The USINE propagation code and recent results from an MCMC analysis

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1 The USINE propagation code and recent results from an MCMC analysis Antje Putze B. Coste (LPSC), L. Derome (LPSC), F. Donato (INFN Torino), & D. Maurin (LPSC) The Oskar Klein Centre for Cosmoparticle Physics Stockholm University

2 Phenomenology of nuclear cosmic rays Why study cosmic-ray propagation? Study of the standard cosmic-ray astrophysics; Indirect search for dark matter. Propagation models: USINE Statistical tools: MCMC Experimental data: AMS = = used for the first time in the context of cosmic-ray physics [Putze et al., A&A (29 211)]. Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 2/1

3 The USINE propagation code Slide from D. Maurin Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 3/1

4 Diffusion Model USINE semi-analytical propagation code [D. Maurin] Diffusion model with minimal reacceleration, constant Galactic wind Galaxy is divided into two zones: 1 a thin disk of size h; 2 a diffusive halo of size L h. K(R) = K β η T R δ Q(R) = qβ η S R α n d = n, n h = Free parameters 6 transport par.: K [kpc 2 /Myr], η T, δ, V c and V a [km/s], L [kpc]. 3 source par.: q in (m 3 s GeV/n) 1, η S, α Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 4/1

5 Stable nuclei: constraining transport parameters B/C [Putze et al., A&A 516 (21), A66] Configuration with V c and V a preferred: L = 4 kpc fixed V c = km/s δ = K = kpc2 /Myr V a = km/s Kolmogorov spectral index (δ = 1/3) disfavoured. Systematic uncertainties are greater than the statistical ones! Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 5/1

6 Stable nuclei: constraining transport parameters 3 He/ 4 He B/C: abundant; elemental separation. Secondary-to-primary ratio (TOA) He/ He (TOA) Balloon72 (4 MV) Balloon73 (5 MV) Balloon77+Voyager (4 MV) Balloon89 (14 MV) IMP7+Pioneer1 (54 MV) ISEE3 (74 MV) ISEE3(HIST) (5 MV) Voyager87 (36 MV) IMAX92 (75 MV) SMILI-I (12 MV) SMILI-II (12 MV) AMS-1 (6 MV) BESS98 (7 MV) CAPRICE98 (7 MV) 3 He/ 4 He:.1 very abundant; isotopic separation Model II with prior (φ = 7 MV) Model III with prior (φ = 7 MV) Model II (φ = 7 MV) Model III (φ = 7 MV) [Coste et al., in preparation; ID 175] 2 1 E k/n [GeV/n] Data V c δ K 1 2 V a (km s 1 ) - (kpc 2 Myr 1 ) (km s 1 ) 3 He/ 4 He B/C Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 6/1

7 Radioactive secondaries: constraining the halo size L Be/ Be Al/ Al 36 Cl/Cl 1 9 Be/ Be + L [kpc] Al/ Al + Model III = r h 36 Cl/Cl Results with 1 Be/ 9 Be data without local bubble: L = kpc.6 L [kpc] Be/ Be Al/ Al 36 Cl/Cl 1 9 Be/ Be Al/ Al + 36 Cl/Cl 25 2 [kpc] r h Model III r h with local bubble: L = kpc, r h = pc [Putze et al., A&A 516 (21), A66] Local bubble underdensity in the LISM modelled as a hole in the disc exponential decrease of radioactive fluxes [Donato et al., A&A 381 (22), 539] Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 7/1

8 MCMC Constraints on CR parameters Conclusion Primary nuclei: constraining source parameters = Model ηt Kbest 12 (kpc2 Myr 1 ) δ best Vcbest (km s 1 ) Vabest (km s 1 ) χ2 /d.o.f II III I/ III/II [Maurin et al., A&A 516 (21), A67] Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 8/1

9 Primary nuclei: p and He [Putze et al., A&A 526 (211), A11] [Putze et al., A&A 526 (211), A11] α well constrained between 2.2 and 2.5 (independent of model and data) asymptotic regime (γ asymp = α + δ) not reached same results for heavier nuclei Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 9/1

10 Primary nuclei: p and He Preliminary [Putze et al., A&A 526 (211), A11] [Putze et al., in preparation] α well constrained between 2.2 and 2.5 (independent of model and data) asymptotic regime (γ asymp = α + δ) not reached same results for heavier nuclei Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 9/1

11 Be/ 26 Al/ 9 Be 27 Al 36 Cl/Cl Be/ Be + Al/ Al + Cl/Cl Conclusion Successful posterior PDF extraction of the propagation parameters of the one dimensional diffusion model First estimation of the Galactic halo size L and the radius r h of the local bubble.6 L [kpc] Model III r h r h [kpc] Good constraints of the spectral slope α implicating a universality for primary nuclei MCMC is a robust tool allowing an excellent parameter estimation in high dimensional parameter spaces. Antje Putze Oskar Klein Centre (SU) ICRC 211 USINE & results from an MCMC analysis 1/1