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Observationally, how can this be established?

What is known theoretically about the process?

Are there any reference papers to read?

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This seems one of the better questins on Astronomy SE lately, I don't know why it received a downvote. –  Rob Jeffries Feb 28 at 10:11

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The phenomenon of tidal locking occurs primarily in short period binary systems with convective envelopes. The tides raise bulges in the stars and these interact with convective motions to dissipate energy and to synchronise the orbital and rotational periods of stars and circularise their orbits. The process is much less efficient in stars with radiative envelopes.

How can we tell observationally? Well, we have to show that the rotation period of a star is the same as its orbital period. The orbital period is easily found, either by measuring eclipses, in the case of binary systems with a high inclination, or by measuring the motions of the star(s) using the doppler shift in their spectra.

Measuring rotation periods is also not so difficult. Fast-rotating stars with convective envelopes have magnetic activity and starspots (analogous to sunspots, but covering a larger area). As the star rotates then the light from the star goes up and down depending on what starspots are on the visible surface. This modulation gives the rotation period. In eclipsing binaries it canbe difficult to separate out spots from eclipses, but here one can use the known orbital inclination and known radii of the stars to see whether their projected rotation velocities (measured fro the widths of spectral absorption lines) matches the predictions from a tidally locked orbit.

There are many known tidally locked bnaries. Any low-mass binary with an orbital period of less than a few days is almost certainly tidally locked, but the situation at orbital periods greater than about about 6-8 days becomes more complicated (e.g. Meibom et al. 2006). The plot below is taken from a review by Mazeh (2008), showing the rotation vs orbital periods from some small, but well-defined samples.

Orbital vs rotation period from Mazeh (2008).

The absolutely classic, must-read, theoretical work on this is by Zahn (1989). The timescale for synchronisation depends on structural properties of the stars, their moments of inertia, the binary mass ratio and the ratio of their separation to their radii to the power of 6. It is this latter property that means tidal locking is nearly bimodal; binaries with periods shorter than some threshold (about 6 days) are usually tidally locked, but those with slightly longer periods almost never are.

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Any reference papers about "Any low-mass binary with an orbital period of less than a few days is almost certainly tidally locked." ? How to tell tidally locked binaries are stable all the time? A giant flare may affect their motions in a short time, like glitch in pulsars. –  questionhang Feb 28 at 19:47
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@questionhang I have added some more observational details and references, but that's as far as I'm going with this answer - the references I have given are open-access... Your other point appears to be beyond the realm of "normal stars" - a flare does not affect the rotation rate in any significant way. –  Rob Jeffries Mar 1 at 0:44

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