Michael Kachelrieß NTNU, Trondheim · 2017. 9. 27. · Development of the elmag. cascade: analytical estimate: [Strong ’74, Berezinsky, Smirnov ’75] Jγ(E) = K(E/ε X)−3/2

[]

Minimal Model for Cosmic Rays and Neutrinos

Michael Kachelrieß

NTNU, Trondheim

Introduction Outline

Outline of the talk

1 Introduction

◮ CR–γ–ν connection

◮ CR composition

◮ elmag. cascades

◮ constraints & wishes

2 Escape model for Galactic CRs

◮ main properties

◮ neutrinos from starburst galaxies

3 Minimal model for UHECRs and neutrinos

◮ with only Ap interactions

◮ with Aγ and Ap interactions

4 Conclusions

Michael Kachelrieß (NTNU Trondheim) Minimal Models for Cosmic Rays and NeutrinosPAHEN, Napoli, 26. Sep. ’17 2 / 19


Outline of the talk

1 Introduction


◮ CR composition

◮ elmag. cascades



◮ main properties





4 Conclusions



Outline of the talk

1 Introduction


◮ CR composition

◮ elmag. cascades



◮ main properties





4 Conclusions


Introduction CR–γ–ν connection

The CR–γ–ν connection:

HE neutrinos and photons are unavoidable byproducts of HECRs

astrophysical models, cosmogenic flux:◮ ratio Iν/Ip determined by nuclear composition of UHECRs and source

evolution◮ ratio Iν/Iγ determined by isospin







astrophysical models, direct flux:◮ stronger model dependence:

⋆ target density⋆ photons may cascade in source







astrophysical models, direct flux:◮ stronger model dependence:

⋆ target density⋆ photons may cascade in source

Our aim:◮ is a single source class responsible for extragalactic CRs, photons and

neutrinos?


Introduction CR composition

Composition of CRs: KASCADE-Grande 2013

primary energy E/eV

1510

1610 1710

1810

)1

.5 e

V-1

s-1

sr

-2 / (

m2

.5 E

dif

f. f

lux

dJ

/dE

·

1510

1610

1710

Akeno (J.Phys.G18(1992)423)AGASA (ICRC 2003)HiResI (PRL100(2008)101101)HiResII (PRL100(2008)101101)AUGER (arXiv:1107:4809)AUGER AMIGA infill (ICRC 2011)

EAS-TOP (Astrop.Phys.10(1999)1)Tibet-III, QGSJET 01 (ApJ678(2008)1165)GAMMA (ICRC 2011)IceTop (arXiv:1202.3039v1)TUNKA-133 (ICRC 2011)Yakutsk (NewJ.Phys11(2008)065008)KASCADE-Grande, QGSJET II (Astrop.Phys.36(2012)183)

KASCADE-Grande, all-part., QGSJET II (this work)KASCADE-Grande, light (p), QGSJET II (this work)KASCADE-Grande, medium (He+C+Si), QGSJET II (this work)KASCADE-Grande, heavy (Fe), QGSJET II (this work)

KASCADE, all-part., QGSJET II (see Appendix A)KASCADE, light (p), QGSJET II (see Appendix A)

KASCADE, medium (He+C+Si), QGSJET II (see Appendix A)KASCADE, heavy (Fe), QGSJET II (see Appendix A)



Composition of CRs: Auger [arXiv:1409.5083 ]

0

100

200

300

400

500

600

500 600 700 800 900 1000

N

Sibyll 2.1

log(E/eV) = 17.8-17.9

p < 10-4

500 600 700 800 900 1000

Sibyll 2.1

log(E/eV) = 17.8-17.9

p = 0.013

500 600 700 800 900 1000

Sibyll 2.1

log(E/eV) = 17.8-17.9

p = 0.235

FeN

Hep

Auger

0

100

200

300

400

500

600

500 600 700 800 900 1000

N

QGSJET II-04

log(E/eV) = 17.8-17.9

p < 10-4

500 600 700 800 900 1000

QGSJET II-04

log(E/eV) = 17.8-17.9

p < 10-3

500 600 700 800 900 1000

QGSJET II-04

log(E/eV) = 17.8-17.9

p = 0.326

0

100

200

300

400

500

600

500 600 700 800 900 1000

N

Xmax [g/cm2]

EPOS-LHC

log(E/eV) = 17.8-17.9

p < 10-4

500 600 700 800 900 1000

Xmax [g/cm2]

EPOS-LHC

log(E/eV) = 17.8-17.9

p = 0.776

500 600 700 800 900 1000

Xmax [g/cm2]

EPOS-LHC

log(E/eV) = 17.8-17.9

p = 0.769



Composition of CRs: Auger [arXiv:1409.5083 ]

0

100

200

300

400

500

600

500 600 700 800 900 1000

N

Sibyll 2.1

log(E/eV) = 17.8-17.9

p < 10-4

500 600 700 800 900 1000

Sibyll 2.1

log(E/eV) = 17.8-17.9

p = 0.013

500 600 700 800 900 1000

Sibyll 2.1

log(E/eV) = 17.8-17.9

p = 0.235

FeN

Hep

Auger

0

100

200

300

400

500

600

500 600 700 800 900 1000

N

QGSJET II-04

log(E/eV) = 17.8-17.9

p < 10-4

500 600 700 800 900 1000

QGSJET II-04

log(E/eV) = 17.8-17.9

p < 10-3

500 600 700 800 900 1000

QGSJET II-04

log(E/eV) = 17.8-17.9

p = 0.326

0

100

200

300

400

500

600

500 600 700 800 900 1000

N

Xmax [g/cm2]

EPOS-LHC

log(E/eV) = 17.8-17.9

p < 10-4

500 600 700 800 900 1000

Xmax [g/cm2]

EPOS-LHC

log(E/eV) = 17.8-17.9

p = 0.776

500 600 700 800 900 1000

Xmax [g/cm2]

EPOS-LHC

log(E/eV) = 17.8-17.9

p = 0.769

composition 6 × 1017 − 5 × 10

18 eV consistent with

◮ 50% p, 50% He+N, < 20%Fe



Composition of CRs:

0

100

200

300

400

500

600

500 600 700 800 900 1000

N

Sibyll 2.1

log(E/eV) = 17.8-17.9

p < 10-4

500 600 700 800 900 1000

Sibyll 2.1

log(E/eV) = 17.8-17.9

p = 0.013

500 600 700 800 900 1000

Sibyll 2.1

log(E/eV) = 17.8-17.9

p = 0.235

FeN

Hep

Auger

0

100

200

300

400

500

600

500 600 700 800 900 1000

N

QGSJET II-04

log(E/eV) = 17.8-17.9

p < 10-4

500 600 700 800 900 1000

QGSJET II-04

log(E/eV) = 17.8-17.9

p < 10-3

500 600 700 800 900 1000

QGSJET II-04

log(E/eV) = 17.8-17.9

p = 0.326

0

100

200

300

400

500

600

500 600 700 800 900 1000

N

Xmax [g/cm2]

EPOS-LHC

log(E/eV) = 17.8-17.9

p < 10-4

500 600 700 800 900 1000

Xmax [g/cm2]

EPOS-LHC

log(E/eV) = 17.8-17.9

p = 0.776

500 600 700 800 900 1000

Xmax [g/cm2]

EPOS-LHC

log(E/eV) = 17.8-17.9

p = 0.769

composition 6 × 1017 − 5 × 10

18 eV consistent with

◮ 50% p, 50% He+N, < 20%Fe

◮ early transition from Galactic to extragalactic CRs



Transition to extragalactic CRs – anisotropy limits

dipole quadrupole

E [EeV]1 10

Upp

er L

imit

- D

ipol

e A

mpl

itude

-210

-110

1

Z=1Z=26

E [EeV]1 10

+λU

pper

Lim

it - A

mpl

itude

-210

-110

1

Z=1Z=26



Transition to extragalactic CRs – anisotropy limits

dipole quadrupole

E [EeV]1 10

Upp

er L

imit

- D

ipol

e A

mpl

itude

-210

-110

1

Z=1Z=26

E [EeV]1 10

+λU

pper

Lim

it - A

mpl

itude

-210

-110

1

Z=1Z=26

dominant light Galactic composition around E = 1018 eV excluded[Giacinti, MK, Semikoz, Sigl (’12), PAO ’13 ]



Effect of heavier nuclei

models reproducing UHECR composition

◮ neutrino flux Iν(E) ∝ A1−αIp(E)






◮ Peter’s cycle: Emax,A = ZEmax,p

◮ require threshold ⇒ based on Aγ interactions






◮ Peter’s cycle: Emax,A = ZEmax,p

◮ require threshold ⇒ based on Aγ interactions

ν flux is too small, at too high E



ν and mixed composition [e.g. Unger, Farrar, Anchordoqui ’15 ]


Introduction Constraints & wishes

IceCube searches for sources: transient sources


Introduction Constraints & wishes

IceCube searches for sources: stationary sources


Introduction Cascade spectrum

Development of the elmag. cascade:



Development of the elmag. cascade:

analytical estimate: [Strong ’74, Berezinsky, Smirnov ’75 ]

Jγ(E) =

K(E/εX)−3/2 at E ≤ εX

K(E/εX)−2 at εX ≤ E ≤ εa

0 at E > εa

three regimes:◮ Thomson cooling:

Eγ =4

3

εbbE2

e

m2e

≈ 100 MeV

(

Ee

1TeV

)2

◮ plateau region: ICS Eγ ∼ Ee

◮ above pair-creation threshold smin = 4Eγεbb = 4m2

e:flux exponentially suppressed



Cascade limit: α = 2.1

1

10

100

1000

10000

1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17

E2 J

(E)

[eV

/cm

2 s s

r]

E/eV

gammanu

Fermi EGRB




1

10

100

1000

10000

1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17

E2 J

(E)

[eV

/cm

2 s s

r]

E/eV

gammanu

Fermi EGRB




1

10

100

1000

10000

1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17

E2 J

(E)

[eV

/cm

2 s s

r]

E/eV

gammanu

Fermi EGRB



Blazars as neutrino sources?

unresolved blazars dominate HE part of EGRB





stacked analysis of gamma-ray and muon neutrino flux from blazars

⇒ disfavors blazars as HE neutrino source

[IceCube ’16, A.Neronov, D.V.Semikoz, K.Ptitsyna ’16 ]





stacked analysis of gamma-ray and muon neutrino flux from blazars

⇒ disfavors blazars as HE neutrino source

[IceCube ’16, A.Neronov, D.V.Semikoz, K.Ptitsyna ’16 ]

leptonic blazar models favored to explain EGRB

neutrino sources should give sub-dominant contribution to EGRB



Constraints on a minimal model:

a single source class that

fits the extragalactic UHECR flux and composition

fits the (extragalactic) neutrino flux



Constraints on a minimal model:

a single source class that

fits the extragalactic UHECR flux and composition

fits the (extragalactic) neutrino flux

gives subdominant contribution to EGRB

consistent with early Galactic to extragalactic transition

⇒ ankle has to be a feature of source spectrum


Escape model

Escape model for Galactic cosmic rays [Giacinti, MK, Semikoz ’14+ ]

reproduces fluxes of individual CR groups

1010

1011

1012

1013

1014 1015 1016 1017 1018 1019 1020

E2.

5 F(E

) [e

V2.

5 /cm

2 /s/s

r]

E [eV]

TibetKASCADEGrandeAuger 2013PHeCNOSiFetotal


Escape model



explains dipole anisotropy

10-5

10-4

10-3

10-2

1011 1012 1013 1014 1015 1016 1017 1018

100 TeV

1 PeV

δ

E [eV]

all dataIceCube 2013

fit 1 SNGalactic

totalGalactic


Escape model




fixes extragalactic flux: F iexgal(E) = F i

obs(E) − F igal(E)


Escape model




fixes extragalactic flux: F iexgal(E) = F i

obs(E) − F igal(E)

escape model applies also to other normal galaxies as starburstgalaxies:

◮ magnetic fields factor 100 higher:

◮ if knee is caused by⋆ diffusion: Ecr ∼ B, neutrino knee at few ×10

16 eV

⋆ source: Emax ∼ BCR, neutrino knee at few ×1014 eV


Escape model Exgal. protons, γ’s and ν’s

Normal and starburst galaxies:

assume E−2.2 source spectrum

normalisation from escape model

starburst: B ∼ 100BMW ⇒ rescale grammage and Emax

fix QCR via SN/star formation rate

vary gas density



Normal and starburst galaxies: [Giacinti, MK, Kalashev, Neronov, Semikoz ’15 ]

0.1

1

10

100

1000

108 1010 1012 1014 1016 1018 1020

jE2 , e

V c

m-2

s-1

sr-1

E, eV

νgal(98%)

pγ

νEGKASCADE 2013

KASCADE Grande EGAuger 2013 Protons



Normal and starburst galaxies: [Giacinti, MK, Kalashev, Neronov, Semikoz ’15 ]

0.1

1

10

100

1000

108 1010 1012 1014 1016 1018 1020

jE2 , e

V c

m-2

s-1

sr-1

E, eV

νgal(98%)

pγ

νEGKASCADE 2013

KASCADE Grande EGAuger 2013 Protons

can not explain exgal. protons

sources can not be dominant sources of both EGRB and neutrinos


Minimal model

Source model:

3 zones

◮ core: rigidity dependent acceleration dN/dR ∝ R−α exp(−R/Rmax)

◮ inner zone: Aγ interactions

◮ outer zone: Ap interactions

diffusion: increase of effective τint

source evolution

◮ BL Lac ≃ peaked at late times

◮ AGN ≃ peaked at early times


Minimal model

Source model:

3 zones





source evolution




Minimal model

Source model:

3 zones





source evolution




Minimal model

Late evol., only interactions on gas: α = 1.8, τpp

0= 0.035 at E0 = 10

19 eV

10-2

10-1

100

101

102

103

104

105

1010 1012 1014 1016 1018 1020

Fermi LAT

IceCube Auger

KASCADE Grande

γν

E2 F

(E)

[eV

/cm

2 /s/s

r]

E [eV]

total EGtotal Gal

p2-4

5-1617-2829-56

[MK, Kalashev, Ostapchenko, Semikoz ’17 ]


Minimal model


0= 0.035 at E0 = 10

19 eV

550

600

650

700

750

800

850

900

1017 1018 1019 1020

Xm

ax [g

/cm

2 ]

E [eV]

Augerp EPOS LHC

Fe EPOS LHCp QGSJetII-4

Fe QGSJetII-4model QGSJetII-4

model EPOS



Minimal model


0= 0.035 at E0 = 10

19 eV

10

20

30

40

50

60

70

80

1017 1018 1019 1020

RM

S(X

max

) [g

/cm

2 ]

E [eV]

Augerp EPOS LHC



model EPOS



Minimal model

AGN evol., gas and photons: α = 1.5, τpp

0= 0.035 and τ

pγ

0= 0.29

10-2

10-1

100

101

102

103

104

105

1010 1012 1014 1016 1018 1020

γ ν

Fermi LAT

IceCube Auger

KASCADE Grande

E2 F

(E)

[eV

/cm

2 /s/s

r]

E [eV]

total EGtotal Gal

p2-4

5-1617-2829-56



Minimal model


0= 0.035 and τ

pγ

0= 0.29

550

600

650

700

750

800

850

900

1017 1018 1019 1020

Xm

ax [g

/cm

2 ]

E [eV]

Augerp EPOS LHC


Fe QGSJetII-4model QGSJetII-4model EPOS-LHC



Minimal model


0= 0.035 and τ

pγ

0= 0.29

10

20

30

40

50

60

70

80

1017 1018 1019 1020

RM

S(X

max

) [g

/cm

2 ]

E [eV]

Augerp EPOS LHC



model EPOS

10

20

30

40

50

60

70

80

1017 1018 1019 1020

RM

S(X

max

) [g

/cm

2 ]

E [eV]

Augerp EPOS LHC



model EPOS



Summary

Summary1 EGRB constrains stronly neutrino sources:

◮ slope of extragal. neutrino α <∼

2.3

◮ neutrino sources are not main source class of EGRB

2 neutrino signal in IceCube:

◮ isotropy favours dominant extragalactic origin above 10–100 TeV

◮ steeper additional contribution dominating at low energies (?)

3 common source class for UHECRs and neutrinos?

◮ several candidates as GRBs are already disfavoured

◮ (subclasses of) AGNs remain attractive option

◮ large neutrino flux at “low” energies requires Ap interactions

◮ UHECR composition favours nuclei with Aγ

◮ sources with both Ap and Aγ interactions favoured


Documents

Michael Kachelrieß NTNU, Trondheim · 2017. 9. 27. · Development of the elmag. cascade: analytical estimate: [Strong ’74, Berezinsky, Smirnov ’75] Jγ(E) = K(E/ε X)−3/2