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 ...possible explanations ...data break in the CR diffusion Proton and He spectra (and coefficient heavier) the effect of a nearby source ∼ 200 − 300 GeV NLDSA: concavity and ∆ γ ∼ 0 . 1 − 0 . 2 reverse shocks ATIC-2, PAMELA, CREAM, distinct populations of CR AMS-02 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 observation 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 ...found B amplification self-regulating Caprioli (2012) mechanism NLDSA maximum ξ CR ≈ 30% + B amplification by CR compression factor close streaming instability to 4 (test particle limit + B in the jump of DSA) condition at the shock spectra close to power + velocity of Alfv` en laws waves (computed in spectral slope amplified B) ∼ 2 . 1 − 2 . 6 steeper spectrum at larger ξ CR S. Recchia CR spectral hardening APS 7th Meeting 5 / 10
NLDSA revisited: simple calculation ξ CR input parameter ∼ 0 . 03 − 0 . 3 small shock modification neglected ( ξ CR � 30%) power law spectrum amplified B by CR streaming instability compression factor + v A compression factor R= u 1 / u 2 γ +1 M 2 − ( γ − 1) R eff = u 1 − v A 1 � 1 � 1 R ≈ 1 + R 1 − 2 1 + Λ B u 2 M A B amplification M A 1 = u 1 / v A 1 � 2 � �� Λ B = W 1 + R γ − 1 � 2 � 5 1 − (1 − ξ CR ) 4 A = 4 M 2 M 2 3 W = γ 25 (1 − ξ CR ) 1 4 M 2 2 A S. Recchia CR spectral hardening APS 7th Meeting 6 / 10
Results: γ ( ξ CR ) 3 R eff γ CR = R eff − 1 4 M 1 =100 ξ =0.1 4.6 ξ =0.2 ξ =0.3 3.8 4.4 4.2 3.6 4 R eff 3.4 3.8 3.6 3.2 3.4 R 3.2 R eff 3 γ CR 3 10 20 30 40 50 60 70 80 90 100 0.05 0.1 0.15 0.2 0.25 0.3 M 1 ξ CR S. Recchia CR spectral hardening APS 7th Meeting 7 / 10
Results: comparison with data diffusive propagation D ( R ) = D 0 ( R / GV ) δ + spallation for He spectral slope of accelerated particles depends on ξ CR case with ξ CR flat distributed in ∼ 0 . 03 − 0 . 3 case with two populations of sources with ξ CR = 3% and 30% S. Recchia CR spectral hardening APS 7th Meeting 8 / 10
Results: comparison with data D 0 ∼ 8 × 10 28 cm 2 / s δ ∼ 0 . 4 grammage ∼ 10 − 12 g / cm 2 at 10 GeV/n H ∼ 4 kpc AMS-02 AMS-02 proton flux PAMELA PAMELA He flux 2.7 Flux(E k )[(GeV/n) 1.7 /(s sr m 2 )] 2.7 Flux(E k )[(GeV/n) 1.7 /(s sr m 2 )] CREAM CREAM ξ uniformly distributed ξ uniformly distributed two populations two populations 10 3 10 4 E k E k 10 2 10 3 10 4 10 5 10 2 10 3 10 4 10 5 E k (GeV) E k (GeV/n) 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
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