# (P)lanetary (O)rbital (E)volution due to (T)ides (POET)¶

Planetary Orbital Evolution due to Tides (POET) is a tool for simulating the evolution of single stars, binary stars, and star–planet systems under the combined effects of:

• Tides in one or both of the objects

• Age dependent stellar structure

• Stars losing angular momentum to wind

• The internal redistribution of angular momentum between the surface and the interior of stars

POET is capable of evolution calculations for orbits ranging from circular to highly eccentric, and for fully flexible prescription for the tidal dissipation efficiency.

Briefly, stars in POET are split into a number of zones each of which experiences:

• Boundaries evolving both in mass and radius

• Its own tidal coupling to the companion

• Exchange of angular momentum with its neighboring zones, both due to “friction” and due to the exchange of material as the zone boundaries evolve.

In addition, the surface zone loses angular momentum due to winds, modeled after, Stauffer and Hartmann 1987, Kawaler 1988, and Barnes and Sofia 1996, as

$\dot{L} = K_w \omega \min(\omega, \omega_{sat})^2 \sqrt{(R_\star/R_\odot)(M_\odot/M_\star)}$

where $$K_w$$ parameterizes the strength of the wind, $$\omega_{sat}$$ is a saturation frequency required by observations, and $$R_\star$$ and $$M_\star$$ are the mass and radius (evolving) of the star. The coupling torque between neighboring zones is such that it would cause exponential decay of the differential rotation on a timescale $$\tau_c$$ (separately defined for each pair of zones) if everything else was turned off.

Stellar evolution is incorporated using interpolation within a grid of stellar properties as a function of mass, metallicity and age.

At the moment, POET comes with a pre–computed grid of stellar evolutions for interpolation for $$0.4 M_\odot \leq M_\star < 1.4 M_\odot$$, which was generated using the publicly available stellar evolution code MESA (Paxton et. al. 2011).

Tidal evolution uses an extended version of the formalism descrsibed in Lai 2012, which was extended to allow for eccentric orbits, where a series expansion in eccentricity is used, up to a dynamically adjusted maximum order.

## Citing POET¶

If you use POET in your publications, and/or presentations, please cite Penev, Zhang and Jackson 2014 and the Astrophysics Source Code Library entry