Galactic Sources, Magnetic Fields and the Energy-Dependent - - PowerPoint PPT Presentation

Antoine Calvez TeV Particle Astrophysics 2010

Galactic Sources, Magnetic Fields and the Energy-Dependent composition of UHECRs.

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Antoine Calvez TeV Particle Astrophysics 2010

Outline

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Antoine Calvez TeV Particle Astrophysics 2010

Outline

• The cosmic ray spectrum

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Antoine Calvez TeV Particle Astrophysics 2010

Outline

• The cosmic ray spectrum
• The Pierre Auger Observatory (PAO) and its energy-dependent chemical

composition

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Antoine Calvez TeV Particle Astrophysics 2010

Outline

• The cosmic ray spectrum
• The Pierre Auger Observatory (PAO) and its energy-dependent chemical

composition

• The role of galactic sources

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Antoine Calvez TeV Particle Astrophysics 2010

Outline

• The cosmic ray spectrum
• The Pierre Auger Observatory (PAO) and its energy-dependent chemical

composition

• The role of galactic sources
• diffusion, anisotropy, spectral features

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Antoine Calvez TeV Particle Astrophysics 2010

Outline

• The cosmic ray spectrum
• The Pierre Auger Observatory (PAO) and its energy-dependent chemical

composition

• The role of galactic sources
• diffusion, anisotropy, spectral features

[AC, Kusenko, Nagataki]

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Antoine Calvez TeV Particle Astrophysics 2010

UHECR

• E < 1 GeV solar modulation make

studies of the primary cosmic ray spectrum very complex

• 1 GeV < E < 105 GeV galactic
• rigin (SNR)
• 105 GeV < E < 109 GeV galactic
• rigin (supernova explosion into

stellar wind)

• E > 109 GeV Ultra High Energy

Cosmic Rays (UHECRs)

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Antoine Calvez TeV Particle Astrophysics 2010

Above the Ankle

UHECRs above the ”ankle” (E > 109 GeV) are believed to be of extragalactic

• rigin for two reasons:

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Antoine Calvez TeV Particle Astrophysics 2010

Above the Ankle

UHECRs above the ”ankle” (E > 109 GeV) are believed to be of extragalactic

• rigin for two reasons:
• lack of plausible galactic sources

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Antoine Calvez TeV Particle Astrophysics 2010

Above the Ankle

UHECRs above the ”ankle” (E > 109 GeV) are believed to be of extragalactic

• rigin for two reasons:
• lack of plausible galactic sources
• lack of galactocentric anisotropy, inconsistent with retaining protons in Galactic

micro-Gauss fields.

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Antoine Calvez TeV Particle Astrophysics 2010

Above the Ankle

UHECRs above the ”ankle” (E > 109 GeV) are believed to be of extragalactic

• rigin for two reasons:
• lack of plausible galactic sources
• lack of galactocentric anisotropy, inconsistent with retaining protons in Galactic

micro-Gauss fields. Both of these reasons can be challenged

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Antoine Calvez TeV Particle Astrophysics 2010

Above the Ankle

UHECRs above the ”ankle” (E > 109 GeV) are believed to be of extragalactic

• rigin for two reasons:
• lack of plausible galactic sources
• lack of galactocentric anisotropy, inconsistent with retaining protons in Galactic

micro-Gauss fields. Both of these reasons can be challenged Both of these reasons should be challenged in view of a recent PAO discovery

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Antoine Calvez TeV Particle Astrophysics 2010

Pierre Auger energy-dependent chemical composition

[Auger PRL 104 (2010) 091101] 5

Antoine Calvez TeV Particle Astrophysics 2010

Pierre Auger energy-dependent chemical composition

[Auger PRL 104 (2010) 091101]

The composition gets heavier with energy

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Antoine Calvez TeV Particle Astrophysics 2010

Pierre Auger energy-dependent chemical composition

[Auger PRL 104 (2010) 091101]

The composition gets heavier with energy What could cause this effect?

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Antoine Calvez TeV Particle Astrophysics 2010

Not Observed by HiRes

[Auger PRL 104 (2010) 091101, HiRes ApJ 622 (2005) 910, HiRes arXiv:0910.4184] 6

Antoine Calvez TeV Particle Astrophysics 2010

Interpreting the PAO Results

There exist two possible solutions to this puzzle:

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Antoine Calvez TeV Particle Astrophysics 2010

Interpreting the PAO Results

There exist two possible solutions to this puzzle:

• The segregation occurs at the source with a heavy element favored acceleration

mechanism. This is unlikely because of photodissociation

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Antoine Calvez TeV Particle Astrophysics 2010

Interpreting the PAO Results

There exist two possible solutions to this puzzle:

• The segregation occurs at the source with a heavy element favored acceleration

mechanism. This is unlikely because of photodissociation

• The acceleration mechanism affects all the particles the same way and the

segregation occurs during the transport of the nuclei.

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Antoine Calvez TeV Particle Astrophysics 2010

Interpreting the PAO Results

There exist two possible solutions to this puzzle:

• The segregation occurs at the source with a heavy element favored acceleration

mechanism. This is unlikely because of photodissociation

• The acceleration mechanism affects all the particles the same way and the

segregation occurs during the transport of the nuclei.

This is exactly what you would expect for Galactic sources...

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Antoine Calvez TeV Particle Astrophysics 2010

Interpreting the PAO Results

There exist two possible solutions to this puzzle:

• The segregation occurs at the source with a heavy element favored acceleration

mechanism. This is unlikely because of photodissociation

• The acceleration mechanism affects all the particles the same way and the

segregation occurs during the transport of the nuclei.

This is exactly what you would expect for Galactic sources... Why?

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Antoine Calvez TeV Particle Astrophysics 2010

Diffusion

B

l

B

l

c

Two different regimes depending on the energy of the particle

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Antoine Calvez TeV Particle Astrophysics 2010

Diffusion

critical energy E0 where rL = lc for E < E0, we get lc >> rL

• mean free path ∼ l
• D = l

3 ≡ D0

for E > E0, we get lc ∼ rL

• mean free path >> l
• D = D0

(

E E0

)2

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Antoine Calvez TeV Particle Astrophysics 2010

Diffusion

critical energy E0 where rL = lc for E < E0, we get lc >> rL

• mean free path ∼ l
• D = l

3 ≡ D0

for E > E0, we get lc ∼ rL

• mean free path >> l
• D = D0

(

E E0

)2 E0 depends on the charge of the nuclei

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Antoine Calvez TeV Particle Astrophysics 2010

Diffusion with Non-Unit Charge

For a particle with charge qi = eZi, we get a critical energy E0,i with rL,i = lc:

• rL,i =

E Bqi

• E0,i = eBlcZi
• E0,i = Zi ×

( 108 eV ) (

B 3×10−6 G

) (

lc 0.3 kpc

)

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Antoine Calvez TeV Particle Astrophysics 2010

Diffusion with Non-Unit Charge

For a particle with charge qi = eZi, we get a critical energy E0,i with rL,i = lc:

• rL,i =

E Bqi

• E0,i = eBlcZi
• E0,i = Zi ×

( 108 eV ) (

B 3×10−6 G

) (

lc 0.3 kpc

) The diffusion coefficient is therefore: Di(E) =      D0 (

E E0,i

)δ1 E ≤ E0,i, D0 (

E E0,i

)(2−δ2) E > E0,i

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Antoine Calvez TeV Particle Astrophysics 2010

Diffusion Equation

For a point-like source: Qi(E,⃗ r) = Q0ξi ( E E0,i )−γ δ(⃗ r) We solve the following differential equation: ∂ni ∂t − ⃗ ∇(Di⃗ ∇ni) + ∂ ∂E(bini) = Qi(E,⃗ r, t) + ∑

k

∫ Pik(E, E′)nk(E′)dE′

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Antoine Calvez TeV Particle Astrophysics 2010

Diffusion Equation

For a point-like source: Qi(E,⃗ r) = Q0ξi ( E E0,i )−γ δ(⃗ r) We solve the following differential equation: ∂ni ∂t − ⃗ ∇(Di⃗ ∇ni) + ∂ ∂E(bini) = Qi(E,⃗ r, t) + ∑

k

∫ Pik(E, E′)nk(E′)dE′ Below GZK energies, energy losses are negligible thus we only consider diffusion terms.

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Antoine Calvez TeV Particle Astrophysics 2010

Solution

The flux is: ni(E, r) = Q0 4πrDi(E) ( E E0,i )−γ with diffusion time tD: tD ∼ R2 Di ∼ 107yr ( R 10 kpc )2 (26 Zi × 1019 eV E )2−δ2

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Antoine Calvez TeV Particle Astrophysics 2010

Consequences

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Antoine Calvez TeV Particle Astrophysics 2010

Consequences

• Diffusion is energy denpendent

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Antoine Calvez TeV Particle Astrophysics 2010

Consequences

• Diffusion is energy denpendent

The spectral slope changes at E ∼ E0,i

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Antoine Calvez TeV Particle Astrophysics 2010

Consequences

• Diffusion is energy denpendent

The spectral slope changes at E ∼ E0,i

• The flux drops dramatically because the particles escape from the galaxy

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Antoine Calvez TeV Particle Astrophysics 2010

Consequences

• Diffusion is energy denpendent

The spectral slope changes at E ∼ E0,i

• The flux drops dramatically because the particles escape from the galaxy
• Diffusion time depends on charge

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Antoine Calvez TeV Particle Astrophysics 2010

Consequences

• Diffusion is energy denpendent

The spectral slope changes at E ∼ E0,i

• The flux drops dramatically because the particles escape from the galaxy
• Diffusion time depends on charge

Diffusion times for nuclei are longer than for protons of the same energy

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Antoine Calvez TeV Particle Astrophysics 2010

Consequences

• Diffusion is energy denpendent

The spectral slope changes at E ∼ E0,i

• The flux drops dramatically because the particles escape from the galaxy
• Diffusion time depends on charge

Diffusion times for nuclei are longer than for protons of the same energy

• The flux drops for protons at lower energies than heavy nuclei

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Antoine Calvez TeV Particle Astrophysics 2010

The Source Problem

Galactic sources are likely to exist, and more pertinently, to have existed:

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Antoine Calvez TeV Particle Astrophysics 2010

The Source Problem

Galactic sources are likely to exist, and more pertinently, to have existed:

• Hypernovae

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Antoine Calvez TeV Particle Astrophysics 2010

The Source Problem

Galactic sources are likely to exist, and more pertinently, to have existed:

• Hypernovae
• Collapsars

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Antoine Calvez TeV Particle Astrophysics 2010

The Source Problem

Galactic sources are likely to exist, and more pertinently, to have existed:

• Hypernovae
• Collapsars
• Unusual Supernovae

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Antoine Calvez TeV Particle Astrophysics 2010

The Source Problem

Galactic sources are likely to exist, and more pertinently, to have existed:

• Hypernovae
• Collapsars
• Unusual Supernovae
• GRBs

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Antoine Calvez TeV Particle Astrophysics 2010

GRBs as Possible Galactic Candidates

• GRBs have been proposed as sources of extragalactic UHECRs

[Vietri; Waxman; Dermer]

• Galactic GRBs have been considered as sources of UHECRs

[Dermer et al., Biermann et al.]

• Long GRBs: probably unusual supernova explosions or hypernovae. Short GRBs:

probably mergers of compact stars.

• Both should have happened in our own Galaxy in the past, at a combined rate
• f one per 104 − 105 years.
• Past Galactic GRBs have been considered as the explanation of 511 keV line

from the Galactic Center [Bertone, et al.; Parizot et al.; AC, Kusenko], as well as the electron excess of PAMELA/Fermi [Ioka; AC, Kusenko]

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Antoine Calvez TeV Particle Astrophysics 2010

Distribution of GRBs in the Milky Way

Supernovae or long GRBs, assuming they follow star counts [Bahcall et al.] Short GRBs, based

• n
• bserved

distribution in other galaxies [Cui, Aoi, Nagataki]

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Antoine Calvez TeV Particle Astrophysics 2010

Comparison with Pierre Auger data Protons, Fe, Overall Spectrum

• 5108 1109

5109 11010 51010 1.01011 1.01012 5.01011 2.01011 2.01012 3.01011 1.51011 1.51012 7.01011 E GeV E3dNdE GeV2 km2 s1 sr1

[AC, Kusenko, Nagataki]

Energy in UHECR per source (GRB, hypernova, etc.) is 1044 erg above 1019 eV.

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Antoine Calvez TeV Particle Astrophysics 2010

Galactocentric anisotropy (sources follow stars)

1108 5108 1109 5109 11010 0.02 0.05 0.10 0.20 E GeV ∆ Total Fe p

[AC, Kusenko, Nagataki]

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Antoine Calvez TeV Particle Astrophysics 2010

Clusters of events from recent/closest GRBs supernovae/long GRBs short GRBs

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Antoine Calvez TeV Particle Astrophysics 2010

Clusters of events from recent/closest GRBs supernovae/long GRBs short GRBs

Extragalactic protons would also contribute to the overall spectrum above 1018 eV, and any anisotropy would be diluted by magnetic fields

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Antoine Calvez TeV Particle Astrophysics 2010

Summary

The energy-dependent composition observed by PAO motivates alternative solutions to the origin of UHECRs: Galactic Sources

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Antoine Calvez TeV Particle Astrophysics 2010

Summary

The energy-dependent composition observed by PAO motivates alternative solutions to the origin of UHECRs: Galactic Sources

• Energy dependent diffusion coefficient offers a solution to the dominance of

nuclei at 1018 − 1019 eV

• The diffusion process within galactic magnetic fields maintains the galactocentric

anisotropy below a few percents

• Many possible source exist within the Milky Way

As long as event rate exceeds 1/108 year

• The apparent clustering could be the result of the most recent event

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Antoine Calvez TeV Particle Astrophysics 2010

Extra Slides

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Antoine Calvez TeV Particle Astrophysics 2010

Magnetic Field Length Scale

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Antoine Calvez TeV Particle Astrophysics 2010

Magnetic Field Length Scale

• Best fit for average random field and scale length B ∼ 5 µG and lc ∼ 55 pc

[Rand & Kulkarni, ApJ 343, 760]

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Antoine Calvez TeV Particle Astrophysics 2010

Magnetic Field Length Scale

• Best fit for average random field and scale length B ∼ 5 µG and lc ∼ 55 pc

[Rand & Kulkarni, ApJ 343, 760]

Based on single cell-size models of Galactic random fields

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Antoine Calvez TeV Particle Astrophysics 2010

Magnetic Field Length Scale

• Best fit for average random field and scale length B ∼ 5 µG and lc ∼ 55 pc

[Rand & Kulkarni, ApJ 343, 760]

Based on single cell-size models of Galactic random fields

• Stellar wind and supernova explosions inject turbulent energy into ISM on the

10 − 100 pc scales

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Antoine Calvez TeV Particle Astrophysics 2010

Magnetic Field Length Scale

• Best fit for average random field and scale length B ∼ 5 µG and lc ∼ 55 pc

[Rand & Kulkarni, ApJ 343, 760]

Based on single cell-size models of Galactic random fields

• Stellar wind and supernova explosions inject turbulent energy into ISM on the

10 − 100 pc scales Energy transferred to smaller scales via direct cascade

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Antoine Calvez TeV Particle Astrophysics 2010

Magnetic Field Length Scale

• Best fit for average random field and scale length B ∼ 5 µG and lc ∼ 55 pc

[Rand & Kulkarni, ApJ 343, 760]

Based on single cell-size models of Galactic random fields

• Stellar wind and supernova explosions inject turbulent energy into ISM on the

10 − 100 pc scales Energy transferred to smaller scales via direct cascade Energy transferred to larger scales via inverse cascade of magnetic helicity

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Antoine Calvez TeV Particle Astrophysics 2010

Magnetic Field Length Scale

• Best fit for average random field and scale length B ∼ 5 µG and lc ∼ 55 pc

[Rand & Kulkarni, ApJ 343, 760]

Based on single cell-size models of Galactic random fields

• Stellar wind and supernova explosions inject turbulent energy into ISM on the

10 − 100 pc scales Energy transferred to smaller scales via direct cascade Energy transferred to larger scales via inverse cascade of magnetic helicity Dramatic change in the spectral slope of the magnetic energy EB(k) around ∼ 0.1 kpc

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Antoine Calvez TeV Particle Astrophysics 2010

Composite Magnetic Energy Spectrum

[Han, Ferriere and Manchester,ApJ. 610, 820 (2004)] 23

Antoine Calvez TeV Particle Astrophysics 2010

Composition

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Antoine Calvez TeV Particle Astrophysics 2010

Composition

External Shock

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Antoine Calvez TeV Particle Astrophysics 2010

Composition

External Shock

• Large dissipation radii

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Antoine Calvez TeV Particle Astrophysics 2010

Composition

External Shock

• Large dissipation radii
• Nuclei can easily survive

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Antoine Calvez TeV Particle Astrophysics 2010

Composition

External Shock

• Large dissipation radii
• Nuclei can easily survive

Internal Shock The nuclei can survive if:

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Antoine Calvez TeV Particle Astrophysics 2010

Composition

External Shock

• Large dissipation radii
• Nuclei can easily survive

Internal Shock The nuclei can survive if:

• Internal shock radius is large

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Antoine Calvez TeV Particle Astrophysics 2010

Composition

External Shock

• Large dissipation radii
• Nuclei can easily survive

Internal Shock The nuclei can survive if:

• Internal shock radius is large
• Large Lorentz factor of the relativistic jets

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Antoine Calvez TeV Particle Astrophysics 2010

Composition

External Shock

• Large dissipation radii
• Nuclei can easily survive

Internal Shock The nuclei can survive if:

• Internal shock radius is large
• Large Lorentz factor of the relativistic jets
• (And/Or) In the presence of a synchrotron self-absorption break

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