Forward Models

BeAR currently includes the following forward models:

The latter two models are usually used to check if the observational data is more likely explained by more simpler models, such as a flat line.

Each model requires its own config file forward_model.config that are discussed below.

Model postprocessing

After the retrieval calculations are finished, the BeAR will perform a postprocessing on the resulting posterior sample. Depending on the chosen forward model, different postprocessing steps can be used, including saving all posterior spectra or temperature profiles. Details can be found in the section on output files.

These postprocessing steps can also be configured in the optional post_process.config file. If this file is not present, BeAR will use default settings for the postprocessing. Depending on the forward model, available options are currently:

  • Delete unused MultiNest files - This will option will delete all MultiNest files that are not used in the post processing. Available options: Yes or No.

  • Save spectra - Compute the spectra for each model in the posterior sample. Spectral will be saved for each observational/instrument individually. Additionally, a high-resolution spectrum of the best-fit model will be computed and saved. Available options: Yes or No.

  • Save temperature structures - Compute and save the temperature profile for each model in the posterior sample. Available options: Yes or No.

  • Save effective temperatures - Compute and save the effective temperature for each model in posterior sample. Available options: Yes or No.

  • Save contribution functions - Compute and save the contribution functions for each observational/instrument for the best-fit model. Available options: Yes or No.

  • Save chemical species - Save the mixing ratio profiles for selected chemical species for all posterior samples. The options for this parameter are the forumulas of the chemical species that should be saved, separated by white spaces. For example, H2O CO2 will save the mixing ratios of water and carbon dioxide. Species that BeAR does not know will be ignored.

Flat line

This model simply fits a flat line through the observational data. Usually, this model is used to test if the use of a more complex model is warranted to explain the observation. The test is normally done by comparing their Bayesian evidences.

In the main retrieval config file retrieval.config it is selected by choosing:

#Forward model
flat_line

Model config file

The flat line model does not need a forward_model.config file since it has no configurable parameters. In the prior distribution file this model requires a single free parameter that determines the flat line.

This parameter needs to have the same units as the observational data. For example, in case of a transmission spectrum, this parameter refers to the transit depth in ppm, while for an emission spectrum, it needs to have units of \(\mathrm{W} \mathrm{m^{-2}} \mathrm{\mu m^{-1}}\).

Model postprocessing

The optional postprocessing file post_process.config has the following structure and options:

#Delete unused MultiNest files
Yes

#Compute spectra
Yes

The default options that are used when this file is not present are:

  • Delete unused MultiNest files : No

  • Compute spectra : No

Transmission spectrum

This forward model computes the wavelength-dependent transit depth \(D(\lambda)\) of an exoplanet atmosphere, given by

\[D(\lambda) = \left(\frac{R_p(\lambda)}{R_*}\right)^2 \ ,\]

where \(R_p(\lambda)\) is the wavelength-dependent planetary radius and \(R_*\) the radius of the host star. In BeAR, \(D(\lambda)\) has units of ppm.

In the retrieval config file retrieval.config it is selected by choosing:

#Forward model
transmission

The transmission spectrum forward model has three general free parameters that have to be added to the priors configuration file in the following order:

  • logarithm of surface gravity \(\log g\) in cgs units

  • planet radius

  • stellar radius

Model config file

The forward_model.config file for the transmission spectrum model has the following structure:

#Number of levels
150

#Bottom of atmosphere pressure (bar)
10

#Top of atmosphere pressure (bar)
1e-6

#Fit for mean molecular weight (mmw) or scale height (sh)
no

#Temperature profile
const

#Cloud model
none

#Optional modules
none

#Retrieved chemical species
iso H2O TiO VO K
bg  H2He

#Opacity species&folders
CIA-H2-H2   CIA/H2-H2
CIA-H2-He   CIA/H2-He
H2          Rayleigh
He          Rayleigh
H2O         Molecules/1H2-16O__POKAZATEL_e2b
TiO         Molecules/48Ti-16O__Toto_e2b
VO          Molecules/51V-16O__VOMYT_e2b

The first three entries refer to the vertical discretisation of the atmosphere. This includes the number of atmospheric layers as well as the bottom and top-of-atmosphere pressures in units of bars.

With the next entry, the retrieval of the mean molecular or the scale height can be chosen. Usually, BeAR will determine the mean molecular based on the chemical abundances of the species included in the retrieval. Sometimes, however, the background species in an atmosphere might not be known. For such a case, BeAR can use the mean molecular weight as a free parameter.

Furthermore, for transmission spectra, the surface gravity, the mean molecular weight, and the temperature might become degenerate in a retrieval. This is often the case when no constraints on the surface gravity can be provided and the dominating background species is not known. In such a scenario, BeAR can use the (constant) atmospheric scale height in units of km as a free parameter.

For the standard case, the keyword no needs to be used here. If BeAR should use the mean molecular weight as a free parameter mmw is used, while sh is used when the scale should be used as a free parameter instead. If either the mean molecular weight or the scale height is chosen as a free parameter, a corresponding prior needs to be added as a fourth model parameter in the prior configuration file.

With the next two entries, the parametrisation for the temperature profile and the cloud models are set. After that, optional modules can be added to the forward model.

Finally, the different chemistry models, chemical species, and the opacity sources are selected. It is important to note that chemical species that are used as part of the chemistry models, should normally also have an associated opacity source. Otherwise, the impact of that species on the resulting spectrum might be negligible and, therefore, its abundance will be likely be unconstrained.

On the other hand, it is theoretically also possible to add opacity species without including this species in any of the chemistry models. In this case, the abundance of this species will be zero and, thus, won’t show up in the spectrum.

Model postprocessing

The optional postprocessing file post_process.config has the following structure and options:

#Delete unused MultiNest files
Yes

#Compute spectra
Yes

#Save temperature structures
No

#Save chemical species
none

The default options that are used when this file is not present are:

  • Delete unused MultiNest files : No

  • Compute spectra : Yes

  • Save temperature structures : No

  • Save chemical species : None

Secondary eclipse spectrum

This forward model computes the wavelength-dependent secondary eclipse (or occultation) depth \(D(\lambda)\) of an exoplanet atmosphere, given by

\[D(\lambda) = \frac{F_p(\lambda)}{F_*(\lambda)} \left(\frac{R_p}{R_*}\right)^2 \ ,\]

where \(F_p(\lambda)\) is the outgoing flux at top of the planet’s atmosphere, \(F_*(\lambda)\) is the stellar photospheric flux, \(R_p\) is the planetary radius and \(R_*\) the radius of the host star. In BeAR, \(D(\lambda)\) has units of ppm.

In the retrieval config file retrieval.config it is selected by choosing:

#Forward model
secondary_eclipse

The secondary eclipse spectrum forward model has two general free parameters that have to be added to the priors configuration file in the following order:

  • logarithm of surface gravity \(\log g\) in cgs units

  • ratio of the planet’s and stellar radius \(\mathrm{R_p/R_*}\)

Model config file

The forward_model.config file for the secondary eclipse spectrum model has the following structure:

#Number of levels
70

#Bottom of atmosphere pressure (bar)
100

#Top of atmosphere pressure (bar)
1e-3

#Temperature profile
poly 6 1

#stellar spectrum
file SecondaryEclipseExample/WASP-43.dat

#cloud layer
none

#Radiative transfer (scm/disort)
scm

#Retrieved chemical species
eq fastchem_parameters.dat

#Opacity species&folders
CIA-H2-H2   CIA/H2-H2
CIA-H2-He   CIA/H2-He
Na          Alkali_Allard/Na
K           Alkali_Allard/K
H2O         Molecules/H2O_pokazatel
CO          Molecules/12C-16O__Li2015_e2b
TiO         Molecules/48Ti-16O__Toto_e2b
VO          Molecules/51V-16O__VOMYT_e2b
SH          Molecules/32S-1H__GYT_e2b
H2S         Molecules/1H2-32S__AYT2_e2b
FeH         Molecules/56Fe-1H__Yueqi_e2b
CH4         Molecules/12C-1H4__YT34to10_e2b
CO2         Molecules/12C-16O2__CDSD_4000_e2b
HCN         Molecules/1H-12C-14N__Harris_e2b
MgH         Molecules/26Mg-1H__Yadin_e2b
TiH         Molecules/48Ti-1H__MoLLIST_e2b
CrH         Molecules/52Cr-1H__Yueqi_e2b
CaH         Molecules/40Ca-1H__MoLLIST_e2b

The first three entries refer to the vertical discretisation of the atmosphere. This includes the number of atmospheric layers as well as the bottom and top-of-atmosphere pressures in units of bars.

With the next two entries, the parametrisation for the temperature profile, the stellar spectrum, and the cloud models are set.

After that, the radiative transfer scheme is chosen. There are currently two different options:

  • scm - the short characteristic method, available for CPU and GPU

  • disort - the discrete-ordinate solver DISORT, only available for CPU

Finally, the different chemistry models, chemical species, and the opacity sources are selected. It is important to note that chemical species that are used as part of the chemistry models, should normally also have an associated opacity source. Otherwise, the impact of that species on the resulting spectrum might be negligible and, therefore, its abundance will be likely be unconstrained.

On the other hand, it is theoretically also possible to add opacity species without including this species in any of the chemistry models. In this case, the abundance of this species will be zero and, thus, won’t show up in the spectrum.

Model postprocessing

The optional postprocessing file post_process.config has the following structure and options:

#Delete unused MultiNest files
Yes

#Save spectra
Yes

#Save temperature structures
Yes

#Save contribution functions
No

#Save chemical species
H2O CO CO2 CH4 NH3

The default options that are used when this file is not present are:

  • Delete unused MultiNest files : No

  • Compute spectra : Yes

  • Save temperature structures : Yes

  • Save contribution functions : No

  • Save chemical species : None

Secondary eclipse spectrum with planetary blackbody

This forward model computes the wavelength-dependent secondary eclipse (or occultation) depth \(D(\lambda)\) of an exoplanet atmosphere, given by

\[D(\lambda) = \frac{F_p(\lambda)}{F_*(\lambda)} \left(\frac{R_p}{R_*}\right)^2 \ ,\]

where \(F_p(\lambda)\) is the outgoing flux at top of the planet’s atmosphere, \(F_*(\lambda)\) is the stellar photospheric flux, \(R_p\) is the planetary radius and \(R_*\) the radius of the host star. In BeAR, \(D(\lambda)\) has units of ppm.

This model is a special case of the secondary eclipse spectrum model, where the planet’s flux is assumed to be blackbody radiation. This is often used to test if the observational data warrants a more complex model or when only a few, usually photometric, data points are available.

In the retrieval config file retrieval.config it is selected by choosing:

#Forward model
secondary_eclipse_bb

This forward model has two general free parameters that have to be added to the priors configuration file in the following order:

  • the planet’s effective temperature in Kelvin

  • ratio of the planet’s and stellar radius \(\mathrm{R_p/R_*}\)

Model config file

The forward_model.config file for the secondary eclipse spectrum model has the following structure:

#Stellar Spectrum
blackbody

It contains a single option related to description of the stellar spectrum. Information on the available options can be found in the section on stellar spectra.

Model postprocessing

The optional postprocessing file post_process.config has the following structure and options:

#Delete unused MultiNest files
Yes

#Compute spectra
Yes

The default options that are used when this file is not present are:

  • Delete unused MultiNest files : No

  • Compute spectra : Yes

Emission spectrum

This forward model computes the emission spectrum \(F(\lambda)\) of an exoplanet or brown dwarf atmosphere. In BeAR, \(F(\lambda)\) has units of \(\mathrm{W} \mathrm{m^{-2}} \mathrm{\mu m^{-1}}\).

In the retrieval config file retrieval.config it is selected by choosing:

#Forward model
emission

The emission spectrum forward model has two general free parameters that have to be added to the priors configuration file in the following order:

  • logarithm of surface gravity \(\log g\) in cgs units

  • a scaling factor \(f\) for the radius/distance relationship, where the radius is internally set to 1 Jupiter radius

  • distance to the object

Model config file

The forward_model.config file for the emission spectrum model has the following structure:

#Number of levels
70

#Bottom of atmosphere pressure (bar)
300

#Top of atmosphere pressure (bar)
1e-3

#Temperature profile
cubicbspline 5

#Cloud model
none

#Radiative transfer (scm/disort)
scm

#Retrieved chemical species
iso H2O CH4 NH3 K H2S CO2
bg H2He

#Opacity species&folders
CIA-H2-H2   CIA/H2-H2
CIA-H2-He   CIA/H2-He
K           Alkali_Allard/K
Na          Alkali_Allard/Na
H2O         Molecules/1H2-16O__POKAZATEL_e2b
CH4         Molecules/12C-1H4__YT34to10_e2b
NH3         Molecules/14N-1H3__CoYuTe_e2b
H2S         Molecules/1H2-32S__AYT2_e2b
CO2         Molecules/12C-16O2__CDSD_4000_e2b

The first three entries refer to the vertical discretisation of the atmosphere. This includes the number of atmospheric layers as well as the bottom and top-of-atmosphere pressures in units of bars.

With the next two entries, the parametrisation for the temperature profile and the cloud models are set.

After that, the radiative transfer scheme is set. There are currently two different options:

  • scm - the short characteristic method, available for CPU and GPU

  • disort - the discrete-ordinate solver DISORT, only available for CPU

Finally, the different chemistry models, chemical species, and the opacity sources are selected. It is important to note that chemical species that are used as part of the chemistry models, should normally also have an associated opacity source. Otherwise, the impact of that species on the resulting spectrum might be negligible and, therefore, its abundance will be likely be unconstrained.

On the other hand, it is theoretically also possible to add opacity species without including this species in any of the chemistry models. In this case, the abundance of this species will be zero and, thus, won’t show up in the spectrum.

Model postprocessing

The optional postprocessing file post_process.config has the following structure and options:

#Delete unused MultiNest files
Yes

#Save spectra
Yes

#Save temperature structures
Yes

#Save effective temperatures
Yes

#Save contribution functions
No

#Save chemical species
none

The default options that are used when this file is not present are:

  • Delete unused MultiNest files : No

  • Compute spectra : Yes

  • Save temperature structures : Yes

  • Save effective temperatures : Yes

  • Save contribution functions : No

  • Save chemical species : None