The Two Point Angular Autocorrelation Function and the Origin of the Highest Energy Cosmic Rays

R.W. Clay , B.R.Dawson , L. Kewley , M. Johnston-Hollitt, PASA, 17 (3), 207.

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Cosmic Ray Directions and Sources

Cosmic rays are charged particles with very high energies. As such, there is an expectation that, at some energy, they will have a tendency to travel in approximately straight lines through intergalactic magnetic fields. The magnitude of those fields is uncertain. Within clusters of galaxies, the fields may have strengths as high as tens of microgauss but they could be a thousand times weaker in intercluster space. Clay et al. (1998) have discussed such propagation on the assumption that those fields are turbulent and found that energies approaching 1020eV are likely to be sufficient for approximately linear motion to apply under most fields such as those just mentioned.

An important component in that conclusion is the interaction of the highest energy cosmic rays with the 3K microwave background (eg Lampard et al. 1997a, Muecke et al. 1999). Above about

$6\times10^{19}$eV, there is a photopion interaction between cosmic ray protons and blue-shifted 3K photons which severely restricts the possible distances to sources of particles at those energies (Lampard et al. 1997b). The interaction is not catastrophic but source distances are limited to a volume with a radius of the order of 100Mpc, which depends somewhat on the hardness of the source spectrum.

Catalogues of arrival directions for cosmic rays with energies above 1020eV contain directions from all over the sky. There are no clear point sources from which the majority of particles appear to originate. There are some suggestive directions in the north where there is apparent clustering on angular scales which are comparable with detector angular uncertainties but, even if those are real, there are still many remaining directions which are spread over the sky. One is forced to conclude that there are either many sources spread over the sky and within a distance of a few hundred megaparsecs or a limited number of sources over the same volume but with directions which are spread by scattering in intergalactic magnetic fields.

Unless the production of these particles is episodic, it appears that we can eliminate galaxies such as our own as sources at the highest energies since there is no evidence for a cosmic ray version of the ``Milky Way'' although there is evidence that, up to 1018eV, our galactic centre may be a cosmic ray source (e.g. Hayashida et al. 1999, Clay et al. 2000). In the same way, Centaurus A, our nearest active galaxy shows no evidence for cosmic ray acceleration to these energies although there is some evidence at lower energies (e.g. Allen et al. 1993, Clay et al. 1994). If this applies as a general rule for FR I sources (centrally concentrated double-lobed extended radio sources as opposed to FR II sources which have widely separated regions of maximum brightness - see Jackson 1999) such as Cen A, we have to look to very esoteric objects for the origins of the highest energy cosmic rays. All powerful sources, such as Cen A, within a few hundred megaparsecs are known and are catalogued. They are rather few and, in general, are not identified with the arrival directions which have been measured. It appears that many of the highest energy cosmic rays must come from distances large enough that they suffer appreciable intergalactic scattering and that we should look for rather broad scale directional spreads from a limited number of very unusual sources.

The search for sources of the highest energy cosmic rays can then be pursued by looking in cosmic ray directional data for preferred directions, or preferred areas of the sky, and then looking in suitable astronomical catalogues for candidate sources in those areas. The requirements for candidate sources have been discussed in many studies but Hillas (1984) has encapsulated the arguments in a readily accessible exposition. It is noteworthy that the energy of the detected particle is not the one for consideration when examining possible source mechanisms since there is a progressive energy loss due to the photopion mechanism. The source criteria are thus more stringent than might appear at first sight.

We usually assume that acceleration is through some form of progressive shock acceleration, although rotating objects with strong magnetic fields may alternatively provide a single voltage of the required magnitude. In the case of shock acceleration, large objects are required since the particles must be contained for long periods and scattered many times whilst energy is gained. Large volumes containing clusters of galaxies or the hot spots of radio lobes associated with FR II radio sources are possible source candidates.


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