Cosmic-ray propagation in the light of the Myriad model Yoann - - PowerPoint PPT Presentation
Cosmic-ray propagation in the light of the Myriad model Yoann Genolini In collaboration with: Pasquale Serpico, Pierre Salati & Richard Taillet Annecy-Le-Vieux, FRANCE BUSAN July 17th, 2017 1 A break in Galactic cosmic rays nuclei S.Ting
Yoann Genolini
BUSAN July 17th, 2017
Annecy-Le-Vieux, FRANCE In collaboration with: Pasquale Serpico, Pierre Salati & Richard Taillet
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S.Ting presentation, CERN, december 2016 ⇒ A universal kinck at R ≥ 200GV ? ∆kinck ≈ 0.12 − 0.13 2
Yang presentation, XSCR, march 2017 ⇒ A universal kinck at R ≥ 200GV ? ∆kinck ≈ 0.12 − 0.13 2
Standard expectation ?
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⇒Explanation 1 : break in the diffusion coefficient ?
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⇒Explanation 2 : break in the source spectrum ?
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⇒Explanation 3 : local source contribution ?
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⇒ Explanation 3 : local source contribution ?
Genolini, Y., Salati, P., Serpico, P. D., & Taillet, R. (2017). Stable laws and cosmic ray physics. A&A, 600, A68.
⇒ Explanation 1 : break in the diffusion coefficient ?
Indications for a high-rigidity break in the cosmic-ray diffusion coefficient, Preprint arxiv: 1706.09812 4
⇒ Explanation 3 : local source contribution ?
Genolini, Y., Salati, P., Serpico, P. D., & Taillet, R. (2017). Stable laws and cosmic ray physics. A&A, 600, A68.
⇒ Explanation 1 : break in the diffusion coefficient ?
Indications for a high-rigidity break in the cosmic-ray diffusion coefficient, Preprint arxiv: 1706.09812 4
May a particular configuration of the sources explain break features ?
1 10 102 103 104 105 Kinetic Energy Ek [GeV] 2 103 6 103 104 1.4 104 Φp.Ek 2.7
Fiducial CREAM 2005 AMS 2015
⇒ P(Ψ) ?
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∂Ψ ∂t − ∇r.(K∇rΨ) = Q(r, E) ⇒ Time independent equation !
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− ∇r.(K∇rΨ) = Q(r, E) ⇒ Time independent equation ! ⇒ Continuous production in space and time !
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− ∇r.(K∇rΨ) = Q(r, E) ⇒ Time independent equation ! ⇒ Continuous production in space and time !
i
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− ∇r.(K∇rΨ) = Q(r, E) ⇒ Time independent equation ! ⇒ Continuous production in space and time !
i
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− ∇r.(K∇rΨ) = Q(r, E) ⇒ Time independent equation ! ⇒ Continuous production in space and time !
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q ν VMW Θ(h − |z|) Θ(Rgal − r)
VMW = 2 h πR2 and ν ≈ 3 SNs/century 6
7 VMW = 2 h πR2 ν ≈ 3 SNs/century
Büsching, I., Kopp, A., Pohl, M., Schlickeiser, R., Perrot, C., & Grenier, I. (2005). The Astrophysical Journal, 619(1), 314.
→ Stochastic behaviour !
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The flux from N sources writes : Ψ =
N
ψi ⇒ Ψ =
N
ψ = N ψ One can expect to compute ψ from p(ψ) : ψ = ∞ dψ ψ p(ψ) With : p(ψ) =
D(rs, ts)
and time for one source
drs dts (1) Integration over the domain of space and time that gives a flux between ψ and ψ + dψ.
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p(ψ) =
D(rs, ts) drs dts (2) Vψ : domain of space and time that gives a flux between ψ and ψ + dψ. Surface equation in pure diffusive regime : ψ =
q (4 π K t)3/2 exp
4 K t
limiting behaviours, 2D or 3D ! For : ψ ≫ ψ we have, p(ψ) ∝
3D ψ−7/3 2D
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Ψ =
N
ψi ⇒ p(ψ) → P(Ψ) Central limit theorem ? σ2
Ψ = Ψ2 − Ψ2 = N σ2 ψ = Nψ2 − Ψ2
N ψ2 = ∞ ψ2 p(ψ)dψ ∝ ψ1/3∞
cte = ∞
3D
cte = ∞
2D The variance diverges
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Generalised central limit theorem ?
The heavy tail behaviour conditioned the stable law limit ! ∀ψ 0, C(ψ) ≡ ∞
ψ
p(ψ′) dψ′ → lim
ψ→∞ ψαC(ψ) = η > 0
For N sufficiently large : P(Ψ) → 1 σN S[α, 1, 1, 0; 1] Ψ − Ψ σN
3D 4/3 2D and σN =
2Γ(α) sin (α π/2) 1/α
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σN = 1, α = 5/3 → 3D, α = 4/3 → 2D
⇒ So one can define confidence intervals, pvalues...
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For example at 1TeV :
10−6 10−5 10−4 10−3 10−2 10−1 100 pvalue E=1TeV −0.06 −0.04 −0.02 0.00 0.02 0.04 0.06 log10 (Ψ/Ψsim) −50 50 ∆[%] 10−4 10−3 10−2 10−1 100 101 pd f E=1TeV
Stable law α = 4/3 Stable law α = 5/3 Gaussian law σsim Simulations
0.0 0.2 0.4 0.6 0.8 1.0 log10 (Ψ/Ψsim) −50 50 10−6 10−5 10−4 10−3 10−2 10−1 100 pvalue E=1TeV 0.0 0.5 1.0 1.5 2.0 2.5 log10 (Ψ/Ψsim) −50 50
Simulation generated 106 configurations of galaxies. Transition from the 2D to the 3D regime ! ⇒Genolini, Y., Salati, P., Serpico, P. D., & Taillet, R. (2017).
Stable laws and cosmic ray physics. A&A, 600, A68. 14
The diffusive propagator is not causal for some region in space and time...
◮ Loophole : reevaluation of
p(ψ) =
ψ
D(rs, ts) drs dts
◮ p(ψ) ∝
for : ψ < ψc ψ−11/3 for : ψ > ψc The variance converges again!
Shall we use the central limit theorem ?...Not really if ψc is very large. Simulations : Stable law is a very good approximation till 10TeV !
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May a particular configuration of the sources explain break features ?
1 10 102 103 104 105 Kinetic Energy Ek [GeV] 2 103 6 103 104 1.4 104 Φp.Ek 2.7
Fiducial CREAM 2005 AMS 2015
⇒ P(Ψ) ?
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We compute an upper value of the probability that a particular configuration of the sources gives a flux Ψ at 12.8TeV : pvalue = ∞
Ψexp
dψexp +∞ dψth p(ψexp|ψth) p(ψth|Model), Example for the benchmark models : Models MIN MED MAX Probabilities(Stable law 4/3) 0.031 0.0082 0.0013
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More generally.. Effect of stochasticity @ a given energy Could be great to include energy correlations Theoretical uncertainty that should be taken into account
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More details in :
Genolini, Y., Salati, P., Serpico, P. D., & Taillet, R. (2017). Stable laws and cosmic ray physics. A&A, 600, A68. 19
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[Kachelrieß et al., 2015]
2Myr old SNR in order to explain the knee..
⇒ P(Ψ) can be used for an homogeneous diffusion model. Models MIN MED MAX Probabilities 0.0072 0.0012 0.00016
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[Tomassetti et al., 2015]
component model, without prior on their number
⇒ P(Ψ) can be used ! The probability @10GeV is 8.6 × 10−5 !
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