Kepler-223 Migration Code

Written by: Cezary Migazewski

This is code used to compute the planetary migration simulations in 
Mills, Fabrycky, Migazewski, Ford, Petigura, and Isaacson, "A resonant chain of four transiting, sub-Neptune planets," Nature, 2016, 533, 509.
An identical version of this code is available as a supplement to the article, available for download at https://www.nature.com/articles/nature17445.
If you make use of this code, please cite Mills et al. 2016 and acknowledge the use of this code. 


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Compilation (flags -O2 -m64 -msse3 are optional, also other flags may be added):

gcc -O2 -m64 -msse3 -lm -o migration migration.c

Execution:

./migration

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Input file:

start_migration.in

Subsequent input variables:

- integer enumerating the output,
- number of planets,

- integration time in years,
- integer controlling output density, i.e., 1000 means that every 1000th integration step will be written out,
- variable controlling time-step of the integration (dt), i.e., 60.0 means that dt = period of the outermost planet/60.0,
- mass of the star (in Solar masses).

Planets masses and initial orbits (the system is coplanar, thus inclination and longitude of the ascending node are both 0.0):

For each planet:
- mass (in Solar masses), semi-major axis (in AU), eccentricity, argument of pericenter (in degrees), mean anomaly (in degrees).

Migration parameters:
- T (years)
- tau0 (years)
- alpha
- kappa
- beta

The time-scale of migration:

tau_a = tau0 * exp(t/T) * (r/AU)^alpha * (m/mE)^beta.

The time-scale of circularization:

tau_e = tau_a/kappa, 

where t is time in years, r in planet's astrocentric distance (in AU), m is planet's mass and mE is the Earth mass.

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Output file:

evolution_?.out

? is the integer enumerating the output (first variable in start_migration.in)

Subsequent columns:

- time (years),

For each planet there are six columns:

- semi-major axis (AU),
- eccentricity,
- inclination (radians),
- longitude of the ascending node (radians),
- argument of pericenter (radians),
- mean anomaly (radians).

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