OL18 module

OL18.eps_23(eps2D, eps3D): The mixing expressions to transition between 3D and 2D. Essentially, eps23 = min(eps2D, eps3D).

OL18.eps_2D(tau, qp, eta, delVy, **dumargs): Calculate accretion efficiency in 2D regime.

OL18.eps_2D_bal(tau, qp, eta, delV, Rp, **dumargs): Equation (A.15) of Paper I

OL18.eps_3D(tau, qp, eta, heff, **dumargs): Calculate accretion efficiency in 3D regime.

OL18.eps_3D_bal(tau, qp, eta, delV, Rp, hP, **dumargs): Equation (A.15) of Paper I

OL18.eps_set(tau, qp, eta, hgas, alphaz): Provides settling efficiency WITHOUT accounting for the f_set modulation factor or ballistic interactions. ASSUMING zero eccentricities, inclinations and standard.

OL18.epsilon_general(mode='', **pars)

Returns the pebble accretion efficiency.

Accepts a variety of “mode” strings that combine to select between pebble accretion modes, e.g., 2d vs 3d, ballistic or settling. This code has not been modified from the original of Ormel & Liu.

Parameters:

mode{[2d, 3d,], [f,], [set, bal,]}

Used to designate accretion modes, can use in combination.

[2d, 3d,] 2d (planar) limit; 3d limit; or mix (default)

[f,] inclusion of fset modulation factor

[set, bal,] settling only; ballistic only; mix (default); (mix always triggers calculation of fset factor)

Examples

2dset 2d (planar), settling regime; EqA4, Paper I

3dsetf 3d regime, w/ modulation factor; Eq21 Paper II

set interpolation b/w 2d and 3d limits, Eq38 Paper II

2dbalf 2d, ballistic regime; EqA15 Paper I

3dbalf 3d, ballistic regime; EqA16 Paper I

'' all effects

**pars

A list of keyword arguments.

qp: planet-to-star mass ratio
tau: dimensionless stoping time (tstop*Omega)
alphaz: turbulence diffusivity parameterization in z-direction
taucorr: dimensionless turbulence correlation time (tcorr*Omega)
hgas: gas aspect ratio
eta: gas dimensionless pressure gradient
sigvec: turbulence rms velocity components
nvec: relative strengths (x,y,z) turbulent velocity components
Rp: planet radius over orbital radius (for ballistic regime)

Notes

SM: The calculations of this module remain unchanged from originals, but this documentation has been modified to comply with numpydoc style.

OL: In case of turbulence, please specify the rms-velocities explicitly via sigvec OR based on alphaz using nvec method. If none is given then nvec = (1,1,1) is assumed.

OL18.f_set(delVvec, sigPvec, vast): Exponential decay function to account for transition between settling and ballistic regimes.

OL18.f_set_i(delVi, sigi, vast): Calculates fset for a single direction.

OL18.heff_app(hP, ip): Approximation to the effective scaleheight in case of planet inclination (ip<>0). Eq. 26 of OL18.

OL18.hp_YL07(tau, hgas, alphaz, taucorr=1.0, **dumargs): Returns the particle scaleheight according to Eq.-21 and -28 of Youdin & Lithwick (2007).

OL18.sig_turb(alphaz, hgas, taucorr=1.0, **dumargs)

OL18.v_ast(tau, qp, **dumargs): Characteristic velocity for pebble accretion.

OL18.v_circ(tau, eta, qp, **dumargs): Circular velocity, Eqs. XXXX of Paper I.