The Beam Properties at the Distance of the Earth

As a check on the properties of propagation in the turbulent field, we ran the program with a purely random field. Clay et al. 1998 have previously calculated the properties of proton propagation in turbulent intergalactic fields and, apart from energy loss issues as discussed by Clay et al. (1998, 2000) and details of the field strength, their broad results should offer a check on our propagation. We find that, as expected, the mean angular deviation of the observed particles from the direction of the galactic centre is inversely proportional to energy for small angular spreads. At 10¹⁹eV it has a value of , fortuitously almost identical to that expected on the basis of the previous work and their simple argument concerning energy losses. At 10¹⁸eV, a decade lower in energy, the propagation is close to diffusive with an almost complete loss of directionality.

When the regular field is introduced, a shift of the mean direction of the observed particles from the direction of the galactic plane results. The magnitude of this deviation depends on the energy of the particles but the dependence is not simple. For our assumed regular magnetic field, we find an overall deflection of the observation direction to the north from the galactic plane. This is to be expected for the local field direction used in the model. However, the magnitude of the deflection is not now inversely proportional to energy except, perhaps, above 10¹⁹eV.

There are at least two contributing factors to this complexity. As we have just noted, the deflection due to the random field is significant at energies appreciably below 10¹⁹eV and, in such a situation, one does not expect linearity to apply to the mean deflection. Also, the spatial period of the regular field as viewed by a particle travelling from the Galactic Centre is of the order of the gyroradius of a particle at these energies. We might well expect that the propagation would show systematic changes in character with energy but it is unreasonable to expect a simple relationship so close to a resonant situation. At 10¹⁹eV, the systematic deflection north of the direction of the galactic plane is of the order of .

The complexity of the dependence of the propagation on local conditions is emphasised if one considers potential observations at different positions within the spiral arm magnetic field. The Earth is towards the inside edge of our spiral arm. Propagation to us is therefore influenced by both our spiral arm field and the field of the next arm inwards, which is in the reverse direction. This emphasises that the detailed properties of the propagation, and the resulting observed arrival directions, depend rather critically on knowing the correct placement of the observation point within the galactic magnetic field.

In reaching the distance of the Earth from the Galactic Centre, a particle must travel through systematic fields which tend to deflect it away from the galactic plane. It is clear that many particles which have gyroradii smaller than the galactocentric distance of the Earth, are unlikely to reach us without some assistance. That assistance may well come from the turbulent field. Using our simple magnetic field model as an example, if we take protons with an energy of

eV and investigate the situation 1kpc more distant than us, the number of observed particles per particle emitted from the Galactic Centre increases by over 20 times for a factor of 4 increase in the strength of the random field. At the position of the Earth, there is a similar, but weaker, effect. Clearly, the random field can have the effect of returning some wayward particles back towards the direction of the galactic plane. Reversing the argument, one could also note that a regular field of value greater than only about 0.03 times that of the random field is sufficient to produce an observable reduction in the detection rate when compared to a purely random field.

In general, it is very difficult for a particle to reach the galactocentric distance of the Earth if its energy is below about

eV, with this threshold depending on the detail of the assumed field. With our best model of the field and the position of the Earth, about one particle in one thousand reached the galactocentric distance of the Earth at

eV. If the Earth had been assumed to be close to the centre of our spiral arm (i.e. a little more distant then we have assumed so far) this would fall to below one in ten thousand. At 10¹⁹eV, the success rate increased to about one in five for our best model, approaching the value to be expected on solid angle arguments for the targetted band of distances from the galactic plane at the distance of the Galactic Centre.

б© Copyright Astronomical Society of Australia 1997