Propagation Modelling and the Magnetic Fields

When galactic cosmic ray trajectory calculations have been made in the past (e.g. Lee and Clay 1995), they have often been based on the reverse propagation of anti-protons from the Earth. This allows one to follow the path of incoming particles and to determine their path lengths within the galaxy as a function of arrival direction. In the case of a source at the galactic centre, this procedure is not possible as both a particular source and an end point are specified. For this procedure to be practical, we have used the galactic centre as the source of protons and accepted particles which reach the galactocentric distance of the Earth over a range of distances above or below the galactic plane. That distance was chosen to be 1kpc. The azimuthal symmetry of our assumed field allows us to use any particle reaching that distance from the centre.

In this work, we followed Lee and Clay (1995) and adopted the axisymmetric galactic magnetic field model of Rand and Kulkarni (1989). This models the spiral arms as concentric rings. The rings correspond to the distances from us of the galactic spiral arms and the magnetic field is assumed to be in azimuthal directions. In this case, we assume that the Earth is at a distance of 8.5kpc from the Galactic Centre and that the centres of the spiral arm ``rings'' are at distances of 9.4kpc and 3.4kpc from the Centre for one field polarity and at 6.4kpc for the reverse polarity. The field strength in the rings is assumed to vary sinusoidally with distance from the galactic centre with an amplitude of . Locally, the field is then towards a galactic longitude of . Following Lee and Clay, we have included a random magnetic field component at a similar magnitude to that which is observed locally with the assumption that the magnitude of the random field is proportional to the magnitude of the local regular field. We have followed protons of different energies through fields of different strengths with various relative strengths of the regular and random components.

Compared to Lee and Clay, we assume a rather weaker dependence of the field on distance above and below the galactic plane. We assumed an e-folding distance with z of 500pc rather than 100pc. This doubled the number of events available in our resulting dataset. Additionally, we placed the Earth at a galactocentric distance of 8.5kpc rather than the previous 10kpc. This is rather closer to present convention. The regular field strength varies sinusoidally with distance from the galactic centre with a spatial period of 6kpc to simulate both the effect of increased field strength in the spiral arms and the reversal from one arm to the next. A random magnetic field was added to make up the complete field. This turbulent field had a Kolmogorov spectrum and a maximum scale size of 100pc (see Lee and Clay 1995). The field strength associated with the maximum scale size was 2.5 times that of the regular field.

Cosmic ray protons were launched from the position of the galactic centre. They were assumed to be lost from the galaxy if their distance above or below the plane exceeded 1kpc. For this reason, their initial elevations were chosen randomly from a solid angle distribution limited to within of the galactic plane. Experience showed that particles with elevations outside this range were soon lost from the galaxy. The protons were followed until they left the galaxy at a distance of 1kpc above or below the galactic plane, or reached a distance of 8.5kpc from the centre, thus reaching the ``Earth'' target. As noted above, the choice of 1kpc was dictated by the need to retain a significant number of events. The distribution of final distances above or below the plane was, however, broad.

On reaching the distance of the ``Earth'', the position of the proton was recorded together with its current velocity vector, the reverse of which would correspond to the direction of its apparent source as recorded by a cosmic ray detector.

б© Copyright Astronomical Society of Australia 1997