IL NUOVO CIMENTO

NOTE BREVI

VOL. 108 B, N. 7 Luglio 1993

S u p e r c o n d u c t i n g S tr ings as Sources o f H i g h - E n e r g y C o s m i c Rays.

J. R. MORRIS Department of Chemistry/Physics/Astronomy, Indiana University Northwest Gary, IN 46408, USA

(ricevuto 1'11 Febbraio 1993; approvato il 27 Luglio 1993)

Summary. -- The possibility is explored that highly charged superconducting strings and vortons ionize neutral atoms and act as high-energy charged-particle accelerators. For strings characterized by a GUT mass scale, it is roughly estimated (neglecting radiative losses) that charged particles such as protons and heavier nuclei may reach an energy scale I> 1021 eV.

PACS 98.80.Cq - Particle-theory models of the early universe. PACS 98.70.Sa - Cosmic-ray sources.

Superconducting cosmic strings can emerge as solutions in certain types of spontaneously broken field-theoretic models [1-3]. These strings can have an electric charge per unit length Q along with a current I[3-5]. In Witten's model[l] the maximum current carried by the string due to bosonic charge carriers could be as large as - 1 0 2 ~ In natural units (h = c = 1)Imax ~ e2~[4], where ~ is the vacuum value of the Higgs field. Using cylindrical coordinates (r, 0, z), the electric and magnetic fields associated with a straight string lying along the z-axis are

Q I (1) E,. ~ - - , Bo .~ - - ,

2zrr 2zrr

for r/> to, where ro is the radius of the string's core. The associated electromagnetic potentials can be taken to be

2~ \ to ' 27: \ to "

Closed loops of charged, current-carrying strings form chiral vortons [6], which have been studied by Davis [6, 7] and Davis and Shellard [8].

Let us consider the possibility that highly charged superconducting strings, either in the form of ,infinite,, straight strings or in the form of chiral vortons, could populate the universe to some degree. In this case we would expect that any neutral atoms which are resident in a region of intergalactic dust or gas coming into close

823

824 J. R. MORRIS

enough contact with a segment of string will be ionized. To fred the ionization radius rl of a segment of string, consider a nonrelativistic atom (in order to ignore magnetic interactions) with an atomic size - a and a characteristic binding energy of magnitude - b. An electron can be removed from the atom when the work done by the electric field of magnitude E becomes comparable to the binding energy b, i.e. eEa ~ b, which gives a critical field strength Ee ~ b/(ea). By (1) the critical radius within which a neutral atom is ionized is roughly

]Q] [Qlea

2 =Ee 2 =b

Subsequent to ionization the charged particles can be accelerated to enormous energies. One of the charges is pulled onto the string, while the other charge is repelled. The particle pulled onto the string experiences a change in electric potential energy

qQ In (4) 5 V = V(ro) - V(rl) ~ - - - 2=

where (2) has been used and we take q - -+ e with qQ < 0. Similarly, the ejected particle experiences a potential-energy change

qQ In (5) a v ' = V(r2) - V( r l ) 2r:

where r2 is taken to be a sufficiently large radius beyond which the string fields become negligible (e.g. due to loop curvature). Let us consider the case where ]E]

I B ], or ] Q ] ~ ]I] (see, e.g. ref. [7]), so that ] Qm~ ] ~ ]/max [ -- e 2 V; since a string can carry such a large charge per unit length for a GUT mass scale value of V, the electromagnetic potential energies, and hence the accured charged-particle kinetic energies, can have magnitudes of similar scale.

Taking e 2 - 0.i, a - 1A - 5.105 GeV -1, b N 10eV = 10 -s GeV, IQ[ - e2~, and -1015 GeV, we roughly estimate rl N 2.4.1026 GeV-1 ~ 5 . 1 0 7 km for the critical

radius. Thus, because of the enormity of Q due to 7, the critical radius for ionization (larger than the Sun's radiusD can be quite sizable. From (4) and (5),

(6) ] AV] max, ] 5 V ' I m~x I> - 5" 1012 G e V = - 5" 10 21 e V .

Therefore, a GUT-scale superconducting string with maximal linear charge density and current may be able to accelerate charged particles to extraordinarily high energies. Without taking radiative losses into account, the maximal kinetic energies, by (6), may be i > - 1021eV. When bremsstrahlung and synchrotron radiation are taken into account (especially for electrons), it is expected that there will also be a flux of high-energy photons.

In summary, it is interesting to note that the interaction of such highly charged strings with otherwise ordinary neutral matter could result in the production of ultra-high-energy cosmic rays.

SUPERCONDUCTING STRINGS AS SOURCES OF HIGH-ENERGY COSMIC RAYS 825

R E F E R E N C E S

[1] E. WITTEN: NucL Phys. B, 249, 557 (1985). [2] A. E. EVERETT: Phys. Rev. Lett., 61, 1807 (1988). [3] O. F. DAYI, H. J. W. MULLER-KIRSTEN, A. V. SHURGAIA and D. H. TCHRAKIAN: Phys. Lett.

B, 286, 234 (1992). [4] D. N. SPERGEL, T. PIRAN and J. GOODMAN: Nucl. Phys. B, 291, 847 (1987). [5] M, ARYAL, A. VILENKIN and T. VACHASPATI: Phys. Lett. B, 194, 25 (1987). [6] R. L. DAVIS: Phys. Rev. D, 38, 3722 (1988). [7] R. L. DAVIS: in The Formation and Evolution of Cosmic Strings, edited by G. GIBBONS,

S. HAWKING and T. VACHASPATI (Cambridge University Press, 1990). [8] R. L. DAVIS and E. P. S. SHELLARD: Nucl. Phys. B, 323, 209 (1989).