Документ взят из кэша поисковой машины. Адрес оригинального документа : http://nuclphys.sinp.msu.ru/conf/epp10/Berezinsky.pdf Дата изменения: Sat Sep 7 14:54:16 2013 Дата индексирования: Fri Feb 28 02:50:51 2014 Кодировка: IBM-866

STATUS of ANKLE in UHECR
V. Berezinsky INFN, Laboratori Nazionali del Gran Sasso, Italy


Total CR spectrum and features
104 102 10-1 10-4 10-7 10-10 10-13 10-16 10-19

Flux (m2 sr s GeV)-1

Knee

(1 particle per m2-year)

2 nd knee
10-22 10-25 10-28 109 1011 1013 1015 1017 1019 1021

(1 particle per km2-year)

Ankle

Energy (eV)


SPECTRA and EXPERIMENTS


OBSERVED CR FEATURES § Knees Proton knee: MSU, Khristiansen and Kulikov 1958 Ep (2 - 3) PeV. Iron knee: KASCADE grande 2012 EFe = Z Ep 80 PeV. § Ankle: Volcano Ranch, Linsley 1963, Ea 10 EeV.
1017 eV electron-poor sample electron-poor sample electron-poor sample
= -2.76 0.02


dI/dE x E2.7 (m-2sr-1s-1eV1.7)

1018 eV
(fig.4) (52108 events) (YCIC>0.845) (17173 events) (k+0.2) (24789 events)

10

19

= -2.69 0.03


= -3.24 0.05


KASCADE-Grande 16.5 17

= -3.16 0.08

17.5

18

log10(E/eV)




OBSERVED CR FEATURES (continued)
Flux*E3/1024 (eV2 m-2 s-1 sr-1)
10

HiRes-I Monocular HiRes-II Monocular Auger Combined

1

-1

10

17

17.5

18

18.5

19

19.5

20

20.5

21

log10(E) (eV)

Observed ankle in power-law approximation HiRes : Ea = 4.5 ‘ 0.5 EeV TA : Ea = 4.9 ‘ 0.3 EeV Auger : Ea = 4.2 ‘ 0.1 EeV GZK cutoff : p + N + , E HiRes : Egzk = 56.2+5.4 EeV -4.9 TA : Egzk = 48 ‘ 1.0 EeV Auger : Ecut =25.7+1.1 . EeV - 1. 2
gzk

50 EeV, E

1 /2

= 52.5 EeV

log E1/2 = 19.73 ‘ 0.07 log E1/2 = 19.69 ‘ 0.1 theory BG 1988 : log E1/2 = 19.72


Signatures of particle propagation through CMB and EBL

10-7

CMB + EBL
10
-8

-1

E-1 dE/dt(E), yr

10

-9

total

10

-10

adiabatic EBL

10-11

e+e10-12 10
18

pion production

10

19

10

20

10

21

10

22

10

23

E, eV

Eeq1 = 2.4 Ѕ 1018 eV,

Eeq2 = 6.1 Ѕ 1019 eV


INTERACTION SIGNATURES AND MODEL-DEPENDENT SIGNATURES

We want to see observational signatures of interaction, but in our calculations model-dependent quantities also appear, such as distances between sources, their cosmological evolution, modes of propagation (from rectilinear to diffusion), local source overdensity or deficit etc. Energy spectrum in terms of modification factor characterizes well the interaction signatures.


MODIFICATION FACTOR Jp (E ) (E ) = unm Jp (E ) unm where Jp (E ) = K E -g includes only adiabatic energy losses. Since many physical phenomena in numerator and denominator compensate or cancel each other, dip in terms of modification factor is less model-dependent than Jp (E ).
It depends very weakly on: g and Emax , modes of propagation (rect or diff), large-scale source inhomogeneity, source separation within 1-50 Mpc, local source overdensity or deficit,.. It is modified by presence of nuclei > ( 15%). Experimental modification factor: exp (E ) = Jobs (E )/K E -g .
1

e+ e

-

10-1 (E) 10-2

g = 2.1 - 3.0

total

10-3

1018

1019 1020 E, eV

1021

1022


Comparison of pair-production dip with observations

10

0

10
ee

0

modification factor

modification factor





ee

10

-1

10

-1

Akeno-AGASA
10
-2

Yakutsk
-2

g=2.7
10
17



to ta l

10

g=2.7
10
17



to ta l

10

18

10

19

10

20

10

21

10

18

10

19

10

20

10

21

E, eV

E, eV

modification factor



ee

10

-1

modification factor

10

0

1

ee

10

-1

HiRes I - HiRes II


TA MD TA SD
10-2

10

-2

g=2.7
10
17

to ta l

=2.6
g



total

10

18

10

19

10

20

10

21

10

18

10

19

10

20

1021

E, eV

E, eV


DIP in AUGER 2011 DATA In modification factor presentation 2011 2 is large. 2 can be reached min in model-dependent presentation in terms of natural spectrum E 3 J (E ), using energy shift = 1.22 and cosmological evolution. As a result of 2 -minimization absolute Auger flux coincides with HiRes and TA.

-1

E J(E), eV2m-2s-1sr

1024
HR 1 HR 2 TA MD

E J(E), eV2m-2s-1sr

-1

1024
HR 1 HR 2 TA MD

3

3

1023

TA SD PAO g = 2.5, Emax= 10 eV, zmax=4, m=3
22

1023

TA SD PAO with 22% energy upscale g = 2.5, Emax= 1022 eV, zmax=4, m=3

1019

1020

1019

1020

E, eV

E, eV


GZK CUTOFF IN HiRes DIFFERENTIAL SPECTRUM

10

0

modification factor



ee

10

-1

HiRes I - HiRes II


10

-2

g=2.7
10
17

to ta l

10

18

10

19

10

20

10

21

E, eV


GZK CUTOFF IN HiRes INTEGRAL SPECTRUM
1.2

1

J(>E)/KE

-

0.8

0.6

0.4

0.2

0

17

17.5

18

18.5

19

19.5

20

20.5

21

log10(E) (eV)

E1/2 in HiRes integral spectrum confirms that steepening in the differential spectrum is the GZK cutoff: E
meas 1/2

= 1019.73

‘0.07

eV

cf

Etheor = 1019 1/2

.72

eV


MASS COMPOSITION: HIRES (top) vs AUGER (bottom)


ANISOTROPY and ANKLE According to measurements of all three largest detectors, Auger, HiRes and Telescope Array, the mass composition at (1 - 3) EeV. i.e. below the ankle, is proton-dominated, or p + He - dominated. If galactic, such composition is excluded by recent measurements of anisotropy (Auger 2011 and 2012). Then ankle with Ea (4 - 5) EeV cannot be the feature of transition from galactic to extragalactic cosmic rays. Transition should occur at lower energy in agreement with dip model. Recent MC simulation for galactic particles (Giacinti et al 2012) confirms this conclusion Thus ankle can be interpreted either as intrinsic property of pairproduction dip or, in case of Auger results, like transition from extragalactic protons to extragalactic nuclei.


ed cb Da `Y XW V ) &p $

U TS RQ P y v y

i gh gq $ w v u s r

gq $

i &h gf $

gf $

8x y v y

8 u v s r y v y 8 u v ts r

8x y v y

8x u v ts r jU

123 g% $ 5 14 4 87 6 @9 A DC B 6 E CBF DG B F 7HF I9

u y v y 8x y v y

v u s r

8x w v u ts r

б !в е г и иж й из ж ед вг вб б #е " ж з з и й из ж ед вг вб вб г ид вж и б вб gg fe iU &% $ gg fe hU &% $

&d g в # и t & # 0) (' &% $

'Small' 700 Ѕ 700 m2 array with scintillation and muon detectors. p+He component is separated by muon content with properties: § p+He component at 0.1 - 1.0 EeV separated as 'electron-rich' using special event criteria, 6300 events. § extragalactic, otherwise anisotropy at E 1 EeV. § flat spectrum = 2.79 ‘ 0.08, cf = 3.24 ‘ 0.08 for total. KASCADE-Grande: 2013 BREAK-THROUGH


Significance of Light-Kascade-Component If this component is extragalactic, flat (g 2.7, cf = 2.79 ‘ 0.08) > and Emax is large (Emax 1 Ѕ 1020 eV) one obtains dip model. If Emax is low (Emax < 1 Ѕ 1019 ) this component provides the necessary element to build the Auger-based models (Aloisio, VB, Blasi 2013):
10
sr )
25
g=1.0, E
max=5Zx10 18

10
eV p He CNO MgAlSi Fe

25
g(A>4)=1.0, g(p,He)=2.7 Emax=3Zx1019 eV p He CNO MgAlSi Fe

sr-1) E3 J(E) (eV2 m
-2

-1

-1

E J(E) (eV m

-2

s

s

-1

10

24

10

24

10

2

23

10

23

3

10

22

10

22

10

21

10

18

10

19

10 E (eV)

20

10

21

10

21

1018

10

19

1020 E (eV)

10

21


SHORT CONCLUSIONS Two models for ankle at Ea (4 - 5) EeV: (i) transition from galactic to extragalactic CRs and (ii) intrinsic feature of pair-production dip. § Ankle as transition is excluded because of anisotropy of galactic component at E < Ea . § The main problem at present is contradiction between HiRes/TA and PAO on mass composition at E > (3 - 5) EeV : § HiRes/TA observe proton dominance and signatures of proton interaction with CMB: pair-production dip and GZK cutoff in differential and integral spectra. § PAO reports the nuclei composition steadily heavier with energy. § The KASCADE observed ankle-like component at 0.1 1 EeV automatically produces dip model in case Emax 1020 eV, and Auger-based model in case Emax < 1 Ѕ 1019 < < E > 1Ѕ eV.


AUGER - BASED MODELS § According Auger at E > 3 GeV Z steadily grows with E. < < § At 1 E 3 EeV data of Auger and HiRes agree with proton composition. max § If this component is extragalactic, then Ep 4 EeV, otherwise protons dominate at E > 3 EeV. Aloisio, VB, Gazizov 2009: Disappointing model. max Eimax = Zi Ep , g = 2.0


MIXED COMPOSITION MODEL Allard 2011
max max Parameters: Ei = Zi Ep , Ep = 4 EeV, g = 2.0, enriched by heavy elements.


DIP in AUGER 2007 DATA
In 2007 Auger data agree reasonably well with the dip. Later, tremendously increasing statistics made error bars much smaller. Observational data include model-dependent effects (e.g. evolution), while theoretical modification factor does not.

Hybrid and combined events 2007

Combined events 2007,


PAIR-PRODUCTION DIP as ENERGY CALIBRATOR Pair-production dip has a fixed energy position, serving as a standard candle. Energy scale of each detector has to be shifted by factor to minimize 2 . Equality of fluxes after recalibration is confirmation of pair-production nature of the dip. V. Berezinsky, A. Gazizov, S. Grigorieva 2006

10

25

10

25

1

J( ) ,eV m s sr EE

J(E)E , eV m s sr

1

2

2

2

-2

-1

-1

10

24

10

24

3

H i es I-H i es I R R I A keno -A G A S A Y akut k s Auger( om b)-Auger( ybr) c h
23

3

10

10

17

10

18

10

19

10

20

10

23

10

17

10

18

10

19

10

20

E,eV

E, eV


GZK CUTOFF IN AUGER SPECTRUM 2007 (combined and hybrid events)


GZK CUTOFF IN AUGER SPECTRUM 2010
S. Grigorieva


GZK CUTOFF IN AUGER SPECTRUM 2011
S. Grigorieva
10
25

10

25

g=2.35, m=4.5, E

max

=1 0 e V, z

22

max

=4.0

10

24

J(E)E , (m s sr eV )

1

J(E)E3, eV2 (m2 s sr)-1

2

-1

10

24

-1

Au g e r 2 0 1 1

Auger 2011 10
23

J(E)E , = 1.0 3 J(E)E , = 1.2 3 J(E)E , = 1.3
3

3

-2

10

23

homogeneous
10
25 17

1 - g=2.6, m=0

10

22

10

18

10

19

10

20

10

18

10

19

10

20

E, eV

E, e V
10

10

25

g=2.2, m=5.0, E

max

=1 0 e V, z

22

max

=4.0

g=2.2, m=5.0, Emax=7.10

19

eV, zmax=4.0

J(E)E , (m s sr eV )

2

10

-1

24

J(E)E , (m s sr eV )

Au g e r 2 0 1 1

-1

2

10

24

-1

-2

Au g e r 2 0 1 1 homogeneous rectilinear: d =5 0 M p c d =1 0 0 M p c
17

10

23

homogeneous with local deficit: 1 - 50 Mpc 2 - 100 Mpc 3 - 200 Mpc 4 - 300 Mpc
17

3

3

-2

-1

10

23

4
10
19

32
10
20

1
10

10

10

18

10

18

10

19

10

20

E, e V

E, e V