Recycling Galactic Cosmic-Ray Nuclei by Shear Acceleration: A Radio Galaxy Model for Ultrahigh-Energy Cosmic Rays Shigeo S. Kimura Center for Particle Astrophys. PSU (IGC Fellow) Dept. Astronomy & Astrophys., PSU Dept. Physics, PSU ref) SSK, T.B. Zhang, K. Murase in prep. Collaborators Bing Theodore Zhang (Beijing Univ.), Kohta Murase (PSU, YITP)
Outline • Introduction • Shear Acceleration in FR-I radio galaxies • UHECRs as Reaccelerated Galactic Cosmic Rays • Summary
Outline • Introduction • Shear Acceleration in FR-I radio galaxies • UHECRs as Reaccelerated Galactic Cosmic Rays • Summary
Ultra-High Energy Cosmic Rays E[eV] 10 18 19 20 10 10 10 ] 22217 -1 13210 7774 4611 )) sr 2639 24.5 3491 2238 1405 3450 5221 2629 569 2006 888 2 7585 10991 1344 60423 eV 34861 -1 26325 16317 267 s 130 -2 -1 m sr 54 24 2 -1 [ eV s -2 1 10 J /(m 23.5 4 24 /10 1 AGASA 3 3 E ( E Auger 23 × HiRes-I 10 J(E) log HiRes-II 22.5 Auger (ICRC 2015 preliminary) TA SD -1 17.5 18 18.5 19 19.5 20 20.5 10 17 17.5 18 18.5 19 19.5 20 20.5 log (E/eV) 10 log (E/eV) Auger (ICRC 15) 10 Abu-zayyat+13 • Air shower experiments reveal the existence of extremely efficient accelerators in the Universe. • E cut ~ 40—50 EeV ~ GZK cutoff energy
Luminosity density E[eV] 18 19 20 10 10 10 waxman 11 22217 3 13210 10 7774 4611 )) 2639 24.5 3491 2238 1405 3450 5221 2629 569 2006 888 2 7585 10991 1344 60423 eV 34861 26325 16317 267 130 -1 ( α − 1)t eff *c (Mpc) sr 54 24 -1 s -2 10 J /(m 23.5 m=0 α =2 4 m=0 α =2.7 2 1 10 m=0 α =3 3 ( E m=3 α =2 23 m=3 α =2.7 10 m=3 α =3 log − 1 exp( − E c, π /E)+2H 0 ) − 1 ( τ − 1 0,ep exp( − E c,ep /E)+ τ 0, π 22.5 Auger (ICRC 2015 preliminary) 19 20 17.5 18 18.5 19 19.5 20 20.5 10 10 log (E/eV) E(eV) 10 • UHECR flux: ~ 0.1 particle km -2 yr -1 @100 EeV • Mean-free path of UHECRs: 100 Mpc • Luminosity density: 3x10 43 erg Mpc -3 yr -1
Source Candidates 1 AU 1 pc 1 kpc 1 Mpc 10 15 Neutron star Hillas 84 • AGN jets Kotera+11 Takahara 90 10 10 P Murase+12 r o t o ≤ n Araudo+16 1 E max 0 21 e V • GRBs F e White ≤ 10 5 E max 1 dwarf 0 20 AGN e V Waxman 95 B (G) G R Globus+15 B Asano+16 A 10 0 G N j e t s • Pulsars Hot spots SNR Blasi + 00, 10 –5 Fang+12 IGM shocks 10 –10 10 5 10 10 10 20 10 25 10 15 R (cm)
Composition 850 <X max > [gm/cm 2 ] Data QGSJETII − 03 QGSJET − 01c SYBILL 2.1 Auger ICRC 15 800 Proton 750 Iron 700 TA 15 650 18.5 19 19.5 20 Energy log 10 (E/eV) • Proton @ E~ EeV, • gradually becomes heavier for higher energy • Data is consistent for two experiments, but interpretation can be changed by analysis
Fitting requirement 1000 Auger 2014 850 E Fe, max =10 20.2 eV protons E 2 dN/dE [eV cm -2 s -1 sr -1 ] 100 α =0.6 800 <X max > [g cm -2 ] 10 750 1 700 A=1-2 0.1 A=3-6 Iron A=7-19 650 A=20-39 A=40-56 0.01 17.5 18 18.5 19 19.5 20 20.5 17.5 18 18.5 19 19.5 20 20.5 log 10 Energy [eV] log 10 Energy [eV] Aloisio+14, Taylor+15 • E max,p ~ 6 EeV • Hard source spectrum: s ≲ 1 • Abundance for Auger data: much heavier than the Galactic composition ratio • Need another EeV component
Espresso Acceleration E 2.7 Flux(E) [m -2 s -1 sr -1 GeV 1.7 ] b � m - - m ln (A) ( ) m º ¢ = G - b = G - bm ( ) 4 Caprioli 15 ¢ - ¢ = ¢ m ¢ º ¢ ¢ f = - ´ ¢ + m b • Re-acceleration of galactic CRs by AGN jets ¢ = G - bm + bm m = ¢ + bm —> composition & spectrum is well fitted m ¹ m • However, this model require extremely strong jets » ¹ —> No source inside the UHECR horizon g G � ¢ = - m b ¢ = - ¢ z D J » � < b - g > f µ ¶ f µ W¢ ¢ + G W¢ ¢ µ µ » G - b � - = ~ m r » D J - + g d µ j ¢ º W¢ ¢ p ¢ = ¢ Î j p j p p F p � g � » F p D J � - µ r µ r ¢ ´ m � D J � - � j ¢ á ñ = G j ¢
Auger: Galactic coordinate TA: equatorial coordinate Anisotropy Auger 15 TA 14 (d) 4 • weakly clustering, but not statistically significant + - Auger 15 • the result of cross correlation analysis is consistent with isotropic arrival —> N source ≳ 10 -6 Mpc -3 Takami+ 12 - = ´ • Luminous sources are disfavored Fang+16 + - a d = > y y = y = = - = ´ a d = � - � = - � ) = 3
Purpose Re-cycling galactic CRs works for the composition • —> consider AGN Jets Harder spectrum is required • —> Shear acceleration High source density is favorable from anisotropy constraints • —> FR-I galaxies Consider recycling galactic cosmic rays by shear acceleration in the FR-I radio galaxies
Outline • Introduction • Shear Acceleration in FR-I radio galaxies • UHECRs as Reaccelerated Galactic Cosmic Rays • Summary
á d ñ d á d ñ d á d ñ d á d ñ d µ Shear Acceleration á ñ • region 1 & 3: á ñ p ¶ p ¶ ¶ ò ò á ñ = = = tail-on collision ¶ ¶ ¶ —> E ⤵ • region 2 & 4: head-on collision p ¶ —> E ⤴ ò á ñ = ¶ = = = = p = x Earl 88, Subramanian 99, Rieger+ 06 For continuous shear layer, distribution function diffuses in p space á ñ ò x x x ¶ ¶ ⎛ ¶ ⎞ - = f p ( ) 1 f p ( ) = - + 2 p p D + ⎜ ⎟ p ¶ ¶ ¶ 2 t p ⎝ p ⎠ = + = = d d - ) = = = = g = = á d ñ = d d = + d - = = =
Shear Acceleration • gyro radius > size of shear layer → discrete shear • Discrete shear: no analytic formulation From MC simu., dN/dE ~ E 0
Model Setup Cocoon Jet B jet R jet R esc B ext Kchekhovskoy+16 • Consider kpc away from the core • Jet becomes cylindrical around kpc scale • Mildly relativistic jet β j ~ 0.6 • Jet is long, L jet ~ 20 kpc >> R jet ~ 300 pc
Model Setup Cocoon Jet B jet R jet R esc B ext Kchekhovskoy+16 • We perform Monte Carlo simulation • Bohm diffusion, λ ~ r g c/3 • isotropic scattering at the fluid rest frame • R esc ~ 10 R jet
Simulation results EL E [s -1 ] E[eV] • Hard spectrum owing to shear acceleration • dN/dE ~ E 0 for E<E peak Consistent with previous works
from simulation results Analytic Estimate • Acceleration Time: e t acc = ⟨ ∆ t ⟩ p / ⟨ ∆ E/E ⟩ p , w as ⟨ ∆ E/E ⟩ p ≃ 4 Γ 2 j β 2 j / 3 on ⟨ ∆ t ⟩ p ∼ 2 R coc / ( c ), e energy gain per cycl , we can write t ≃ 3 e t acc ≃ 3 R coc / (2 β 2 j c ). ssion only for a transr • Escape time: , t esc ∼ R 2 coc / (6 D Bohm ). tting t acc ≃ t esc , w E peak ≃ eZ s 3 Γ 2 j β 2 j B coc R coc ∼ 2 . 1 Z s B 4 R 3 β 2 6 EeV , Consistent with the MC simulations Achieve a few EeV for protons
Outline • Introduction • Shear Acceleration in FR-I radio galaxies • UHECRs as Reaccelerated Galactic Cosmic Rays • Summary
Halo cocoon jet Low-E CR High-E CR Re-acceleration of galactic cosmic rays • Galactic cosmic rays (GCRs) are diffusing in halo • Jet penetrates halo: Low-E GCRs (< E inj ) are advected & cools down, High-E GCRs (> E inj ) are injected to the shear accel.
Re-acceleration of galactic cosmic rays E 2 L E [erg s -1 ] SSK+ in prep Since FR-I radio galaxies are • elliptical, we enhance metal abundance for injected CRs. p, He : the Galactic CR • others : the Galactic CR x3 E[eV] We can obtain hard spectrum & heavier composition • (f H , f He , f C-O , f Ne-Al , f Si-K , f Ca-Mn , f Fe ) =(72, 21, 4.3, 1.1, 0.54, 0.14, 0.38 ) • Luminosity ~ 10 41 erg/s, number density ~ 10 -5 Mpc -3 • —> consistent with the expected luminosity density & anisotropy
Propagation of IGM Batista + 16 • Using CRpropa code that includes a) decay of nuclei b) photomeson production: p+ γ —> p + π c) photodisintegration : N A + γ —> N A-1 + p d) photo-pair production: p+ γ —> p + e + + e - (the code includes other channels) • Radiation fields: EBL (infrared), CMB (radio) G. Müller+ ICRC 13 Neutrino, Photon EeV Nucleus
Spectrum at the Earth SSK+ in prep • Compatible with the Auger result. • A bit lower flux around E ~ 30 EeV • We need another EeV component cf.) Aloisio+14
Composition at the Earth SSK+ in prep • Consistent with the Auger feature: heavier for higher E • < ln A> is heavier for E > 10 EeV • σ 2 (ln A) is comparable • For higher E peak model, <ln A> is better, but the spectrum is worse
Outline • Introduction • Shear Acceleration in FR-I radio galaxies • UHECRs as Reaccelerated Galactic Cosmic Rays • Summary
Summary • Experiments for UHECRs show a) Cutoff energy: 40-50 EeV b) Luminosity density: 3x10 43 erg Mpc -3 yr -1 c) Heavier composition for higher energy d) Large number density: n >10 -6 Mpc -3 • The model of re-acceleration of galactic CRs by shear in FR-I radio galaxies are consistent with all the requirement above. E 2 L E [erg s -1 ] E[eV]
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