On the CR spectrum releasedby a type II SNR expandingin the presupernova wind

Astroparticle Physics 201423-28 June 2014, Amsterdam

Martina Cardillo, Pasquale Blasi, Elena Amato INAF-Osservatorio Astrofisico di Arcetri

June 23, 2014

Index

• Expectations from Bell non-resonant instability: Why do we need it? Maximum energy

• Conclusions

• Description of our toy-model: Spectrum Energetics Comparison with KASKADE-GRANDE data Comparison with ARGO data

Non-resonant Bell Instability

RESONANTINSTABILITY

(Skilling 1975)

NONRESONANTINSTABILITY(Bell 2004)

Excitation of Alfvén waves with λ ≅ rL

Purely growing waves at wavelengths non-resonant with rL (λ << rL), driven by the CR current jCR.

Growth rate dependence on the shock velocity (α vs2) and on

plasma density (α n⅙)

Very YoungSNRs

Non-resonant Bell instability: E-max

ISM

WIND

ρ = cost

ρ α R-2

• Independent from the B field strength• Proportional to CR efficiency (ξCR)• Strong dependence on shock velocity

EDphase

Spectrum of escaping particlesAcceleration

spectrum

STARTING POINT

WIND

ρej α R-k k=[7,9]

p=[3,4] No sharp cut-off

above EM!

Caprioli et al. 2010,Schure&Bell 2013

Observed spectrumObserved Spectrum

Diffusion Spallation

Fixed Variables

Mej= 1 M

dM/dt= 10-5 M/yrs

Vw= 10 km/sRd= 10 kpc

H= 3 kpc

D0= 3 x 1028 cm2 s-1

δ= 0.65

nd= 1 cm-3 kpc

σsp= α(E) Αβ(E)

ESN= Supernova energyR = Explosion rate

EM t0 V0

ξCR

Standard energetics: k=7

ESN= 1051 ergR= 1/30 yrs

EM= 6.6 x 1014 eVξCR= 12%

t0= 96 yrsv0=10.445 km/s

Standard energetics: k=8

ESN= 1051 ergR= 1/30 yrs

EM= 6.4 x 1014 eVξCR= 10 %

t0= 88 yrsv0=11.339 km/s

Standard energetics: k=9

ESN= 1051 ergR= 1/30 yrs

EM= 6.3 x 1014 eVξCR= 8.5 %

t0= 84.5 yrsv0=11.830 km/s

Time problem

~3x1015 ~2x1012

• τdyn> τpp≅ 103 s

• τdyn> τIC ≅ 106 s

• τdyn> τph ≅ 109 s

KASKADE Grande (Apel,2013)

k=9ESN= 1052 ergR= 1/950 yrs

EM ≅ 9.4 x 1015 eVξCR ≅ 13 %

t0 ≅ 27 yrsv0 ≅37.500 km/s

EM ≅ 9.4 x 1015 eVξCR ≅ 13 %

t0 ≅ 27 yrsv0 ≅37.500 km/s

k=9ESN= 1052 ergR= 1/950 yrs

KASKADE Grande + ARGO (Di Sciascio, 2014)

ARGO

EM ≅ 6.3 x 1014 eVξCR ≅ 8.5 %

t0 ≅ 84 yrsv0 ≅11.800 km/s

k=9ESN= 1051 ergR= 1/30 yrs

k=9ESN= 4 x 1051 ergR= 1/60 yrs

EM ≅ 1.2 x 1015 eVξCR ≅ 4.5 %

t0 ≅ 42 yrsv0 ≅23.700 km/s

Uncertainty on the data?

Additional component?

ARGO (Di Sciascio, 2014)

Conclusions

Our toy-model shows that the NRI leads to the release of a steep power-law spectrum in the ejecta dominated phase

KASKADE Grande data can be fitted only by requiring a challengingly large energetics of a SNR

Our model can fit ARGO data of the light component but a fit to the overall spectrum requires the existence of another population of very energetic particles in addition to the SNR one.

The “knee” provided by our model is at E < 3x1015 eV for standard energetics

Bell non-resonant instability (NRI) predicts that very energetic SNRs can reach PeV energies

Thank you

very much!