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）

Part 0 Introduction

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)

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

Energetics of cosmic rays Total local energy density: –(4p/c) ∫ Ef(E) dE ~ erg/cm 3 ~ B 2 / 8p Power needed: (4p/c) ∫ Ef(E) / t esc (E) dE galactic t esc ~ 10 7 E -0.6 yrs Power ~ erg/cm 3 s Supernova power: erg per SN ~3 SN per century in disk ~ erg/cm 3 s SN model of galactic CR Power spectrum from shock acceleration, propagation Spectral Energy Distribution (linear plot shows most E < 100 GeV) (4p/c) Ef(E) = local differential CR energy density

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. Mewaldt et al., A.I.P. Conf. Proc. 598 (2001) 165

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

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

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

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

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

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

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

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

22-year modulation cycle ( positive negative positivenegative

22-year modulation cycle Flat Shar p ( positive negative positivenegative

Observation by BESS

Energy spectrum

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

Charge dependence (A>0, 30deg)

Charge dependence (A>0, 30deg)

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. The modifications on the heliospheric structure at polar region are required.

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

Simplified Stationary 1-dimensional Model Spectrum bends at Solar modulationGalactic modulation R max PC bend

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

→Power law spectrum ～ E -2.7 (<3×10 15 eV) ～ E -3.0 (3×10 15 ｰ eV) →Spectral break around eV (refered to as the ‘knee’) CR all particle spectrum ∝ E -2.7 ∝ E -3 3×10 15 eV SNR origin unknown knee Total Energy E (eV/particle) [Differetial Flux (m -2 s -1 sr -1 (GeV/particle) -1 ) ]×E 2.5

→SNRs have the necessary power and the Fermi shock acceleration mechanism provides the observed spectrum. ※ CRs above the ‘knee’ is still unknown ! SNR origin of CRs below eV (1) Energetics (2) Shock acceleration mechanism (3) Elemental and Isotopic Composition (Muraishi et al. 2000; Enomoto et al. 2002; Aharonian et al. 2004) Synchrotron radio emission from SNRs π 0 decay γ-rays from several SNRs by EGRET Synchrotron X-rays from several SNRs (SN1006, RXJ1713,…) (Esposito et al. 1996) (Koyama et al. 1995; Koyama et al. 1997, etc.) (1) GeV CRs (2) TeV CRs General arguments Direct evidence TeV γ-rays from SNRs RX J have been detected !!

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

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

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

Total Energy E (eV/particle) ∝ E -3 3×10 15 eV knee [Differetial Flux (m -2 s -1 sr -1 (GeV/particle) -1 ) ]×E 2.5 hypothetical extragalactic CRs ∝ E -3 Intergalactic space Galactic sphere Boundary R G.C. Galactic wind Solar system r = 8.5 kpc Schematic view of our model

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

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

∝ E -3 ・ magnetic field: ・ radial distance of the galactic sphere: ・ speed of the galactic wind: Galactic modulated spectra of protons at Earth (r = 8.5 kpc) (Zirakashvili et al. 1996) → 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. (Zirakashvili et al. 1996)

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

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

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

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

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

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

∝ E -3 Composite model for F modul (E ) (ex3) F Modul = f Modul + f Modul + f Modul + f Modul + f Modul Fe protonHe CNO NeMgSi →we can also reproduce the spectrum using the model with a composite hypothetical CRs

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

4. Discussion － Energetics of hypothetical extragalactic CRs － Possible origin

If the hypothetical CRs pervade the intergalactic space uniformly and the spectrum extends down to their rest mass energy ( ), ( ～ ) Corresponding density parameter Upper limit (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? ★ Energetics of the hypothetical CRs hypothetical extragalactic CRs ∝ E -3

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

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

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. 5. Conclusion All-particle spectrum of CRs around “the knee” region is reproduced well by a superposition of the two components,

Supplement

High speed solar wind

Forward in time heliolatitude radial distance 80 AU particle energy ~ 3 GeV ▪ The tilt angle near the sun is ~. ▪ The solar activity strengthening. Entrance point :

Explanation for High Energy Cosmic Ray Data: Inject -2.2 spectrum (relativistic shock acceleration); spectral modiffications due to CR scattering on the MHD turbulence Knee in CR spectrum: results from the knee in the spectrum of MHD turbulence in the Galaxy, rigidity dependece of the knee due to interaction with the same spectrum of turbulence. “Second knee”: results from the decline of turbulence with wavelengths >100 pc transition between galactic and extragalactic components occurs between the second knee and ankle. Transition to CRs from Galactic SNR occurs at ~100 TeV (or lower) Fits imply large baryon load: f b ~ Predict detectable neutrino flux from strong GRBs