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6.1. Astrophysical footprints

Cosmic strings, with or without current carrying capabilities, are predicted by many theories of high energy physics, and they have been postulated ad hoc as a possible explanation of various phenomena, many of which we have explained above. If indeed present in our universe, cosmic strings could help in the reconciliation between theory and observations in many cases, as well as lead to interesting and testable predictions in others. These areas include galactic magnetic fields, stable string loops (vortons) as a possible dark matter candidate, gravitational waves from strings, etc.

Strings and galactic magnetic fields

There are many outstanding astrophysical problems that may perhaps be explained with the help of superconducting cosmic strings. One of these concerns how galactic magnetic fields are generated. In the most commonly held scenario, the magnetic fields possessed by galaxies today arose from smaller seed fields that already existed before galaxies themselves formed. These seed fields would have only a small coherence length - the average size of a region with a roughly uniform field - but standard magnetohydrodynamic theory allows both the strength of the field and its coherence length to grow to galactic scales.

A field incorporated into a protogalactic structure remains trapped as that structure grows; in particular, as the protogalaxy shrinks under its own gravity, the magnetic flux within it is compressed too, increasing the strength (flux per unit area) of the field. Rotation of the evolving system may then increase the field strength further, through a dynamo effect, to the value typical of galactic magnetic fields, roughly 10-6 gauss. However, this scenario is not universally accepted, and other models are being studied that would produce tiny primordial fields that already have a large coherence length.

Superconducting cosmic strings may be able to do the job. They carry electric currents, and in fact fairly large ones. As we saw, Witten [1985] was the first to suggest that strings could become superconducting, and he went on to calculate a maximum current based on the mass and charge of a string's current-carrying fermion: some curlyJmax ~ 1020A for particles on the grand unified mass scale - a huge value not so often met even in astrophysics. Magnetic fields are produced when an electrically charged object moves in space; theoretically this is precisely what cosmic strings are and what they do. Calculations suggest that superconducting strings could generate interesting seed magnetic fields with strengths of about 10-20 gauss and with coherence scales of roughly 100 kiloparsecs. This corresponds to the size of protogalaxies, and dynamo effects could then increase the field strength to the observed values. The string's motion through the turbulent primordial plasma might induce vorticity that could also amplify field strengths. Conducting strings could thus easily provide magnetic fields that would evolve into modern galactic fields [see, e.g., Martins & Shellard, 1998].

Cosmic rays from cosmic strings

A second problem is much closer to home. Earth's atmosphere is constantly assaulted by lots of particles, such as photons, electrons, protons and heavier nuclei. Recent detections have recorded astonishingly energetic cosmic-ray events, with energies on the order of a few hundred exaelectron-volts (1 EeV = 1018 electron-volts). This is roughly the kinetic energy of a tennis ball traveling at over 150 kilometers an hour, all concentrated into an atomic particle. Particles with such energies cannot easily move through intergalactic space, which, far from being empty, is pervaded by cosmic background radiation fields, including the already mentioned microwave background (CMB) as well as diffuse radio backgrounds. From the perspective of particles moving faster than some critical velocity, these fields look like bunches of very damaging photons, which degrade the particle's energy through collisions and scattering. For example, a proton that reaches Earth's atmosphere with the necessary energy to explain these ultra-energetic events could not have come from farther away than about 30 million parsecs, according to a result known as the Greisen-Zatsepin-Kuz'min (GZK) cutoff [see, e.g., Bhattacharjee & Sigl, 2000].

One might therefore conclude that the ultra-high-energy cosmic rays (uhecrons) must come from sources that are close (astrophysically speaking) to our galaxy. However, unusual and energetic objects like quasars and active galactic nuclei are mostly too far away. The high-energy particles remain a mystery because when one looks back in the direction they came from, there is nothing nearby that could have given them the necessary kick. So what are they, and how did they manage to reach us?

For the time being, standard astrophysics seems unable to answer these questions, and in fact essentially states that we should not receive any such rays. As Ludwik Celnikier from the Observatoire de Paris-Meudon has said, comparing cosmological dark matter to ultra-high-energy cosmic rays: the former is a form of matter which should exist, but until further notice doesn't, whereas the high-energy rays are particles which do exist but perhaps shouldn't.

This is where topological defects, and in particular superconducting cosmic strings, can lend a hand. They offer two ways to deliver extremely energetic particles: they may directly emit particles with tremendous energies, or, more excitingly, they may send off tiny loops of superconducting cosmic string which would then be misinterpreted as ordinary but very energetic particles.

The first mechanism arises because the currents carried by strings can be thought of as streams of trapped particles, which would in general be extremely massive and unstable. Like neutrons, however, which decay in a few minutes when left by themselves but live happily inside nuclei, these heavy particles can exist indefinitely when confined within strings. Indeed, cosmic strings are the only objects that could preserve such particles from their origin to the present time. The trapped particles can nonetheless emerge occasionally when strings suffer violent events. A single string may bend sharply to create a kink or cusp (21), or a pair of strings may intersect in such a way that their ends switch partners. In these events some trapped particles can find their way out of the string, at which time they would almost instantly decay. They are so massive, however, that the light particles produced in their decay would be energetic enough to qualify as ultra-high-energy cosmic rays.

Disintegration of superconducting strings has also been proposed as the origin of ultra high energy cosmic rays [Hill, Schramm & Walker, 1987; see however Gill & Kibble, 1994], with the advantage of getting round the difficulties of the conventional shock acceleration of cosmic rays. This mechanism will also produce neutrinos of up to 1018 eV energies. Horizontal air shower measurements, like the Akeno Giant Air Shower Array (AGASA) experiment [Yoshida, et al., 1995], however, constrain nue + nubare fluxes, and current estimates from superconducting strings seem to exceed these bounds [Blanco-Pillado, Vazquez & Zas, 1997].

Vortons as uhecrons

A second possibility was proposed by Bonazzola & Peter [1997] who have recently suggested that the high-energy cosmic rays are in fact vortons. As we saw, vortons typically have more than a hundred times the charge of an electron, Q = Ze, and thus they are efficiently accelerated along electric field lines in active galactic nuclei. Their huge mass, moreover, means that compared to protons they need smaller velocities to attain equivalently high energies, and these lower velocities mean they can travel enormous distances without running up against the GZK cutoff. A vorton hitting any air molecule in the atmosphere would decay as if it were a very energetic but otherwise ordinary particle. The interaction of the trapped current carriers in the vorton with the quarks within atmospheric protons would proceed with a characteristic energy spectrum (Figure 1.20), which would be mirrored by the energy spectrum of observed high-energy rays.

Figure 20

Figure 1.20. Interaction of a vorton with a proton in Earth's atmosphere varies with energy in a way that depends on the interaction of quarks inside the proton with current-carrying particle states in the string loop [Bonazzola & Peter, 1997]. Ultra-high-energy cosmic rays created in this way might have a characteristic energy spectrum that would identify vorton collisions as their origin.

Other interesting possibilities in which defects play themselves the rôle of high-energy cosmic rays have been proposed in the literature in connection with gauge monopoles [e.g., Huguet & Peter, 2000; Wick, Kephart, Weiler & Biermann, 2000]. It is hoped that the enigma of ultra-high-energy cosmic rays will be clarified in the near future with the data gathered in the very large Pierre Auger Observatory (22).

21 Movies of a cosmic string cusp simulation can be found at Back.

22 See the internet sites and Back.

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