petitRADTRANS.temperature_profiles

Submodules

• petitRADTRANS.temperature_profiles.gradient
• petitRADTRANS.temperature_profiles.guillot
• petitRADTRANS.temperature_profiles.isothermal
• petitRADTRANS.temperature_profiles.madhusudhan
• petitRADTRANS.temperature_profiles.molliere
• petitRADTRANS.temperature_profiles.power_law
• petitRADTRANS.temperature_profiles.spline

Functions

zhang_2023_temperature_profile(→ jax.Array)	This function takes the temperature gradient at a set number of spline points and interpolates a temperature
guillot_temperature_profile(→ jax.Array)	Returns a temperature array, in units of K, of the same dimensions as the pressure P (in bar).
guillot_dayside_temperature_profile(→ jax.Array)	Returns a dayside temperature array, in units of K, using the Guillot (2010) model.
guillot_global_temperature_profile(→ jax.Array)	Returns a global average temperature array, in units of K, using the Guillot (2010) model.
guillot_global_ret_temperature_profile(→ jax.Array)	Global Guillot P-T formula for retrievals, with kappa/gravity replaced by delta.
guillot_metallic_temperature_profile(→ jax.Array)	Get a Guillot temperature profile depending on metallicity.
guillot_modif_temperature_profile(→ jax.Array)	Modified Guillot P-T formula for retrievals.
isothermal_temperature_profile(→ jax.Array)	Returns an isothermal temperature profile.
madhusudhan_seager_temperature_profile(→ jax.Array)	Calculate temperatures based on the Madhusudhan and Seager (2009) parameterization.
molliere_2020_temperature_profile(temperature_nodes, ...)	Self-luminous retrieval P-T model.
power_law_temperature_profile(→ jax.Array)	Compute a power law profile for temperature; log(T) = a*log(P) + b.
linear_spline_temperature_profile(...)	Compute a linear spline profile for temperature based on pressure points.
cubic_spline_temperature_profile(→ tuple[jax.Array, float])	Compute a cubic spline profile for temperature based on pressure points.

Package Contents

petitRADTRANS.temperature_profiles.zhang_2023_temperature_profile(pressures: jax.typing.ArrayLike, num_layer: int, layer_pt_slopes: jax.typing.ArrayLike, t_bottom: float, top_of_atmosphere_pressure: float = -3, bottom_of_atmosphere_pressure: float = 3) → jax.Array

This function takes the temperature gradient at a set number of spline points and interpolates a temperature profile as a function of pressure. Based on the method described in Zhang et al. (2023).

Args:

pressures: The pressure array in bar. num_layer: The number of layers. Default for covering 10^3 to 10^-3 bar as in Zhang 2023 is 6.

To cover 10^3 to 10^-6 bar 10 is recommended.

layer_pt_slopes: The temperature gradient (d(ln T) / d(ln P)) at the spline points. t_bottom: The temperature at the bottom of the atmosphere. top_of_atmosphere_pressure: Minimum atmospheric pressure in log bar. If the pressure array extends

beyond this value, the temperature structure at lower pressures will be isothermal.

bottom_of_atmosphere_pressure: Maximum atmospheric pressure in log bar.

Returns:

The temperature profile in K.

petitRADTRANS.temperature_profiles.guillot_temperature_profile(pressures: jax.typing.ArrayLike, infrared_mean_opacity: float, gamma: float, gravities: jax.typing.ArrayLike, intrinsic_temperature: float, equilibrium_temperature: float, redistribution_coefficient: float = 0.25) → jax.Array

Returns a temperature array, in units of K, of the same dimensions as the pressure P (in bar).

For this the temperature model of Guillot (2010) is used (his Equation 29). Source: https://doi.org/10.1051/0004-6361/200913396

Args:

pressures: Array of pressures in bar. infrared_mean_opacity: The infrared mean opacity in units of cm^2/g. gamma: The ratio between the visual and infrared mean opacities. gravities: The planetary gravity at the given pressures in units of cm/s^2. intrinsic_temperature: The planetary intrinsic temperature in K. equilibrium_temperature: The planetary equilibrium temperature in K. redistribution_coefficient: The redistribution coefficient of the irradiance. A value of 1 corresponds to the

substellar point, 1/2 for the day-side average and 1/4 for the global average.

Returns:

The temperature profile in K.

petitRADTRANS.temperature_profiles.guillot_dayside_temperature_profile(pressures: jax.typing.ArrayLike, infrared_mean_opacity: float, gamma: float, gravities: jax.typing.ArrayLike, intrinsic_temperature: float, equilibrium_temperature: float) → jax.Array

Returns a dayside temperature array, in units of K, using the Guillot (2010) model.

This is a wrapper for guillot_temperature_profile with redistribution_coefficient set to 0.5, which corresponds to an average over the day side of the planet.

Args:

pressures: Array of pressures in bar. infrared_mean_opacity: The infrared mean opacity in units of cm^2/g. gamma: The ratio between the visual and infrared mean opacities. gravities: The planetary gravity at the given pressures in units of cm/s^2. intrinsic_temperature: The planetary intrinsic temperature in K. equilibrium_temperature: The planetary equilibrium temperature in K.

Returns:

The temperature profile in K.

petitRADTRANS.temperature_profiles.guillot_global_temperature_profile(pressures: jax.typing.ArrayLike, infrared_mean_opacity: float, gamma: float, gravities: jax.typing.ArrayLike, intrinsic_temperature: float, equilibrium_temperature: float) → jax.Array

Returns a global average temperature array, in units of K, using the Guillot (2010) model.

This is a wrapper for guillot_temperature_profile with redistribution_coefficient set to 0.25, which corresponds to an average over the whole planetary surface.

Args:

pressures: Array of pressures in bar. infrared_mean_opacity: The infrared mean opacity in units of cm^2/g. gamma: The ratio between the visual and infrared mean opacities. gravities: The planetary gravity at the given pressures in units of cm/s^2. intrinsic_temperature: The planetary intrinsic temperature in K. equilibrium_temperature: The planetary equilibrium temperature in K.

Returns:

The temperature profile in K.

petitRADTRANS.temperature_profiles.guillot_global_ret_temperature_profile(pressures: jax.typing.ArrayLike, delta: float, gamma: float, intrinsic_temperature: float, equilibrium_temperature: float) → jax.Array

Global Guillot P-T formula for retrievals, with kappa/gravity replaced by delta.

This function is a variation of the Guillot (2010) temperature profile, where the ratio of the mean infrared opacity to gravity (kappa/g) is replaced by a single parameter, delta. This is useful for retrieval applications where gravity is fixed and opacity is a parameter.

Args:

pressures: Array of pressures in bar. delta: Proportionality factor for optical depth, equal to kappa_ir / g, where kappa_ir is the

infrared mean opacity (cm^2/g) and g is the gravity (cm/s^2).

gamma: The ratio between the visual and infrared mean opacities. intrinsic_temperature: The planetary intrinsic temperature in K. equilibrium_temperature: The planetary equilibrium temperature in K.

Returns:

The temperature profile in K.

petitRADTRANS.temperature_profiles.guillot_metallic_temperature_profile(pressures: jax.typing.ArrayLike, gamma: float, reference_gravity: jax.typing.ArrayLike, intrinsic_temperature: float, equilibrium_temperature: float, infrared_mean_opacity_solar_metallicity: float, metallicity: float | None = None) → jax.Array

Get a Guillot temperature profile depending on metallicity.

This function calculates a global average Guillot temperature profile, where the infrared mean opacity is scaled with metallicity.

Args:

pressures: Array of pressures in bar. gamma: Ratio between visual and infrared opacity. reference_gravity: Surface gravity in cm/s^2. intrinsic_temperature: Intrinsic temperature in K. equilibrium_temperature: Equilibrium temperature in K. infrared_mean_opacity_solar_metallicity: Infrared mean opacity for a solar metallicity (Z=1)

atmosphere, in cm^2/g.

metallicity: Ratio of heavy elements abundance over H abundance with respect to the solar ratio.

If None, solar metallicity is assumed.

Returns:

The temperature profile in K.

petitRADTRANS.temperature_profiles.guillot_modif_temperature_profile(pressures: jax.typing.ArrayLike, delta: float, gamma: float, intrinsic_temperature: float, equilibrium_temperature: float, ptrans: float, alpha: float) → jax.Array

Modified Guillot P-T formula for retrievals.

This function uses the guillot_global_ret_temperature_profile and applies a modifying factor to the temperature profile. The modification is controlled by alpha and ptrans, which can shape the profile around a transition pressure.

Args:

pressures: Array of pressures in bar. delta: Proportionality factor for optical depth, equal to kappa_ir / g. gamma: The ratio between the visual and infrared mean opacities. intrinsic_temperature: The planetary intrinsic temperature in K. equilibrium_temperature: The planetary equilibrium temperature in K. ptrans: Transition pressure in bar, where the modification is centered. alpha: A parameter controlling the strength and shape of the temperature modification.

Returns:

The modified temperature profile in K.

petitRADTRANS.temperature_profiles.isothermal_temperature_profile(pressures: jax.typing.ArrayLike, temperature: float) → jax.Array

Returns an isothermal temperature profile.

Args:

pressures: An array of pressures. The shape is preserved for the output temperatures. temperature: The constant temperature value for the profile.

Returns:

An array of temperatures with the same shape as pressures, all set to the input temperature.

petitRADTRANS.temperature_profiles.madhusudhan_seager_temperature_profile(pressures: jax.typing.ArrayLike, log_pressure_points: tuple[float], temperature_reference: float, alpha_points: tuple[float], beta_points: tuple[float]) → jax.Array

Calculate temperatures based on the Madhusudhan and Seager (2009) parameterization.

This function computes temperatures using the Madhu and Seager (2009) parameterization for a given set of pressure values, pressure breakpoints, temperature breakpoints, alpha values, and beta values.

Based off of the POSEIDON implementation: MartianColonist/POSEIDON

Parameters:

pressures(numpy.ndarray)

An array of pressure values (in bar) at which to calculate temperatures.

log_pressure_points(list)

A list of log10 pressure breakpoints defining different temperature regimes. The zeroth element is the minimum pressure, should be log10(press[0]). The first element is the 1-2 boundary The second element is the level of the inversion The third element is the 2-3 boundary. The fourth element is the pressure at which the temperature is set (P_set).

temperature_reference(float)

A temperature at log_pressure_points[4] used to constrain the temperature profile.

alpha_points(list)

A list of alpha values used in the parameterization for different regimes. Must have length 2.

beta_points(list)

A list of beta values used in the parameterization for different regimes. By default, b[0] == b[1] == 0.5, unclear how well this will work if these aren’t used! Must have length 2.

Returns:

temperatures(numpy.ndarray)

An array of calculated temperatures (in K) corresponding to the input pressure values.

Reference: - Madhusudhan, N., & Seager, S. (2009). A Temperature and Abundance Retrieval Method for Exoplanet Atmospheres.

The Astrophysical Journal, 707(1), 24-39. https://doi.org/10.1088/0004-637X/707/1/24

petitRADTRANS.temperature_profiles.molliere_2020_temperature_profile(temperature_nodes, delta, alpha, t_internal, pressures, metallicity, co_ratio, conv)

Self-luminous retrieval P-T model. Args:

temperature_nodesjnp.array([t1, t2, t3])

temperature points to be added on top radiative Eddington structure (above tau = 0.1). Use spline interpolation, t1 < t2 < t3 < tconnect as prior.

deltafloat

proportionality factor in tau = delta * pressures_cgs**alpha

alphafloat

power law index in tau = delta * pressures_cgs**alpha For the tau model: use proximity to kappa_rosseland photosphere as prior.

t_internalfloat

internal temperature of the Eddington model

pressuresjnp.ndarray

input pressure profile in bar

convbool

enforce convective adiabat yes/no

co_ratiofloat

C/O for the nabla_ad interpolation

metallicityfloat

metallicity for the nabla_ad interpolation

Returns:

Tretjnp.ndarray

The temperature as a function of atmospheric pressure.

petitRADTRANS.temperature_profiles.power_law_temperature_profile(pressures: jax.typing.ArrayLike, alpha: float, T0: float) → jax.Array

Compute a power law profile for temperature; log(T) = a*log(P) + b.

This function computes a cubic spline profile for temperature using pressure and temperature data points, along with a curvature prior.

Args:

pressures (array-like): An array or list of pressure data points. alpha (float): power law exponent (how steep is the profile) T0 (float): multiplicative factor (offsets the profile)

Returns:

temperatures (array): temperature values for each pressure value

petitRADTRANS.temperature_profiles.linear_spline_temperature_profile(pressures: jax.typing.ArrayLike, temperature_points: jax.typing.ArrayLike, gamma: float, nnodes: int = 0) → tuple[jax.typing.ArrayLike, float]

Compute a linear spline profile for temperature based on pressure points.

This function computes a linear spline profile for temperature using pressure and temperature data points, along with a curvature prior.

Args:

pressures: An array of pressure data points. temperature_points: An array of temperature data points. gamma: A parameter controlling the curvature of the spline. nnodes: Number of nodes to use in the spline interpolation.

Defaults to 0, which means automatic determination of nodes.

Returns:

A tuple containing:

• interpolated_temperatures: Interpolated temperature values based on the linear spline.

• prior: Curvature prior value calculated for the spline.

petitRADTRANS.temperature_profiles.cubic_spline_temperature_profile(pressures: jax.typing.ArrayLike, temperature_points: jax.typing.ArrayLike, gamma: float, nnodes: int = 0) → tuple[jax.Array, float]

Compute a cubic spline profile for temperature based on pressure points.

This function computes a cubic spline profile for temperature using pressure and temperature data points, along with a curvature prior.

Args:

pressures: An array of pressure data points. temperature_points: An array of temperature data points. gamma: A parameter controlling the curvature of the spline. nnodes: Number of nodes to use in the spline interpolation.

Defaults to 0, which means automatic determination of nodes.

Returns:

A tuple containing:

• interpolated_temperatures: Interpolated temperature values based on the cubic spline.

• prior: Curvature prior value calculated for the spline.