Non-linear acceleration at supernova remnant shocks and the - - PowerPoint PPT Presentation

Non-linear acceleration at supernova remnant shocks and the hardening in the cosmic ray spectrum

• S. Recchia
• S. Gabici

APC-Univerity Paris 7

Amsterdam-Paris-Stockholm 7th Meeting 11 October 2017 - 13 October 2017

• S. Recchia

CR spectral hardening APS 7th Meeting 1 / 10

Overview

Observed spectral hardening in the p and He spectra NLDSA revisited dispersion in the spectral slope of cosmic rays steeper spectra corresponding to larger acceleration efficiencies

• S. Recchia

CR spectral hardening APS 7th Meeting 2 / 10

Cosmic ray spectral hardening

...data

Proton and He spectra (and heavier) ∼ 200 − 300 GeV ∆γ ∼ 0.1 − 0.2 ATIC-2, PAMELA, CREAM, AMS-02

...possible explanations

break in the CR diffusion coefficient the effect of a nearby source NLDSA: concavity and reverse shocks distinct populations of CR sources

• S. Recchia

CR spectral hardening APS 7th Meeting 3 / 10

Cosmic ray acceleration

efficient magnetic field amplification detected in several SNRs necessary for acceleration of CRs to the knee

• bservation of γ-rays in SNRs

large dispersion in the slope of CRs in SNRs steep CR spectra ∝ E −2.1 − E −2.5 in contrast with standard predictions of NLDSA test particle DSA predicts ∝ E −2 CR pressure generate precursor in the upstream region concave spectra, hard (∝ E −1.5) above few GeV large acceleration efficiencies

• S. Recchia

CR spectral hardening APS 7th Meeting 4 / 10

NLDSA revisited

Caprioli (2012)

NLDSA + B amplification by CR streaming instability + B in the jump condition at the shock + velocity of Alfv` en waves (computed in amplified B)

...found

B amplification self-regulating mechanism maximum ξCR ≈ 30% compression factor close to 4 (test particle limit

• f DSA)

spectra close to power laws spectral slope ∼ 2.1 − 2.6 steeper spectrum at larger ξCR

• S. Recchia

CR spectral hardening APS 7th Meeting 5 / 10

NLDSA revisited: simple calculation

ξCR input parameter ∼ 0.03 − 0.3 small shock modification neglected (ξCR 30%) power law spectrum amplified B by CR streaming instability

compression factor R= u1/u2

M2

1

2

γ+1 R

− (γ − 1) 1 + ΛB ≈ 1

B amplification MA1 = u1/vA1

M2

A = 4

25

• 1 − (1 − ξCR)

5 4

2 (1 − ξCR)

3 4

compression factor + vA

Reff = u1 − vA1 u2 + R

• 1 −

1 MA

• ΛB = W
• 1 + R

2 γ − 1

• W = γ

2 M2

1

M2

A

• S. Recchia

CR spectral hardening APS 7th Meeting 6 / 10

Results: γ(ξCR)

γCR = 3Reff Reff − 1

3 3.2 3.4 3.6 3.8 4 10 20 30 40 50 60 70 80 90 100 Reff M1 ξ=0.1 ξ=0.2 ξ=0.3 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 0.05 0.1 0.15 0.2 0.25 0.3 ξCR M1=100 R Reff γCR

• S. Recchia

CR spectral hardening APS 7th Meeting 7 / 10

Results: comparison with data

diffusive propagation D(R) = D0(R/GV)δ + spallation for He spectral slope of accelerated particles depends on ξCR case with ξCR flat distributed in ∼ 0.03 − 0.3 case with two populations of sources with ξCR = 3% and 30%

• S. Recchia

CR spectral hardening APS 7th Meeting 8 / 10

Results: comparison with data

δ ∼ 0.4 D0 ∼ 8 × 1028cm2/s H ∼ 4 kpc grammage ∼ 10 − 12 g/cm2 at 10 GeV/n

104 102 103 104 105 Ek

2.7Flux(Ek)[(GeV/n)1.7/(s sr m2)]

Ek (GeV) proton flux AMS-02 PAMELA CREAM ξ uniformly distributed two populations 103 102 103 104 105 Ek

2.7Flux(Ek)[(GeV/n)1.7/(s sr m2)]

Ek (GeV/n) He flux AMS-02 PAMELA CREAM ξ uniformly distributed two populations

• S. Recchia

CR spectral hardening APS 7th Meeting 9 / 10

Conclusions

Revisited NLDSA dispersion in the CR acceleration efficiency and spectral slope steeper spectra correspond larger efficiencies CR spectra at the sources in agreement with γ−ray data in SNRs spectral hardening in the proton and helium spectrum can be naturally accounted for

• S. Recchia

CR spectral hardening APS 7th Meeting 10 / 10