Orbital period modulation and quadrupole moment changes in magnetically active close binaries

We discuss the main characteristics of the orbital period modulation in clo se binaries with tate-type components. We focus on the various physical sce narios proposed to explain this phenomenon and, in particular, Hall's (1989 ) suggestion that it may be connected with magnetic activity. Starting from the work of Applegate (1992) and Lanza et al. (1998a), we develop an integ ral approach to evaluate the gravitational quadrupole moment of an active s tar and its variations, which we consider to be an important driver of the observed orbital period changes. The method applies the tensor virial theor em after Chandrasekhar (1961) and directly relates the variation of the qua drupole moment with the changes of kinetic and magnetic energy of the stell ar hydromagnetic dynamo. Particular effort has been applied in minimizing t he number of free parameters entering the problem. A sample of 46 close binaries with period changes of alternate signs has be en studied by our method. The amplitude of the quadrupole moment change app ears to decrease with increasing angular velocity, implying that the time-v ariable part of the kinetic energy of rotation varies as delta T/T proporti onal to Omega(-0.93+/-0.10), With a correlation coefficient of 0.83. The le ngth of the cycle of the orbital period modulation seems to be correlated w ith the angular velocity as P-mod proportional to Omega(-0.36+/-0.10), but With a Smaller correlation coefficient of 0.62. These results support the s uggestion that a distributed non-linear dynamo is at work in the convective envelopes of very active stars and that it strongly affects the differenti al rotation. We also discuss the energy budget of the process responsible f or the quadrupole moment variation and find that, on average, only similar to 10% of the energy required to maintain the differential rotation may be lost by dissipation in the turbulent convective envelope during a cycle of the orbital period change. The problems of the magnetic field geometry and stability and the relationship between the length of the activity cycle, as determined by the change of the area of the starspots and the orbital peri od modulation, respectively, are also addressed.