Applegate mechanism

The Applegate mechanism (Applegate's mechanism or Applegate effect) explains long term orbital period variations seen in certain eclipsing binaries. As a main sequence star goes through an activity cycle, the outer layers of the star are subject to a magnetic torque changing the distribution of angular momentum, resulting in a change in the star's oblateness. The orbit of the stars in the binary pair is gravitationally coupled to their shape changes, so that the period shows modulations (typically on the order of ∆P/P ∼ 10⁻⁵) on the same time scale as the activity cycles (typically on the order of decades).

Careful timing of eclipsing binaries has shown that systems showing orbital period modulations on the order of ∆P/P ∼ 10⁻⁵ over a period of decades are quite common. A striking example of such a system is Algol, for which the detailed observational record extends back over two centuries. Over this span of time, a graph of the time dependence of the difference between the observed times of eclipses versus the predicted times shows a feature (termed the "great inequality") with a full amplitude of 0.3 days and a recurrent time scale of centuries. Superimposed on this feature is a secondary modulation with a full amplitude of 0.06 days and a recurrent time scale of about 30 years. Orbital period modulations of similar amplitude are seen in other Algol binaries as well.

Although recurrent, these period modulations do not follow a strictly regular cycle. Irregular recurrence rules out attempts to explain these period modulations as being due to apsidal precession or the presence of distant, unseen companions. Apsidal precession explanations also have the problem that they require an eccentric orbit, but the systems in which these modulations are observed often show orbits of little eccentricity. Furthermore, third body explanations have the issue that in many cases, a third body massive enough to produce the observed modulation should not have managed to escape optical detection, unless the third body were quite exotic.

Another phenomenon observed in certain Algol binaries has been monotonic period increases. This is quite distinct from the far more common observations of alternating period increases and decreases explained by the Applegate mechanism. Monotonic period increases have been attributed to mass transfer, usually (but not always) from the less massive to the more massive star

The time scale and recurrence patterns of these orbital period modulations suggested to Matese and Whitmire (1983) a mechanism invoking changes in the quadrupole moment of one star with subsequent spin-orbit coupling. However, they could not provide any convincing explanation for what might cause such fluctuations in the quadrupole moment.

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