Discussion

An examination of Figure 1 shows that, in the north, the anisotropy has a peak at about 21 hours in right ascension. The southern anisotropy shows a dip at about 7 hours right ascension. Given the uncertainties of the data of one to two hours due to limited statistics and the combination of only first and second harmonics, these data are remarkably consistent in the sense that the peak is in almost an opposite direction on the sky to the trough. Such a situation is that which would be expected for a unidirectional anisotropy due to net cosmic ray streaming (e.g. Jacklyn 1986). That is, the cosmic rays have a diffusive flow from the direction of greatest intensity and show a minimum in intensity in the opposite direction. An ideal unidirectional anisotropy would have a cosinusoidal variation with the angle from maximum intensity. The case shown in figure 1 deviates from this but retains an intensity peak in the forward direction and a trough behind. We are not able to identify the diffusion process with such confidence from northern data alone.

The majority of both the northern and southern data are at mid-latitudes and we can identify the direction of the cosmic ray flow as from the spiral arm inwards direction which is at about 20hrs in right ascension and 35 degrees in declination (Jacklyn 1986). Studies of the galactic magnetic field identify the spiral arm as the local direction of the overall galactic magnetic field which has a broad-scale value of a few microgauss.

The amplitude of the anisotropy is of the order of 0.2%. Simple diffusion ideas (see e.g. Allan 1972) suggest that this value would be roughly equal to the ratio of the scattering mean free path to a characteristic dimension of the containment region (perhaps the central galactic region with a scale of 10kpc). In this case, a plausible mean free path of about 20pc is found - perhaps 20 gyro radii. Alternatively, one could take cosmic ray lifetimes of about yr and estimate the size of the containment region as the product of the anisotropy and the lifetime. That lifetime has been measured at low energies through studies of radioactive nuclei. As energies increase, it still appears to apply up to eV based on a number of propagation calculations as discussed by Clay and Smith (1996). A containment dimension of the order of 10kpc is thus found which is a consistent, albeit crude, check of our ideas.

It is possible that there may be a local source of cosmic rays, perhaps associated with the local bubble (Clay and Smith 1997, Erlykin and Wolfendale 1997). The direction of any anisotropy associated with such a bubble is proposed by Clay and Smith (1997) and is not compatible with the observations presented here. The data presented by Erlykin and Wolfendale (1997) for a local single source are not a good fit to observations at the energy discussed in this paper.

A knowledge of the amplitude of the anisotropy and the suggestion that it is associated with streaming along the spiral arm allows one to estimate the rate of energy injection into galactic cosmic rays. It is assumed that the outward cosmic ray flow is dominated by streaming along the spiral arm. This is supported by the anisotropy data for, if there was poor containment and the galactic central regions were the source of the cosmic rays, there would be some suggestion in the data of flow from those regions and this is not observed. If we take the spiral arm cross section as 1000pc in the galactic plane and 100pc perpendicular, we can estimate the area through which the cosmic rays diffuse. The magnitude of the anisotropy gives us rather directly the speed of the diffusive drift (the speed of light multiplied by the amplitude of the anisotropy) and we can then use our knowledge of the local cosmic ray energy density for all cosmic ray particles (1eV/cc to the level of approximation which we are using) to derive the rate of cosmic ray energy flow past us. Since we observe the cosmic ray flow to be along the spiral arm, this rate of about erg/sec corresponds to the necessary rate of energy injection and is significantly less than that which we would have derived assuming diffusion through the whole galactic surface.

The anisotropy at lower energies is less than at eV (see e.g. Clay and Smith 1997, Speller et al. 1972) and below about eV it may be even smaller, being dominated by other effects such as the motion of the solar system through the galaxy. This implies that, as would be expected, the diffusive flow is slower at lower energies where the gyro radii are smaller in the galactic field and the particles follow the small scale random field components more effectively. Our estimate of the power will thus be an upper limit, high by at least a factor of ten. We thus make our estimate of the power injection into galactic cosmic rays as less than or of the order of ergs/sec (watts). This power requirement is modest compared to some in the literature and reflects the relative lack of high energy activity in our galaxy. It is not far above the estimate by Ginzburg (1969) of to ergs/s for the average power of cosmic rays only from stars like our Sun in the galaxy. Such stars will not provide particles up to eV but we can see that they might well contribute the bulk of the power requirements.

© Copyright Astronomical Society of Australia 1997