January 22, 2015. Protons (85 %) Nuclei (13%) Electrons/Positrons (2%) Galactic Origin α=2.7.

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!


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


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


Observational problem!

Our model: diffusion and spallation

B/C ratio

flat

steep


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


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)


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


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


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


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.

Thank you

very much!

January 22, 2015. Protons (85 %) Nuclei (13%) Electrons/Positrons (2%) Galactic Origin α=2.7.

Documents

Transcript of January 22, 2015. Protons (85 %) Nuclei (13%) Electrons/Positrons (2%) Galactic Origin α=2.7.