Comparison of The Energy Spectra Between Single Shock and Converging Double-Shock Speaker: Wang Xin Co-authors: Yan Yihua, Ding Mingde, Wang Na, & Shan Hao Xinjiang Astronomical Observatory, Chinese Academy of Sciences CAS Key Laboratory of Solar Activity, NAOC email: wangxin@xao.ac.cn The 35th International Cosmic Ray Conference Bexco, Busan, Korea 10-20,July,2017
Previous Studies Using MC Method 1, The dynamical shock structures, A & A, Wang & Yan (2011). 2, Injection rate, ApJS, Wang, et al (2013). 3, CME-driven shock, RAA, Wang & Yan (2012). 4, E max in an Isolated shock, RAA,Wang, et al (2016) 5, E max in two converging shocks, ApJ, Wang, et al (2017). 1
Motivation -1 Dec-14-2006 SEP (Mewaldt et al., 2008) 2
Simulate the“Break”Using MC Method 1, Up to now, it is hardly predicted by numerical methods. ApJ, (Malkov et al., 2013). 2, Simulated E max ∼ 4MeV, in single bow shock. ApJ, (Knerr+,1996) 3, Simulated E max ∼ 5MeV, in single CME shock RAA, (Wang+,2012) 4, Simulated E max ∼ 20MeV, in double converging shocks. ApJ, (Wang+,2017) 3
Single Shock Model The Schematic Diagram of the Simulation Box U 1 =−600km s −1 |U 2 |>|U|>|U 1 | U 2 =−1042km s −1 V shock V shock ICME reflective wall ∆ U=442km s −1 Xfeb = 300R e V L B 0 Precursor V V L Foreshock U V th =46kms −1 Shock τ 0 =13" FEB 300 250 200 150 100 50 0 X (X max =1000R e ) Downstream Upstream FEB 4
Spectra of Single Bow Shock ApJ (Knerr+1996): E max @ ∼ 3-4MeV 5
Spectra of Single CME Shock The Energy Spectrum 10 10 Final Energy Spectrum Initial Energy Spectrum Flux ( cm 2 .s.sr.MeV ) −1 8 10 6 10 E −1.1074 4 10 2 10 0 10 −3 −2 −1 0 1 10 10 10 10 10 Energy (MeV) RAA (Wang et al., 2012): E max @ ∼ 5MeV 6
Emax in an Isolated Shock Maximum Energy E max in Cases with Different τ 25 5.5506 The Maximum Energy Particles (MeV) Shape−preserving interpolant C 3.7031 3.5620 20 3.0489 2.8381 2.9780 D F B A E 15 Cases in A,B,C,D,E,F ( σ = π , µ =0) shape−preserving 10 T0 T0/2 T0/3 T0/4 T0/5 T0/12.5 The Constants of the Scattering Time τ E max saturation @ ∼ 5.5MeV (RAA, Wang+2016) 7
Spectra in Isolated Shock The Energy Spectrum in Different Scattering Time 1 10 A,T0 (Emax=2.9780MeV) B,T0/2 (Emax=3.0489MeV) 0 10 C,T0/3 (Emax=5.5506MeV) D,T0/4 (Emax=3.7031MeV) E,T0/5 (Emax=2.8381MeV) −1 10 F,T0/12.5(Emax=3.562MeV) Flux ( [ cm 2 .s.sr.keV ] −1 ) Initial Spectrum −2 10 −3 10 −4 10 −5 10 −6 10 −7 10 0 1 2 3 4 5 6 7 10 10 10 10 10 10 10 10 Energy (eV) 8
Double Converging Shocks The Schematic Diagram of the Simulation Box in Double Shocks Model U0 1 V sh1 V L V sh2 V L Earth reflective wall CME reflective wall IMF U0 2 V L V Precursor2 Precursor1 u 600 500 400 300 200 100 0 X Downstream1 Upstream1 Upstream2 Downstream2 9
Velocity Profiles 10
Density Profiles 11
Particles Acceleration in Double Shocks Particle Acceleration (Q=8) Vmax=37.3926 40 30 Velocity 20 10 0 600 250 400 200 150 Position 200 100 50 Time 0 0 12
Particles Acceleration in Double Shocks Comparison of the Energy Spectra 10 10 Protons 12/13:0200 − 12/14:2200 9 10 E −1.17 ± 0.11 E −1.07 Protons / (cm 2 −sr−MeV ) 8 10 E −2.55 ± 0.10 7 10 E −2.45 E −2.48 ± 0.12 6 10 Observed Spectrum Simulated Spectrum 5 10 −1 0 1 2 10 10 10 10 Kinetic Energy (MeV) ApJ (Wang et al., 2017): E br ∼ 5MeV 13
Comparison of Spectra Comparison of the Energy Spectra 10 10 The Energy Spectrum Protons 10 12/13:0200 − 12/14:2200 10 Final Energy Spectrum 9 10 E −1.17 ± 0.11 Initial Energy Spectrum E −1.07 Flux ( cm 2 .s.sr.MeV ) −1 8 Protons / (cm 2 −sr−MeV ) 10 8 10 6 E −2.55 ± 0.10 10 7 E −1.1074 10 E −2.45 4 10 E −2.48 ± 0.12 6 2 10 10 Observed Spectrum Simulated Spectrum 0 5 10 10 −3 −2 −1 0 1 −1 0 1 2 10 10 10 10 10 10 10 10 10 Kinetic Energy (MeV) Energy (MeV) Converging-Shock Model < ———- > Single-Shock Model 14
Summary and Conclusions 1,Find the saturation of the E max ∼ 5MeV in single shock model. Fit to the obser- vation at lower energy range. 2,Obtain the extensive energy spectral range up to E max ∼ 20MeV in double converging-shock model. 3,Identify the energy“break”E break ∼ 5MeV in double converging-shock model. 4,We suggest converging-shock interac- tion can produce the energy “break”. 15
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