petitRADTRANS.physics

Stores useful physical functions.

Functions

compute_dist(t_irr, dist, t_star, r_star, mode, mode_what)
compute_effective_temperature(→ float)	Calculates the effective temperature by integrating the model and using the stefan boltzmann law.
power_law_temperature_profile(→ numpy.typing.NDArray)	Compute a power law profile for temperature; log(T) = a*log(P) + b.
cubic_spline_profile(→ tuple[numpy.typing.NDArray, float])	Compute a cubic spline profile for temperature based on pressure points.
doppler_shift(→ numpy.typing.NDArray | float)	Calculate the Doppler-shifted wavelength for electromagnetic waves.
flux_cm2flux_hz(→ numpy.typing.NDArray | float)	Convert a flux from [flux units]/cm to [flux units]/Hz at a given wavelength.
flux_hz2flux_cm(→ numpy.typing.NDArray | float)	Convert a flux from [flux units]/Hz to [flux units]/cm at a given frequency.
flux2irradiance(→ numpy.typing.NDArray | float)	Calculate the spectral irradiance of a spherical source on a target from its flux (spectral radiosity).
frequency2wavelength(→ numpy.typing.NDArray | float)	Convert frequencies into wavelength in centimeter.
hz2um(→ numpy.typing.NDArray | float)	Convert frequencies into wavelengths in micrometer.
linear_spline_profile(→ tuple[numpy.typing.NDArray, float])	Compute a linear spline profile for temperature based on pressure points.
make_press_temp(rad_trans_params)	Function to make temp
make_press_temp_iso(rad_trans_params)	Function to make temp
madhu_seager_2009(pressures, log_pressure_points, ...)	Calculate temperatures based on the Madhusudhan and Seager (2009) parameterization.
planck_function_cm(→ numpy.typing.NDArray | float)	Returns the Planck function \(B_{\lambda}(T)\) in units of
planck_function_hz(→ numpy.typing.NDArray | float)	Returns the Planck function \(B_{\nu}(T)\) in units of
planck_function_hz_temperature_derivative(...)	Returns the derivative of the Planck function with respect to the temperature in units of
rebin_spectrum(→ numpy.typing.NDArray)	Re-bin the spectrum using the Fortran rebin_spectrum function, and catch errors occurring there.
rebin_spectrum_bin(→ numpy.typing.NDArray)	Re-bin the spectrum using the Fortran rebin_spectrum_bin function, and catch errors occurring there.
temperature_profile_function_guillot(...)	Returns a temperature array, in units of K,
temperature_profile_function_guillot_dayside(...)	Returns a temperature array, in units of K,
temperature_profile_function_guillot_global(...)	Returns a temperature array, in units of K,
temperature_profile_function_guillot_global_ret(...)	Global Guillot P-T formula with kappa/gravity replaced by delta.
temperature_profile_function_guillot_metallic(...)	Get a Guillot temperature profile depending on metallicity.
temperature_profile_function_guillot_modif(...)	Modified Guillot P-T formula
temperature_profile_function_isothermal(...)
temperature_profile_function_ret_model(rad_trans_params)	Self-luminous retrieval P-T model.
temperature_curvature_prior(press, temps, gamma)	Compute a curvature prior for a temperature-pressure profile.
dtdp_temperature_profile(press, num_layer, ...[, ...])	This function takes the temperature gradient at a set number of spline points and interpolates a temperature
um2hz(→ numpy.typing.NDArray | float)	Convert wavelengths in micrometer into frequencies.
wavelength2frequency(→ numpy.typing.NDArray | float)	Convert wavelengths in centimeter to frequencies.

Module Contents

petitRADTRANS.physics.compute_dist(t_irr, dist, t_star, r_star, mode, mode_what)

petitRADTRANS.physics.compute_effective_temperature(wavelengths: numpy.typing.NDArray, flux: numpy.typing.NDArray, orbit_semi_major_axis: float = 1.0, planet_radius: float = 1.0, use_si_units: bool = False) → float

Calculates the effective temperature by integrating the model and using the stefan boltzmann law.

Args:

wavelengthsnumpy.ndarray

Wavelength grid

fluxnumpy.ndarray

Flux density grid

orbit_semi_major_axisOptional(float)

Distance to the object. Must have same units as planet_radius

planet_radiusOptional(float)

Object radius. Must have same units as orbit_semi_major_axis

use_si_unitsOptional(bool)

If the flux is in W/m2/micron, this should be true

petitRADTRANS.physics.power_law_temperature_profile(press: numpy.typing.NDArray, alpha: float, T0: float) → numpy.typing.NDArray

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:

press (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.physics.cubic_spline_profile(press: numpy.typing.NDArray, temperature_points: numpy.typing.NDArray, gamma: float, nnodes: int = 0) → tuple[numpy.typing.NDArray, 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:

press (array-like): An array or list of pressure data points. temperature_points (array-like): An array or list of temperature data points. gamma (float): A parameter controlling the curvature of the spline. nnodes (int, optional): Number of nodes to use in the spline interpolation.

Defaults to 0, which means automatic determination of nodes.

Returns:

tuple: A tuple containing two elements:

• interpolated_temps (array-like): Interpolated temperature values based on the cubic spline.

• prior (array-like): Curvature prior values calculated for the spline.

petitRADTRANS.physics.doppler_shift(wavelength_0: numpy.typing.NDArray | float, velocity: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Calculate the Doppler-shifted wavelength for electromagnetic waves.

A negative velocity means that the source is going toward the observer. A positive velocity means the source is going away from the observer.

Args:

wavelength_0: (cm) wavelength of the wave in the referential of the source velocity: (cm.s-1) velocity of the source relative to the observer

Returns:

900. the wavelength of the source as measured by the observer

petitRADTRANS.physics.flux_cm2flux_hz(flux_cm: numpy.typing.NDArray | float, wavelength: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Convert a flux from [flux units]/cm to [flux units]/Hz at a given wavelength. Flux units can be, e.g., erg.s-1.cm-2.

Steps:

[cm] = c[cm.s-1] / [Hz] => d[cm]/d[Hz] = d(c / [Hz])/d[Hz] => d[cm]/d[Hz] = c / [Hz]**2 integral of flux must be conserved: flux_cm * d[cm] = flux_hz * d[Hz] flux_hz = flux_cm * d[cm]/d[Hz] => flux_hz = flux_cm * wavelength**2 / c

Args:

flux_cm: ([flux units]/cm) wavelength: (cm)

Returns:

([flux units]/Hz) the radiosity in converted units

petitRADTRANS.physics.flux_hz2flux_cm(flux_hz: numpy.typing.NDArray | float, frequency: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Convert a flux from [flux units]/Hz to [flux units]/cm at a given frequency. Flux units can be, e.g., erg.s-1.cm-2.

Steps:

[cm] = c[cm.s-1] / [Hz] => d[cm]/d[Hz] = d(c / [Hz])/d[Hz] => d[cm]/d[Hz] = c / [Hz]**2 => d[Hz]/d[cm] = [Hz]**2 / c integral of flux must be conserved: flux_cm * d[cm] = flux_hz * d[Hz] flux_cm = flux_hz * d[Hz]/d[cm] => flux_cm = flux_hz * frequency**2 / c

Args:

flux_hz: (erg.s-1.cm-2.sr-1/Hz) frequency: (Hz)

Returns:

(erg.s-1.cm-2.sr-1/cm) the radiosity in converted units

petitRADTRANS.physics.flux2irradiance(flux: numpy.typing.NDArray | float, source_radius: float, target_distance: float) → numpy.typing.NDArray | float

Calculate the spectral irradiance of a spherical source on a target from its flux (spectral radiosity).

Args:

flux: (M.L-1.T-3) flux of the source source_radius: (L) radius of the spherical source target_distance: (L) distance from the source to the target

Returns:

The irradiance of the source on the target (M.L-1.T-3).

petitRADTRANS.physics.frequency2wavelength(frequency: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Convert frequencies into wavelength in centimeter.

Args:

frequency: frequency: (Hz) the frequency to convert

Returns:

900. the corresponding wavelengths

petitRADTRANS.physics.hz2um(frequency: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Convert frequencies into wavelengths in micrometer.

Args:

frequency: (Hz) the frequency to convert

Returns:

(um) the corresponding wavelengths

petitRADTRANS.physics.linear_spline_profile(press: numpy.typing.NDArray, temperature_points: numpy.typing.NDArray, gamma: float, nnodes: int = 0) → tuple[numpy.typing.NDArray, 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:

press (array-like): An array or list of pressure data points. temperature_points (array-like): An array or list of temperature data points. gamma (float): A parameter controlling the curvature of the spline. nnodes (int, optional): Number of nodes to use in the spline interpolation.

Defaults to 0, which means automatic determination of nodes.

Returns:

tuple: A tuple containing two elements:

• interpolated_temps (array-like): Interpolated temperature values based on the linear spline.

• prior (array-like): Curvature prior values calculated for the spline.

petitRADTRANS.physics.make_press_temp(rad_trans_params)

Function to make temp

petitRADTRANS.physics.make_press_temp_iso(rad_trans_params)

Function to make temp

petitRADTRANS.physics.madhu_seager_2009(pressures, log_pressure_points, T_set, alpha_points, beta_points)

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).

T_set(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.physics.planck_function_cm(temperature: float, wavelength: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Returns the Planck function \(B_{\lambda}(T)\) in units of \(\rm erg/s/cm^2/cm/steradian\).

Args:

temperature (float):

Temperature in K.

wavelength:

Array containing the wavelength in cm.

petitRADTRANS.physics.planck_function_hz(temperature: float, frequency: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Returns the Planck function \(B_{\nu}(T)\) in units of \(\rm erg/s/cm^2/Hz/steradian\).

Args:

temperature (float):

Temperature in K.

frequency:

Array containing the frequency in Hz.

petitRADTRANS.physics.planck_function_hz_temperature_derivative(temperature: float, frequency: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Returns the derivative of the Planck function with respect to the temperature in units of \(\rm erg/s/cm^2/Hz/steradian\). # TODO unused?

Args:

temperature:

Temperature in K.

frequency:

Array containing the frequency in Hz.

Returns:

petitRADTRANS.physics.rebin_spectrum(input_wavelengths: numpy.typing.NDArray, input_spectrum: numpy.typing.NDArray, rebinned_wavelengths: numpy.typing.NDArray) → numpy.typing.NDArray

Re-bin the spectrum using the Fortran rebin_spectrum function, and catch errors occurring there. The fortran rebin function raises non-blocking errors. In that case, the function outputs an array of -1.

Args:

input_wavelengths: wavelengths of the input spectrum input_spectrum: spectrum to re-bin rebinned_wavelengths: wavelengths to re-bin the spectrum to. Must be contained within input_wavelengths

Returns:

The re-binned spectrum on the re-binned wavelengths

petitRADTRANS.physics.rebin_spectrum_bin(input_wavelengths: numpy.typing.NDArray, input_spectrum: numpy.typing.NDArray, rebinned_wavelengths: numpy.typing.NDArray, bin_widths: numpy.typing.NDArray) → numpy.typing.NDArray

Re-bin the spectrum using the Fortran rebin_spectrum_bin function, and catch errors occurring there. The fortran rebin function raises non-blocking errors. In that case, the function outputs an array of -1.

Args:

input_wavelengths: wavelengths of the input spectrum input_spectrum: spectrum to re-bin rebinned_wavelengths: wavelengths to re-bin the spectrum to. Must be contained within input_wavelengths bin_widths: bin widths of the wavelengths to re-bin the spectrum to.

Returns:

The re-binned spectrum on the re-binned wavelengths

petitRADTRANS.physics.temperature_profile_function_guillot(pressures: numpy.typing.NDArray, infrared_mean_opacity: float, gamma: float, gravities: numpy.typing.NDArray, intrinsic_temperature: float, equilibrium_temperature: float, redistribution_coefficient: float = 0.25) → numpy.typing.NDArray

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:

numpy array of floats, containing the input pressure in bars.

infrared_mean_opacity:

The infrared mean opacity in units of \(\rm cm^2/s\).

gamma:

The ratio between the visual and infrared mean opacities.

gravities:

The planetary gravity at the given pressures in units of \(\rm cm/s^2\).

intrinsic_temperature:

The planetary intrinsic temperature (in units of K).

equilibrium_temperature:

The planetary equilibrium temperature (in units of 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.

petitRADTRANS.physics.temperature_profile_function_guillot_dayside(pressures: numpy.typing.NDArray, infrared_mean_opacity: float, gamma: float, gravities: numpy.typing.NDArray, intrinsic_temperature: float, equilibrium_temperature: float) → numpy.typing.NDArray

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), in the case of averaging the flux over the day side of the planet.

Args:

pressures:

numpy array of floats, containing the input pressure in bars.

infrared_mean_opacity (float):

The infrared opacity in units of \(\rm cm^2/s\).

gamma (float):

The ratio between the visual and infrared opacity.

gravities (float):

The planetary surface gravity in units of \(\rm cm/s^2\).

intrinsic_temperature (float):

The planetary internal temperature (in units of K).

equilibrium_temperature (float):

The planetary equilibrium temperature (in units of K).

petitRADTRANS.physics.temperature_profile_function_guillot_global(pressures: numpy.typing.NDArray, infrared_mean_opacity: float, gamma: float, gravities: numpy.typing.NDArray, intrinsic_temperature: float, equilibrium_temperature: float) → numpy.typing.NDArray

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), in the case of averaging the flux over the whole planetary surface.

Args:

pressures:

numpy array of floats, containing the input pressure in bars.

infrared_mean_opacity (float):

The infrared opacity in units of \(\rm cm^2/s\).

gamma (float):

The ratio between the visual and infrared opacity.

gravities (float):

The planetary surface gravity in units of \(\rm cm/s^2\).

intrinsic_temperature (float):

The planetary internal temperature (in units of K).

equilibrium_temperature (float):

The planetary equilibrium temperature (in units of K).

petitRADTRANS.physics.temperature_profile_function_guillot_global_ret(pressures: numpy.typing.NDArray, delta: float, gamma: float, intrinsic_temperature: float, equilibrium_temperature: float) → numpy.typing.NDArray

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

petitRADTRANS.physics.temperature_profile_function_guillot_metallic(pressures: numpy.typing.NDArray, gamma: float, reference_gravity: numpy.typing.NDArray, intrinsic_temperature: float, equilibrium_temperature: float, infrared_mean_opacity_solar_metallicity: float, metallicity: float | None = None) → numpy.typing.NDArray

Get a Guillot temperature profile depending on metallicity.

Args:

pressures: (bar) pressures of the profile gamma: ratio between visual and infrared opacity reference_gravity: (cm.s-2) surface gravity intrinsic_temperature: (K) intrinsic temperature equilibrium_temperature: (K) equilibrium temperature infrared_mean_opacity_solar_metallicity:

(cm2.s-1) infrared mean opacity for a solar metallicity (Z = 1) atmosphere

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

Returns:

temperatures: (K) the temperature at each pressures of the atmosphere

petitRADTRANS.physics.temperature_profile_function_guillot_modif(pressures: numpy.typing.NDArray, delta: float, gamma: float, intrinsic_temperature: float, equilibrium_temperature: float, ptrans: float, alpha: float) → numpy.typing.NDArray

Modified Guillot P-T formula

petitRADTRANS.physics.temperature_profile_function_isothermal(pressures: numpy.typing.NDArray, temperature: float) → numpy.typing.NDArray

petitRADTRANS.physics.temperature_profile_function_ret_model(rad_trans_params)

Self-luminous retrieval P-T model.

Args:

t3np.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 * press_cgs**alpha

alphafloat

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

tintfloat

internal temperature of the Eddington model

pressnp.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:

Tretnp.ndarray

The temperature as a function of atmospheric pressure.

petitRADTRANS.physics.temperature_curvature_prior(press, temps, gamma)

Compute a curvature prior for a temperature-pressure profile.

This function calculates a curvature prior for a temperature-pressure profile, penalizing deviations from a smooth, low-curvature profile, based on Line 2015

Args:

press (array-like): An array or list of pressure data points. temps (array-like): An array or list of temperature data points. gamma (float): The curvature penalization factor.

Returns:

float: The curvature prior value.

petitRADTRANS.physics.dtdp_temperature_profile(press, num_layer, layer_pt_slopes, t_bottom, top_of_atmosphere_pressure=-3, bottom_of_atmosphere_pressure=3)

This function takes the temperature gradient at a set number of spline points and interpolates a temperature profile as a function of pressure.

Args:

pressarray_like

The pressure array.

num_layerint

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_slopesarray_like

The temperature gradient at the spline points.

t_bottomfloat

The temperature at the bottom of the atmosphere.

top_of_atmosphere_pressurefloat

Minimum atmospheric pressure in log bar. If the pressure array extends beyond this value, the temperature structure at lower pressures than this value will be isothermal.

bottom_of_atmosphere_pressurefloat

Maximum atmospheric pressure in log bar.

Returns:

temperaturesarray_like

The temperature profile.

petitRADTRANS.physics.um2hz(wavelength: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Convert wavelengths in micrometer into frequencies.

Args:

wavelength: (um) the wavelengths to convert

Returns:

(Hz) the corresponding frequencies

petitRADTRANS.physics.wavelength2frequency(wavelength: numpy.typing.NDArray | float) → numpy.typing.NDArray | float

Convert wavelengths in centimeter to frequencies.

Args:

wavelength: (cm) the wavelengths to convert

Returns:

(Hz) the converted frequencies