spectrum released by a type II SNR e xpanding in the presupernova wind Astroparticle Physics 2014 2328 June 2014 Amsterdam Martina Cardillo Pasquale Blasi ID: 236613
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Slide1
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, 2014Slide2
Index Expectations from Bell non-resonant instability:Why do we need it?Maximum energy Conclusions Description of our toy-model:SpectrumEnergeticsComparison with KASKADE-GRANDE dataComparison with ARGO dataSlide3
Non-resonant Bell InstabilityRESONANTINSTABILITY(Skilling 1975)NONRESONANTINSTABILITY(Bell 2004)Excitation of Alfvén waves with λ ≅ rLPurely 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 YoungSNRsSlide4
Non-resonant Bell instability: E-maxISMWINDρ = costρ α R-2
Independent from the B field strength Proportional to CR efficiency (ξCR) Strong dependence on shock velocity
EDphaseSlide5
Spectrum of escaping particlesAcceleration spectrumSTARTING POINTWINDρej α R-kk=[7,9]
p
=[3,4]
No sharp cut-off
above E
M
!
Caprioli
et al. 2010,
Schure&Bell
2013Slide6
Observed spectrumObserved SpectrumDiffusionSpallationFixedVariablesMej= 1 MdM/dt= 10-5 M/yrsVw= 10 km/sRd= 10 kpcH= 3 kpcD0= 3 x 1028 cm2 s-1
δ= 0.65nd= 1 cm-3 kpcσsp= α(E) Αβ(E)ESN= Supernova energy
R = Explosion rateEM
t
0
V
0
ξ
CRSlide7
Standard energetics: k=7ESN= 1051 ergR= 1/30 yrsEM= 6.6 x 1014 eVξCR= 12%t0= 96 yrsv0=10.445 km/sSlide8
Standard energetics: k=8ESN= 1051 ergR= 1/30 yrsEM= 6.4 x 1014 eVξCR= 10 %t0= 88 yrsv0=11.339 km/sSlide9
Standard energetics: k=9ESN= 1051 ergR= 1/30 yrsEM= 6.3 x 1014 eVξCR= 8.5 %t0= 84.5 yrsv0=11.830 km/sSlide10
Time problem~3x1015~2x1012τdyn> τpp≅ 103 sτdyn> τIC ≅ 106 sτdyn> τph ≅ 109 sSlide11
KASKADE Grande (Apel,2013)k=9ESN= 1052 ergR= 1/950 yrsEM ≅ 9.4 x 1015 eVξCR ≅ 13 %t0 ≅ 27 yrsv0 ≅37.500 km/sSlide12
EM ≅ 9.4 x 1015 eVξCR ≅ 13 %t0 ≅ 27 yrsv0 ≅37.500 km/sk=9ESN= 1052 ergR= 1/950 yrsKASKADE Grande + ARGO (Di Sciascio, 2014) Slide13
ARGO EM ≅ 6.3 x 1014 eVξCR ≅ 8.5 %t0 ≅ 84 yrsv0 ≅11.800 km/sk=9ESN= 1051 ergR= 1/30 yrsSlide14
k=9ESN= 4 x 1051 ergR= 1/60 yrsEM ≅ 1.2 x 1015 eVξCR ≅ 4.5 %t0 ≅ 42 yrsv0 ≅23.700 km/sUncertainty on the data?Additional component?ARGO (Di Sciascio, 2014) Slide15
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 energiesSlide16
Thank youvery much!