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Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia

Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia. N cr ~ 10 -10 cm -3 - total number density w cr ~ 1.5 eV/cm 3 - energy density E max ~ 3x10 20 eV - max. observed energy δ cr ~ 10 -3 at 10 12 - 10 14 eV - anisotropy

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Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia

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  1. Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia

  2. Ncr ~ 10-10 cm-3- total number density wcr ~ 1.5 eV/cm3- energy density Emax ~ 3x1020 eV - max. observed energy δcr ~ 10-3 at 1012 - 1014 eV - anisotropy rg ~ 1E/(Z×3×1015 eV) pc - Larmor radius ulsar

  3. energy balanceGinzburg & Syrovatskii 1964 • required source power3×1038 erg/(s kpc2) • SN kinetic energy 2×1039 erg/(s kpc2) • (Wsn=1051 erg, νGal = 0.03 yr-1 • local SN rate 50 Myr-1kpc-2) ~ 15% - efficiency of CR acceleration in SNRs acceleration by external shock: a) “normal” composition after correction on atomic properties (FIP, volatility) b) delay between nuclear synthesis and acceleration (Soutoul test: 59Ni 59Co, high obs. 59Co/56Fe gives δt > 105yr Leske 1993) other Galactic accelerators: pulsars [2×1050 (10 ms/τ)2 erg], stellar winds [2×1038 erg/s kpc2], Galactic GRBs [1051 erg/105 yr], micro quasars, Galactic Center …

  4. diffusive shock acceleration Fermi 1949, Krymsky 1977, Bell 1978 • average gain • of momentum D(p) SNR ush distribution function (test particles) shock CR intensity time of acceleration resonant diffusion kres~1/rg Larmor radius

  5. maximum energy condition of acceleration, critical Pecklet number (parameter of modulation) SNR Wsn=1051erg • maximum value -typical in interstellar medium ism n0=1cm-3 diffusion should be anomalously slow near the shock (upstream and downstream) cosmic ray streaming instability in shock precursor Bell 1978, Lagage & Cesarsky 1983, McKenzie & Vőlk 1982, Achterberg 1983, Vőlk et al. 1988, Fedorenko 1990, Bell & Lucek 2000, 2001

  6. Bohm limit standard assumption δB ~ Bism Bohm diffusion Nagano & Watson 2000 extra- galactic? galactic knee

  7. nonlinear shock modification by cosmic ray pressure for high Mach shocks not power law spectrum at the shock Berezhko & Elliison 1999 Axford 1977, 1981 Eichler 1984 Berezhko et al. 1996 Malkov et al. 2000

  8. This composite image shows Cassiopeia A at many different wavelengths: radio polarization in red (VLA), X-rays in green (CHANDRA) and optical in blue (HST). Notice the outer shock, visible only in X-rays, as the thin green rim most visible at the top of the image. Also notice the bright ring which is visible at all three wavelengths, and the many different filamentary structures seen at each wavelength. The compact remains of the exploded star are visible only in X-rays, as the bright green spot slightly below and to the left of the geometric center of the bright ring.

  9. observations nonthermal X-rays εkeV = 1 BμG(Ee/120 TeV)2 εmax ~ 100 TeV SN1006 Koyama et al. 1995 Cas AAllen et al. 1997 RX J1713-39Koyama et al. 1997 RX J0852-46 (“Vela jr”) Slane et 2001 radio emission νMHz = 4.6 BμGEe,GeV2 E = 50 MeV – 30 GeV (100 GeV for IR) γ = 1.9 – 2.5 We = 1048 – 1049 erg Ginzburg & Syrovatskii 1964 Shklovsky 1976 synchrotron γ e SNR inverse Compton εγ = ε0(Ee/mec2)2 γ p TeV γ – rays electrons/protons εmax ~ 100 TeV SN1006 Tanimori et al 1998 RX J1713Muraishi et al. 2000 Aharonian et al. 2004 Cas AAharonian et al. 2001 RX J0852-46 (“Vela jr”) G338.3-0.0; G23.3-0.3; G8.7-0.1 Aharonian et al. 2005 e π0 not confirmed by HESS (2004) ! γ γ-rays (π0) Ε = 30-3000 MeV γ Cygni, IC443 Esposito et al. 1996 Sturner & Dermer 1996

  10. confrontation with observations problems: • Galactic sources should work up to (1-3)×1018 eV (Fe ?) • no VHE gamma-rays from not very young SNRstsnr ≥ 3×103 yr • average cosmic ray source spectrum γs = 2.1 - 2.4(depending on propagation model)

  11. abandonment of Bohm limit hypotheses maximum momentum of accelerated protons • strong cosmic-ray streaming instability (δB B0),Bell & Lucek 2000, 2001- non-linear wave interactions of Kolmogorov type in shock precursorPtuskin & Zirakashvili 2003, 2005 Ptuskin & Zirakashvili 2003 > < δB > B0 δB < B0 under extreme conditions: Emax ≈ 1017Z(ush/3×104km/s)2 ×(ξcr/0.5)Mej1/3n1/6 eV δBmax ≈ 103(ush/3×104km/s)n1/2μG Wsn = 1051 erg, Bism = 5 μG, n0 = 0.4 cm-3 ξcr = 0.5, κ = 0.04, a = 0.3

  12. average source spectrum step function spectrum at the shock delta function instantaneous SNR luminosity in run-away cosmic rays SN rate adiabatic stage Q ~ ξcrνsnWsnp-4 (Sedov)- universal spectrum ! average cosmic-ray source spectrum ejecta-dominated stage SNII in RSG wind: Q~ p-6.5at ρstar~ r -10 SNI in uniform medium: Q ~ p-7.0 (Chevalier – Nadyozhin)

  13. Weaver et al. 1977 Chevalier & Liang 1989 ism R=60pc n=1cm-3 ρstar~ r-10 ∙ M=10-5 uw=10km/s Rw=2pc · Eknee ≈ 6×1015 Z eV, ~ ξcrWsnM1/2(Mejuw)-1 Emax ≈ 4×1016 Z eVat tmin = 7 days dense RSG wind SNII hot bubble 0.013 cm-3, 3μG expected break of all particle spectrum δγ = 0.5 Ptuskin & Zirakashvili 2004 Roth et al. 2003 KASCADE

  14. extra- galactic? galactic knee 2nd knee dispersion of SNs? reacceleration? early transition to extragalactic CRs? Nagano & Watson 2000

  15. OB association: u=3×103 km/s, B=10-5 G, R=30 pc R u f ~ 1/p3 ta ~ R/(Fshu) at Di < uR ~ D/(Fshu2) at Di > uR • Reacceleration by multiple shocks SNR SNR Emax ~ 1017Z eV Axford & Ip 1991, Bykov & Toptygin 1990, 2001 Klepach et al. 2000 SNR • Reacceleration in plerions Ω Crab pulsar few msec pulsar δΦ Ｅθ= Bφur/c pulsar wind u δΦ = 4×1015Z eV – 1019Z eV Bell 1991, 2000, Berezhko 1993 SNR termination shock

  16. Summary • Maximum energy of accelerated particles strongly depends on SNR age in the presence of cosmic-ray streaming instability accompanied by non-linear wave dissipation. Emax can reach 1017Z eV in very young SNRs (with corresponding increase of random magnetic field to up to 10-3 G) and may fall down to less than 1011Z eV at the end of Sedov stage. Standard estimate of Emax based on the Bohm limit calculated for interstellar magnetic filed strength is not justified. • This gives a clue to understanding why SNRs are not bright in very high energy γ-rays at t > 3×103 yr. • Average source spectrum ~ p-4 up to ~ 6×1015Z eV is formed during adiabatic (Sedov) stage of SNR evolution provided constant fraction of incoming gas momentum flux goes to cosmic ray pressure at the shock. Steep power-law spectrum above this energy is produced at the preceding ejecta-dominated stage. The knee observed at 4×1015 eV may mark the transition from ejecta-dominated to adiabatic evolution of SNR shocks which accelerate cosmic rays.

  17. strong streaming instability and non-linear wave interactions in shock precursor():abandonment of Bohm limit hypotheses Ptuskin & Zirakashvili 2003 eq. for maximum momentum eq. for cosmic rays (1D, u=const) eq. for mhd waves (wk is spectral energy density) nonlinear wave interactions of Kolmogorov type ~ kδB(>k)/(4πρ)1/2 Verma et al. 1996 supersonic convection linear damping growth rate …D∇f in agreement with Bell & Lucek 2001

  18. diffusion coefficient: growth rate:

  19. streaming instability in shock precursor(no damping) cosmic-ray pressure ~ 0.5 for very strong shock Alfven velocity wave energy density weak random field: strong random field: characteristic velocity of waves

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