Acceleration of Cosmic Rays in a System of Rotating Stars

朱 光 华 (Chu, Kwang-Hua )

内蒙古科技大学 数学物理科学与生物工程学院 （包头市） School of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Sciecne and Technology (Baotou)

2011-Aug-10

The author thanks the Financial Support from ICRC2011 LOC andStarting Funds for 2011-IMUST Scientific Researcher.

Outline

• ● Introduction

• ● Mathematical Formulations

• ● Physical Applications

• ● Discussions

• ● Recent and Future Works

Differential energy spectrum of cosmic rays of energy above 1011 eV multiplied by E2.

arXiv: 1103.0031

If cosmic-rays originate from cosmological distances, their flux at the highest energies (E ≥ 6 × 1019 eV) should be suppressed due to interactions with the cosmological background photons,creating a feature in the spectrum called the GZK cutoff.

K. Greisen, Phys. Rev. Lett. 16, 748 (1966).G. Zatsepin and V. Kuzmin, J. Exp. Theor. Phys. Lett. 4, 78 (1966).

R. U. Abbasi et al., Phys. Rev. Lett. 100, 101101 (2008) [arXiv:astro-ph/0703099].J. Abraham et al., Phys. Lett. B 685, 239 (2010) [arXiv:1002.1975].

Schematic evolution of an hadronic cascade. At each step roughly 1/3rd of the energy is transferred from the hadronic cascade to the electromagnetic one.

Note that the plausible UHECR sources tend to be found in directions of lower 100μm flux,[UHECR coinciding source directions present IRAS fluxes 0.614 ± 0.022 MJy sr−1 whereas the directions towards those galaxies non-coincident with UHECRs presnet 1.68±0.63 MJy sr−1.] To the extent that the 100μm flux traces the Galactic dust and magnetic field, then CRs are likely to be better aligned with their sources in directions of low flux. (Rep. Prog. Phys. 67 1663 (2006))

IRAS 100μm view of the North GalacticPole (white = high flux, dark (blue) = low flux), towards the region of several QRs (quasar remnants)that appear to coincide with UHECRs. Small circles mark the 12 galaxies (candidate QRs) in the sample of [astro-ph/0204419]. Dark (red) circles mark Galaxies perhaps associated with UHECRs; white circles mark galaxies without associated UHECRs.

a spinning supermassive black hole, threaded by magnetic fields generated by currents flowing in a disc or torus, induces an emf which, if vaccum breakdown is prevented and in the absence of severe energy losses, accelerate a particle near the full voltage.

Quasar remnants (QRs) as UHECR emitters

Boldt E and Ghosh P 1999 Mon. Not. R. Astron. Soc. 307 491 [astro-ph/9902342]Boldt E and Loewenstein M 2000 Mon. Not. R. Astron. Soc. 316 L29 [astro-ph/0006221]

UltraHigh Energy Cosmic Rays (UHECRs)

Magnetars : isolated neutron stars with extremely strong surface dipole fields of

order Bd 1015 G and fast rotation at birth with initial rotation period Pi 1 ms.

Hillas plot for candidate acceleration sites, relating their size and magnetic field strength. To accelerate a given particle species above 100 EeV objects must lie above the corresponding lines.

β represents the velocity of the accelerating shock wave or the efficiency of the accelerator.

[arXiv:1103.0031]

How to Accelerate w/o Additional Energy?

Borrow idea from the flying objects :

Free Dive (in a Potential)!

Discrete Boltzmann Models

Quantum Discrete Boltzmann Models发表文章 : Possible Phase Diagram for Localization tuned by the Disorder and Pauli-blocking effects , Phys. Rev. B, vol. 68(20) 205308 (2003).

Possible acoustical probe for the metamagnetic transition, Physical Review B vol. 70 174421 (2004).

Spectral Problem for Dilute Atomic Gases using Discrete Uehling-Uhlenbeck Operators, Phys. Rev. E, vol. 66 047106 (2002).

Dispersion Relations for Waves in Dilute Hard-Sphere Bose Gases, J. Phys. B Atom. Mol. Opt. Phys., vol. 34(22) pp. L711-L717 (2001).

发表文章 :

Ultrasound propagation by the discrete kinetic theory, J. Phys. : Condensed Matter, vol. 11(45) pp. 8819-8828 (1999).

Spectral problems for the discrete velocity models, European Physical Journal B, vol. 10(1) pp. 1-4 (1999).

Spectral problems for the four-velocity model: Revisited, Appl. Math. Lett., vol. 14(3) pp. 275-278 (2001).

Possible Localization of the Sound Propagation in Hard-Sphere Gases, J. Phys. A Math. & General, vol. 34 pp. L673-L680 (2001).

Multiple Scattering and Possible Localization of the Sound Propagation in Hard-Sphere Gases, J. Phys. A Math. & General, vol. 35 pp. 1919-1926 (2002).

Enhanced stationary flow due to grazing collisions, J. Phys. A : Math. & General, vol. 33(40) pp. 7103-7108 (2000).

Schematic plot for a collision. M and M1 are the associated angular momenta which have opposite sign.

t

+ u ·x

+ γ ·u

i

i

= Fi

γ : External field force per unit mass

( ) Ni

θ

Possible External Field Effects θ

Study the Plane Wave Propagationand the relevant Dispersion Relations.

=cos()sin(),

Anderson (1958) : noninteracting electrons in an extendedsystem might have either localized or extended eigenstates according to whether the degree of disorder in the system was high or low, and that localized electrons would nothave the ability to transport charge or energy which is assumed in the theory of metals.

Localizations

BosonFermion

Acoustical Wave Attenuation

θ= 0

Possible Amplification

Discussions★

the cosmic ray passing through this plane-wave (e.g., acoustic)-amplified channel might be Accelerated

⊕

⊕

the possible acceleration (due to amplification) is proportional to h ( c S N0) which is also proportional to Z (a nucleus charge number, considering the effective scattering cross-section S)

Future Works

•● Experimental Data Included

•● Quantitative Results Obtained

•● Acceleration of Universe in Phantom Type

Dark Energy