[PPT] - Anomalies in Cosmic Ray Composition: Explanation Based on Mass to PowerPoint Presentation

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Anomalies in Cosmic Ray Composition: Explanation Based

n Mass to Charge Ratio

Adrian Hanusch, Tatyana Liseykina, Mikhail Malkov Universität Rostock Institut für Physik

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Hypothesis of CR origin

supernova SN 1006 remnant

X-ray Chandra image

acceleration by a 1st order Fermi mechanism diffusive shock acceleration (DSA)

particles gain energy by crossing the

shock front

scattering by magnetic perturbations
power-law spectrum

f(p) ∼ p−q with q = 3 r r − 1 = 4 1 − M −2

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Anomalies in CR composition

Measurements

M. Aguilar et al., PRL, 115(21):211101, (2015).

∆q ≈ 0.1 is in conflict with the DSA

EOM in terms of rigidity R = p c/Z e 1 c dR dt = E (r, t) + R × B (r, t)

R2

0 + R2

1 c dr dt = R

R2

0 + R2

◮ same phase-space trajectories for R ≫ R0 = A mp c2/Z e

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Content

Anomalies in cosmic ray composition Scenarios Hybrid simulation Basics Simulation set-up Results Particle spectra Injection efficiency Proton-to-helium ratio Summary and Outlook

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Anomalies in CR composition

Scenarios

1. contribution from several SNRs with different p-He mixtures
V. I. Zatsepin and N. V. Sokolskaya, Astron. Astrophys. 458, 5 (2006).
2. CR spallation in the ISM
P. Blasi and E. Amato, J. Cosmol. Astropart. Phys. 01 (2012).
3. time-dependence of the shock evolution

3.1 effect of SNR environment

Y. Ohira and K. Ioka, Astrophys. J. Lett. 729, L13+ (2011).

3.2 time-dependence of shock strength

M. A. Malkov, P. H. Diamond, and R. Z. Sagdeev, PRL 108(8), 081104 (2012).
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Anomalies in CR composition

Scenarios

1. contribution from several SNRs with different p-He mixtures
V. I. Zatsepin and N. V. Sokolskaya, Astron. Astrophys. 458, 5 (2006).

→ not testable

2. CR spallation in the ISM
P. Blasi and E. Amato, J. Cosmol. Astropart. Phys. 01 (2012).
3. time-dependence of the shock evolution

3.1 effect of SNR environment

Y. Ohira and K. Ioka, Astrophys. J. Lett. 729, L13+ (2011).

3.2 time-dependence of shock strength

M. A. Malkov, P. H. Diamond, and R. Z. Sagdeev, PRL 108(8), 081104 (2012).
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Anomalies in CR composition

Scenarios

1. contribution from several SNRs with different p-He mixtures
V. I. Zatsepin and N. V. Sokolskaya, Astron. Astrophys. 458, 5 (2006).

→ not testable

2. CR spallation in the ISM
P. Blasi and E. Amato, J. Cosmol. Astropart. Phys. 01 (2012).

→ not sufficient for explaining the p/He ratio

A. E. Vladimirov, G. Jóhannesson, I. V. Moskalenko, and T. A. Porter, Astrophys. J. 752, 68 (2012).
3. time-dependence of the shock evolution

3.1 effect of SNR environment

Y. Ohira and K. Ioka, Astrophys. J. Lett. 729, L13+ (2011).

3.2 time-dependence of shock strength

M. A. Malkov, P. H. Diamond, and R. Z. Sagdeev, PRL 108(8), 081104 (2012).
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Anomalies in CR composition

Scenarios

1. contribution from several SNRs with different p-He mixtures
V. I. Zatsepin and N. V. Sokolskaya, Astron. Astrophys. 458, 5 (2006).

→ not testable

2. CR spallation in the ISM
P. Blasi and E. Amato, J. Cosmol. Astropart. Phys. 01 (2012).

→ not sufficient for explaining the p/He ratio

A. E. Vladimirov, G. Jóhannesson, I. V. Moskalenko, and T. A. Porter, Astrophys. J. 752, 68 (2012).
3. time-dependence of the shock evolution

3.1 effect of SNR environment

Y. Ohira and K. Ioka, Astrophys. J. Lett. 729, L13+ (2011).

→ C/He and O/He ratios are independent of R 3.2 time-dependence of shock strength

M. A. Malkov, P. H. Diamond, and R. Z. Sagdeev, PRL 108(8), 081104 (2012).
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Anomalies in CR composition

Mass-to-charge ratio

M. Aguilar et al., PRL, 115(21):211101, (2015).
C/He and O/He ratios are independent of R

AMS-02 Collaboration, http://www.ams02.org/wp-content/uploads/2016/12/Final.pdf. (2016).

assumption

mass-to-charge dependence of

injection

power law exponent:

q(M) = 4 1 − M −2

shock strength decreases with

time

if He2+ is injected more readily

at earlier times

◮

harder integrated spectra

◮ fractions of different species can probe properties of CR accelerators

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Hybrid simulation

Basics

ions determine the relevant scales electrons are treated as a massless fluid ne m dve dt = 0 = −e ne

E + 1

c ve × B

− ∇pe + e ne η J

ions are treated kinetically (PIC) mi dv dt = qi

E + 1

c v × B − η J

dx

dt = v

non-relativistic
low-frequency magnetostatic model:

∇ × B = 4π

c J 1 c ∂t B = ∇ × E

adiabatic relation for electron pressure:

pe ∼ nγe with γe = 5

3

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Hybrid simulation

Simulation set-up

1D spatially, 3D velocity
super-alfvénic plasma flow

enters from the right

B0 = B0 x
realistic composition: 10%

He2+ in number density units: t − inverse proton gyrofrequency 1/ωc n − upstream density n0 x − proton inertial length c/ωp B − upstream magnetic v − Alfvén velocity vA field B0 ∆x = 0.2 c/ωp, ∆t = 0.01/v0, N α

ppc = 100,

Lx up to 17 · 103 c/ωp

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Hybrid simulation

Simulation set-up

1D spatially, 3D velocity
super-alfvénic plasma flow

enters from the right

B0 = B0 x
realistic composition: 10%

He2+ in number density units: t − inverse proton gyrofrequency 1/ωc n − upstream density n0 x − proton inertial length c/ωp B − upstream magnetic v − Alfvén velocity vA field B0 ∆x = 0.2 c/ωp, ∆t = 0.01/v0, N α

ppc = 100,

Lx up to 17 · 103 c/ωp

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Results

Particle spectra

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 100 101 102 103 104 105 106 f(E) / arb. units E / E0

Energy distribution: v0 = 15 vA, t = 1000 1/ωc

fp(E) fHe(E)

E0 = 1

2 mp v2 A

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Results

Particle spectra

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 100 101 102 103 104 105 106 Tp = 39.26 THe = 170.08 f(E) / arb. units E / E0

Energy distribution: v0 = 15 vA, t = 1000 1/ωc

fp(E) fth(E) fHe(E) fth(E)

E0 = 1

2 mp v2 A

thermal distribution

fth(E) ∝ E1/2 exp(−E/T)

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Results

Particle spectra

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 100 101 102 103 104 105 106 Tp = 39.26 THe = 170.08 f(E) / arb. units E / E0

Energy distribution: v0 = 15 vA, t = 1000 1/ωc

fp(E) fth(E) fpow(E) fHe(E) fth(E) fpow(E)

E0 = 1

2 mp v2 A

thermal distribution

fth(E) ∝ E1/2 exp(−E/T)

power-law with cut-off

fpow(E) ∼ E−q exp(−E/Ecut)

supra-thermal particles
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Results

Injection efficiency

definition of the injection efficiency ηinj = f(Einj) ∞ fth(E) dE with Einj from fpow(Einj) = fth(Einj)

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 100 101 102 103 104 105 106 Tp = 39.26 THe = 170.08 f(E) / arb. units E / E0

Energy distribution: v0 = 15 vA, t = 1000 1/ωc

fp(E) fth(E) fpow(E) fHe(E) fth(E) fpow(E)

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Results

Injection efficiency

definition of the injection efficiency ηinj = f(Einj) ∞ fth(E) dE with Einj from fpow(Einj) = fth(Einj)

0.01 0.02 0.03 0.04 0.05 10 20 30 40 50 injection efficiency / % M p+ He2+ fit fit

agreement with theoretical

prediction ηinj ∼ M −1 ln(M/M∗) at high M

M. A. Malkov, Phys. Rev. E 58, 4911, (1998).
fit η(M) = a · (M − b) · M −c
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Results

Injection efficiency

definition of the injection efficiency ηinj = f(Einj) ∞ fth(E) dE with Einj from fpow(Einj) = fth(Einj)

0.01 0.02 0.03 0.04 0.05 10 20 30 40 50 injection efficiency / % M p+ He2+ fit fit

agreement with theoretical

prediction ηinj ∼ M −1 ln(M/M∗) at high M

M. A. Malkov, Phys. Rev. E 58, 4911, (1998).
fit η(M) = a · (M − b) · M −c

◮ proton injection dominant at low M shocks ◮ slight prevalence of He2+ injection at high M

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Results

Proton-to-helium ratio

expansion of a SNR: Sedov-Taylor phase Rs = C1/5

ST t2/5

and Vs = 2 5C1/5

ST t−3/5 = 2

5C5/2

ST R−3/2 s

with: CST = 25 ESN 4π ρ0 number of CRs of species α in the shock interior Nα(p) ∝ Rmax

Rmin

fα(p, M(R))R2 dR ∝ M−2

min

M−2

max

fα(p, M) dM −2 with fα ∝ ηα(M) (R/Rinj)−q(M) q(M) =

4 1−M−2

10 1 10 100 1000 Np/NHe rigidity R / GV PAMELA AMS-02 fit Malkov et al. 2012 simulation

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Summary & Outlook

Summary

series of hybrid simulations focused on particle injection
injection efficiency depends on Mach number and A/Z

ratio

good agreement between simulation and measured p/He

ratio for R > 10 GV Outlook

two-dimensional simulations
detailed investigation of the trajectories of injected particles

Acknowledgements financial support by RFBR NASA ATP-program computational resources

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Summary & Outlook

Summary

series of hybrid simulations focused on particle injection
injection efficiency depends on Mach number and A/Z

ratio

good agreement between simulation and measured p/He

ratio for R > 10 GV Outlook

two-dimensional simulations
detailed investigation of the trajectories of injected particles

Acknowledgements financial support by RFBR NASA ATP-program computational resources

Thank you for your attention

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