We make publicly available an efficient, versatile, easy to use and extend tool for calculating the evolution of circular aligned planetary orbits due to the tidal dissipation in the host star. This is the first model to fully account for the evoluti
on of the angular momentum of the stellar convective envelope by the tidal coupling, the transfer of angular momentum between the stellar convective and radiative zones, the effects of the stellar evolution on the tidal dissipation efficiency and stellar core and envelope spins, the loss of stellar convective zone angular momentum to a magnetically launched wind and frequency dependent tidal dissipation. This is only a first release and further development is under way to allow calculating the evolution of inclined and eccentric orbits, with the latter including the tidal dissipation in the planet and its feedback on planetary structure. Considerable effort has been devoted to providing extensive documentation detailing both the usage and the complete implementation details, in order to make it as easy as possible for independent groups to use and/or extend the code for their purposes. POET represents a significant improvement over some previous models for planetary tidal evolution and so has many astrophysical applications. In this article, we describe and illustrate several key examples.
We use the distribution of extrasolar planets in circular orbits around stars with surface convective zones detected by ground based transit searches to constrain how efficiently tides raised by the planet are dissipated on the parent star. We parame
terize this efficiency as a tidal quality factor (Q*). We conclude that the population of currently known planets is inconsistent with Q*<10^7 at the 99% level. Previous studies show that values of Q* between 10^5 and 10^7 are required in order to explain the orbital circularization of main sequence low mass binary stars in clusters, suggesting that different dissipation mechanisms might be acting in the two cases, most likely due to the very different tidal forcing frequencies relative to the stellar rotation frequency occurring for star--star versus planet--star systems.
In recent years it has been shown that the tidal coupling between extrasolar planets and their stars could be an important mechanism leading to orbital evolution. Both the tides the planet raises on the star and vice versa are important and dissipati
on efficiencies ranging over four orders of magnitude are being used. In addition, the discovery of extrasolar planets extremely close to their stars has made it clear that the estimates of the tidal quality factor, Q, of the stars based on Jupiter and its satellite system and on main sequence binary star observations are too low, resulting in lifetimes for the closest planets orders of magnitude smaller than their age. We argue that those estimates of the tidal dissipation efficiency are not applicable for stars with spin periods much longer than the extrasolar planets orbital period. We address the problem by applying our own values for the dissipation efficiency of tides, based on our numerical simulations of externally perturbed volumes of stellar-like convection. The range of dissipation we find for main-sequence stars corresponds to stellar $Q_*$ of $10^8$ to $3{times}10^9$. The derived orbit lifetimes are comparable to, or much longer than the ages of the observed extrasolar planetary systems. The predicted orbital decay transit timing variations due to the tidal coupling are below the rate of ms/yr for currently known systems, but within reach of an extended Kepler mission provided such objects are found in its field.
The current understanding of the turbulent dissipation in stellar convective zones is based on the assumption that the turbulence follows Kolmogorov scaling. This assumption is valid for some cases in which the time frequency of the external shear is
high (e.g., solar p modes). However, for many cases of astrophysical interest (e.g., binary orbits, stellar pulsations, etc.), the timescales of interest lie outside the regime of applicability of Kolmogorov scaling. We present direct calculations of the dissipation efficiency of the turbulent convective flow in this regime, using simulations of anelastic convection with external forcing. We show that the effects of the turbulent flow are well represented by an effective viscosity coefficient, we provide the values of the effective viscosity as a function of the perturbation frequency and compare our results to the perturbative method for finding the effective viscosity of Penev et al. that can be applied to actual simulations of the surface convective zones of stars.
We extend the analysis of Penev et al. (2007) to calculate effective viscosities for the surface convective zones of three main sequence stars of 0.775Msun, 0.85Msun and the present day Sun. In addition we also pay careful attention to all normalizat
ion factors and assumptions in order to derive actual numerical prescriptions for the effective viscosity as a function of the period and direction of the external shear. Our results are applicable for periods that are too long to correspond to eddies that fall within the inertial subrange of Kolmogorov scaling, but no larger than the convective turnover time, when the assumptions of the calculation break down. We find linear scaling of effective viscosity with period and magnitudes at least three times larger than the Zahn (1966, 1989) prescription.
We have adapted the anelastic spectral code of Barranco & Marcus (2006) to simulate a turbulent convective layer with the intention of studying the effectiveness of turbulent eddies in dissipating external shear (e.g. tides). We derive the anelastic
equations, show the time integration scheme we use to evolve these equations and present the tests we ran to confirm that our code does what we expect. Further we apply a perturbative approach to find an approximate scaling of the effective eddy viscosity with frequency, and find that it is in general agreement with an estimate obtained by applying the same procedure to a realistic simulation of the upper layers of the solar convective zone.
