woma 1.1

WorldMaker

Create models of rotating and non-rotating planets by solving the differential equations for hydrostatic equilibrium, and create initial conditions for e.g. smoothed particle hydrodynamics (SPH) simulations by placing particles that precisely match the planet's profiles.

See the tutorial.ipynb notebook for a full tutorial and examples (https://github.com/srbonilla/WoMa), with additional documentation in this file, below.

Presented in Ruiz-Bonilla et al. (2020, https://arxiv.org/abs/2007.02965).

Includes SEAGen (https://github.com/jkeger/seagen; Kegerreis et al. 2019, MNRAS 487:4) with modifications for spinning planets.

Sergio Ruiz-Bonilla: [e-mail]
Jacob Kegerreis: [e-mail]

If you find any bugs, potential improvements, or features worth adding, then please let us know!

Files

• tutorial.ipynb Jupyter notebook tutorial and examples.
• woma/ Code directory.
  • main.py The main program classes and functions.
  • data/ Data for equation of state (EoS) tables.
  • eos/ EoS and temperature-density relations.
  • spherical_funcs/ Functions for spherical profiles.
  • spin_funcs/ Functions for spinning profiles.
  • misc/ Miscellaneous functions and constants.
• README.md This file. General info and documentation.
• LICENSE.txt GNU general public license v3+.
• setup.py, setup.cfg, MANIFEST.in PyPI package files.

Requirements

• Python 3 (tested with 3.6.9).
• PyPI: Automatically install the package with pip install woma, see https://pypi.org/project/woma/

Notation etc.

• Formatted with black.
• Arrays are explicitly labelled with a prefix A1_, or An_ for an n-dimensional array.

Documentation

See the tutorial.ipynb notebook for a full tutorial and examples. This documentation summarises the different options available.

Full documentation is provided in the class and function docstrings.

Most functions take an optional verbosity argument that controls the amount of printed information. Set 0 for no printing, 1 for standard output, or 2 for extra details.

Contents

1. Spherical profiles
2. Spinning profiles
3. Particle placement

1. Spherical profiles

All profiles require the temperature and either the pressure or density at the surface: T_s and P_s or rho_s, plus the material and temperature-density relation for each layer (see below): A1_mat_layer and A1_T_rho_type.

The optional parameter num_prof sets the number of profile integration steps. Default 1000.

Equations of state (EoS)

It is important to check that the EoS you use are appropriate for your application.

So far, we have implemented several Tillotson, ANEOS, SESAME, and Hubbard & MacFarlane (1980) materials, with more on the way.

Materials are set for each layer with A1_mat_layer using the following material names, which are converted internally into material IDs, set by a base type ID (multiplied by 100) plus a minor type:

• Tillotson (Melosh 1989; Benz & Asphaug 1999): 1
  • Iron: Til_iron : 100
  • Granite: Til_granite : 101
  • Water: Til_water : 102
  • Basalt: Til_basalt : 103
• Hubbard & MacFarlane (1980): 2
  • Hydrogen-helium atmosphere: HM80_HHe : 200
  • Ice H20-CH4-NH3 mix: HM80_ice : 201
  • Rock SiO2-MgO-FeS-FeO mix: HM80_rock : 202
• SESAME (Lyon & Johnson 1992) and similar: 3
  • Iron (2140): SESAME_iron : 300
  • Basalt (7530): SESAME_basalt : 301
  • Water (7154): SESAME_water : 302
  • Senft & Stewart (2008) water in a SESAME-style table: SS08_water : 303
• ANEOS (in SESAME-style tables): 4
  • Forsterite (Stewart et al. 2019): ANEOS_forsterite : 400
  • Iron (Stewart, zenodo.org/record/3866507): ANEOS_iron : 401
  • Fe85Si15 (Stewart, zenodo.org/record/3866550): ANEOS_Fe85Si15 : 402

These are defined in woma/misc/glob_vars.py.

Temperature-density relations

These relations are set for each layer with A1_T_rho_type:

• "adiabatic": Adiabatic, only available for some EoS.
• "power=a" where a is a float: A power law T ~ rho^a. So e.g. "power=0" for isothermal.

Profile generation

There are several options for which additional parameters are set and which unknowns are found, depending on the number of layers in the planet.

Most of these functions are simple iterative bisection searches over the unknown parameter(s) to find a valid planet in hydrostatic equilibrium that satisfies the set attribute values.

The additional function arguments like R_max set things like the upper bound for an iteration so usually do not need to be precise.

Optional arguments for these functions (in addition to the verbosity) set:

• tol: The tolerance for finding unknown parameters as a fractional difference between two consecutive iterations. Default usually 0.001, depending on the method.
• num_attempt: The maximum number of iteration attempts if the tolerance has still not been reached. Default usually 40, depending on the method.

If the outer radii or masses of some but not all layers are required as inputs, then the unknown elements in the input arrays can be left as None, e.g.: A1_R_layer = [3.1415, None] or A1_M_layer = [None, 1.23, 4.56].

1 layer

• gen_prof_L1_find_R_given_M(), requires:
  • Total mass: self.M
  • Maximum radius: R_max
• gen_prof_L1_find_M_given_R(), requires:
  • Total radius: self.R
  • Maximum mass: M_max

2 layers

• gen_prof_L2_find_R1_given_M_R(), requires:
  • Total radius: self.R
  • Total mass: self.M
• gen_prof_L2_find_M_given_R_R1(), requires:
  • Total radius: self.R
  • Layer 1 outer radius: self.A1_R_layer[0]
  • Maximum mass: M_max
• gen_prof_L2_find_R_given_M_R1(), requires:
  • Total mass: self.M
  • Layer 1 outer radius: self.A1_R_layer[0]
  • Maximum radius: R_max
• gen_prof_L2_find_R_R1_given_M1_M2(), requires:
  • Layer 1 and 2 masses: self.A1_M_layer
  • Minimum and maximum radii: R_min, R_max

3 layers

• gen_prof_L3_find_M_given_R_R1_R2(), requires:
  • Layer 1, 2, and 3 outer radii: self.A1_R_layer
• gen_prof_L3_find_R1_given_M_R_R2(), requires:
  • Total mass: self.M
  • Total radius: self.R
  • Layer 2 outer radius: self.A1_R_layer[1]
• gen_prof_L3_find_R2_given_M_R_R1(), requires:
  • Total mass: self.M
  • Total radius: self.R
  • Layer 1 outer radius: self.A1_R_layer[0]
• gen_prof_L3_find_R_given_M_R1_R2(), requires:
  • Total mass: self.M
  • Layer 1 and 2 outer radii: self.A1_R_layer[0], [1]
• gen_prof_L3_find_R1_R2_given_M_R_I(), requires:
  • Total mass: self.M

Adding layers

• gen_prof_given_inner_prof(): After generating an initial planet, a new layer can be added on top by integrating outwards. Requires:
  • Name of the material in the new layer: mat
  • Temperature-density relation in the new layer: T_rho_type
  • Minimum density at which the new layer will stop: rho_min
  • Minimum pressure at which the new layer will stop: P_min

Additional parameters

See the main.py and other docstrings for full details.

The class's num_prof parameter sets the number of radial profile steps, while the profile generating functions take arguments like tol and/or num_attempt that control the convergence criterion and maximum number of iterations to do to find the unknown parameters.

2. Spinning profiles

See tutorial.ipynb for the main usage:

spherical_planet = woma.Planet( . . . ) 

spin_planet = woma.SpinPlanet(
    planet = spherical_planet,
    period = 24,  # hours
)

The output attributes available from the spin_planet object are documented in the SpinPlanet class docstring in woma/main.py.

The primary outputs are the arrays of properties of the nested spheroids, including their equatorial and polar radii (semi-major and semi-minor axes), A1_R and A1_Z, and for example their masses, densities, pressures, and temperatures, A1_m, A1_rho, A1_P, and A1_T.

Additional parameters are similar to those in the spherical case mentioned above. See the docstrings for full details.

3. Particle placement

See tutorial.ipynb for the main usage:

planet = woma.Planet( . . . ) 
# or 
planet = woma.SpinPlanet( . . . )

N_particles = 1e7
N_ngb = 48 # Optional number of neighbours for approximate SPH smoothing lengths

particles = woma.ParticleSet(planet, N_particles, N_ngb=N_ngb)

The output attributes available from the particles object are documented in the ParticlePlanet class docstring in woma/main.py.