE particle detection will be possible, f. e. by South and North parts of Pierre Auger Observatory. 5. CONCLUSIONS 1. It is impossible to solve finally the problem of the cutoff without solving the knee problem. The best and apparently the only way for solution of the knee problem is to search for VHE muons which are generated in primary cosmic ray particle interactions with energies above the knee. 2. In any case, at interpretation of results of cutoff investigations, especially with EAS arrays of new generation (f.e. South part of PAO), it is necessary to take into account the possibility of existence of primary spectrum with a constant slope. In future projects, such as North part of PAO in US, it is necessary to decrease the distance between surface defectors in order to have possibility of measurements of EAS with energies around the ankle. ACKNOWLEDGMENTS This work was partially supported by CRDF Award RP2-2557-MO-03. Many thanks to B.A.Trubnikov for numerous very fruitful discussions and to N.S.Barbashina,
R.P.Kokoulin and I.I.Yashin preparation of this paper.
223
for help in
REFERENCES 1. A.A.Petrukhin, Nucl. Phys. B (Proc Suppl.) 110 (2002) 484 and 122 (2003) 259. 2. A.A.Petrukhin, Proc. XIth Rencontres de Blois "Frontiers of Matter", Blois, 1999, ed. J. Tran Thanh Van, The Gioi Publishers, 401. 3. B.A.Trubnikov et al., Proc. Int. Conf. on Plasma Physics, New Delhi, 1, (1989) 257 and in the book "Hydrodynamics of Unstable Media", CRC Press (1996) 114. 4. S.A.Slavatinski, Nucl. Phys. B (Proc. Suppl.) 122 (2003) 3. 5. V.I.Yakovlev, Nucl. Phys. B (Proc. Suppl.) 122 (2003) 201 and 417. 6. V.A.Antonova et al., Nucl. Phys. B (Proc. Suppl.) 75A (1999) 333. 7. N.P.Il'ina et al., Proc. 24th ICRC , Roma, 1 (1995) 524. 8. O.G.Ryazhskaya, Nucl. Phys. B (Proc. Suppl.) 87 (2000) 423. 9. T.Matano et al., Proc. 9th ICCR, London, 2 (1965) 1045. 10. A.A.Petrukhin, Proc. Vulcano Workshop 2000 "Frontier Objects in Astrophysics and Particle Physics", eds. F.Giovannelli & G. Mannocchi, 375. 11. A.A.Petrukhin, Proc. Vulcano Workshop 2002 "Frontier Objects in Astrophysics and Particle Physics", eds. F.Giovannelli & G. Mannocchi, 527. 12. A.A.Petrukhin, Proc. Vulcano Workshop 2004 "Frontier Objects in Astrophysics and Particle Physics", eds. F.Giovannelli & G. Mannocchi (in press).
Cutoff of primary cosmic ray energy spectrum without the knee and the ankle A.A.Petrukhin Moscow Engineering Physics Institute, Kashirskoe shosse, 31, Moscow 115409, Russia Experimental and theoretical situation in investigations of cosmic rays with energies higher than the knee is considered. The evidences of new state of matter production in interactions of PeV cosmic rays are analysed. Theoretical model of cosmic ray acceleration in cosmic plasma pinches with constant slope of energy spectrum γ = 3 is described. Consequences for future experiments and for interpretation of their results around the cutoff are discussed. 1. INTRODUCTION
Usually cutoff problem in considered in relation with cosmic ray acceleration and propagation. In this case, the cutoff shape and position strongly depend on the distance to the source of the production of cosmic rays or/and their propagation time. Considerably less attention is paid to the problem of correctness of primary particle energy evaluation. Since no direct measurements of EHE particles exist, the results of EAS investigations can be used only. At that, theoretical models of EAS development are used to evaluate primary particle energy. And if to suppose that the model of interaction is changed with the increase of energy, our knowledge about primary spectrum behavior at EHE energies may be very far from the reality. As it is known, the measured EAS energy spectrum has two peculiarities: the knee at about 3 − 5 PeV and the ankle near 5 EeV. At present, most part of cosmic ray investigators believe that these peculiarities has the primary spectrum. In papers [1], a possibility of explanation of the knee and the ankle appearance as a result of a drastic change of hadron interaction at energies 0920-5632/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2004.10.065
around the knee and the ankle was analysed on the basis of the hypothesis [2] about the production of a new heavy short-lived particle (state of matter) with mass about 1 TeV. To the present, many evidences in support of this hypothesis have been found. The situation in theoretical description of cosmic ray acceleration and propagation has been also changed. Practically all well-known theoretical models cannot describe energy spectrum in the whole energy range and cannot predict unambiguously the value of the integral spectrum slope γ ≈ 1.7. To obtain the necessary value, it is usually supposed that the energy spectrum is steepening with ∆γ ~ 0.5 during propagation of cosmic rays in the Galaxy. But very long life time of cosmic rays in Galaxy is required for that. In these models, the knee position is the maximal energy of cosmic rays which can be kept by magnetic fields in the Galaxy. Correspondingly, the ankle is the energy at which the flux of extragalactic particles will prevail galactic cosmic rays. Meanwhile, the model of acceleration of particles in cosmic
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
plasma pinches exists, which predicts unambiguous value of γ = 3 and does not require separation of cosmic rays on galactic and extragalactic ones [3]. Unfortunately, this very interesting model was practically unknown among cosmic ray physicists. Therefore the purpose of this paper is the consideration of these new circumstances and the analysis of possible consequences for primary spectrum behavior near cutoff. 2. EXPERIMENTAL SITUATION To the present, a wide set of experimental data which evidence for the inclusion of new physical processes in PeV energy region has been accumulated. Of course as a rule it is impossible to evaluate the energy of primary particles in cosmic ray experiments with a good accuracy. But certainly all unusual experimental data have the energy threshold in PeV interval. These phenomena cannot be explained in frame of existing theories of particle interactions or have negligibly small probability. Unusual experimental data can be separated in three groups: unusual events detected in hadron experiments, unexpected behavior of EAS characteristics, and evidences of the excess of VHE muons. Most important unusual events in hadron interactions were observed in experiments "Pamir" and "Chacaltaya" [4] and in Tien-Shan hadron calorimeter [5]. Among them: Halos, Alignment, Centauros, Anti-Centauros, Penetraiting cascades and Long-flying particles. More detailed description of these events may be found elsewhere [4, 5]. The attempts to describe these phenomena in frame of existing theoretical models were unsuccessful, and for their explanation different new approaches were suggested. But too large number of new ideas
219
has lead to a skeptical attitude of most part of physicists to them. Measured EAS characteristics at knee energies and higher did not give direct indications on new physical process inclusion but many obtained results appeared unexpected in comparison with lower energies. And since the EAS development depends not only on hadron interaction model but also on primary cosmic ray composition, changes of observed EAS characteristics were interpreted as a consequence of the change in composition of primary cosmic rays. Among them: Nµ/Ne-ratio, dependence of Xmax on Ne, fraction of young showers, various anomalies in lateral distribution. In the last years, the phenomenon of copious production of delayed neutrons near the EAS core was observed [6]. Study of VHE muons (i.e. muons with energy > 100 TeV) is a very hard problem because of a very steep muon energy spectrum with γ ∼ 2.7, and there are only two experiments which touch this energy region [7, 8], and two observations of individual VHE muons [9, 10]. These results indicate some excess of VHE muons and can evidence for new physics inclusion since for their explanation the flux of muons from the known sources of muon generation is not sufficient [11]. To explain all listed unusual (unexpected) results from a single point of view the production of new heavy particle (state of matter) is most applicable. Large mass explains the threshold of its appearance and the absence of any serious evidences of its existence in accelerator experiments. Particle with such large mass has to decay into W±, Z0-bosons, which in their turn can decay into both leptons (eνe), (µνµ), (τντ) and hadrons (on average, about 20 secondary particles, mainly pions). This circumstance can explain big fluctuations in detected events and in EAS development.
220
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
Generation of neutrinos with large energies, which are not detected in EAS experiments, leads to a missing energy and allows to explain the knee appearance and a big spread in results of different experiments in conditions of limited statistics. Calculations show that in decays of heavy particles with PeV energies, muons with energies more 100 TeV are generated [2]. The appearance of additional flux of VHE muons allows to explain many unusual results obtained in hadron experiments, f.e. production of penetrating cascades, generation of AntiCentauros, long-flying component etc, since any hadron detector should register muon interactions. Of course, this additional flux explains all evidences of VHE muon excess observation. And finally, new proposed physical object can be considered as a resonance state. In this case, according to Chew-Frautschi diagram, it must have spin about 106. Of course, this value is unusual and unaccustomed, but there are no principal limitations for Chew-Frautschi diagram application. The resonance state with such large momentum may be considered as a quasiclassical object, and Fig.1 illustrates some possible consequences of such object decays. More detailed consideration of possible explanation of various unusual experimental data in frame of the discussed hypotheses is given elsewhere [12]. The main conclusion for the present paper is the following: the inclusion of new physics with production of massive shortlived particles allows to explain the knee as the result of change of interaction but not as the result of primary spectrum changes. As it was shown in [1], within the frame of the considered hypothesis it is possible to explain the ankle also, if to suppose that the ankle energy (∼ 5 EeV) is the critical energy for new particles in the atmosphere (as, f.e., 100 GeV is the critical energy for pions and 700 GeV
is that for kaons). At critical energy, the probabilities of decay and interaction in the atmosphere become equal. For higher energies new particles mostly interact, the fraction of missing energy is decreasing, and the measured integral spectrum slope returns to initial value γ ∼ 1.7.
Figure 1. Halo and alignment production in decays of a resonance state with a large spin.
3. THEORETICAL DESCRIPTION OF PRIMARY ENERGY SPECTRUM The theoretical models of cosmic ray production and acceleration can be divided in
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
two basic groups: explosion type, f.e. Supernova, and multiple interaction type, f.e. Fermi mechanism. The main problem for models of the first type is the absence the point sources of cosmic rays. The main problem for models of the second type is relatively low limit of maximal energy of accelerated particles. In a whole, there is no model, which describes primary spectrum in the full energy range. And finally, though in all models the spectrum is assumed in the form N ∼ E-γ, there is no model, which unambiguously predicts the value of γ. Practically all these problems were solved 15 years ago [3]. Since the results of [3] were obtained by plasma physicists, reported at conferences and published in magazines and books on plasma physics, these results are almost unknown among cosmic ray community. Therefore the basic ideas and results of this model are given below. In this model, charged particles of cosmic rays are produced and accelerated in cosmic plasma, and mechanism of their production and acceleration is the following. In cosmic plasma (of any origin) the electrical discharges – "cosmic lightnings" − can occur, at which cylindrical pinches are formed, similar to laboratory ones. Two basic instabilities of plasma pinches are known: snaky and neck (Fig.2). In the latter case plasma jets are squeezed out of pinch neck. These jets are the accelerated particle beams. For description of this process the well-known equations of plasma physics are used only. This model has no free parameters except for absolute intensity. The main results of this model: − Integral energy spectrum slope has unambiguous value γ = 3 ≈ 1.73, which does not depend on pinch sizes, currents in pinches and other parameters. These parameters determine coefficient of proportionality only. − Accelerated particle energy has no limitation since density in plasma pinch neck goes to infinity when its radius tends to zero.
221
Of course, the considered model cannot close other models of cosmic ray production and acceleration, but if to suppose that generation of cosmic rays in plasma pinches is the main source of cosmic rays in Universe, in this case some problems of cosmic ray physics will be solved and answers to many questions will be obtained.
Figure 2. Acceleration of particles in pinches of cosmic plasma. For example, this model does not require additional change of γ during long time propagation of cosmic rays in the Galaxy. Apparently, it is not necessary to divide cosmic rays in galactic and extragalactic ones, since the contribution of various sources of cosmic plasma (stars, Supernovae, Galaxy, black holes, etc.) can be summed, and it explains the absence of point sources of cosmic rays, since even near Supernova the plasma pinches can be oriented in any direction. At the same time, generation of cosmic rays in narrow jets can explain the appearance of correlated particles in cosmic rays. Very simple solution for cosmic ray composition
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
problem is obtained also. The composition of cosmic rays must be the same as composition of cosmic plasma, which consists mainly of hydrogen and must not depend on particle energy, since all equations for plasma pinches are solved for the variable E/m = 1/ 1 - β2 . Naturally, near the Earth, the Sun, Galaxy nuclei, etc. energy spectrum and composition of cosmic rays may be changed due to the influence of local magnetic field, additional sources of accelerated particles, etc. If to combine constant energy spectrum slope of primary cosmic rays and the hypothesis about the origin of the knee and the ankle as a result of changes in the interaction, then new approach to cutoff problem will be necessary.
curve 4 shows the same spectrum but without cutoff. Of course, the appearance of "bump" is possible in traditional model also if the extragalactic spectrum has the slope less than 1.7. 10
E2.7 dN/dE (cm-2 sr-1 s-1 GeV1.7)
222
5 4
2 1
3
0.5
2
0.2 0.1
1
1014
4. CUTOFF PROBLEM New approach to cutoff problem has to take into account the following circumstances. Firstly, a possibility of generation of particles in the Galaxy (in plasma pinches) without limitation of energy, which will have no cutoff due to a short distance between points of production and observation. Secondly, if the knee and the ankle are results of particle interaction change, the behavior of energy spectrum above the ankle will be changed. Fig.3 illustrates the difference of existing model and proposed behavior of the energy spectrum. Curve 1 in the figure shows the cutoff for the case when the energy spectrum above the ankle is represented by the extragalactic component with the same slope (γ ~ 1.7). Curve 2 shows energy spectrum for the case of a single primary spectrum with constant γ = 1.7. Cutoff will have the same place in energy scale, but the famous "bump" appears. If cosmic rays from our Galaxy and other nearest galaxies give considerable part of primary particles at these energies cutoff appears at larger energy (curve 3). And at last
1016
1018 E (eV/nucleus)
1020
1022
Figure 3. Cutoff in various models of primary spectrum: 1 − with the knee and the ankle; 2, 3, 4 − without them (2 − uniform spectrum; 3 − spectrum from Galaxy; 4 − without cutoff). The choice between two approaches is very difficult but some ideas can be suggested. Firstly, it is necessary to confirm or to reject the change of interaction in PeV energy region. For that, investigation of VHE muons in EAS below and higher the knee is the best way. The absence of VHE muons in EAS below the knee and their appearance above the knee will be irrefutable proof of new physics existence. In the opposite case, it is necessary to wait for LHC results. Secondly, it is desirable to conduct EAS investigations in maximal wide intervals of energies. This will allow to match more correctly experimental data obtained for different energy intervals. And, at last, it is very important to measure energy-lateral distribution of HE muons in EAS with energies more than 1017 eV. These energies correspond to energies more than 14 TeV in the center-of-mass system and will not be
A.A. Petrukhin / Nuclear Physics B (Proc. Suppl.) 136 (2004) 218–223
investigated at accelerators in the visible future. Of course, the development of theoretical evaluations for description of EAS in the atmosphere for various suppositions about primary spectrum and interaction models is required. Let us mark one more interesting opportunity. If the idea of generation of cosmic rays in plasma pinches is correct and particles are accelerated in jets, then attempts of correlated EHE particle detection will be possible, f. e. by South and North parts of Pierre Auger Observatory. 5. CONCLUSIONS 1. It is impossible to solve finally the problem of the cutoff without solving the knee problem. The best and apparently the only way for solution of the knee problem is to search for VHE muons which are generated in primary cosmic ray particle interactions with energies above the knee. 2. In any case, at interpretation of results of cutoff investigations, especially with EAS arrays of new generation (f.e. South part of PAO), it is necessary to take into account the possibility of existence of primary spectrum with a constant slope. In future projects, such as North part of PAO in US, it is necessary to decrease the distance between surface defectors in order to have possibility of measurements of EAS with energies around the ankle. ACKNOWLEDGMENTS This work was partially supported by CRDF Award RP2-2557-MO-03. Many thanks to B.A.Trubnikov for numerous very fruitful discussions and to N.S.Barbashina,
R.P.Kokoulin and I.I.Yashin preparation of this paper.
223
for help in
REFERENCES 1. A.A.Petrukhin, Nucl. Phys. B (Proc Suppl.) 110 (2002) 484 and 122 (2003) 259. 2. A.A.Petrukhin, Proc. XIth Rencontres de Blois "Frontiers of Matter", Blois, 1999, ed. J. Tran Thanh Van, The Gioi Publishers, 401. 3. B.A.Trubnikov et al., Proc. Int. Conf. on Plasma Physics, New Delhi, 1, (1989) 257 and in the book "Hydrodynamics of Unstable Media", CRC Press (1996) 114. 4. S.A.Slavatinski, Nucl. Phys. B (Proc. Suppl.) 122 (2003) 3. 5. V.I.Yakovlev, Nucl. Phys. B (Proc. Suppl.) 122 (2003) 201 and 417. 6. V.A.Antonova et al., Nucl. Phys. B (Proc. Suppl.) 75A (1999) 333. 7. N.P.Il'ina et al., Proc. 24th ICRC , Roma, 1 (1995) 524. 8. O.G.Ryazhskaya, Nucl. Phys. B (Proc. Suppl.) 87 (2000) 423. 9. T.Matano et al., Proc. 9th ICCR, London, 2 (1965) 1045. 10. A.A.Petrukhin, Proc. Vulcano Workshop 2000 "Frontier Objects in Astrophysics and Particle Physics", eds. F.Giovannelli & G. Mannocchi, 375. 11. A.A.Petrukhin, Proc. Vulcano Workshop 2002 "Frontier Objects in Astrophysics and Particle Physics", eds. F.Giovannelli & G. Mannocchi, 527. 12. A.A.Petrukhin, Proc. Vulcano Workshop 2004 "Frontier Objects in Astrophysics and Particle Physics", eds. F.Giovannelli & G. Mannocchi (in press).