The Effective Tidal Viscosity in Close Solar-Type Binaries


  Itzhak Goldman  
Afeka, Tel Aviv Academic College of Engineering


A major problem confronting the understanding of tidal evolution of close solar-type binaries is the inefficiency of the turbulent  convection. The  value  of the effective viscosity estimated, in the framework of the mixing length theory (MLT), implies  circularization  timescales   which are almost  two orders of magnitude longer than observed. Moreover, the reduction of the effective viscosity due to the fast time-variation of the tidal shear in short period binaries,  increases the discrepancy to about  three orders of magnitude. This state of affairs has motivated suggestions that tidal orbital evolution, notably circularization occurs mainly during the pre-main-sequence phase. However, observational data accumulated over the recent decades imply that circularization does occur during the the main-sequence phase (Mazeh 2008).

We examine the possibility that the apparent inefficiency of turbulent convection   is merely a shortcoming of  MLT  approach.  Indeed,  a recent 3D numerical simulation (Penev et al. 2007),  suggests that the true convective viscosity is probably larger than the MLT value and that the reduction due to the time-variation of the shear is not drastic.
We  employ a  model for stellar turbulent convection (Canuto, Goldman & Mazzitelli 1996) to evaluate the effective viscosity both for a steady for  and time dependent tidal shear.
The model is physically based, self-consistent, and accounts for the full spectrum of the turbulent eddies. It has been found   advantageous, compared to the MLT, in many applications.
We use an  analytic approximation to  the turbulent spectrum to obtain the reduction of the efficiency due to the time-variation of the tide. The results are:
(i) an enhanced effective viscosity ( by a factor of ~4.5) and more importantly

(ii) only a mild  reduction due to the time-variation of the tidal shear.

Overall,  for binaries with orbital period of 15 days the discrepancy is "only" a factor of ~30 down from a factor of ~1000.