Consequences of the common origin of the knee and the ankle in Cosmic Ray Physics

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Consequences of the common origin of the knee
and the ankle in Cosmic Ray Physics

• Antonio Codino
• INFN and Dipartimento di Fisica
• dell'Università degli Studi di Perugia, Italia

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The knee and the ankle have a common origin

• Introduction
• Some consequences of this common origin
• I The chemical composition of the cosmic
  radiation above 1017 eV up to 1020 eV.
• II Some basic constraints on the real engine
  accelerating cosmic
• rays in the Milky Way.
• III The trend of the residence time of the
  galactic cosmic rays versus energy up to 1019
  eV implied by the common origin of the knee and
  ankle (the problem of isotropy of the cosmic
  radiation at any energy).

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Papers on the knee and the ankle

• The present explanation of the knee and the
  ankle, in collaboration with François Plouin,
  may be found in
• The origin of the ankle (10 pages) Nuclear
  Physics B, 165 (2007) (Proc. Suppl.) 307-316. and
  Astro-ph/0701593, 20 january 2007.
• A unique mechanism generating the knee and the
  ankle in the local galactic zone (25 pages)
  Vulcano Conference (2006) e Astro-ph/0701521, 18
  january 2007.
• Galactic basins of helium and iron around the
  knee energy (42 pages) Internal report
  INFN/TC-06/05, February 20th 2006 duplicated in
• Astro-ph/0701498 del 17 january 2007.
• The reading of The extension and shape of the
  collecting zones of the galactic cosmic rays from
  helium to iron requires the notion of the
  galactic basin introduced in The Astrophysical
  Journal (2006) 639, 173-184 Codino-Plouin, (12
  pages).
• The method of calculation may be found in
  Brunetti-Codino, (10 pages) The Astrophysical
  Journal (2000), 528, 789-798

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ION BLEND

• Normalization energy 1014 eV

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Postulating constant spectral indices in the
cosmic ray spectrum.This is the heading of a
paragraph in the paper The origin of the
ankle

• The spectral indices of all ions of the
  cosmic radiation are taken constant in the
  interval
• 100 GeV - 5 1019 eV (iron ankle
  energy).

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An acceleration mechanism predicting constant
spectral indices of 2,5 up to 5 x 1019 eV

• G. Pizzella, Nature 226434 (1970).
• The mechanism would operate in the dipole
  magnet fields of neutron stars in a plasma
  atmosphere.
• G. Trubnikov et al.
• Pisma v ZhETF, Vol. 62, iss. 2, pp.
  86-90, 1995.
• About possible generation of cosmic rays and
  gamma-bursts in plasma pinches

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Chemical composition from 1017 eV to above 1019
eV.

• An analysis of giant air showers detected
  by the Flys Eye starting at energies 1017 eV
  leads to the following conclusion
• .It contains, however, an emerging light
  component that grows to about 40 per cent of the
  total flux above 1018 eV.
• Comments on Astrophysics, T. K. Gaisser et al.
  Vol . 17 numbers 2 and 3, (1993).

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Ion abundances at 1014 eV ( high energy ion
blend)

• I0 23,30 10-2 particles/(m2 s TeV sr) Energy
  1014 eV

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Ion abondances at 1 TeV (well below the
knee energy region)

• I0 27,1 10-2 particles/(m2 s TeV sr)
  Energy 1012 eV

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Let s analyze now a second implication of the
common origin of the knee and the ankle

• If the theory of the knee and the ankle is
  correct,
• then it follows that the engine, the real
  engine accelerating cosmic rays in the Milky
  Way, must provide constant spectral indices for
  each ion, in the complete energy range explored,
• namely, from hundreds GeV up 5 x 1019 eV
  (iron ankle energy).

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Maximum electron energy measured in young
supernovae remnant S. P. Reynolds and J.W.
Keohane, ApJ, 525, 368 (1999)
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There is a maximum energy Emax gained by
nucleiin supernovae remnants

• (C.J. Cesarsky and P.O. Lagage, (1983) Astron.
  and Astrophys. 118, 223 e 125, 249)
• Emax 3/20 (u1/c) Z e B(u1TA)
• Z e electric charge of the nucleus
• u1 shock wave velocity (5000 km/s)
• B magnetic field strength (3 µG)
• C sound speed in the medium (300 km/s)
• TA acceleration time 103 years
• Special mechanisms have been conceived to
  extend Emax
• H. J. Völk and P.L. Biermann, (1988),
  Astro. Journ. Letters 333, L65.
• A. R. Bell and S. G. Lucek, (2001),
  Mon. Not. R. Astron. Soc. 321, 433-438.

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• If the diffusive shock acceleration believed
  to operate in supernovae remnants has a maximum
  limit in energy (1014 or 1017 eV)
• and
• If the spectral indices are constant up to 5
  x 1019 eV
• the necessary conclusion is that a variety of
• acceleration mechanisms is at work.

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Different acceleration mechanisms ...

• active with variable efficiencies in different
  energy intervals
• operating in quite dissimilar cosmic regions
• injecting uneven amounts of ions from hydrogen to
  uranium
• at very different distances from the Earth

... would finally cooperate to yield a unique
spectral index in the solar system of the Milky
Way.
In my opinion, this hypothetical situation is
unnatural and unplausible.
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Conclusions

• The computed chemical composition of the
  cosmic radiation, e.g. lnltAgt, has the
  characteristic features
• of increasing from 1,8 up to 3,2 in the interval
• 1015 3x1017 eV
• 2) and of becoming lighter above
• 3x1017 eV up to 4x1018 eV.

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Conclusions (cont.)

• The transition from heavy to light composition
  occurs at 3x1017 eV, a value independent from the
  ion blend.
• These basic characteristics are in accord with
  the experiments.
• This transition is generated only by the galactic
  component of the cosmic radiation due to its
  intrisic properties, and not by the appearence
  of an extragalactic component.

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Conclusions (cont.)

• For example, Yakutsk data are compatible with
  our calculations in the range 1015 1019 eV and
  those from Flys Eye in the range 3x1017 1019
  eV.

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Conclusions (cont.)
On the contrary, data from other experiments
(Auger and Hires) disagree with these
calculations. These experiments measure a very
light component in the range 3x1017 5 1019 eV.
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Fin du séminaire
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Fin du séminaire
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Fin du séminaire
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From Trevor Weeks
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Position of the sources in the Galaxy
Galactic wind
The solution of the knee and ankle problem
Grammage
Asymmetries in the arrival directions of the
cosmic rays
Method of calculation
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Champ magnétique spirale
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Trajectoires des rayons cosmiques dans le disque

• Brunetti Codino, ApJ, 2000, 528, 789

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Illuminating the Galaxy by an ion beam emitted
from the Earth and counting the number of nuclear
collisions in the disk
nuclear collisions
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Energia massima per i nuclei

• (C.J. Cesarsky and P.O. Lagage, (1983) Astron.
  and Astrophys. 118, 223 e 125, 249)
• Emax 3/20 (u1/c) Z e B(u1TA)
• Z e carica del nucleo
• u1 velocità dellonda (5000 km/s)
• B campo magnetico (3 µG)
• C velocità del suono nel mezzo (300 km/s)
• TA 103 anni
• Due scappatoie per accrescere lenergia massima
  Emax
• Mezzo interstellare con proprietà particolari.
• Particelle accelerate nel vento stellare della
  stella genitrice.
• ( H. J. Völk P.L. Biermann,
  (1988) Astro. Journ. Letters 333, L65)

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Energia massima per gli elettroni

• (GAISSER, pagina 160)
• Emax 23 TeV u1/c 1/vB 220 TeV
• Nellarticolo citato (Lagage e Cesarsky) il
  processo di accelerazione avviene prima che la
  massa espulsa al tempo TA si è diluita nello
  spazio interstellare imponendo che la densità
  della massa espulsa uguagli quella del mezzo
  interstellare imperturbato si ha
• 4/3 p Rrs3 ?mi Mes
• Rrs raggio del resto di supernova e Mes massa
  espulsa.
• Approssimando Rrs con u1TA si ottiene TA di
  1000 anni circa con u15000 km/s e Mes 10 masse
  solari (1,989 x 1034 grammi)
• TA tempo utile per laccelerazione delle
  particelle nel resto delle supernova

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Acceleratori astrofisici

• Esplosioni di supernove
• Pulsar giovani
• Stelle di neutroni con stelle compagne

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Brunetti Codino, ApJ, 2000, 528, 789
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Sd
g grammage (g/cm2) is the the gas column
swept out by the cosmic rays
LD trajectory length nH number of atoms
per cubic centimeter mH hydrogen mass
g mHnHLD
l A / (s g
NA)
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