POSEIDON.geometry

Functions to compute geometric aspects of the model atmosphere.

Module Contents

Functions

atmosphere_regions(Atmosphere_dimension, TwoD_type, ...)

Establish the number of azimuthal sectors (Evening-Morning) and zenith

angular_grids(Atmosphere_dimension, TwoD_type, ...)

Compute the grids of angles (sector / zone centres, edges, and differential

opening_angle(R_p_ref, T, mu, g[, log_sigma, log_X, ...])

Calculate the predicted terminator opening angle using the analytic equation
POSEIDON.geometry.atmosphere_regions(Atmosphere_dimension, TwoD_type, N_slice_EM, N_slice_DN)

Establish the number of azimuthal sectors (Evening-Morning) and zenith zones (Day-Night) required to discretise the background atmosphere.

Parameters:

  • Atmosphere_dimension (int) – The dimensionality of the model atmosphere (Options: 1 / 2 / 3).

  • TwoD_type (str) – For 2D models, specifies whether the model considers day-night gradients or evening-morning gradients (Options: D-N / E-M).

  • N_slice_EM (even int) – Number of azimuthal slices in the evening-morning transition region.

  • N_slice_DN (even int) – Number of zenith slices in the day-night transition region.

Returns:

Number of azimuthal sectors comprising the background atmosphere. N_zones (int):

Number of zenith zones comprising the background atmosphere.

Return type:

N_sectors (int)

POSEIDON.geometry.angular_grids(Atmosphere_dimension, TwoD_type, N_slice_EM, N_slice_DN, alpha, beta, sharp_DN_transition)

Compute the grids of angles (sector / zone centres, edges, and differential extents) for a given discretised atmosphere.

By convention, the angles are defined as:

phi: angle in terminator plane measured clockwise from North pole. theta: angle from terminator plane measured towards nightside.

Due to (assumed) North-South symmetry in all cases, we only need to consider theta > -pi/2 and/or phi < pi/2 (i.e. northern hemisphere).

Parameters:

  • Atmosphere_dimension (int) – The dimensionality of the model atmosphere (Options: 1 / 2 / 3).

  • TwoD_type (str) – For 2D models, specifies whether the model considers day-night gradients or evening-morning gradients (Options: D-N / E-M).

  • N_slice_EM (even int) – Number of azimuthal slices in the evening-morning transition region.

  • N_slice_DN (even int) – Number of zenith slices in the day-night transition region.

  • alpha (float) – Terminator opening angle (degrees).

  • beta (float) – Day-night opening angle (degrees).

  • sharp_DN_transition (bool) – For 2D / 3D models, sets day-night transition width (beta) to 0.

Returns:

Mid-sector angles (radians). theta (np.array of float):

Mid-zone angles (radians).

phi_edge (np.array of float):

Boundary angles for each sector (radians).

theta_edge (np.array of float):

Boundary angles for each zone (radians).

dphi (np.array of float):

Angular width of each sector (radians).

dtheta (np.array of float):

Angular width of each zone (radians).

Return type:

phi (np.array of float)

POSEIDON.geometry.opening_angle(R_p_ref, T, mu, g, log_sigma=-25.3, log_X=-3.3, tau_0=0.56, P_ref=0.01, gamma=0.01)

Calculate the predicted terminator opening angle using the analytic equation from Wardenier+2022 (their Eq. 10).

This analytic prescription is valid for a 1D isothermal atmosphere with constant gravity with opacity dominated by a single chemical species with constant cross section. Despite these caveats, the formula performs rather well compared to full radiative transfer models. Therefore, this offers a good first-order estimate for the angular width about the terminator plane for which transmission spectrum are sensitive.

Parameters:

  • R_p_ref (float) – Planetary radius at the reference pressure P_ref (typically the white light transit radius).

  • T (float) – Representative planet temperature (typically T_eq) (K).

  • mu (float) – Mean molecular mass of the atmosphere (kg).

  • g (float) – Gravitational field strength of planet (m/s^2).

  • log_sigma (float) – Absorption cross section of dominant opacity source (log_10 (m^2)).

  • log_X (float) – Mixing ratio of chemical species dominating the opacity.

  • tau_0 (float) – Slant optical depth for impact parameter corresponding to the opening angle (0.56 default corresponds to Lecavelier des Etangs+2008).

  • P_ref (float) – Reference pressure corresponding to R_p_ref.

  • gamma (float) – ‘Tolerance factor’ for the opening angle, such that the angle encloses a fraction gamma -> (1 - gamma) of the total slant optical depth. The default corresponds to the 1-99 % optical depth region. Note: relabelled from ‘beta’ in Wardenier+2022, since POSEIDON uses beta for the opening angle itself.

Returns:

Day-night opening angle (degrees).

Return type:

beta (float)