The Applegate mechanism is a theoretical model proposed to explain observed long-term cyclic period changes in various types of variable stars, particularly pulsating white dwarfs (ZZ Ceti stars) and the orbital periods of certain close binary systems, such as cataclysmic variable (CV) systems. It was primarily developed by Donald Applegate and his collaborators in the early 1990s.
The core idea behind the Applegate mechanism involves cyclic changes in the internal magnetic field of a star, analogous to the solar cycle. These magnetic cycles are thought to occur within a convective envelope (or the entire star in the case of some pulsating white dwarfs or the secondary star in a binary system). The mechanism proceeds as follows:
- Magnetic Field Cycle: The star's internal magnetic field undergoes periodic strengthening and weakening.
- Angular Momentum Redistribution: As the magnetic field varies, it interacts with the differentially rotating stellar material, particularly within the convection zone. This interaction leads to a redistribution of angular momentum within the star. Magnetic stresses can transfer angular momentum between different parts of the star, such as between the core and the envelope.
- Oblateness Change: To conserve total angular momentum, a redistribution of angular momentum within the star requires a change in its overall shape, specifically its oblateness (the degree of its equatorial bulge). For example, if angular momentum is transferred from the core to the envelope, the envelope spins up and becomes more oblate, while the core spins down and becomes less oblate. The overall effective radius of the star can also change.
- Moment of Inertia and Stellar Structure: Changes in the star's oblateness and radius directly affect its moment of inertia. This, in turn, subtly alters the star's overall gravitational potential and internal structure.
- Period Variation: For pulsating stars, changes in internal structure and gravitational potential affect the propagation of stellar pulsations (e.g., pressure modes or gravity modes), leading to observable changes in their pulsation periods. For binary systems, changes in the radius or moment of inertia of one of the component stars (typically the secondary donor star in a CV system) can alter its gravitational quadrupole moment. This change, in conjunction with the system's orbital angular momentum, leads to a modulation of the orbital period.
The Applegate mechanism has been invoked to explain the observed period variations in:
- ZZ Ceti stars: These are pulsating white dwarfs that exhibit changes in their non-radial pulsation periods that are too large and too rapid to be explained solely by secular evolutionary cooling.
- Cataclysmic Variable (CV) systems: Specifically, the cyclic modulations observed in the orbital periods of some short-period CVs (like AM CVn stars) and ultracompact X-ray binaries. In these cases, it is often proposed that magnetic cycles within the convective secondary (donor) star cause its radius to expand and contract periodically, leading to changes in the orbital separation and thus the orbital period.
While the Applegate mechanism provides a compelling physical explanation for observed period changes that are difficult to account for otherwise, the precise details and the magnitude of the effects required to match observations are still subjects of active astrophysical research and debate.