1. Cosmic-ray helium hardening 1. Galactic cosmic ray 3. Cosmic-ray helium hardening 4. Summary Contents Yutaka Ohira and Kunihito Ioka High energy accelerator organization (KEK) 2. Escape of cosmic ray Ref: Ohira, Y. and Ioka, K., 2011, ApJL, 729, L13

2. Galactic cosmic ray E knee =10 15.5 eV (1particle /m 2 /yr) Gaisser 2006 SNRs are though to be the origin of the Galactic CR. N(E) ∝ E -2.7 (E<10 15.5 eV) Considering the propagation effect Q sour ∝ E -2.1-2.4 Observed Galactic CR spectrum DSA model Q ∝ E -2 What Type? Isolated or in superbubbles? Inconsistent ?

3. Recent CR Observations The spectrum of CR He is harder than that of CR p. All CR spectra becomes hard at around 200 GeV/n. Ahn et al. ApJL, 2010, 714, L89 CREAM, ATIC-2, PAMELA Ahn et al. ApJL, 2010, 714, L89

4. Escape of Cosmic Rays Free expansion phase ( t < 200yr ): age limited E knee E max t Sedov t E m,esc is obtained from t esc = t acc Sedov phase ( t < 10 5 yr ) : escape limited E max = E knee ( t / t Sedov ) E m,esc decreases with time SNR R diff ∝ (Dt age ) 1/2 R sh = R Sedov × (t age / t Sedov ) ( t age < t Sedov ) (t age / t Sedov ) 2/5 ( t age > t Sedov ) t acc ~ D u sh 2, t esc ~ D R sh 2, D =  g cE 3eB (B should be amplified) E max ∝ = E knee (t / t Sedov ) -  B(t)t -1/5 g(t)g(t)

5. Spectrum of runaway CRs dN/dE E E max ∝ t -α N ∝ t β E -s esc Runaway CR spectrum f esc (E) Maximum energy E max ∝ t -α, α > 0 CR number N(E=mc 2 ) ∝ t β, β 0 > f esc ∝ E -s esc s esc = s + α β s ≠ s esc f esc (E) dE = f SNR dt dE max dt Total CR spectrum in the SNR f SNR ∝ t β E -s Y. Ohira, K. Murase, R. Yamazaki, 2010, A&A, 513, A17 E -s (Ptuskin&Zirakashvili(2005), Ohira&Ioka(2011), Caprioli et al.(2010), Drury(2011)) escape

6. Application to the CR He hardening Δs = 0.08 means that He/p at 10 14 eV is about 3 times higher than that at 10 9 eV. However, the mean He abundance in the universe is constant after the BBN. We should consider the inhomogeneous abundance region. For example, superbubbles. Many SNe explode in superbubbles. Ejecta dominates around the center of superbubles. Higdon et al.(1998) He/p is larger than that of the solar value.

7. Schismatic picture For simplicity, n p = const n He ∝ r -δ

8. Spectral hardening at 200 GeV/n Spectral index At least one of s, α, and β has a time dependence or γ has an energy dependence or the source of CR is two components. Recent CREAM observations show that spectra of all CR composition become hard at 200 GeV/n Here, we consider the time (energy) dependence of s Sedov solution Galactic diffusion D∝pD∝p  tot (R sh )=m p (n p (R sh )+4n He (R sh ))

9. Comparison of our model and CR obs. Ohira, Y. & Ioka, K., 2011, ApJL T = 10 6 K He p n p = const. Hardening at around 200GeV Φ = 450MV n He ∝ r -0.715 D ∝ p 0.43 T = 10 6 K CR He hardening  Superbubble! N CR,i ∝ n i E max ∝ ZR sh -6.5

10. Summary f esc ∝ E -s esc s esc = s + α β f SNR ∝ t β E -s, E max ∝ t -α Considering the inhomogeneous abundance region, the spectrum of runway CR He becomes harder than that of CR p. Considering the Mach number evolution with 10 6 K, runaway CR spectra of all CRs become hard at 200 GeV/n. the spectrum of CR He is harder than that of CR p, The runaway CR spectrum is different from that in the accelerator. Recently, CREAM shows that and all CR spectra become hard at round 200 GeV/n. CR Observations suggest the CR origin is SNRs in superbubbles.  He <  p 

11. Evolution of the maximum energy （ E max ∝ R sh -α ） E max = E knee at t = t Sedov (R sh = R Sedov ) E max = m p c 2 at t = 10 2.5 t Sedov (R sh = 10R Sedov ) E max = E knee R sh R Sedov -6.5 α = 6.5 So, we phenomenologically assume 300 radio SNRs have been observed in a part of our galaxy. SN rate ~ 0.03 / yr 300×5 = 1500 radio SNRs in our galaxy Life time×SN rate = 1500 (Case & Bhattacharya, 1998, ApJ)  Life time ~ 5×10 4 yr ~ 10 2.5 t Sedov (t Sedov ~200yr)

12. Thermal leakage injection p max = Zp knee R sh R Sedov -α Z : charge ρ tot (R sh ) = m p ( n p (R sh ) + 4n He (R sh ) ) u sh ∝ ρ(R sh ) -1/2 R sh -3/2 p inj ∝ u sh p inj,i 3 f i (p inj ) ∝ n i (R sh )f i (p) ∝ p -(s+2) F SNR,i (R sh, m p c) ∝ R sh 3 f i (m p c) ∝ R sh 3 p inj s+2 f i (p inj ) ∝ R sh 3 n i (R sh ) p inj s-1 ∝ n i (R sh )  tot (R sh ) (1-s)/2 R sh 3(3-s)/2

13. Superbubble ~700pc ~30pc R sh (t end )~200pc R sh (t Sedov ) Superbubble size ~ 700pc Star cluster size ~ 30pc SNR size at t Sedov ~ 20pc SNR size at t end ~ 200pc SN ejecta dominate within 1/3 of 700pc ~ 230pc Higdon et al. (1998) ISM Weaver et al.(1997)

14. Spectrum of our model p max = Zp knee R sh R Sedov -α-α n p (R sh ) = n p,0, n He (R sh ) = 10 -1+6.5δ/α n p,0 R sh R Sedov -δ-δ D ∝ p γ T ε Ohira, Y. & Ioka, K., 2011, ApJL

15. Mach number T = 10 6 K