1. Introduction

Planetary nebulae are among the most beautiful objects in the sky. Despite their name, they have nothing to do with planets: they are the gaseous envelopes ejected by intermediate-mass stars (0.8 to 8 solar masses) at the end of their lives. The Sun will form a planetary nebula in about 5 billion years. Many of these nebulae display spectacular spiral structures.

2. Formation of Planetary Nebulae

When an intermediate-mass star exhausts its central hydrogen, it swells into a red giant. In the asymptotic giant branch (AGB) phase, the star loses mass at a high rate (10^-7 to 10^-4 solar masses per year) as slow stellar winds. Then a fast wind from the central white dwarf catches up and compresses the slow wind, creating the visible nebula. The central star, now a hot white dwarf, ionizes the surrounding gas which emits light.

3. Observed Spiral Structures

Several planetary nebulae display remarkable spiral structures. The Helix Nebula (NGC 7293) shows regularly spaced concentric arcs, interpreted as periodic mass ejections. The Ant Nebula (Mz 3) presents bipolar jets and helical structures. AFGL 3068 (the Spiral Nebula) shows a near-perfect spiral, one of the most beautiful spiral structures known in a nebula.

4. Mechanisms of Spiral Formation

Two main mechanisms explain spiral structures in planetary nebulae. The first is the presence of a binary companion: if the AGB star has a companion (star, brown dwarf or even giant planet), the stellar wind is modulated by the companion's orbit. The wind forms an Archimedean spiral in the orbital plane, with spacing between arms equal to the distance traveled in one orbital period. The second mechanism is the rotation of the star itself, which can create helical structures in polar jets.

5. Conclusion

Planetary nebulae illustrate how the death of stars can produce geometrically beautiful structures. The observed spirals are archives of the star's mass-loss history, encoding in their geometry the presence of binary companions and variations in the stellar wind over thousands of years.