On the CR spectrumreleased by a type II SNR
expandingin the presupernova wind
SUGAR 2015, GenevaJanuary 21-23
Martina Cardillo, Elena Amato, Pasquale Blasi INAF-Osservatorio Astrofisico di Arcetri
January 22, 2015
Knee energyproblem
Non-resonantinstability Type II SNae
Spectrum(from ED toST phase)
Maximum energy
KASCADE-Grande
&ARGO
Magnetic field amplification
RESONANTINSTABILITY
(Skilling 1975)
NONRESONANTINSTABILITY(Bell 2004)
Excitation of Alfvén waves with λ ≅ rL
saturation at δB/B ≅ 1 EM< 1 PeV
Purely growing waves at wavelengths λ << rL, driven by the CR current jCR generation of power at larger spatial scales up to λ ≅ rL larger EM
General case: Estimation of the maximum energy
Current at distance R
Balance
Growth Rate
e-folding
Maximum EnergyCardillo, Amato & Blasi 2015
SourceSpectrum
General case: Estimation of the escaping spectrum
Escape Spectrum
Shock Radius
Shock Velocity CR Current
Cardillo, Amato & Blasi 2015
Type Im=0, k=7
No sharp
cut-off
above E M!
Cardillo, Amato & Blasi 2015
Type IIm=2, k=9
General case: Estimation of the escaping spectrum
Ejecta density
Medium density
Shock radius
k=[7,10]
Our model: SNR parameters
Cardillo, Amato & Blasi 2015
Ejecta Mass
ISM density
Wind density
ST radius
Ejecta density
ST time
Shock radius
Shock velocity
ISM
WIND
• Type II SNR provide higher maximum energy • Proportional to CR efficiency (ξCR)• Strong dependence on shock velocity
EDphase
Our model: maximum energy
Cardillo, Amato & Blasi 2015
Observational problem!
Our model: diffusion and spallation
B/C ratio
flat
steep
Cardillo, Amato & Blasi 2015
Diffusion
Spallation
(Ptuskin 2009)
Cross Section(Horandel 2007)
Grammage
Our model: Observed spectrum
Diffusion SpallationAssumption
sVariablesMej= 1 M
dM/dt= 10-5 M/yrs
Vw= 10 km/sRd= 10 kpc
X(E)=k(Rg/ 3GV)-δ
δ= 2.65 - pinj
nd= 1 cm-3
σsp= α(E) Αβ(E)
ESN= Supernova energyR = Explosion rate
EM t0 V0
ξCR
Escape
Cardillo, Amato & Blasi 2015
From TRACERand CREAM
Our model: SN energy behavior
flat
steep
EM= 1 PeV Ra= 1/30 yrs ξCR= 11% (for standard Esn=1051 erg)
EM= 1 PeV Ra= 1/800 yrs ξCR= 240% (!!) (for standard Esn=1051 erg)
Cardillo, Amato & Blasi 2015
EM > 1 PeV
EM > 1 PeV
Our model: Standard energetics
ESN= 1051 ergR= 1/30 yrs
EM= 1 PeVξCR= 11%
t0= 85 yrsv0=15.700 km/s
Cardillo, Amato & Blasi 2015
k=9ESN= 2 x 1051 ergR= 1/110 yrs
EM ≅ 3.7 x 1015 eVξCR ≅ 20 %t0 ≅ 60 yrsv0 ≅22.200 km/s
Model and data
Cardillo, Amato & Blasi 2015
k=9ESN= 1051 ergR= 1/15 yrs
EM ≅ 507 TeVξCR ≅ 5.2 %t0 ≅ 85 yrsv0 ≅15.700 km/s
KASCADE Grande (Apel 2013)
ARGO(Di Sciascio 2014)
k=9ESN= 2 x 1051 ergR= 1/110 yrs
EM ≅ 3.7 x 1015 eVξCR ≅ 20 %t0 ≅ 60 yrsv0 ≅22.200 km/s
Model and data
Cardillo, Amato & Blasi 2015
k=9ESN= 1051 ergR= 1/15 yrs
EM ≅ 507 TeVξCR ≅ 5.2 %t0 ≅ 85 yrsv0 ≅15.700 km/s
ARGO(Di Sciascio 2014)
Uncertainty on the data?
Additional component?
KASCADE Grande (Apel 2013)
Conclusions
NHR instability leads to the release of a steep power-law spectrum in the ejecta dominated phase no sharp cut-off!
KASCADE Grande and ARGO data can be fitted with reasonable values of SN parameters.
No model that can fit both ARGO and KASCADE-Grande data need a better data understanding with a consequent theory improvement.
Type II SNRs can accelerate particles up to the knee at very early time detection problem.
Bell non-resonant instability predicts that very energetic SNRs can reach PeV energies.
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