LATITUDINAL EFFECT OF COSMIC RADIATION AND THE MAGNETIC MOMENT OF THE SUN

The existence of a latitudinal effect of cosmic radiation was proved about 20 years ago[^1]. This effect consists in an increase in the intensity of cosmic rays when the point of observation is moved from the geomagnetic equator toward the poles. It is explained by the deflecting action that the Earth’s magnetic field exerts on the primary cosmic radiation arriving at the Earth from space. The presence of a latitudinal effect in cosmic radiation was the first proof that primary cosmic radiation is electrically charged. It is known that, to a first approximation, the Earth’s magnetic field is described by the field of a magnetic dipole possessing a magnetic moment

\[ M = 8.1 \cdot 10^{25}\ \text{gauss}\cdot\text{cm}^3. \]

Charged particles falling vertically onto the Earth at its magnetic poles move along the lines of force of this dipole and do not experience the deflecting action of the magnetic field. Particles falling onto the Earth at the equator are subject to the deflecting action of the Earth’s magnetic field to the greatest degree. It is therefore natural to expect that the intensity of cosmic rays will increase when moving from the equator toward the poles. In Fig. 1 are shown the curves of the latitudinal effect obtained by Compton at sea level and at altitudes of 2000 and 4360 m. We see that these curves do indeed show a monotonic increase in the intensity of ionization from the equator toward the poles. At the same time, the curves shown are characterized by the presence of “saturation,” occurring at a latitude of 50°; at latitudes greater than 50° the intensity of cosmic radiation does not change with latitude. The absence of a latitudinal effect between 50° and the pole for considerably greater altitudes followed from the experiments of Carmichael and Dymond[^2], who made their measurements (telescopes of Geiger–Müller counters raised on sounding balloons) at various latitudes up to 88° N latitude, at which an altitude of 22 km was reached.

They found that, within the errors of the experiment, the altitude dependence of the intensity of cosmic rays coincides with the altitude dependence of the inten-

siveness obtained by Pfotzer at \(49^\circ\) N latitude, i.e. that the latitude effect between \(49^\circ\) and \(88^\circ\) N latitude is practically absent. From the theory of the latitude effect it is known that, for particles incident vertically on the surface of the Earth, for each latitude \(\lambda\) there is a certain critical momentum, \(p_{\mathrm{cr}}\), such that all charged particles possessing a smaller momentum are deflected by the magnetic field and go back without reaching the Earth. The dependence of \(p_{\mathrm{cr}}\) on latitude is given by the expression

\[ p_{\mathrm{cr}} = 15000 \cos^4 \lambda \ \text{MeV}/c. \]

For \(50^\circ\) N latitude, \(p_{\mathrm{cr}} \simeq 3000\) MeV/\(c\). The first explanation of the “saturation” of the latitude-effect curve consisted in the following. Suppose that the minimum energy required by primary particles to penetrate through the entire atmosphere is equal to or greater than 3000 MeV. (This assumption agrees with reality: a relativistic particle loses \(60\)–\(2\cdot 10^9\) eV in passing through the whole atmosphere.) Then all primary particles responsible for producing the latitude effect at latitude \(50^\circ\) and higher (and the secondary particles formed by them) are absorbed in the atmosphere and cannot participate in producing the latitude effect; in other words, primary particles sensitive to the Earth’s magnetic field do not reach sea level at latitude \(50^\circ\) and higher. If this hypothesis were correct, the latitude at which “saturation” begins would change with altitude. Meanwhile, from the data of Compton and Kozinets it followed that saturation begins at all altitudes at one and the same latitude. For more than ten years another explanation of the “saturation” of the latitude-effect curve, due to Janossy, was regarded as generally accepted; he proposed that, in the primary spectrum of the radiation incident on the Earth, particles with energies below 3000 MeV are entirely absent. He put forward the hypothesis that the absence of such energies in the primary spectrum is caused by the deflecting action of the Sun’s magnetic field. It should be noted that the data on the Sun’s magnetic field are highly contradictory. Hale\(^{4}\), on the basis of a study of Zeeman splitting of solar-spectrum lines, suggested that the Sun has a magnetic dipole moment approximately equal to \(1.7\cdot 10^{34}\) gauss·cm\(^3\).

Fig. 1.

At the same time, analogous investigations by other authors did not reveal the existence of a measurable magnetic field of the Sun by spectroscopic methods. Calculations by Vallarta and Al. showed that the magnitude of the Sun’s magnetic moment, equal to \(1.7 \cdot 10^{34}\), would be sufficient to explain the “saturation” of the latitude effect curve. Thus, the existence of “saturation” could be regarded as an independent confirmation of the presence of a magnetic moment in the Sun. In the paper under review

Fig. 2.

Pomerantz\(^5\), devoted to measuring the altitude variation of cosmic radiation at 52 and 69° N latitude, showed that the latitude effect at high altitudes also occurs for these latitudes. This result means that “saturation” in the curve of the latitude effect is absent at high altitudes. It is not consistent with previous measurements, in particular those of Carmichael and Dymond, and, if it is correct, means that the magnetic moment of the Sun is much less than \(1.7 \cdot 10^{34}\) gauss·cm\(^3\). The experiment carried out by Pomerantz consisted of repeated ascents into the stratosphere on parachute-equipped assemblies of identical telescopes made of Geiger–Müller counters and radio equipment that transmitted to the ground signals on the atmospheric pressure, the temperature inside the gondola where the apparatus was placed, and the intensity of cosmic rays recorded by the telescope. The author paid special attention to ensuring that the separate telescope assemblies and the radio equipment working together with them were identical. As an illustration of the extent to which this was achieved, we note that in 20 flights 20 installations were used, and the intensity recorded by these 20 installations at sea level varied from \(0.886 \pm 0.010\) to \(0.920 \pm 0.014\) coincidences per hour at

average value of \(0.905 \pm 0.003\) coincidences per hour. In Fig. 2, two of the curves obtained by the author for the altitude variation of the intensity of cosmic rays are presented. Along the ordinate axis is plotted the intensity recorded by the telescope, when a lead filter \(6.5\ \mathrm{cm}\) thick was placed between its rows; along the abscissa axis, the pressure in mm Hg. The upper curve was taken during flights at \(69^\circ\) N latitude, the lower one during flights at \(52^\circ\) N latitude. We see that up to an altitude corresponding to a pressure of \(150\ \mathrm{mm}\) Hg (\(12\ \mathrm{km}\)), the intensity variation at both latitudes is practically the same, and this means that at these altitudes the intensity of cosmic radiation does not in fact change between these latitudes. However, with increasing altitude the latitude effect begins to appear. At the maximum altitude, corresponding to a pressure of \(7.5\ \mathrm{mm}\) Hg, the magnitude of the latitude effect, measured by the ratio of the intensity at latitude \(69^\circ\) to the intensity at latitude \(52^\circ\), reaches the value 1.43. The author also measured the altitude variation of intensity for the case in which a lead filter \(1\ \mathrm{cm}\) thick was placed between the rows of the telescope, and for the case of a telescope free of any absorbers (except for the walls of the counters). Both these series of curves likewise unambiguously indicate the existence of a significant latitude effect, beginning at an altitude corresponding to about \(150\ \mathrm{mm}\) Hg. As we have already indicated, this finding is in contradiction with all previous measurements made at great altitudes. Nevertheless, there is no basis for doubting the data reported by the author. But if “saturation” of the latitude-effect curve is absent, it follows from this that the magnetic field of the Sun is considerably less than \(1.7 \cdot 10^{34}\ \mathrm{gauss}\cdot\mathrm{cm}^{3}\). The author points out that the maximum value of the magnetic moment that does not contradict the latitude effect observed by him is \(0.6 \cdot 10^{33}\ \mathrm{gauss}\cdot\mathrm{cm}^{3}\), i.e., almost 30 times smaller than the value given by Hale.

A. V.

References

1. Compton, Phys. Rev. 43, 387 (1933).
2. Carmichael and Dymond, Proc. Roy. Soc. A171, 321 [(1939).
3. Cosyns, Nature 137, 616 (1936).
4. Hale, Astrophys. Journ. 47, 206 (1918).
5. M. A. Pomerantz, Phys. Rev. 77, 830 (1950).