NONLINEAR COSMIC RAY TRANSPORT Elena Amato INAFOsservatorio Astrofisico

NON-LINEAR COSMIC RAY TRANSPORT Elena Amato INAF-Osservatorio Astrofisico di Arcetri

OUTLINE • RECENT FINDINGS BY PAMELA AND AMS-02: • BREAKS IN THE SPECTRA OF PRIMARIES • UNEXPECTED BEHAVIOR OF SECONDARIES • SUMMARY OF STANDARD PREDICTIONS • EXPLANATION OF BREAKS BASED ON CR NONLINEAR DIFFUSION • CONSEQUENCES ON CR INJECTION SPECTRA • CR SELF-CONFINEMENT CLOSE TO THE SOURCES • POSITRONS 2

THE COSMIC RAY SPECTRUM N(E) E- =2. 7 10<E Ge. V<3 106 =3. 1 E Ge. V >3 106 Ø 98% OF PARTICLES ARE PROTONS AND NUCLEI • 87% PROTONS • 12% He • 1% HEAVIER NUCLEI Ø 2% ARE ELECTRONS Ø ABOUT 10 -3 ARE ANTIMATTER PARTICLES (POSITRONS AND ANTI-PROTONS) FOR A LONG TIME ONLY KNEE AND ANKLE THE GALACTIC COMPONENT USED TO HAVE A FEATURELESS SPECTRUM 3

SPECTRAL BREAKS Adriani et al 11 NOW MORE BREAKS Ahn et al 10

AMS 02 CONFIRMS Aguilar et al 15

ODDITIES OF ANTIMATTER

ANTIMATTER VS SECONDARY NUCLEI Aguilar et al 16 B/C IS WELL BEHAVED: DECREASES WITH ENERGY anti-p/p DOES NOT Aguilar et al 16 NOR DOES e+/p

THE STANDARD PICTURE H INDEP. OF E PROPAGATION INJECTION STEADY STATE LEAKY BOX MODEL PROTON SPECTRUM BREAKS MIGHT BE TELLING US ABOUT INJECTION OR DIFFUSION…. 8

SECONDARIES VS PRIMARIES: EXPECTATION SPECTRUM OF PRIMARIES SPECTRUM OF STABLE SECONDARIES ANALOGOUSLY AND WITH EXTRA ASSUMPTION THAT ELECTRONS’ γINJ SAME AS PROTONS 9

BREAKS FIRST BREAK AT E ≈200 -300 Ge. V PAMELA (Adriani et al 10) AMS 02 (Aguilar et al 15) AMS 02 (Aguilar et 15) THAT LOW ENERGY CRs COULD SELF-GENERATE THE TURBULENCE FOR THEIR SCATTERING IS AN OLD SUGGESTION (e. g. Wentzel 74) 10

INTERACTION OF A COSMIC RAY WITH AN ALFVÉN WAVE INTERACTION MOST EFFECTIVE AT RESONANCE: ∼r. L 11

PARTICLE DIFFUSION AND WAVE GROWTH IF CR ARE ISOTROPIZED BY THE WAVES… BEFORE SCATTERING: PCR=n. CRm CRvd AFTER SCATTERING: PCR=n. CRm CRv. A FOR RESONANT ALFVÉN WAVES MOMENTUM HAS GONE TO THE WAVES with SUPERALFVÉNIC STREAMING OF CRs WAVE GROWTH UP TO WHAT SCALE/ENERGY SELF-GENERATED WAVES ARE DOMINANT? 12

A SIMPLE ESTIMATE TRANSITION BETWEEN DIFFERENT DIFFUSION REGIMES OCCURS AT SCALE WHERE EXTERNAL TURBULENCE (SNE WITH LC ≈100 pc? ) EQUALS IN ENERGY DENSITY THE SELF-GENERATED TURBULENCE ASSUMPTIONS: • QUASI-LINEAR THEORY APPLIES • THE EXTERNAL TURBULENCE HAS A KOLMOGOROV SPECTRUM • MAIN SOURCE OF DAMPING IS NON-LINEAR DAMPING • DIFFUSION IN EXTERNAL TURBULENCE EXPLAINS MEASURED HIGH ENERGY FLUX WITH SNRs INJECTING CRs WITH 10% EFFICIENCY THE RESULT IS Blasi, EA, Serpico 12 13

BREAK FROM SELF-GENERATED TURBULENCE Blasi, EA, Serpico, 12 14

TAKING ALL INTO ACCOUNT. . Aloisio+ 15 IMPLICATION: AT TEV ENERGIES CRs ARE INJECTED IN THE GALAXY WITH A E-2. 3/2. 4 SPECTRUM ü OK WITH AMS-02 B/C ü GOOD FOR ANISOTROPY (e. g. Blasi&EA 12) X BAD FOR MAX. EN. IN SNRs 15

CRs FROM DISCRETE SOURCES N(E) E-( inj+ e) inj=2. 34 (Blasi & EA, 12) e=1/3 inj+ e=2. 67 D(E) E e CONTRIBUTION FROM EXTRAGALACTIC CRs inj=2. 07 e=0. 6 inj+ e=2. 67 16

DIFFUSION AND ANISOTROPY inj=2. 07 e=0. 6 inj+ e=2. 67 e=2. 34 inj=2. 34 e=1/3 inj+ e=2. 67 §ANISITROPY IS TOO LARGE FOR =0. 6 (Blasi & EA 12 b, Ptuskin et al 07, Sveshnikova et al 13, Pohl & Eichler 13) 17 §FOR =1/3 CONFIGURATIONS THAT RESEMBLE THE DATA CAN BE FOUND

DIFFUSION COEFFICIENT AT HIGH ENERGY ASIDE FROM THEORETICAL CONSIDERATIONS Aguilar et al 16 AMS 02 DATA POINT TO δe～ 0. 4 -0. 5 A PROBLEM FOR ACCELERATION UP TO THE KNEE…. (Schure & Bell 13, Cardillo, EA, Blasi 15) AGAIN STEEP INJECTION SPECTRA ARE SUGGESTED 18

MAXIMUM ENERGY IN SNRs • MFA (Bell 04) DUE TO CURRENT OF ESCAPING PARTICLES • GROWTH RATE PROPTO JCR WHICH DEPENDS ON SPECTRUM AT THE SHOCK, PMAX AND VS (Schure & Bell 13, Cardillo, EA, Blasi 15) SELF-REGULATION MECHANISM LITTLE TURBULENCE LARGE ESCAPE FRACTION LARGE CURRENT DECREASES EFFICIENT ACCELERATION TURBULENCE INCREASES 19

PEVATRONS TYPE II Cardillo, EA, Blasi 15 ESN=1051 erg/s ξCR=0. 1 v. WIND=10 km/s Mej=MSUN MLOSS=10 -5 MSUN/yr RELEASED SPECTRUM ΓCR >2 IF ΓSRC >2 ΓCR =2 IF ΓSRC ≤ 2 STEEP SPECTRA AND EFFICIENT PARTICLE ACCELERATION? ?

IN NLDSA THEORY… Caprioli 11 STEEP SPECTRA DUE TO AMPLIFIED FIELDS (Ptuskin & Zirakashvili 08) Morlino & Caprioli 11 TYCHO ALSO NEUTRALS MIGHT PRODUCE SOME STEEPENING (Morlino+, 12, 13, 14) 21

MAXIMUM ENERGY AND SOURCE SPECTRUM E-2 WITH ΓCR >2, Pmax=Pe. V REQUIRES: • RARE (<1/1000 yr-1) • EXTREME EVENTS (ESN>1052 erg) • EXTREME EFFICIENCY (ξCR>30%) E-2. 3

BUT WHERE IS THE KNEE? KASCADE-Grande Data: Apel + 13 ξCR ≈15% EMAX ≈4 Pe. V R≈1/100 yr-1 ESN ≈2 x 1051 ξCR ≈5. 2% EMAX ≈500 Te. V R≈1/15 yr-1 ESN ≈1051 SOME INCONSISTENCY IN THE DATA? • THE ALL PARTICLE SPECTRUM IS THE SAME • BUT THE PROTON SPECTRUM CUTS OFF AT 10 TIMES LOWER ENERGY ARGO Data: Di Sciascio + 13, De Mitri + 14

ANTIMATTER VS SECONDARY NUCLEI Aguilar et al 16 B/C IS WELL BEHAVED: DECREASES WITH ENERGY anti-p/p DOES NOT Aguilar et al 16 NOR DOES e+/p

ANTI-PROTONS Aloisio + in prep. • FLAT DIFFUSION COEFFICIENT • FLATTENING OF THE PARENT P PRODUCTION CROSSSECTION: INCREASES WITH ENERGY AND LARGE UNCERTAINTIE S(Di Mauro+ 16) NOT A REAL ISSUE

ALTERNATIVE SCENARIOS DECOUPLING B PRODUCTION FROM THE REST (Blum et al 10; Katz et al 13; Cowsik & Burch 10; Cowsik et 1 l 14; Lipari 16) • CR ESCAPE FROM GALAXY IS ENERGY INDEP. • LOW ENERGY CRS ACCUMULATE LARGE GRAMMAGE IN SOURCE VICINITY: B PRODUCED CLOSE TO THE SOURCE B/C STANDARD • POSITRONS AND ANTI-P FROM 10 -20 TIMES LARGER ENERGY P SAME SPECTRA AS PARENT P 26

NON-LINEAR COCOONS? • LOW ENERGY PARTICLES CAN SPEND A LONG TIME CLOSE TO THEIR SOURCES THANKS TO SELF-GENERATED TUBULENCE, IN PRINCIPLE BOTH RESONANT (ECR/UB<c/vs) NON-RESONANT (ECR/UB>c/vs) • FOR THE CASE OF PROPAGATION FROM EXTRAGAL. SOURCES NON-RESONANT INSTABILITY IS VERY EFFICIENT THANKS TO LOW IGM B-FIELD • 1018 e. V PARTICLES CONFINED CLOSE TO THEIR SOURCES FOR THE AGE OF THE UNIVERSE (Blasi, EA, D’Angelo 15) LOW ENERGY CUT-OFF IN EXTRAGAL. CRs? ? • FOR GALACTIC SOURCES RESONANT INSTABILITY PROVIDES A LOWER BOUND ON CONFINEMENT (Nava+ 16, D’Angelo+ 17) 27

WAVE-GENERATION CLOSE TO GALACTIC SOURCES • RELEASE CRs WITH 0. 1 ESN IN 104 YR • LET THEM PROPAGATE IN SELF-GEN. FIELD 1 Ge. V CR OVERDENSITY WAVE ENERGY DENSITY (50 pc) D’Angelo, Blasi, EA 16 28

SELF-CONFINEMENT AROUND GALACTIC SOURCES ESCAPE IN Dsg D’Angelo, Blasi, EA 16 ESCAPE IN Dg CONSIDERABLE GRAMMAGE CAN BE ACCUMULATED IN THE SOURCE VICINITY 29

THE POSITRON “EXCESS” (Aguilar et al 13) (Adriani et al 09) (Ackerman et al 11) MANY IDEAS (& PAPERS): • DARK MATTER • NEW CR PROPAGATION SCENARIOS • ASTROPHYSICAL SOURCES (e. g. Serpico 12, Di Mauro et al 17, EA & Blasi 17) • e+ ONLY SECONDARIES • e- SPECTRUM SAME AS 30

PULSARS AND THEIR NEBULAE EXCELLENT FACTORIES OF LEPTONIC ANTIMATTER IMMEDIATELY SUGGESTED AS THE SOURCES OF e+ EXCESS (e. g. Hooper, Blasi, Serpico 08, Grasso et al 09, Heyl et al 10) MOST ROTATIONAL ENERGY ENDS UP IN PAIR WIND

PULSAR BOW SHOCK NEBULAE MOUSE NEBULA GUITAR NEBULA Gaensler et al 04 Bucciantini, Amato, Del Zanna 05 Bykov, EA, et al 17 MAIN UNKNOWN: HOW MUCH ENERGY IS LEFT IN PAIRS AT ESCAPE, t≈20000 yr. DEPENDS ON SPIN-DOWN: 32

SNRs AND PSRs IN THE GALAXY SNR DISTRIBUTION (Green 05, Faucher-Giguere & Kaspi 06) 80% SNRs HOST A PSR PARAMETERS (B*, P 0, VP) ESCAPE AT≈5 X 104 yr PROTONS AND PRIMARY ELECTRONS INJECTED FROM SNRS WITH SPECTRUM AS FROM NEWEST AMS-02 DATA (Aguilar et al 15) AND 10% EFFICIENCY DIFFUSION THROUGH THE GALAXY A LA KOLMOGOROV: D(E)≈E 1/3 (Aguilar et al 16) 33

POSITRONS FROM PWNe DATA: AMS-02 TOTAL e- EA & Blasi 17 PRIMARY e- TOTAL e+ PWN e+ SECONDARY e+ AND e- PWN ACCELERATION EFFICIENCY 12% INJECTED SPECTRUM E-1. 5 E<500 GEV 34

POSITRON FRACTION AMS-02 DATA PAMELA DATA EA & Blasi 17 35

CONTRIBUTING SOURCES 10 Ge. V 100 Ge. V 1 Te. V GEMINGA? • ENERGY DETERMINATION: PAIRS AT THE PSR POTENTIAL DROP, AS IN GUITAR (Bandiera 08) • PROTONS FROM PSR (e. g. Amato & Arons 06)? • STEEPER SPECTRUM THAN REQUIRED FOR EXCESS? 36

SUMMARY • RECENT FINDINGS BY PAMELA AND AMS-02: • BREAKS IN THE SPECTRA OF PRIMARIES • B/C A LA KOLMOGOROV • FLAT ANTI-PROTONS • RISING POSITRON FRACTION • CHALLENGE TO STANDARD SCENARIO OF CR PROPAGATION? • SO FAR MAINLY SEEM TO SUGGEST THAT NON-LINEARITIES MIGHT PLAY ESSENTIAL ROLE FOR PROPAGATION • WE HAVE ALREADY ACCEPTED THIS VIEW FOR ACCELERATION…. 37

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