宇宙線エネルギースペクトルの解釈

1. 宇宙線エネルギースペクトルの解釈 柳田昭平　（茨城大学） 三宅晶子　（茨城大学） 村石浩　 （北里大学） 吉田龍生　（茨城大学）

2. Part 0 Introduction

3. Generation of the Observed Cosmic Rays C(E,A,Z)=D[M[P[A[I[S(E’,A’,Z’)]]]] Ø(E,A,Z)=M-1[D-1[C(E’,A,Z)]] R. E. Lingenfelter, 16th ICRC(1979)

4. Spectrometers (DA = 1 resolution, good E resolution) Air showers Calorimeters (less good resolution) Air-shower arrays on the ground to overcome low flux. Don’t see primaries directly. Direct measurements Knee Ankle

5. Spectral Energy Distribution (linear plot shows most E < 100 GeV) (4p/c) Ef(E) = local differential CR energy density Energetics of cosmic rays • Total local energy density: • (4p/c) ∫ Ef(E) dE ~ 10-12 erg/cm3 ~ B2 / 8p • Power needed: (4p/c) ∫ Ef(E) /tesc(E) dE galactic tesc ~ 107 E-0.6 yrs Power ~ 10-26 erg/cm3s • Supernova power: 1051 erg per SN ~3 SN per century in disk ~ 10-25 erg/cm3s • SN model of galactic CR Power spectrum from shock acceleration, propagation

6. Lessons from the heliosphere • ACE energetic particle fluences: • Smooth spectrum • composed of several distinct components: • Most shock accelerated • Many events with different shapes contribute at low energy (< 1 MeV) • Few events produce ~10 MeV • Knee ~ Emax of a few events • Ankle at transition from heliospheric to galactic cosmic rays R.A. Mewaldtet al., A.I.P. Conf. Proc. 598 (2001) 165

7. Part 1 Solar Modulation of the Galactic Cosmic Rays Revisit by a Relatively New Method

8. diffusion convection drift adiabatic energy loss : particle guiding center : particle momentum : Wiener process given by Gaussian distribution 1. Motivation Numerical simulation methods Parker’s transport equation(Parker 1965) : solar wind velocity : time : distribution function : gradient-curvature drift velocity : particle momentum : diffusion coefficient tensor SDE equivalent to Parker’s transport eq. (Yamada, Yanagita and Yoshida 1998; Zhang 1999)

9. Stochastic differential equation (SDE) • The SDE method is easy to solve. • The solution of the SDE backward in time provides information not available by other numerical methods. e.g. • distribution of energy loss and arrival time • trajectory of particles • distribution of entrance points of GCRs • (heliolatitude-longitude distribution) What’s new in the present work • steady and 3-D solar modulation problem • flat current sheet Zhang (1999) : ★We developed the time-dependent and 3-D code adapted for the wavy current sheet.

10. ⊙ 2. Model Relevant some parameters • boundary of the heliosphere : • solar wind velocity : • Magnetic field : Parker spiral • diffusion coefficient :

11. ⊙ ⊙ Model of the current sheet change of over the 11-year period : ⊙ ⊙ ⊙ (cf. Jokipii and Thomas 1981) radius of the sun constant

12. 3. Results - Sample trajectories - Distribution of exit point - 22-year modulation cycle - Energy spectrum

13. qA>0 (Positive) qA<0 (Negative) Sample trajectories Drift pattern of a sample particle Red : Positive polarity Blue : Negative polarity

14. Distribution of exit (entrance) point at the boundary Observer : northern the current sheet Observer : southern the current sheet

15. negative negative positive positive (http://neutronm.bartol.udel.edu/modplot.html) 22-year modulation cycle

16. negative negative positive positive Flat Sharp (http://neutronm.bartol.udel.edu/modplot.html) 22-year modulation cycle

17. Observation by BESS

18. Energy spectrum

19. Energy spectrum • existence of the random transverse component of the HMF at the polar regions • (Jokipii and Kota 1989) • fast polar solar wind The particles for Positive polarity will be more modulated.

20. Charge dependence (A>0, 30deg)

21. Charge dependence (A>0, 30deg)

22. 4. Summary • The results anticipated by the drift pattern are obtained for the sample trajectories and the distribution of exit (entrance) point at the heliospheric boundary. • Our simulation based on the SDE method reproduced a 22-year modulation cycle which is qualitatively consistent with observations. • Our model spectrum for qA < 0 agrees with BESS result, however it fails to reproduce the observed spectrum for qA > 0. • The modifications on the heliospheric structure at polar region are required.

23. Part 2 Galactic Modulation of Extragalactic Cosmic Rays Speculation of the Origin of the Knee

24. Simplified Stationary 1-dimensional Model Spectrum bends at Solar modulation Galactic modulation Rmax PCbend

25. 1. Introduction －CR spectrum, origin of CRs, etc.

26. CR all particle spectrum ∝E -2.7 knee ∝E -3 SNR origin [Differetial Flux (m-2 s-1 sr-1 (GeV/particle)-1) ]×E 2.5 unknown Total Energy E (eV/particle) 3×1015eV →Power law spectrum ～E -2.7 (<3×1015 eV) ～E -3.0 (3×1015ｰ 1018 eV) →Spectral break around 1015 eV (refered to as the ‘knee’)

27. SNR origin of CRs below 1015 eV General arguments (1) Energetics (2) Shock acceleration mechanism (3) Elemental and Isotopic Composition • SNRs have the necessary power and the Fermi shock acceleration mechanism provides the observed spectrum. Direct evidence (1) GeV CRs • Synchrotron radio emission from SNRs • π0 decay γ-rays from several SNRs by EGRET (Esposito et al. 1996) (2) TeV CRs • Synchrotron X-rays from several SNRs (SN1006, RXJ1713,…) (Koyama et al. 1995; Koyama et al. 1997, etc.) • TeV γ-rays from SNRs RX J1713.7-3946have been detected !! (Muraishi et al. 2000; Enomoto et al. 2002; Aharonian et al. 2004) ※CRs above the ‘knee’ is still unknown !

28. ※ Possibility of the Galactic modulation of extragalactic CRs ? Muraishi, Yanagita & Yoshida, Prog. Theor. Phys. 113 , pp.721-731(2005) Possible origin of CRs between 1015 and 1018 eV (1) Escape from the galaxy of more energetic particles (Peters 1960) (2) Z dependence of the maximum energy in shock acceleration (Drury 1983, Lagage & Cesarsky 1983) (3) Reacceleration of GCRs (Jokipii & Morfill 1985) (4) Change of the interaction models in EAS (Erlykin & Wolfendale 2000) (5)Necessity of anomalous (extragalactic) CRs ?? (Fichtel & Linsley 1986)

29. 2. Galactic modulation of extragalactic CRs －Motivation －Simulation method and Results

30. Motivation -Possible existence of V.H.E. CRs in IGS - ○ recent observational results from ICM • EUV and hard X-ray emissions from ICM (Ensslin et al. 1999) • Isotropic extragalactic γ-ray background (Loeb & Waxman 2000) →Existence of L.E. CR electron If nuclear components with energy up to 1018 eV also exist in the inter-galactic space including around our galaxy, these components modulated by the galactic wind should be directly observable !!! → We numerically examine such a possibility.

31. Schematic view of our model knee Intergalactic space ∝E-3 ∝E -3 [Differetial Flux (m-2 s-1 sr-1 (GeV/particle)-1) ]×E 2.5 Galactic sphere hypothetical extragalactic CRs Galactic wind Total Energy E (eV/particle) 3×1015eV Solar system r = 8.5 kpc G.C. Boundary R

32. ― Fokker-Plank Eq.(spherical symmetric case) ― (Parker 1965) radial distance time speed of the galactic wind distribution function particle momentum diffusion coefficient for radial propagation ― SDEs equivalent to F-P eq. ― (Yamada, Yanagita & Yoshida 1998) Wiener process given by a Gaussian distribution

33. ☆diffusion coefficient Bohm diffusion coefficient the ratio of diffusion mean free path to Larmor radius magnetic field in the galactic halo

34. Galactic modulated spectra of protons at Earth (r = 8.5 kpc) ・ radial distance of the galactic sphere: ∝E-3 (Zirakashvili et al. 1996) ・ speed of the galactic wind: (Zirakashvili et al. 1996) ・ magnetic field: → The spectrum breaks around the knee energy. → If eta increased by some factor, the break point is shifted to lower energy by the same factor.

35. Modulated spectra of various nuclear components ∝E-3 → The break point of the nuclear components is shifted to higher energy by a factor of Z compared with that for protons. (ex)η=1000

36. Break point in the modulated spectrum of the hypothetical extragalactic CRs ∝E-3 →The resultant modulated spectrum depends on five parameters, η, Z, R, V, and B. →If we difine the breaking energy Ebreak as the energy at which the modulated spectrum becomes maximal, then…

37. 3. A model of the all-particle spectrum near the knee region

38. ― A model of the all-particle spectrum expected all-particle spectrum modulated extragalactic component (←usingour result!) component originating in SNRs in our galaxy atomic number each nuclear components maximum energy attained by proton accelerated in SNRs spectral index of each nuclear components z →We fit fSNR with the results of various direct observation in TeV energy region.

39. Energy spectra obtained using direct measurements and the fitted curves (ex) Emax=500TeV → We define the sum of these components as the SNR component, FSNR .

40. ∝E -3 Single-component model for Fmodul(E ) proton (ex1) FModul(E) = fModul (E) proton → We can replace fModul with another nuclear component, fModul . Z Fe (ex2) FModul(E) = fModul (E) →Our model can reproduces the observed spectrum around the knee fairly well !

41. ∝E -3 proton He FModul = fModul + fModul + fModul + fModul + fModul NeMgSi CNO Fe Composite model for Fmodul(E ) (ex3) →we can also reproduce the spectrum using the model with a composite hypothetical CRs

43. (ex1) Single-component model forFmodul = fModul (ex2) Single-component model forFmodul = fModul proton Fe Expected mean mass of CRs around the knee region all Fe → (ex3) Composite model for He proton FModul = fModul + fModul + fModul + fModul + fModul ＜ln A＞ CNO Fe NeMgSi All proton → → Our model should be tested by future experiments in an energy range much higher than the knee.

45. 4. Discussion 　　－Energetics of hypothetical extragalacticCRs －Possible origin

46. hypothetical extragalactic CRs ∝E-3 ★Energetics of the hypothetical CRs Upper limit • If the hypothetical CRs pervade the intergalactic space uniformly and the spectrum extends down to their rest mass energy ( ), • Corresponding density parameter ( ～ ) (Burles et al. 2001) →CRs contribute to Dark Matter ?? →The spectrum becomes harder in the energy lower than the knee? →CRs are confined in local regions?

47. hypothetical extragalactic CRs ∝E-3 ∝E-2 1014.5 eV Lower limit • If the hypothetical CR spectrum becomes harder with the index of 2 in the energy range lower than 10^14.5 eV, … →much small !

48. ★Possible origin of hypothetical extragalactic CRs • Reacceleration of GCRs ? (Jokipii & Morfill 1985) • Early starburst in galaxy clusters? (Voelk & Atoyan 2000) • Cluster merger ? (Blasi 2001) • Shock acceleration in large-scale • structure formation ? More energetic ! (Miniati et al. 2000) In the future • TeV γ-ray observation from cluster merger →existence of shock accelerated extragalactic CRs →relation between extragalactic CRs and CRs above the knee

49. 5. Conclusion • All-particle spectrum of CRs around “the knee” • region is reproduced well by a superposition of • the two components, GCRs of SNR origion and, the extragalactic CRs modulated by the galactic wind. • The position of “the knee” may give us ideas on the • structure of the galactic sphere (its size, the speed of • the galactic wind, and etc.‥‥etc.) . • Future observations of CRs above the knee region • will tell us the chemical composition of the • extragalactic CRs. • Simulation experiments in more realistic setting • for galactic structure are needed.

50. Supplement