Cosmic Rays, Photons and Neutrinos

Transcription

1 Cosmic Rays, Photons and Neutrinos Michael Kachelrieß NTNU, Trondheim []

2 Introduction Outline Plan of the lectures: Cosmic rays Galactic cosmic rays Basic observations Acceleration Supernova remnants Problems Extragalactic cosmic rays Transition Anisotropies and sources Nuclear composition CR secondaries: photons and neutrinos Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

3 Introduction Outline Milky Way globular clusters disc h = 300pc Sun 8 kpc gas/cr halo Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

4 Introduction Outline Milky Way globular clusters disc h = 300pc Sun 8 kpc gas/cr halo Larmor radius 1 pc = cm R L = cp ZeB 100 pc 3µG B E Z ev pp interaction: σ pp 50 mbarn mbarn = cm 2 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

5 Introduction Outline Milky Way globular clusters disc h = 300pc Sun 8 kpc gas/cr halo Larmor radius 1 pc = cm R L = cp ZeB 100 pc 3µG B E Z ev pp interaction: σ pp 50 mbarn mbarn = cm 2 extragalactic scales: distance to Virgo: 18 Ṁpc observable universe: c/h0 4 Gpc Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

6 1910: Father Wulf measures ionizing radiation in Paris 80m: flux/2

7 300m: flux/2 80m: flux/2

8 Introduction History 1912: Victor Hess discovers cosmic rays The results are most easily explained by the assumption that radiation with very high penetrating power enters the atmosphere from above; the Sun can hardly be considered as the source. Hess and Kolhoerster s results: 80 excess ionization altitude/1000m Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

9 Introduction Observational techniques What do we know 100 years later? solar modulation LHC Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

10 Introduction Observational techniques What do we know 100 years later? solar modulation only few bits of information? energy density ρ cr 0.8eV/cm 3 exponent α of dn/de 1/E α nuclear composition for E < ev isotropic flux for E < ev LHC Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

11 Introduction Observational techniques Observing gamma-rays or cosmic rays: GeV-TeV Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

12 Introduction Observational techniques Observing gamma-rays or cosmic rays: around TeV Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

13 Introduction Observational techniques Pierre Auger Observatory: Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

14 Introduction Observational techniques Pierre Auger Observatory: Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

15 Introduction Observational techniques Three options for HE astronomy: High-energy photons: IACT s (HESS, MAGIC, Veritas) extremely successful new sources, extragal. backgrounds, evidence for hadronic accelerators, M87,... synergy with Fermi-LAT next generation experiment CTA on the way Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

16 Introduction Observational techniques Three options for HE astronomy: VHE photons: successful, but restricted to few Mpc 22 radio log10(e/ev) 16 photon horizon γγ e + e CMB 14 IR kpc 10kpc 100kpc Mpc 10Mpc 100Mpc Gpc Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

17 Introduction Observational techniques Three options for HE astronomy: VHE photons: successful, but restricted to few Mpc hadronic photons vs. synchrotron/compton photons Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

18 Introduction Observational techniques Three options for HE astronomy: astronomy with VHE photons restricted to few Mpc astronomy with HE neutrinos: smoking gun for hadrons but challenging Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

19 Introduction Observational techniques Three options for HE astronomy: astronomy with VHE photons restricted to few Mpc astronomy with HE neutrinos: smoking gun for hadrons but challenging large λν, but also large uncertainty δϑ > 1 small event numbers: < few/yr for PAO or ICECUBE identification of steady sources challenging without additional input Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

20 Introduction Observational techniques Three options for HE astronomy: astronomy with VHE photons restricted to few Mpc astronomy with HE neutrinos: Alternative: smoking gun for hadrons but challenging large λν, but also large uncertainty δϑ > 1 small event numbers: < few/yr for PAO or ICECUBE identification of steady sources challenging without additional input Astronomy with neutrinos possible? Astronomy with charged particles possible? Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

21 Introduction Observational techniques Three options for HE astronomy: 22 proton horizon log10(e/ev) 16 photon horizon γγ e + e CMB 14 IR kpc 10kpc 100kpc Mpc Virgo 10Mpc 100Mpc Gpc Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

22 Introduction Observational techniques Three options for HE astronomy: 22 proton horizon log10(e/ev) 16 if UHECRs 14 are protons: deflections may be small photon horizon γγ e + e use 12 larger statistics of UHECRs well-suited horizon scale 10 kpc 10kpc 100kpc Mpc Virgo 10Mpc 100Mpc CMB IR Gpc Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

23 Introduction Basic observations Basic observations: Solar modulations Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

24 Introduction Basic observations Basic observations: Solar modulations Solar wind carries plasma solar rest frame: electric potential Φ Fish (t) low-energy particles cannot penetrate solar sytem Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

25 Introduction Basic observations Basic observations: Abundances at E/n = 5 GeV Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

26 Introduction Basic observations Basic observations: Abundances at E/n = 5 GeV Li, B and Ti groups strongly enriched Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

27 Introduction Basic observations Basic observations: Abundances at E/n = 5 GeV Li, B and Ti groups strongly enriched spallation product of CRs on gas B/C fixes residence time τ 10 7 yr Low energy CR make random walk Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

28 Introduction Basic observations Basic observations: Abundances at E/n = 5 GeV Li, B and Ti groups strongly enriched spallation product of CRs on gas B/C fixes residence time τ 10 7 yr Low energy CR make random walk diffuse in Galactic magnetic field constrains combination of D0 and h Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

29 Introduction Basic observations Diffusion 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) Cosmic Rays NORDITA School / 30

30 Introduction Basic observations Diffusion 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) Cosmic Rays NORDITA School / 30

31 Introduction Basic observations Diffusion 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 Bohm α = 1 β = 1 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

32 Introduction Basic observations Diffusion 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 Bohm α = 1 β = 1 observed energy spectrum of primaries: injection: dn/de E α observed: dn/de E α β α = 3/2 and β = 1/2 simplest combination Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

33 Sources and acceleration Acceleration Fermi acceleration 1.order, diffusive shock acceleration: SNR, GRB 2.order: superbubbles, continuously? Electromagnetic induction: Pulsar, Kerr BH Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

34 Sources and acceleration Acceleration Fermi acceleration 1.order, diffusive shock acceleration: SNR, GRB 2.order: superbubbles, continuously? Electromagnetic induction: Pulsar, Kerr BH Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

35 Sources and acceleration Acceleration Electromagnetic induction: Pulsar, Kerr BH millisecond pulsar: E max ZB 0R 3 ω 2 c ev Z B ( Ω G 3000 s 1 ) 2 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

36 Sources and acceleration Acceleration Electromagnetic induction: Pulsar, Kerr BH millisecond pulsar: E max ZB 0R 3 ω 2 c ev Z B ( Ω G 3000 s 1 but: gap, curvature radiation, plasma, Lmin : minimal power P dissipated by such an accelerator up to ev? L min = U 2 /R > W = erg/s ) 2 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

37 Sources and acceleration Acceleration Electromagnetic induction: Pulsar, Kerr BH millisecond pulsar: E max ZB 0R 3 ω 2 c ev Z B ( Ω G 3000 s 1 but: gap, curvature radiation, plasma, Lmin : minimal power P dissipated by such an accelerator up to ev? L min = U 2 /R > W = erg/s [density of stationary UHECR sources n s < L/L 10 5 /Mpc 3 ] ) 2 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

38 Sources and acceleration Acceleration Electromagnetic induction: Pulsar, Kerr BH millisecond pulsar: E max ZB 0R 3 ω 2 c ev Z B ( Ω G 3000 s 1 but: gap, curvature radiation, plasma, Lmin : minimal power P dissipated by such an accelerator up to ev? L min = U 2 /R > W = erg/s [density of stationary UHECR sources n s < L/L 10 5 /Mpc 3 ] SMBH may be UHECR sources, pulsars mainly local e + e source ) 2 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

39 Sources and acceleration Possible sources and the Hillas plot: log(b/g) pulsars AU pc AGN cores GRB SNR kpc Galactic halo Mpc radio galaxies cluster log(r/km) Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

40 Sources and acceleration Possible sources and the Hillas plot: log(b/g) pulsars AU pc AGN cores GRB SNR kpc Galactic halo Mpc radio galaxies cluster log(r/km) contains only size constraint; additionally age limitation: SNR, galaxy clusters energy losses: pulsars, AGN Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

41 Sources and acceleration Standard Galactic source: SNRs energetics: sources are SNRs: kinetic energy output of SNe: 10M ejected with v cm/s every 30 yr L SN,kin erg/s explains local energy density of CR ǫcr 1 ev/cm 3 for a escape time from disc τ esc yr and efficiency 1% Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

42 Sources and acceleration Standard Galactic source: SNRs energetics: sources are SNRs: kinetic energy output of SNe: 10M ejected with v cm/s every 30 yr L SN,kin erg/s explains local energy density of CR ǫcr 1 ev/cm 3 for a escape time from disc τ esc yr and efficiency 1% 1.order Fermi shock acceleration dn/de E γ with γ = diffusion in GMF with D(E) τ 1 esc(e) E δ and δ 0.5 explains observed spectrum E 2.6 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

43 Sources and acceleration Standard Galactic source: SNRs energetics: sources are SNRs: kinetic energy output of SNe: 10M ejected with v cm/s every 30 yr L SN,kin erg/s explains local energy density of CR ǫcr 1 ev/cm 3 for a escape time from disc τ esc yr and efficiency 1% 1.order Fermi shock acceleration dn/de E γ with γ = diffusion in GMF with D(E) τ 1 esc(e) E δ and δ 0.5 explains observed spectrum E 2.6 Problems: maximal energy E max too low anisotropy too large (?) Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

44 Sources and acceleration 1.order Fermi acceleration 2.nd order Fermi acceleration consider CR with initial energy E 1 scattering at a cloud moving with velocity V : E p 2 2 θ θ 1 2 V E p 1 1 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

45 Sources and acceleration 1.order Fermi acceleration Energy gain ξ (E 2 E 1 )/E 1? Lorentz transformation 1: lab (unprimed) cloud (primed) E 1 = γe 1 (1 β cos ϑ 1 ) where β = V/c and γ = 1/ 1 β 2 Lorentz transformation 2: cloud lab E 2 = γe 2(1 + β cos ϑ 2) scattering off magnetic irregularities is collisionless, the cloud is very massive E 2 = E 1 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

46 Sources and acceleration 1.order Fermi acceleration Energy gain ξ (E 2 E 1 )/E 1? E 2 = E 1 : Lorentz transformation 1: lab cloud E 1 = γe 1 (1 β cos ϑ 1 ) }{{} where β = V/c and γ = 1/ 1 β 2 Lorentz transformation 2: cloud lab E 2 = γe 2(1 + β cos ϑ 2) ξ = E 2 E 1 E 1 = 1 β cos ϑ 1 + β cos ϑ 2 β2 cos ϑ 1 cos ϑ 2 1 β 2 1. we need average values of cos ϑ 1 and cos ϑ 2 : Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

47 Sources and acceleration 1.order Fermi acceleration Assume: CR scatters off magnetic irregularities many times in cloud its direction is randomized, cos ϑ 2 = 0. collision rate CR cloud: proportional to their relative velocity (v V cos ϑ 1 ): for ultrarelativistic particles, v = c, dn dω 1 (1 β cos ϑ 1 ), and we obtain cos ϑ 1 = dn dn cos ϑ 1 dω 1 / dω 1 = β dω 1 dω 1 3 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

48 Sources and acceleration 1.order Fermi acceleration Energy gain ξ for 2.nd order Fermi: Plugging cos ϑ 2 = 0 and cos ϑ 1 = β 3 since β 1. ξ β 2 > 0 energy gain ξ = 1 + β2 /3 1 β β2 into formula for ξ gives O(ξ) = β 2, because β 1: average energy gain is very small ξ depends on drift velocity of clouds Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

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50 Sources and acceleration Diffusive shock acceleration Diffusive shock acceleration consider CR with initial energy E 1 scattering at a shock moving with velocity V s : E 1 V p θ 1 E 1 V s E 1 E 1 V p E 2 shock E 2 θ 2 E 2 E 2 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

51 Sources and acceleration Diffusive shock acceleration same discussion, but now different angular averages: projection of istropic flux on planar shock: dn d cos ϑ 1 = thus cos ϑ 1 = 2 3 and cos ϑ 2 = 2 3 { 2 cos ϑ1 cos ϑ 1 < 0 0 cos ϑ 1 > 0 ξ 4 3 β = 4 3 (u 1 u 2 ) + ξ β: efficient + test particle approximation + strong shock: universal spectrum dn/de E 2 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

52 Sources and acceleration Diffusive shock acceleration Maximal energy of SNR: Lagage-Cesarsky limit acceleration rate β acc = de dt = 3Ev2 sh acc ζd(e), ζ 8 20 Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

53 Sources and acceleration Diffusive shock acceleration Maximal energy of SNR: Lagage-Cesarsky limit acceleration rate β acc = de dt = 3Ev2 sh acc ζd(e), ζ 8 20 assume Bohm diffusion D(E) = cr L /3 E and B µg Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

54 Sources and acceleration Diffusive shock acceleration Maximal energy of SNR: Lagage-Cesarsky limit acceleration rate β acc = de dt = 3Ev2 sh acc ζd(e), ζ 8 20 assume Bohm diffusion D(E) = cr L /3 E and B µg E max ev Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

55 Sources and acceleration Diffusive shock acceleration Maximal energy of SNR: [Bell, Luzcek 02, Bell 04 ] (resonant) coupling CR Alfven waves Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

56 Sources and acceleration Diffusive shock acceleration Maximal energy of SNR: [Bell, Luzcek 02, Bell 04 ] (resonant) coupling CR Alfven waves non-linear non-resonant magnetic field amplification Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

57 Sources and acceleration Diffusive shock acceleration Maximal energy of SNR: [Bell, Luzcek 02, Bell 04 ] (resonant) coupling CR Alfven waves non-linear non-resonant magnetic field amplification observational evidence for B mg in young SNR rims Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30

58 Sources and acceleration Diffusive shock acceleration SNR RX J changes on δt 1 yr imply B 1mG Michael Kachelrieß (NTNU Trondheim) Cosmic Rays NORDITA School / 30