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**Session 43 - Binary Stars.**

*Display session, Tuesday, January 16*

*North Banquet Hall, Convention Center*

## [43.19] On the Validity of the Classical Apsidal Motion Formula for Tidal Distortion

*E. Quataert, P. Kumar, C. O. Ao (MIT)*
We check the validity of the widely used classical apsidal motion
formula as a function of orbital parameters, stellar structure, and
stellar rotation rate by comparing dynamical calculations of the
periastron advance with the equilibrium tidal formula. We find that
the classical formula gives very accurate results when the periods of
the low order quadrupole g, f and p modes are smaller than the
periastron passage time by a factor of about 7 or more. However, when
this condition is not satisfied, the difference between the classical
formula and the exact result can be quite large, and even periastron
recession can result. The largest difference arises when one of the
low order modes of the star is nearly resonant with an integer
multiple of the orbital frequency minus twice the rotation rate of the
star. The resonance of higher order g-modes (number of radial nodes
greater than about 4) with the orbit is very unlikely to cause
significant deviation from the classical result because of their weak
coupling to the tidal force and thus their small contribution to the
apsidal motion. Resonances involving rotational modes of the star are
also unlikely to make much contribution to the apsidal motion because
of their small overlap with the tidal force, even though they have
periods comparable to the periastron passage time.

We apply our work to two famous binary systems (AS Cam and DI Her)
which show abnormally small apsidal motion, and conclude that
dynamical effects are unimportant for these systems, i.e. the
equilibrium tide assumption is an excellent approximation.

**Program
listing for Tuesday**