We present analysis of precision radial velocities (RV) of 1134 mostly red giant stars in the southern sky, selected as candidate astrometric grid objects for the Space Interferometry Mission (SIM). Only a few (typically, 2 or 3) spectroscopic observ
ations per star have been collected, with the main goal of screening binary systems. The estimated rate of spectroscopic binarity in this sample of red giants is 32% at the 0.95 confidence level, and 46% at the 0.75 confidence. The true binarity rate is likely to be higher, because our method is not quite sensitive to very wide binaries and low-mass companions. The estimated lower and upper bounds of stellar RV jitter for the entire sample are 24 and 51 m/s, respectively; the adopted mean value is 37 m/s. A few objects of interest are identified with large variations of radial velocities, implying abnormally high mass ratios.
A formula for the tidal dissipation rate in a spherical body is derived from first principles, to correct some mathematical inaccuracies found in the literature. The development is combined with the Darwin-Kaula formalism for tides. Our intermediate
results are compared with those by Zschau (1978) and Platzman (1984). When restricted to the special case of an incompressible spherical planet spinning synchronously without libration, our final formula can be compared with the commonly used expression from Peale & Cassen (1978, Eqn. 31). The two turn out to differ. In our expression, the contributions from all Fourier modes are positive-definite, this not being the case of the formula from Ibid. (The presence of negative terms in their formula was noticed by Makarov 2013.) Examples of application of our expression for the tidal damping rate are provided in the work by Makarov and Efroimsky (2014).
In Efroimsky & Makarov (2014), we derived from the first principles a formula for the tidal heating rate in a tidally perturbed homogeneous sphere. We compared it with the formulae used in the literature, and pointed out the differences. Using this r
esult, we now present three case studies - Mercury, Kepler-10b, and a triaxial Io. A very sharp frequency-dependence of k2/Q near spin-orbit resonances yields a similarly sharp dependence of k2/Q on the spin rate. This indicates that physical libration may play a major role in tidal heating of synchronously rotating bodies. The magnitude of libration in the spin rate being defined by the planets triaxiality, the latter should be a factor determining the dissipation rate. Other parameters equal, a synchronously rotating body with a stronger triaxiality should generate more heat than a similar body of a more symmetrical shape. Further in the paper, we discuss scenarios where initially triaxial objects melt and lose their triaxiality. Thereafter, dissipation in them becomes less intensive; so the bodies freeze. The tidal bulge becomes a new permanent figure, with a new triaxiality lower than the original. In the paper, we also derive simplified, approximate expressions for dissipation rate in a rocky planet of the Maxwell rheology, with a not too small Maxwell time. The three expressions derived pertain to the cases of a synchronous spin, a 3:2 resonance, and a nonresonant rotation; so they can be applied to most close-in super-Earth exoplanets detected thus far. In such bodies, the rate of tidal heating outside of synchronous rotation is weakly dependent on the eccentricity and obliquity, provided both these parameters are small or moderate. According to our calculation, Kepler-10b could hardly survive the great amount of tidal heating without being synchronised, circularised and also reshaped through a complete or partial melt-down.
We reexamine the popular belief that a telluric planet or satellite on an eccentric orbit can, outside a spin-orbit resonance, be captured in a quasi-static tidal equilibrium called pseudosynchronous rotation. The existence of such configurations was
deduced from oversimplified tidal models assuming either a constant tidal torque or a torque linear in the tidal frequency. A more accurate treatment requires that the torque be decomposed into the Darwin-Kaula series over the tidal modes, and that this decomposition be combined with a realistic choice of rheological properties of the mantle. This development demonstrates that there exist no stable equilibrium states for solid planets and moons, other than spin-orbit resonances.
Tidal torques play a key role in rotational dynamics of celestial bodies. They govern these bodies tidal despinning, and also participate in the subtle process of entrapment of these bodies into spin-orbit resonances. This makes tidal torques directl
y relevant to the studies of habitability of planets and their moons. Our work begins with an explanation of how friction and lagging should be built into the theory of bodily tides. Although much of this material can be found in various publications, a short but self-consistent summary on the topic has been lacking in the hitherto literature, and we are filling the gap. After these preparations, we address a popular concise formula for the tidal torque, which is often used in the literature, for planets or stars.We explain why the derivation of this expression, offered in the paper by Goldreich (1966; AJ 71, 1 - 7) and in the books by Kaula (1968, eqn. 4.5.29), and Murray & Dermott (1999, eqn. 4.159), implicitly sets the time lag to be frequency independent. Accordingly, the ensuing expression for the torque can be applied only to bodies having a very special (and very hypothetical) rheology which makes the time lag frequency independent, i.e, the same for all Fourier modes in the spectrum of tide. This expression for the torque should not be used for bodies of other rheologies. Specifically, the expression cannot be combined with an extra assertion of the geometric lag (or the phase lag) being constant, because at finite eccentricities the said assumption is incompatible with the constant-time-lag condition.
