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!