Astroparticle Physics 1 (1992) 129-131 North-Holland
Cosmic rays and cosmic strings
Xinyu Chi, Charles Dahanayake , Jerzy Wdowczyk 2 and Arnold W. Wolfendale Department of Physics, University of Durham, Durham, DHI SLE, UK
Received 14 May 1992
It has been suggested that the highest-energy cosmic rays might be protons resulting from collapsing cosmic strings in the Universe. We point out that this mechanism, although attractive, has important shortcomings, notably the fact that gamma rays produced along with the protons and those produced by the protons in their interactions with the cosmic background radiation generate cascades in the Universe and result in unacceptably high fluxes of cosmic gamma rays in the region of hundreds of MeV.
The problem of the origin of cosmic radiation is a continuing one. ~though the low-energy particles, those below 10 eV or so, are probably due to supernova remnant (SNR) shocks [l], there are considerable uncertainties at higher energies. The SNR hypothesis can be invoked, with dimin- ishing certainty, for energies up to 1Ol5 eV but above this there is little firm fact and, indeed, it is not clear whether the sources are within the Galaxy or outside it, i.e. are extragalactic (EG). The favoured view  is that EG sources are mainly responsible above 10s eV but the nature of these sources is obscure. We, ourselves, incline to the view that colliding galaxies may play a part but a detailed mechanism has yet to be work out.
An explanation that is, at first sight, attractive concerns cosmic strings [3-51. The idea is that such strings, which are hypothesised to be pro- duced in the early universe and to contain ex- traordinarily condensed regions of X-particles with masses _ lOI GeV (the GUT energy scale),
Correspondence to: A.W. Wolfendale, Department of Physics, University of Durham, Durham, DHl 3LE, UK. On leave from University of Kelaniya, Kelaniya, Sri Lanka. On leave from the Institute of Nuclear Studies, 90-950
are able to shake free the X-particles when they, the strings, intersect or their loops collapse [6,7]. The X-particles in the strings are rendered stable by the potential well associated with their mass density (- 10z2 g cm-> but when released the X-particles decay into a variety of particles amongst which are protons. It is these particles that could, in principle, comprise the ultra-high- energy cosmic rays.
2. The cosmic ray energy spectrum postulated to arise from collapsing cosmic strings
Bhattacharjee  has presented the energy spectrum shown in fig. 1. Here, the characteristic shape of spectrum is given by the details of the decay of the X-particles and the effect of energy losses by interaction of the protons with the cos- mic microwave background (CMB), but the abso- lute intensities come from normalisation to the measured spectrum at 4 x 1019 eV.
An attractive feature of the cosmic string pro- ton spectrum is that it is comparatively flat above 10 eV and thereby holds out the hope of mea- surement by the new much larger extensive air shower arrays which are being planned.
0927-6505/92/%05.00 0 1992 - Elsevier Science Publishers B.V. Ah rights reserved
130 X. Chi et al. / Cosmic rays and cosmic strikgs
- -34 T.
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Fig. 2. The postulated proton spectrum from collapsing cos- mic strings from the work of ~hattacha~ee  fsalid line). The injection spectrum (dashed-dotted line) and the measured
cosmic ray spectrum (dashed line) are indicated.
3. mamma rays resulting from the inte~ctions of extragalactic protons with the CMB
In earlier papers [8,9J we drew attention to the gamma rays which will resuh from extragalactic protons interacting with the CMB. Figure 2 shows the gamma ray spectrum coming from an injec- tion spectrum of protons having the conventional form for shock acceleration: j(E) dE a E- d E. The characteristic shape of the gamma ray spec- trum arises from the form of energy dependence of y-y collisions. Essentially, it is the energy in the shaded area shown in fig. 2 which cascades down to give the gamma ray flux (apart from a small fraction of the energy going into neutrinos).
In practice, the gamma ray energy region where this cascade flux can most easily be seen is at _ 100 MeV. Here, there are results from the SAS-II experiment [lo] on the extragalactic dif- fuse flux which set an upper Iimit to what might be possible from the p-CMB interaction process. With the assumptions in fig. 2, viz a cut-off in the proton injection spectrum at 10 eV, the pre-
10 -10 -12 -14 -16
j(E) -18 (t.m-2g-J -20
sf eV-) 1::
-26 -28 -30 -32 -34 -36 -38 -40
,,l:: ,ob 8 10 12l; 16 18 2$21
Fig. 2. The proton spectrum and the derived y-ray spectrum over the whole energy range for the non-cosmological situa-
tion from the work of Wdowczyk and Wolfendale .
lo3 r Ej(E1 : Injection
eV2 cm-* o
s sr- -1
IO5 4 -
E2j(E) 3 _
eV2 cmm2 2 -
isr- 1 - lb)
E(eVl Fig. 3. Energy spectrum of protons at injection and after modulation by collisions with the cosmic microwave back- ground to give the spectrum expected at earth: (a) after Wdowczyk and Wolfendale , where the EG protons (de- noted EGP) are derived from shock acceleration in distant galaxies, and (b) after Bhattacharjee , where the protons come from collapsing cosmic strings. The energy in the shaded
area is converted into gamma rays by cascading in the uni verse.
X. Chi et al. / Cosmic rays and cosmic strings 131
dieted gamma ray flux is a factor 20 below the observed flux, i.e. there is no inconsistency.
The situation with the cosmic string hypothesis is similar to the extent that there will be a gamma ray cascade generated from the p-CMB interac- tions but its flux will be considerably in excess. Figure 3 shows the situation, where a comparison with our earlier work  is made. Whereas previ- ously we had 1.3 x lo- eV cmP3 liberated, the value now (fig. 3b) is N 5 X 10m6 eV cmP3, i.e. a factor 40 higher. The previous 100 MeV gamma flux which was a factor 20 low now becomes a factor 2 in excess of observation.
The situation is even worse when allowance is made for the gamma rays resulting from the non-nucleons generated in the X-particle decays. The fraction of energy going into gamma rays is not completely clear but it is probably at least ten times that going into nucleons. Thus, a conserva- tive factor for the over production of 100 MeV gamma rays is 20.
It is difficult to escape the conclusion that the detected cosmic ray protons (assuming that this is what they are) are not due to collapsing cosmic strings.
4. Limits to the cosmic string parameters
We can use the argument just developed to set a limit on the fcvpn factor which enters into cosmic string theory: fn < 1.5 X lo- (here f is the fraction of the total energy of all primary loops released into particles within a period of oscillation and n is the dimensionless mass per unit length). Bhattacharjee  quotes an upper limit on 77 from pulsar timing results of 4 X 10u6 so that our result gives f~ 4 x lo-.
The conclusion is that most of the GUT-scale cosmic loops (if they exist) must be in non-col- lapsing configurations. It should be noted that if the collapses which generate ultra-high-energy cosmic rays occurred at large redshifts, then the limit would be depressed still further - by a decade or so (see ref. , for the analogous case with the shock-generated EG particle model).
Notwithstanding the possible existence of cos- mic strings in the universe it appears well nigh impossible to invoke them as significant contribu- tors to the flux of cosmic rays of the highest energy assuming, that is, that the particles are protons. The predicted gamma ray flux is just too great to be reconciled with the detected flux at energies in the region of 100 MeV.
The reason for the assumption about the na- ture of the particles at the highest energy is that, remarkably, their composition is by no means clear. Although we are of the view [ll] that they represent a mixture of protons and heavy nuclei (probably iron) it is not inconceivable that there is a significant flux of extragalactic gamma rays. Thus it might be possible to invoke the gamma rays produced when the X-particles decay as be- ing responsible for many of the cosmic rays of the highest energy without exceeding the low-energy limit; detailed calculations on this aspect will be made. On this hypothesis, the associated protons would be of negligible intensity and essentially non-detectable.
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