Carl Størmer and the Aurorae

Fredrik Carl Mülertz Størmer

Carl Størmer

On September 3, 1874, Norwegian mathematician and geophysicist Carl Størmer was born. Carl Størmer is known both for his work in number theory and for studying the movement of charged particles in the magnetosphere and the formation of aurorae. He also contributed both important photographic observations and mathematical data to the understanding of the polar aurora, of stratospheric and mesospheric clouds, and of the structure of the ionosphere. The discovery of the Van Allen Radiation Belts by James Van Allen confirmed with surprising accuracy Størmer’s theoretical analysis of solar charged particle trajectories in Earth‘s magnetic field.

Carl Størmer studied mathematics at the Royal Frederick University and later moved to Paris where he studied together with Picard, Poincaré, Painlevé, Jordan, Darboux, and Goursat at the Sorbonne. Størmer was appointed professor of mathematics at Kristiania in 1903 and he was elected the first president of the newly formed Norwegian Mathematical Society in 1918.

It is believed that when Størmer observed Kristian Birkeland’s experimental attempts to explain the aurora borealis, he was fascinated by aurorae and related phenomena. His first work on the subject attempted to model mathematically the paths taken by charged particles perturbed by the influence of a magnetized sphere, and Størmer eventually published over 48 papers on the motion of charged particles.

Størmer was able to show that the radius of curvature of any particle’s path is proportional to the square of its distance from the sphere’s center. To solve the resulting differential equations numerically, he used Verlet integration, which is therefore also known as Störmer’s method.

Størmer’s predicted particle motions were later verified by Ernst Brüche and Willard Harrison Bennett. Størmer’s calculations showed that small variations in the trajectories of particles approaching the earth would be magnified by the effects of the Earth’s magnetic field, explaining the convoluted shapes of aurorae.

Further, Størmer considered the possibility that particles might be trapped within the magnetic field, and worked out the orbits of these trapped particles, a prediction that was borne out after his death by the 1958 discovery of the Van Allen radiation belt. Størmer, a keen photographer, also took pictures of around 20 different observatories across Norway. By measuring their heights and latitudes by triangulation, Størmer discovered that the aurora are typically as high as 100 kilometers above ground. He managed to classify them by their shapes and discovered the “solar-illuminated aurora” where the upper parts of an aurora are lit by the sun. Størmer published his work in several book, including From the depths of space to the heart of the atom and The Polar Aurora.

References and Further Reading

  • Carl Størmer at MacTutor History of Mathematics archive, University of St Andrews
  • Carl Størmer Biography at the Biographical Memoirs of Fellows of the Royal Society



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