The Escape Model. Michael Kachelrieß NTNU, Trondheim. with G.Giacinti, O.Kalashev, A.Nernov, V.Savchenko, D.Semikoz
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- Stuart Logan Martin
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![The Escape Model Michael Kachelrieß NTNU, Trondheim []](/docs-images/79/78949848/images/1-0.jpg "with G.Giacinti, O.Kalashev, A.Nernov, V.Savchenko, D.")
1 The Escape Model Michael Kachelrieß NTNU, Trondheim [] with G.Giacinti, O.Kalashev, A.Nernov, V.Savchenko, D.Semikoz
2 Introduction Outline Outline of the talk 1 Introduction Results on Composition 2 Escape model Fluxes of groups of CR nuclei & knee Transition to extragalactic CRs Exgal. protons, γ s and ν s as CR secondaries 3 A recent nearby SN? Anisotropy Antimatter fluxes 4 Conclusions Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
3 Introduction Outline Outline of the talk 1 Introduction Results on Composition 2 Escape model Fluxes of groups of CR nuclei & knee Transition to extragalactic CRs Exgal. protons, γ s and ν s as CR secondaries 3 A recent nearby SN? Anisotropy Antimatter fluxes 4 Conclusions Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
4 Introduction Outline Outline of the talk 1 Introduction Results on Composition 2 Escape model Fluxes of groups of CR nuclei & knee Transition to extragalactic CRs Exgal. protons, γ s and ν s as CR secondaries 3 A recent nearby SN? Anisotropy Antimatter fluxes 4 Conclusions Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
5 Introduction Composition Composition of Galactic CRs: traditional view [Gaisser, Stanev, Tilav 13 ] sr -1 s -1 ] 4 3 Proton_total He_total C_total O_total Fe_total Z=53 group Z=80 group dn/de [GeV 2.6 E 1.6 m Pamela Proton Pamela He CreamII Proton CreamII He CreamII C CreamII O CreamII Mg CreamII Si CreamII Fe Primary Energy, E [GeV] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
6 Introduction Composition Composition of Galactic CRs: KASCADE-Grande 2013 ) 1.5 sr -1 s -1 ev -2 / (m 2.5 E EAS-TOP (Astrop.Phys.(1999)1) Tibet-III, QGSJET 01 (ApJ678(2008)1165) GAMMA (ICRC 2011) IceTop (arxiv: v1) TUNKA-133 (ICRC 2011) Yakutsk (NewJ.Phys11(2008)065008) KASCADE-Grande, QGSJET II (Astrop.Phys.36(2012)183) Akeno (J.Phys.G18(1992)423) AGASA (ICRC 2003) HiResI (PRL0(2008)11) HiResII (PRL0(2008)11) AUGER (arxiv:17:4809) AUGER AMIGA infill (ICRC 2011) diff. flux dj/de 15 KASCADE, all-part., QGSJET II (see Appendix A) KASCADE, light (p), QGSJET II (see Appendix A) KASCADE, medium (He+C+Si), QGSJET II (see Appendix A) KASCADE, heavy (Fe), QGSJET II (see Appendix A) KASCADE-Grande, all-part., QGSJET II (this work) KASCADE-Grande, light (p), QGSJET II (this work) KASCADE-Grande, medium (He+C+Si), QGSJET II (this work) KASCADE-Grande, heavy (Fe), QGSJET II (this work) primary energy E/eV 18 Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
7 Introduction Composition Composition of Galactic CRs: Auger [arxiv: ] 600 Sibyll 2.1 Sibyll 2.1 Sibyll 2.1 Fe N 500 He p Auger 400 log(e/ev) = log(e/ev) = log(e/ev) = N p < -4 p = p = QGSJET II-04 QGSJET II-04 QGSJET II log(e/ev) = log(e/ev) = log(e/ev) = N p < -4 p < -3 p = EPOS-LHC EPOS-LHC EPOS-LHC log(e/ev) = log(e/ev) = log(e/ev) = N p < -4 p = p = X max [g/cm 2 ] X max [g/cm 2 ] X max [g/cm 2 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
8 Introduction Composition Composition of Galactic CRs: Auger [arxiv: ] 600 Sibyll 2.1 Sibyll 2.1 Sibyll 2.1 Fe N 500 He p Auger 400 log(e/ev) = log(e/ev) = log(e/ev) = N p < -4 p = p = QGSJET II-04 QGSJET II-04 QGSJET II log(e/ev) = log(e/ev) = log(e/ev) = N p < -4 p < -3 p = EPOS-LHC EPOS-LHC EPOS-LHC log(e/ev) = log(e/ev) = log(e/ev) = composition ev consistent with N 200 p < -4 p = p = % 0 p, 50% He+N, < 20%Fe X max [g/cm 2 ] X max [g/cm 2 ] X max [g/cm 2 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
9 Introduction Composition Composition of Galactic CRs: 600 Sibyll 2.1 Sibyll 2.1 Sibyll 2.1 Fe N 500 He p Auger 400 log(e/ev) = log(e/ev) = log(e/ev) = N p < -4 p = p = QGSJET II-04 QGSJET II-04 QGSJET II log(e/ev) = log(e/ev) = log(e/ev) = N p < -4 p < -3 p = EPOS-LHC EPOS-LHC EPOS-LHC log(e/ev) = log(e/ev) = log(e/ev) = composition ev consistent with N p < -4 p = p = % 0 p, 50% He+N, < 20%Fe early transition X max [g/cm 2 ] from Galactic X max [g/cm to 2 ] extragalactic X max CRs [g/cm 2 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
10 Introduction Composition Transition to extragalactic CRs anisotropy limits dipole quadrupole Upper Limit - Dipole Amplitude Z=1 Z=26 1 E [EeV] Upper Limit - Amplitude λ Z=1 Z=26 1 E [EeV] dominant light Galactic composition around E = 18 ev excluded [Giacinti, MK, Semikoz, Sigl 12, PAO 13 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
11 Knee explanations Cosmic Ray Knee: steepening γ 0.4 at few 15 ev. ) 1.5 s -1 sr -1 ev -2 J(E) (m RHIC (p-p) HERA (γ-p) Equivalent c.m. energy 3 Tevatron (p-p) 4 7 TeV 14 TeV LHC (p-p) s pp (GeV) 5 HiRes-MIA HiRes I HiRes II Auger Scaled flux E ATIC PROTON RUNJOB KASCADE (QGSJET 01) KASCADE (SIBYLL 2.1) KASCADE-Grande 2009 Tibet ASg (SIBYLL 2.1) Energy 20 (ev/particle) 21 Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
12 Knee explanations Cosmic Ray Knee: 3 explanations. ) Equivalent c.m. energy 3 4 s pp (GeV) 5 6 s -1 sr -1 ev -2 J(E) (m RHIC (p-p) HERA (γ-p) Tevatron (p-p) 7 TeV 14 TeV LHC (p-p) HiRes-MIA HiRes I HiRes II Auger Scaled flux E ATIC KASCADE (QGSJET 01) 14 PROTON RUNJOB KASCADE (SIBYLL 2.1) KASCADE-Grande 2009 Tibet ASg (SIBYLL 2.1) Energy (ev/particle) change of interactions at multi-tev energies: excluded by LHC Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
13 Knee explanations Cosmic Ray Knee: 3 explanations. change of interactions at multi-tev energies: excluded by LHC change of propagation at R L l coh or E c ZeB l coh : change in diffusion from D(E) E 1/3 to Hall diffusion D(E) E small-angle scattering D(E) E 2 something intermediate? unavoidable effect, but for B few µg and l coh 30 pc at too high energy: E c /Z 15 B l c µg pc Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
14 Knee explanations Cosmic Ray Knee: 3 explanations maximal rigidity of dominant CR sources e.g. Hillas model E 2.6 I(E) [GeV 1.6 m -2 sr -1 s -1 ] p He C O Fe total E/eV Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
15 Knee explanations Cosmic Ray Knee: 3 explanations maximal rigidity of dominant CR sources e.g. Hillas model E 2.6 I(E) [GeV 1.6 m -2 sr -1 s -1 ] p He C O Fe total E/eV i = 1,...,3 types of CR sources, with slopes α A,i, rel. fractions f A,i Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
16 Knee explanations Cosmic Ray Knee: 3 explanations maximal rigidity of dominant CR sources e.g. Hillas model E 2.6 I(E) [GeV 1.6 m -2 sr -1 s -1 ] p He C O Fe total E/eV i = 1,...,3 types of CR sources, with slopes α A,i, rel. fractions f A,i no reliable estimate of E max,i, α A,i, and f A,i fit of many-parameter model to two observables: I tot and ln(a) Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
17 Knee explanations Cosmic Ray Knee: 3 explanations maximal energy: Gaisser, Stanev & Tilav version [ ] <lna> IC40/IT40 Kascade Tunka-133 HiResMia HiRes Auger TA H4a H3a Global Fit Global Fit with Population Primary Energy, E [GeV] 9 11 Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
18 Knee explanations Propagation in turbulent magnetic fields: Galactic magnetic field: regular + turbulent component turbulent: fluctuations on scales l min AU to l max ( 150) pc Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
19 Knee explanations Propagation in turbulent magnetic fields: Galactic magnetic field: regular + turbulent component turbulent: fluctuations on scales l min AU to l max ( 150) pc CRs scatter mainly on field fluctuations B(k) with kr L 1. Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
20 Knee explanations Propagation in turbulent magnetic fields: Galactic magnetic field: regular + turbulent component turbulent: fluctuations on scales l min AU to l max ( 150) pc CRs scatter mainly on field fluctuations B(k) with kr L 1. slope of power spectrum P(k) k α determines energy dependence of diffusion coefficient D(E) E β as β = 2 α: Kolmogorov α = 5/3 β = 1/3 Kraichnan α = 3/2 β = 1/2 Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
21 Knee explanations Propagation in turbulent magnetic fields: Galactic magnetic field: regular + turbulent component turbulent: fluctuations on scales l min AU to l max ( 150) pc CRs scatter mainly on field fluctuations B(k) with kr L 1. slope of power spectrum P(k) k α determines energy dependence of diffusion coefficient D(E) E β as β = 2 α: Kolmogorov α = 5/3 β = 1/3 Kraichnan α = 3/2 β = 1/2 observed energy spectrum of primaries: injection: dn/de E δ observed: dn/de E δ β δ and β are degenerated Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
22 Knee explanations Propagation in turbulent magnetic fields: Galactic magnetic field: regular + turbulent component turbulent: fluctuations on scales l min AU to l max ( 150) pc CRs scatter mainly on field fluctuations B(k) with kr L 1. slope of power spectrum P(k) k α determines energy dependence of diffusion coefficient D(E) E β as β = 2 α: Kolmogorov α = 5/3 β = 1/3 Kraichnan α = 3/2 β = 1/2 observed energy spectrum of primaries: injection: dn/de E δ observed: dn/de E δ β δ and β are degenerated anisotropy δ = 3D ij i ln(n) Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
23 Knee explanations Our approach: use model for Galactic magnetic field calculate trajectories x(t) via F L = qv B. Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
24 Knee explanations Our approach: use model for Galactic magnetic field calculate trajectories x(t) via F L = qv B. as preparation, let s calculate diffusion tensor in pure, isotropic turbulent magnetic field Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
25 Knee explanations Eigenvalues of D ij = x i x j /(2t) for E = 15 ev D(1PeV) (cm 2 /s) 1e+29 1e+28 d 3 d 2 d 1D Time (kyr) Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
26 Knee explanations Eigenvalues of D ij = x i x j /(2t) for E = 15 ev D(1PeV) (cm 2 /s) 1e+29 1e+28 d 3 d 2 d 1D Time (kyr) asymptotic value is smaller than extrapolated Galprop value [Giacinti, MK, Semikoz ( 12) ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
27 Knee explanations Knee from Cosmic Ray Escape l coh and regular field B(x) fixed from observations LOFAR: lcoh < pc in disc determine magnitude of random B rms (x) from grammage X(E) Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
28 Knee explanations Knee from Cosmic Ray Escape l coh and regular field B(x) fixed from observations LOFAR: lcoh < pc in disc determine magnitude of random B rms (x) from grammage X(E) X(E) in g/cm β=1, L=pc β=0.1, L=pc 0.01 β=1/8, L=25pc δ=1/3 AMS-02 (a) AMS-02 (b) Jones E/Z in ev Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
29 Knee explanations Knee from Cosmic Ray Escape l coh and regular field B(x) fixed from observations LOFAR: lcoh < pc in disc determine magnitude of random B rms (x) from grammage X(E) X(E) in g/cm β=1, L=pc β=0.1, L=pc 0.01 β=1/8, L=25pc δ=1/3 AMS-02 (a) AMS-02 (b) Jones E/Z in ev prefers weak random fields fluxes I A (E) of all isotopes fixed by low-energy data Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
30 Knee explanations Galactic CRs: KASCADE-Grande 2013 ) 1.5 sr -1 s -1 ev -2 / (m EAS-TOP (Astrop.Phys.(1999)1) Tibet-III, QGSJET 01 (ApJ678(2008)1165) GAMMA (ICRC 2011) IceTop (arxiv: v1) TUNKA-133 (ICRC 2011) Yakutsk (NewJ.Phys11(2008)065008) KASCADE-Grande, QGSJET II (Astrop.Phys.36(2012)183) Akeno (J.Phys.G18(1992)423) AGASA (ICRC 2003) HiResI (PRL0(2008)11) HiResII (PRL0(2008)11) AUGER (arxiv:17:4809) AUGER AMIGA infill (ICRC 2011) diff. flux dj/de E KASCADE, all-part., QGSJET II (see Appendix A) KASCADE, light (p), QGSJET II (see Appendix A) KASCADE, medium (He+C+Si), QGSJET II (see Appendix A) KASCADE, heavy (Fe), QGSJET II (see Appendix A) KASCADE-Grande, all-part., QGSJET II (this work) KASCADE-Grande, light (p), QGSJET II (this work) KASCADE-Grande, medium (He+C+Si), QGSJET II (this work) KASCADE-Grande, heavy (Fe), QGSJET II (this work) primary energy E/eV 18 Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
31 Knee explanations Knee from Cosmic Ray Escape: proton energy spectra 13 E 2.5 F(E) [ev 2.5 /cm 2 /s/sr] KASCADE 2013 KASCADE Grande CREAM-2011 PAMELA pc e+ 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17 E [ev] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
32 Knee explanations Knee from Cosmic Ray Escape: He energy spectra 13 E 2.5 F(E) [ev 2.5 /cm 2 /s/sr] PAMELA 2011 CREAM-2011 KASCADE Grande KASCADE 2013 He 5 pc e+ 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17 E [ev] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
33 Knee explanations Knee from Cosmic Ray Escape: CNO energy spectra 13 E 2.5 F(E) [ev 2.5 /cm 2 /s/sr] KASCADE Grande CNO KASCADE 2013 CREAM C+O 9 CNO 25 pc e+12 1e+13 1e+14 1e+15 1e+16 1e+17 1e+18 1e+19 E [ev] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
34 Knee explanations Knee from Cosmic Ray Escape: total energy spectra E 2.5 F(E) [ev 2.5 /cm 2 /s/sr] Tibet KASCADE Grande Auger 2013 P He CNO Si Fe total E [ev] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
35 Knee explanations Knee from Cosmic Ray Escape: ln(a) ln(a) KASCADE-Grande KASCADE IceCube TUNKA Auger 0% exgal p p/fe exgal. mix 0 1e+15 1e+16 1e+17 1e+18 1e+19 1e+20 E/eV Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
36 Knee explanations Knee from Cosmic Ray Escape: ln(a) ln(a) KASCADE-Grande KASCADE IceCube TUNKA Auger 0% exgal p p/fe exgal. mix 0 1e+15 1e+16 1e+17 1e+18 1e+19 1e+20 E/eV exgal. mix: 60% p, 25% He, 15% N Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
37 Knee explanations Knee from Cosmic Ray Escape: dipole anisotropy -2-3 δ -4 1 PeV all data IceCube 2013 fit 1 SN 0 TeV Galactic total -5 Galactic E [ev] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
38 Knee explanations Knee from Cosmic Ray Escape: dipole anisotropy Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
39 Escape model Exgal. protons, γ s and ν s Extragalactic proton flux in escape model: 6 E 2 F(E) [ev/cm 2 /s/sr] KASCADE KASCADE Grande KASCADE Grande EG P 25 pc with Auger limit -1 Auger 2013 Auger 2013 Protons -2??? E [ev] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
40 Escape model Exgal. protons, γ s and ν s Extragalactic proton flux in escape model: 6 E 2 F(E) [ev/cm 2 /s/sr] KASCADE KASCADE Grande KASCADE Grande EG P 25 pc with Auger limit -1 Auger 2013 Auger 2013 Protons??? what are the sources? E [ev] testable via γ-ray and neutrinos? Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
41 Escape model Exgal. protons, γ s and ν s Normal and starburst galaxies: assume E 2.2 source spectrum starburst: B 0B MW rescale grammage and E max fix Q CR via SN/star formation rate vary gas density Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
42 Escape model Exgal. protons, γ s and ν s Normal and starburst galaxies: 00 ν gal (98%) je 2, ev cm -2 s -1 sr -1 0 p γ 1 ν EG KASCADE 2013 KASCADE Grande EG Auger 2013 Protons E, ev Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
43 Escape model Exgal. protons, γ s and ν s Normal and starburst galaxies: 00 ν gal (98%) je 2, ev cm -2 s -1 sr -1 0 p γ 1 ν EG KASCADE 2013 KASCADE Grande EG Auger 2013 Protons E, ev can not explain exgal. protons sources are thick can not be dominant sources of both EGRB and neutrinos Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
44 Escape model Exgal. protons, γ s and ν s Extragalactic proton flux in escape model: α p = 2.2 requires late redshift evolution: 20 N c (z)/n c (0) BL Lacs ρ. SNII (z)/ρ. SNII (0) z Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
45 Escape model Exgal. protons, γ s and ν s Extragalactic proton flux in escape model: α p = 2.2 requires late redshift evolution: 20 N c (z)/n c (0) BL Lacs ρ. SNII (z)/ρ. SNII (0) z BL Lacs/FR-I are promising sources Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
46 Escape model Exgal. protons, γ s and ν s Extragalactic proton flux in escape model: α p = 2.2 requires late redshift evolution: BL Lacs/FR-I are promising sources E 2 F(E) [ev/cm 2 /s/sr] KASCADE KASCADE Grande KASCADE Grande EG P 25 pc with Auger limit -1 Auger 2013 Auger 2013 Protons BL Lacs E [ev] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
47 Escape model Exgal. protons, γ s and ν s Diffuse fluxes from BL Lacs α = 2.17 and E τ = 3 11 ev 00 ν gal (75%) je 2, ev cm -2 s -1 sr -1 0 p γ 1 ν EG KASCADE 2013 KASCADE Grande EG Auger 2013 Protons E, ev Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
48 Escape model Exgal. protons, γ s and ν s Diffuse fluxes from BL Lacs α = 2.1 and E τ = 3 11 ev je 2, ev cm -2 s -1 sr ν gal (37%) p γ 1 ν EG KASCADE 2013 KASCADE Grande EG Auger 2013 Protons E, ev Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
49 Escape model Exgal. protons, γ s and ν s Diffuse fluxes from BL Lacs α = 2.1 and E τ = 3 14 ev 00 ν gal (85%) je 2, ev cm -2 s -1 sr -1 0 p γ 1 ν EG KASCADE 2013 KASCADE Grande EG Auger 2013 Protons E, ev Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
50 Escape model Exgal. protons, γ s and ν s Diffuse fluxes from BL Lacs 00 ν gal (75%) je 2, ev cm -2 s -1 sr -1 0 p γ 1 ν EG KASCADE 2013 KASCADE Grande EG Auger 2013 Protons E, ev BL Lac s can explain CR proton flux EGRB and large fraction of IceCube ν from pp interactions Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
51 Local source Anisotropies Anisotropy of a single source if only turbulent field: diffusion = random walk = free quantum particle number density is Gaussian with σ 2 = 4DT δ = 3D n c n = 3R 2T what happens for general fields? Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
52 Local source Anisotropies Anisotropy of a single source if only turbulent field: diffusion = random walk = free quantum particle number density is Gaussian with σ 2 = 4DT δ = 3D n c n = 3R 2T what happens for general fields? Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
53 Local source Anisotropies Anisotropy of a single source if only turbulent field: diffusion = random walk = free quantum particle number density is Gaussian with σ 2 = 4DT δ = 3D n c n = 3R 2T what happens for general fields? Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
54 Local source Anisotropies Anisotropy of a single source: only turbulent field B 0 = 0 G 3/2 50 pc / ct 1 kpc 0.1 Anisotropy (R / 50 pc) kpc Years [Savchenko, MK, Semikoz 15 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
55 Local source Anisotropies Anisotropy of a single source: plus regular B 0 = 1 G 3/2 50 pc / ct 1 kpc 0.1 Anisotropy (R / 50 pc) kpc Years [Savchenko, MK, Semikoz 15 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
56 Local source Anisotropies Anisotropy of a single source: B 0 = 1 G 3/2 50 pc / ct 1 kpc 0.1 Anisotropy (R / 50 pc) kpc Years regular field changes n(x), but keeps it Gaussian no change in δ Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
57 Local source Anisotropies Anisotropy of a single source: -3 δ -4 1 PeV all data IceCube TeV fit 1 SN Galactic -5 total [Savchenko, MK, Semikoz 15 ] E [ev] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
58 Local source Antimatter fluxes Single source: other signatures 2 Myr SN explains anomalous 60 Fe sediments [Ellis+ 96 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
59 Local source Antimatter fluxes Single source: other signatures 2 Myr SN explains anomalous 60 Fe sediments [Ellis+ 96 ] secondaries: p diffuse as p leads to constant p/p ratio p/p ratio fixed by source age p flux is predicted e + flux is predicted relative ratio of p and e + depends only on their Z factors Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
60 Local source Antimatter fluxes Single source: other signatures 2 Myr SN explains anomalous 60 Fe sediments [Ellis+ 96 ] secondaries: p diffuse as p leads to constant p/p ratio p/p ratio fixed by source age p flux is predicted e + flux is predicted relative ratio of p and e + depends only on their Z factors may responsible for different slopes of local p and nuclei fluxes Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
61 Local source Antimatter fluxes Single source: proton flux [MK, Neronov, Semikoz 15 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
62 Local source Antimatter fluxes Single source: positrons [MK, Neronov, Semikoz 15 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
63 Local source Antimatter fluxes Single source: antiprotons [MK, Neronov, Semikoz 15 ] Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
64 Conclusions Conclusions I Knee due to CR escape recovery of fluxes as suggested by KASCADE-Grande probes GMF: suggests small Brms and small l coh transition to light-medium extragalactic CRs completed at 18 ev propagation feature is unavoidable, only possible to shift to higher energies source effects may be on top, but seem not necessary Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
65 Conclusions Conclusions I Knee due to CR escape recovery of fluxes as suggested by KASCADE-Grande probes GMF: suggests small Brms and small l coh transition to light-medium extragalactic CRs completed at 18 ev propagation feature is unavoidable, only possible to shift to higher energies source effects may be on top, but seem not necessary Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
66 Conclusions Conclusions I Knee due to CR escape recovery of fluxes as suggested by KASCADE-Grande probes GMF: suggests small Brms and small l coh transition to light-medium extragalactic CRs completed at 18 ev propagation feature is unavoidable, only possible to shift to higher energies source effects may be on top, but seem not necessary Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
67 Conclusions Conclusions I Knee due to CR escape recovery of fluxes as suggested by KASCADE-Grande probes GMF: suggests small Brms and small l coh transition to light-medium extragalactic CRs completed at 18 ev propagation feature is unavoidable, only possible to shift to higher energies source effects may be on top, but seem not necessary Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
68 Conclusions Conclusions II 1 Single source: anisotropy dipole formula δ = 3R/2T holds universally in quasi-gaussian regime plateau of δ points to dominance of single source 2 Single source: antimatter consistent explanation of p, p and e + fluxes consistent with 60 Fe and δ 3 local geometry of GMF is important Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
69 Conclusions Conclusions II 1 Single source: anisotropy dipole formula δ = 3R/2T holds universally in quasi-gaussian regime plateau of δ points to dominance of single source 2 Single source: antimatter consistent explanation of p, p and e + fluxes consistent with 60 Fe and δ 3 local geometry of GMF is important Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
70 Conclusions Conclusions II 1 Single source: anisotropy dipole formula δ = 3R/2T holds universally in quasi-gaussian regime plateau of δ points to dominance of single source 2 Single source: antimatter consistent explanation of p, p and e + fluxes consistent with 60 Fe and δ 3 local geometry of GMF is important Michael Kachelrieß (NTNU Trondheim) Escape Model DESY Zeuthen, / 30
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