exojax.spec package

Submodules

exojax.spec.api module

Molecular database (MDB) class using a common API w/ RADIS = (CAPI), will be renamed.

• MdbExomol is the MDB for ExoMol

• MdbHit is the MDB for HITRAN or HITEMP

class exojax.spec.api.MdbExomol(path, nurange=[- inf, inf], margin=0.0, crit=0.0, Ttyp=1000.0, bkgdatm='H2', broadf=True, gpu_transfer=True, inherit_dataframe=False, local_databases='./')

Bases: radis.api.exomolapi.MdbExomol

molecular database of ExoMol.

MdbExomol is a class for ExoMol.

simple_molecule_name

simple molecule name

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1)

Type

nd array

Sij0

line strength at T=Tref (cm)

Type

nd array

logsij0

log line strength at T=Tref

Type

jnp array

A

Einstein A coeeficient

Type

jnp array

gamma_natural

gamma factor of the natural broadening

Type

DataFrame or jnp array

elower

the lower state energy (cm-1)

Type

DataFrame or jnp array

gpp

statistical weight

Type

DataFrame or jnp array

jlower

J_lower

Type

DataFrame or jnp array

jupper

J_upper

Type

DataFrame or jnp array

n_Texp

temperature exponent

Type

DataFrame or jnp array

dev_nu_lines

line center in device (cm-1)

Type

jnp array

alpha_ref

alpha_ref (gamma0), Lorentzian half-width at reference temperature and pressure in cm-1/bar

Type

jnp array

n_Texp_def

default temperature exponent in .def file, used for jlower not given in .broad

alpha_ref_def

default alpha_ref (gamma0) in .def file, used for jlower not given in .broad

A

QT_interp(T)

interpolated partition function.

Parameters

T – temperature

Returns

Q(T) interpolated in jnp.array

Sij0

compute_load_mask(df)

elower

eupper

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array.

gupper

instances_from_dataframes(df_load_mask)

generate instances from (usually masked) data farame

Parameters

df_load_mask (DataFrame) – (masked) data frame

Raises

ValueError – _description_

jlower

jupper

logsij0

nu_lines

qr_interp(T)

interpolated partition function ratio.

Parameters

T – temperature

Returns

qr(T)=Q(T)/Q(Tref) interpolated in jnp.array

class exojax.spec.api.MdbHitemp(path, nurange=[- inf, inf], margin=0.0, crit=0.0, Ttyp=1000.0, isotope=0, gpu_transfer=False, inherit_dataframe=False)

Bases: radis.api.hitempapi.HITEMPDatabaseManager

molecular database of HITEMP.

simple_molecule_name

simple molecule name

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1)

Type

nd array

Sij0

line strength at T=Tref (cm)

Type

nd array

dev_nu_lines

line center in device (cm-1)

Type

jnp array

logsij0

log line strength at T=Tref

Type

jnp array

A

Einstein A coeeficient

Type

jnp array

gamma_natural

gamma factor of the natural broadening

Type

jnp array

gamma_air

gamma factor of air pressure broadening

Type

jnp array

gamma_self

gamma factor of self pressure broadening

Type

jnp array

elower

the lower state energy (cm-1)

Type

jnp array

gpp

statistical weight

Type

jnp array

n_air

air temperature exponent

Type

jnp array

QT_interp(isotope, T)

interpolated partition function.

Parameters

• isotope – HITRAN isotope number starting from 1

• T – temperature

Returns

Q(idx, T) interpolated in jnp.array

compute_load_mask(df, qrtyp)

exact_isotope_name(isotope)

exact isotope name

Parameters

isotope (int) – isotope number starting from 1

Returns

exact isotope name such as (12C)(16O)

Return type

str

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array.

instances_from_dataframes(df_load_mask)

generate instances from (usually masked) data farame

Parameters

df_load_mask (DataFrame) – (masked) data frame

Raises

ValueError – _description_

qr_interp(isotope, T)

interpolated partition function ratio.

Parameters

• isotope – HITRAN isotope number starting from 1

• T – temperature

Returns

qr(T)=Q(T)/Q(Tref) interpolated in jnp.array

qr_interp_lines(T)

Partition Function ratio using HAPI partition data. (This function works for JAX environment.)

Parameters

T – temperature (K)

Returns

Qr_line, partition function ratio array for lines [Nlines]

Note

Nlines=len(self.nu_lines)

class exojax.spec.api.MdbHitran(path, nurange=[- inf, inf], margin=0.0, crit=0.0, Ttyp=1000.0, isotope=0, gpu_transfer=False, inherit_dataframe=False)

Bases: radis.api.hitranapi.HITRANDatabaseManager

molecular database of HITRAN

simple_molecule_name

simple molecule name

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1)

Type

nd array

Sij0

line strength at T=Tref (cm)

Type

nd array

dev_nu_lines

line center in device (cm-1)

Type

jnp array

logsij0

log line strength at T=Tref

Type

jnp array

A

Einstein A coeeficient

Type

jnp array

gamma_natural

gamma factor of the natural broadening

Type

jnp array

gamma_air

gamma factor of air pressure broadening

Type

jnp array

gamma_self

gamma factor of self pressure broadening

Type

jnp array

elower

the lower state energy (cm-1)

Type

jnp array

gpp

statistical weight

Type

jnp array

n_air

air temperature exponent

Type

jnp array

QT_interp(isotope, T)

interpolated partition function.

Parameters

• isotope – HITRAN isotope number starting from 1

• T – temperature

Returns

Q(idx, T) interpolated in jnp.array

compute_load_mask(df, qrtyp)

exact_isotope_name(isotope)

exact isotope name

Parameters

isotope (int) – isotope number starting from 1

Returns

exact isotope name such as (12C)(16O)

Return type

str

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array.

instances_from_dataframes(df_load_mask)

generate instances from (usually masked) data farame

Parameters

df_load_mask (DataFrame) – (masked) data frame

Raises

ValueError – _description_

qr_interp(isotope, T)

interpolated partition function ratio.

Parameters

• isotope – HITRAN isotope number starting from 1

• T – temperature

Returns

qr(T)=Q(T)/Q(Tref) interpolated in jnp.array

qr_interp_lines(T)

Partition Function ratio using HAPI partition data. (This function works for JAX environment.)

Parameters

T – temperature (K)

Returns

Qr_line, partition function ratio array for lines [Nlines]

Note

Nlines=len(self.nu_lines)

exojax.spec.atomll module

exojax.spec.atomll.Sij0(A, gupper, nu_lines, elower, QTref_284, QTmask, Irwin=False)

Reference Line Strength in Tref=296K, S0.

Parameters

• A – Einstein coefficient (s-1)

• gupper – the upper state statistical weight

• nu_lines – line center wavenumber (cm-1)

• elower – elower

• QTref_284 – partition function Q(Tref)

• QTmask – mask to identify a rows of QTref_284 to apply for each line

• Irwin – if True(1), the partition functions of Irwin1981 is used, otherwise those of Barklem&Collet2016

Returns

Line strength (cm)

Return type

Sij(T)

exojax.spec.atomll.gamma_KA3(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0)

HWHM of Lorentzian (cm-1) caluculated with the 3rd equation in p.4 of Kurucz&Avrett1981.

Parameters

• T – temperature (K)

• PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

• PHH – H2 molecule pressure (bar)

• PHe – helium pressure (bar)

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

• nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

• elower – excitation potential (lower level) [cm-1]

• eupper – excitation potential (upper level) [cm-1]

• atomicmass – atomic mass [amu]

• ionE – ionization potential [eV]

• gamRad – log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

• gamSta – log of gamma of Stark damping (s-1)

• vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

• enh_damp – empirical “enhancement factor” for classical Unsoeld’s damping constant cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

• chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

• C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

• logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

• gam6H – 17*v**(0.6)*C6**(0.4)*N (v:relative velocity, N:number density of neutral perturber) (computed)

• Texp – temperature dependency (gamma6 sim T**((1-α)/2) ranging 0.3–0.4) (computed)

Returns

pressure gamma factor (cm-1)

Return type

gamma

Note

“/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

• Reference of van der Waals damping constant (pressure/collision gamma):

• Kurucz+1981: https://ui.adsabs.harvard.edu/abs/1981SAOSR.391…..K

• Barklem+1998: https://ui.adsabs.harvard.edu/abs/1998MNRAS.300..863B

• Barklem+2000: https://ui.adsabs.harvard.edu/abs/2000A&AS..142..467B

• Gray+2005: https://ui.adsabs.harvard.edu/abs/2005oasp.book…..G

exojax.spec.atomll.gamma_KA3s(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0)

(supplemetary:) HWHM of Lorentzian (cm-1) caluculated with the 3rd equation in p.4 of Kurucz&Avrett1981 but without discriminating iron group elements.

Parameters

• T – temperature (K)

• PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

• PHH – H2 molecule pressure (bar)

• PHe – helium pressure (bar)

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

• nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

• elower – excitation potential (lower level) [cm-1]

• eupper – excitation potential (upper level) [cm-1]

• atomicmass – atomic mass [amu]

• ionE – ionization potential [eV]

• gamRad – log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

• gamSta – log of gamma of Stark damping (s-1)

• vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

• enh_damp – empirical “enhancement factor” for classical Unsoeld’s damping constant cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

• chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

• C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

• logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

• gam6H – 17*v**(0.6)*C6**(0.4)*N (v:relative velocity, N:number density of neutral perturber) (computed)

• Texp – temperature dependency (gamma6 sim T**((1-α)/2) ranging 0.3–0.4)(computed)

Returns

pressure gamma factor (cm-1)

Return type

gamma

Note

“/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

• Reference of van der Waals damping constant (pressure/collision gamma):

• Kurucz+1981: https://ui.adsabs.harvard.edu/abs/1981SAOSR.391…..K

• Barklem+1998: https://ui.adsabs.harvard.edu/abs/1998MNRAS.300..863B

• Barklem+2000: https://ui.adsabs.harvard.edu/abs/2000A&AS..142..467B

• Gray+2005: https://ui.adsabs.harvard.edu/abs/2005oasp.book…..G

exojax.spec.atomll.gamma_KA4(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0)

HWHM of Lorentzian (cm-1) caluculated with the 4rd equation in p.4 of Kurucz&Avrett1981.

Parameters

• T – temperature (K)

• PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

• PHH – H2 molecule pressure (bar)

• PHe – helium pressure (bar)

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

• nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

• elower – excitation potential (lower level) [cm-1]

• eupper – excitation potential (upper level) [cm-1]

• atomicmass – atomic mass [amu]

• ionE – ionization potential [eV]

• gamRad – log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

• gamSta – log of gamma of Stark damping (s-1)

• vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

• enh_damp – empirical “enhancement factor” for classical Unsoeld’s damping constant #cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

• chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

• C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

• logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

• gam6H – 17*v**(0.6)*C6**(0.4)*N (v:relative velocity, N:number density of neutral perturber) (computed)

• Texp – temperature dependency (gamma6 sim T**((1-α)/2) ranging 0.3–0.4) (computed)

Returns

pressure gamma factor (cm-1)

Return type

gamma

Note

Approximation of case4 assume “that the atomic weight A is much greater than 4, and that the mean-square-radius of the lower level <r^2>_lo is small compared to <r^2>_up”.

“/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

• Reference of van der Waals damping constant (pressure/collision gamma):

• Kurucz+1981: https://ui.adsabs.harvard.edu/abs/1981SAOSR.391…..K

• Barklem+1998: https://ui.adsabs.harvard.edu/abs/1998MNRAS.300..863B

• Barklem+2000: https://ui.adsabs.harvard.edu/abs/2000A&AS..142..467B

• Gray+2005: https://ui.adsabs.harvard.edu/abs/2005oasp.book…..G

exojax.spec.atomll.gamma_uns(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0)

HWHM of Lorentzian (cm-1) estimated with the classical approximation by Unsoeld (1955)

Parameters

• T – temperature (K)

• PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

• PHH – H2 molecule pressure (bar)

• PHe – helium pressure (bar)

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

• nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

• elower – excitation potential (lower level) [cm-1]

• eupper – excitation potential (upper level) [cm-1]

• atomicmass – atomic mass [amu]

• ionE – ionization potential [eV]

• gamRad – log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

• gamSta – log of gamma of Stark damping (s-1)

• vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

• enh_damp – empirical “enhancement factor” for classical Unsoeld’s damping constant cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

• chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

• C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

• logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

• gam6H – 17*v**(0.6)*C6**(0.4)*N (v:relative velocity, N:number density of neutral perturber) (computed)

• Texp – temperature dependency (gamma6 sim T**((1-α)/2) ranging 0.3–0.4)(computed)

Returns

pressure gamma factor (cm-1)

Return type

gamma

Note

“/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

• Reference of van der Waals damping constant (pressure/collision gamma):

• Unsöld1955: https://ui.adsabs.harvard.edu/abs/1955psmb.book…..U

• Kurucz+1981: https://ui.adsabs.harvard.edu/abs/1981SAOSR.391…..K

• Barklem+1998: https://ui.adsabs.harvard.edu/abs/1998MNRAS.300..863B

• Barklem+2000: https://ui.adsabs.harvard.edu/abs/2000A&AS..142..467B

• Gray+2005: https://ui.adsabs.harvard.edu/abs/2005oasp.book…..G

exojax.spec.atomll.gamma_vald3(T, PH, PHH, PHe, ielem, iion, nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp, enh_damp=1.0)

HWHM of Lorentzian (cm-1) caluculated as gamma/(4*pi*c) [cm-1] for lines with the van der Waals gamma in the line list (VALD or Kurucz), otherwise estimated according to the Unsoeld (1955)

Parameters

• T – temperature (K)

• PH – hydrogen pressure (bar) #1 bar = 1e6 dyn/cm2

• PHH – H2 molecule pressure (bar)

• PHe – helium pressure (bar)

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

• nu_lines – transition waveNUMBER in [cm-1] (NOT frequency in [s-1])

• elower – excitation potential (lower level) [cm-1]

• eupper – excitation potential (upper level) [cm-1]

• atomicmass – atomic mass [amu]

• ionE – ionization potential [eV]

• gamRad – log of gamma of radiation damping (s-1) (https://www.astro.uu.se/valdwiki/Vald3Format)

• gamSta – log of gamma of Stark damping (s-1)

• vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

• enh_damp – empirical “enhancement factor” for classical Unsoeld’s damping constant cf.) This coefficient (enh_damp) depends on each species in some codes such as Turbospectrum. #tako210917

• chi_lam (=h*nu=1.2398e4/wvl[AA]) – energy of a photon in the line (computed)

• C6 – interaction constant (Eq.11.17 in Gray2005) (computed)

• logg6 – log(gamma6) (Eq.11.29 in Gray2005) (computed)

• gam6H – 17*v**(0.6)*C6**(0.4)*N (computed) (v:relative velocity, N:number density of neutral perturber)

• Texp – temperature dependency (gamma6 sim T**((1-α)/2) ranging 0.3–0.4) (computed)

Returns

pressure gamma factor (cm-1)

Return type

gamma

Note

“/(4*np.pi*ccgs)” means: damping constant -> HWHM of Lorentzian in [cm^-1]

• Reference of van der Waals damping constant (pressure/collision gamma):

• Unsöld1955: https://ui.adsabs.harvard.edu/abs/1955psmb.book…..U

• Kurucz+1981: https://ui.adsabs.harvard.edu/abs/1981SAOSR.391…..K

• Barklem+1998: https://ui.adsabs.harvard.edu/abs/1998MNRAS.300..863B

• Barklem+2000: https://ui.adsabs.harvard.edu/abs/2000A&AS..142..467B

• Gray+2005: https://ui.adsabs.harvard.edu/abs/2005oasp.book…..G

exojax.spec.atomll.get_VMR_uspecies(uspecies, mods_ID=DeviceArray([[0, 0]], dtype=int32), mods=DeviceArray([0], dtype=int32))

Extract VMR arrays of the species that contribute the opacity (“uspecies” made with “get_unique_species”)

Parameters

• uspecies – jnp.array of unique list of the species contributing the opacity [N_species x 2(ielem and iion)]

• mods_ID – jnp.array listing the species whose abundances are different from the solar [N_modified_species x 2(ielem and iion)]

• mods – jnp.array of each abundance deviation from the Sun [dex] for each modified species listed in mods_ID [N_modified_species]

Returns

jnp.array of volume mixing ratio [N_species]

Return type

VMR_uspecies

exojax.spec.atomll.get_VMR_uspecies_FC(FCSpIndex_uspecies, mixing_ratios)

By using FastChem, extract volume mixing ratio (VMR) of the species that contribute the opacity (“uspecies” made with “get_unique_species”)

Parameters

• FCSpIndex_uspecies – SpeciesIndex in FastChem for each species of interest [N_species]

• mixing_ratios – volume mixing ratios of all available gases calculated using fastchem2_call.run_fastchem [N_layer x N_species]

Returns

VMR of each species in each atmospheric layer [N_species x N_layer]

Return type

VMR_uspecies

exojax.spec.atomll.get_unique_species(adb)

Extract a unique list of line contributing species from VALD atomic database (adb)

Parameters

adb – adb instance made by the AdbVald class in moldb.py

Returns

unique elements of the combination of ielem and iion (jnp.array with a shape of N_UniqueSpecies x 2(ielem and iion))

Return type

uspecies

exojax.spec.atomll.ielemion_to_FastChemSymbol(ielem, iion)

Translate atomic number and ionization level into SpeciesSymbol in FastChem.

Parameters

• ielem – atomic number (int) (e.g., Fe=26)

• iion – ionized level (int) (e.g., neutral=1, singly)

Returns

//github.com/exoclime/FastChem/blob/master/input/logK_ext.dat)

Return type

SpeciesSymbol in FastChem (str) (cf. https

exojax.spec.atomll.interp_QT284(T, T_gQT, gQT_284species)

interpolated partition function of all 284 species.

Parameters

• T – temperature

• T_gQT – temperature in the grid obtained from the adb instance [N_grid(42)]

• gQT_284species – partition function in the grid from the adb instance [N_species(284) x N_grid(42)]

Returns

interpolated partition function at T Q(T) for all 284 Atomic Species [284]

Return type

QT_284

exojax.spec.atomll.padding_2Darray_for_each_atom(orig_arr, adb, sp)

Extract only data of the species of interest from 2D-array and pad with zeros to adjust the length.

Parameters

• orig_arr – array [N_any (e.g., N_nu or N_layer), N_line] Note that if your ARRAY is 1D, it must be broadcasted with ARRAY[None,:], and the output must be also reshaped with OUTPUTARRAY.reshape(ARRAY.shape)

• adb – adb instance made by the AdbVald class in moldb.py

• sp – array of [ielem, iion]

Returns

padded_valid_arr

exojax.spec.atomll.sep_arr_of_sp(arr, adb, trans_jnp=True, inttype=False)

Separate by species (atoms or ions) the jnp.array stored as an instance variable in adb, and pad with zeros to adjust the length

Parameters

• arr – array of a parameter (one of the attributes of adb below) to be separated [N_line]

• adb – adb instance made by the AdbVald class in moldb.py

• trans_jnp – if True, the output is converted to jnp.array (dtype=’float32’)

• inttype – if True (along with trans_jnp = True), the output is converted to jnp.array of dtype=’int32’

Returns

species-separated array [N_species x N_line_max]

Return type

arr_stacksp

exojax.spec.atomll.uspecies_info(uspecies, ielem_to_index_of_ipccd, mods_ID=DeviceArray([[0, 0]], dtype=int32), mods=DeviceArray([0], dtype=int32), mods_id_trans=DeviceArray([], dtype=float32))

Provide arrays of information of the species that contribute the opacity (“uspecies” made with “get_unique_species”)

Parameters

• uspecies – jnp.array of unique list of the species contributing the opacity

• ielem_to_index_of_ipccd – jnp.array for conversion from ielem to the index of ipccd

• mods_ID – jnp.array listing the species whose abundances are different from the solar

• mods – jnp.array of each abundance deviation from the Sun [dex] for each modified species in mods_ID

• mods_id_trans – jnp.array for converting index in “mods_ID” of each species into index in uspecies

Returns

jnp.array of mass mixing ratio in the Sun of each species in “uspecies” atomicmass_uspecies_list: jnp.array of atomic mass [amu] of each species in “uspecies” mods_uspecies_list: jnp.array of abundance deviation from the Sun [dex] for each species in “uspecies”

Return type

MMR_uspecies_list

exojax.spec.atomllapi module

API for VALD 3.

exojax.spec.atomllapi.air_to_vac(wlair)

Convert wavelengths [AA] in air into those in vacuum.

• See http://www.astro.uu.se/valdwiki/Air-to-vacuum%20conversion

Parameters

• wlair – wavelengthe in air [Angstrom]

• n – Refractive Index in dry air at 1 atm pressure and 15ºC with 0.045% CO2 by volume (Birch and Downs, 1994, Metrologia, 31, 315)

Returns

wavelength in vacuum [Angstrom]

Return type

wlvac

exojax.spec.atomllapi.load_atomicdata()

load atomic data and solar composition.

• See Asplund et al. 2009, Gerevesse et al. 1996

Returns

table of atomic data

Return type

ipccd (pd.DataFrame)

Note

atomic.txt is in data/atom

exojax.spec.atomllapi.load_ionization_energies()

Load atomic ionization energies.

Returns

table of ionization energies

Return type

df_ionE (pd.DataFrame)

Note

NIST_Atomic_Ionization_Energies.txt is in data/atom

exojax.spec.atomllapi.load_pf_Barklem2016()

load a table of the partition functions for 284 atomic species.

• See Table 8 of Barklem & Collet (2016); https://doi.org/10.1051/0004-6361/201526961

Returns

steps of temperature (K) pfdat (pd.DataFrame): partition functions for 284 atomic species

Return type

pfTdat (pd.DataFrame)

exojax.spec.atomllapi.make_ielem_to_index_of_ipccd()

index conversion for atomll.uspecies_info (Preparation for LPF)

Returns

jnp.array to convert ielem into index of ipccd

Return type

ielem_to_index_of_ipccd

exojax.spec.atomllapi.partfn_Fe(T)

Partition function of Fe I from Irwin_1981.

Parameters

T – temperature

Returns

partition function Q

exojax.spec.atomllapi.pick_ionE(ielem, iion, df_ionE)

Pick up ionization energy of a specific atomic species.

Parameters

• ielem (int) – atomic number (e.g., Fe=26)

• iion (int) – ionized level (e.g., neutral=1, singly ionized=2, etc.)

• df_ionE (pd.DataFrame) – table of ionization energies

Returns

ionization energy

Return type

ionE (float)

Note

NIST_Atomic_Ionization_Energies.txt is in data/atom

exojax.spec.atomllapi.pickup_param(ExAll)

extract transition parameters from VALD3 line list and insert the same DataFrame.

Parameters

ExAll – VALD3 line list as pandas DataFrame (Output of read_ExAll)

Returns

Einstein coefficient in [s-1] nu_lines: transition waveNUMBER in [cm-1] (#NOT frequency in [s-1]) elower: lower excitation potential [cm-1] (#converted from eV) eupper: upper excitation potential [cm-1] (#converted from eV) gupper: upper statistical weight jlower: lower J (rotational quantum number, total angular momentum) jupper: upper J ielem: atomic number (e.g., Fe=26) iion: ionized level (e.g., neutral=1, singly) gamRad: log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format) gamSta: log of gamma of Stark damping (s-1) vdWdamp: log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Return type

A

exojax.spec.atomllapi.read_ExAll(allf)

IO for linelists downloaded from VALD3 with a query of “Long format” in the format of “Extract All” or “Extract Element”.

Note

About input linelists obtained from VALD3 (http://vald.astro.uu.se/). VALD data access is free but requires registration through the Contact form (http://vald.astro.uu.se/~vald/php/vald.php?docpage=contact.html). After the registration, you can login and choose the “Extract Element” mode. For example, if you want the Fe I linelist, the request form should be filled as

>>> Starting wavelength :    1500
>>> Ending wavelength :    100000
>>> Element [ + ionization ] :    Fe 1
>>> Extraction format :    Long format
>>> Retrieve data via :    FTP
>>> Linelist configuration :    Default
>>> Unit selection:    Energy unit: eV - Medium: vacuum - Wavelength unit: angstrom - VdW syntax: default

Please assign the fullpath of the output file sent by VALD ([user_name_at_VALD].[request_number_at_VALD].gz) to the variable “allf”. See https://www.astro.uu.se/valdwiki/presformat_output for the detail of the format.

Parameters

• allf – fullpath to the input VALD linelist (See Notes above for more details.)

• Ion (Elm) –

• WL_vac (AA) –

• gf* (log) –

• E_low (eV) – lower excitation potential

• lo (J) – lower rotational quantum number

• E_up (eV) – upper excitation potential

• up (J) – upper rotational quantum number

• lower (Lande) –

• upper (Lande) –

• mean (Lande) –

• Rad. (Damping) –

• Stark (Damping) –

• Waals (Damping) –

Returns

line data in vaex DataFrame

exojax.spec.atomllapi.read_kurucz(kuruczf)

Input Kurucz line list (http://kurucz.harvard.edu/linelists/)

Parameters

kuruczf – file path

Returns

Einstein coefficient in [s-1] nu_lines: transition waveNUMBER in [cm-1] (#NOT frequency in [s-1]) elower: lower excitation potential [cm-1] (#converted from eV) eupper: upper excitation potential [cm-1] (#converted from eV) gupper: upper statistical weight jlower: lower J (rotational quantum number, total angular momentum) jupper: upper J ielem: atomic number (e.g., Fe=26) iion: ionized level (e.g., neutral=1, singly) gamRad: log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format) gamSta: log of gamma of Stark damping (s-1) gamvdW: log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Return type

A

exojax.spec.atomllapi.vac_to_air(wlvac)

Convert wavelengths [AA] in vacuum into those in air.

• See http://www.astro.uu.se/valdwiki/Air-to-vacuum%20conversion

Parameters

• wlvac – wavelength in vacuum [Angstrom]

• n – Refractive Index in dry air at 1 atm pressure and 15ºC with 0.045% CO2 by volume (Birch and Downs, 1994, Metrologia, 31, 315)

Returns

wavelengthe in air [Angstrom]

Return type

wlair

exojax.spec.autospec module

Automatic Opacity and Spectrum Generator.

class exojax.spec.autospec.AutoRT(nus, gravity, mmw, Tarr, Parr, dParr=None, databasedir='.database', xsmode='auto', autogridconv=True)

Bases: object

exojax auto radiative transfer.

addcia(interaction, mmr1, mmr2)

Parameters

• interaction – e.g. H2-H2, H2-He

• mmr1 – mass mixing ratio for molecule 1

• mmr2 – mass mixing ratio for molecule 2

addmol(database, molecules, mmr, crit=0.0)

Parameters

• database – database= HITRAN, HITEMP, ExoMol

• molecules – molecule name

• mmr – mass mixing ratio (float or ndarray for the layer)

• crit – line strength criterion, ignore lines whose line strength are below crit

rtrun()

running radiative transfer.

Returns

spectrum (F0) in the unit of erg/s/cm2/cm-1

Note

If you want to use the unit of erg/cm2/s/Hz, divide the output by the speed of light in cgs as Fx0=Fx0/ccgs, where ccgs=29979245800.0. See #84

spectrum(nuobs, Rinst, vsini, RV, u1=0.0, u2=0.0, zeta=0.0, betamic=0.0)

generating spectrum.

Parameters

• nuobs – observation wavenumber array

• Rinst – instrumental resolving power

• vsini – vsini for a stellar/planet rotation

• RV – radial velocity (km/s)

• u1 – Limb-darkening coefficient 1

• u2 – Limb-darkening coefficient 2

• zeta – macroturbulence distrubunce (km/s) in the radial-tangential model (Gray2005)

• betamic – microturbulence beta (STD, km/s)

Returns

spectrum (F)

class exojax.spec.autospec.AutoXS(nus, database, molecules, databasedir='.database', memory_size=30, broadf=True, crit=0.0, xsmode='auto', autogridconv=True, pdit=1.5)

Bases: object

exojax auto cross section generator.

autonus(checknus, tag='ESLOG')

init_database()

linest(T)

line strength.

Parameters

T – temperature (K)

Returns

line strength (cm)

nonnegative_xsm(xsm)

check negative value of xsm.

Parameters

xsm – xs matrix

Returns

xsm negative eliminated

select_xsmode(Nline)

xsection(T, P)

cross section.

Parameters

• T – temperature (K)

• P – pressure (bar)

Returns

cross section (cm2)

xsmatrix(Tarr, Parr)

cross section matrix.

Parameters

• Tarr – temperature layer (K)

• Parr – pressure layer (bar)

Returns

cross section (cm2)

exojax.spec.contdb module

Continuum database (CDB) class.

• CdbCIA is the CDB for CIA

class exojax.spec.contdb.CdbCIA(path, nurange=[- inf, inf], margin=10.0)

Bases: object

download()

Downloading HITRAN cia file.

Note

The download URL is written in exojax.utils.url.

exojax.spec.defcia module

Definition of Default cia dataset for autospec.

exojax.spec.defcia.ciafile(interaction)

provide ciafile from interaction.

Parameters

interaction – e.g. H2-H2

Returns

cia file name

exojax.spec.defcia.interaction2mols(interaction)

provide 2 molecules from interaction.

Parameters

interaction – e.g. H2-H2

Returns

mol1, mol2

Examples:

>>> from exojax.spec.defcia import interaction2mols
>>> print(interaction2mols("H2-CH4 (equilibrium)"))
>>> ('H2', 'CH4')
>>> print(interaction2mols("CH4-He"))
>>> ('CH4', 'He')

exojax.spec.defmol module

Definition of Default dataset for autospec.

exojax.spec.defmol.search_molfile(database, molecules)

name identifier of molecular databases.

Parameters

• database – molecular database (HITRAN,HITEMP,ExoMol)

• molecules – molecular name such as (CO, 12C-16O)

Returns

identifier

exojax.spec.dit module

Line profile computation using Discrete Integral Transform.

• Line profile computation of Discrete Integral Transform for rapid spectral synthesis, originally proposed by D.C.M van den Bekerom and E.Pannier.

• This module consists of selected functions in addit package.

• The concept of “folding” can be understood by reading the discussion by D.C.M van den Bekerom.

exojax.spec.dit.dgmatrix(x, dit_grid_resolution=0.1, adopt=True)

DIT GRID MATRIX (alias)

Parameters

• x – simgaD or gammaL matrix (Nlayer x Nline)

• dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns

grid for DIT (Nlayer x NDITgrid)

exojax.spec.dit.ditgrid(x, dit_grid_resolution=0.1, adopt=True)

DIT GRID (deplicated).

Parameters

• x – simgaD or gammaL array (Nline)

• dit_grid_resolution – grid resolution. res=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be res exactly.

Returns

grid for DIT

exojax.spec.dit.dtauM_vald(dParr, g, adb, nus, cnu, indexnu, pmarray, SijM, gammaLM, sigmaDM, uspecies, mods_uspecies_list, MMR_uspecies_list, atomicmass_uspecies_list, dgm_sigmaD, dgm_gammaL)

Compute dtau caused by VALD lines from cross section xs (DIT)

Parameters

• dParr – delta pressure profile (bar) [N_layer]

• g – gravity (cm/s^2)

• adb – adb instance made by the AdbVald class in moldb.py

• nus – wavenumber matrix (cm-1) [N_nus]

• cnu – cont (contribution) jnp.array [N_line]

• indexnu – index (index) jnp.array [N_line]

• pmarray – (+1,-1) array [len(nu_grid)+1,]

• SijM – line intensity matrix [N_layer x N_line]

• gammaLM – gammaL matrix [N_layer x N_line]

• sigmaDM – sigmaD matrix [N_layer x N_line]

• uspecies – unique elements of the combination of ielem and iion [N_UniqueSpecies x 2(ielem and iion)]

• mods_uspecies_list – jnp.array of abundance deviation from the Sun [dex] for each species in “uspecies” [N_UniqueSpecies]

• MMR_uspecies_list – jnp.array of mass mixing ratio in the Sun of each species in “uspecies” [N_UniqueSpecies]

• atomicmass_uspecies_list – jnp.array of atomic mass [amu] of each species in “uspecies” [N_UniqueSpecies]

Returns

optical depth matrix [N_layer, N_nus]

Return type

dtauatom

exojax.spec.dit.dtauM_vald_old(dParr, xsm, g, uspecies, mods_uspecies_list, MMR_uspecies_list, atomicmass_uspecies_list)

Compute dtau caused by VALD lines from cross section xs (DIT)

Parameters

• dParr – delta pressure profile (bar) [N_layer]

• xsm – cross section matrix (cm^2) [N_layer, N_nus]

• g – gravity (cm/s^2)

• uspecies – unique elements of the combination of ielem and iion [N_UniqueSpecies x 2(ielem and iion)]

• mods_uspecies_list – jnp.array of abundance deviation from the Sun [dex] for each species in “uspecies” [N_UniqueSpecies]

• MMR_uspecies_list – jnp.array of mass mixing ratio in the Sun of each species in “uspecies” [N_UniqueSpecies]

• atomicmass_uspecies_list – jnp.array of atomic mass [amu] of each species in “uspecies” [N_UniqueSpecies]

Returns

optical depth matrix [N_layer, N_nus]

Return type

dtauatom

exojax.spec.dit.sigma_voigt(dgm_sigmaD, dgm_gammaL)

compute sigma of the Voigt profile.

Parameters

• dgm_sigmaD – DIT grid matrix for sigmaD

• dgm_gammaL – DIT grid matrix for gammaL

Returns

sigma

exojax.spec.dit.vald(adb, Tarr, PH, PHe, PHH)

(alias of lpf.vald)

Parameters

• adb – adb instance made by the AdbVald class in moldb.py

• Tarr – Temperature array

• PH – Partial pressure array of neutral hydrogen (H)

• PHe – Partial pressure array of neutral helium (He)

• PHH – Partial pressure array of molecular hydrogen (H2)

Returns

line intensity matrix gammaLM: gammaL matrix sigmaDM: sigmaD matrix

Return type

SijM

exojax.spec.dit.xsmatrix(cnu, indexnu, pmarray, sigmaDM, gammaLM, SijM, nu_grid, dgm_sigmaD, dgm_gammaL)

Cross section matrix (DIT/2D+ version)

Parameters

• cnu – contribution by npgetix for wavenumber

• indexnu – index by npgetix for wavenumber

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• sigmaDM – doppler sigma matrix in R^(Nlayer x Nline)

• gammaLM – gamma factor matrix in R^(Nlayer x Nline)

• SijM – line strength matrix in R^(Nlayer x Nline)

• nu_grid – linear wavenumber grid

• dgm_sigmaD – DIT Grid Matrix for sigmaD R^(Nlayer, NDITgrid)

• dgm_gammaL – DIT Grid Matrix for gammaL R^(Nlayer, NDITgrid)

Returns

cross section matrix in R^(Nlayer x Nwav)

Warning

This function have not been well tested.

exojax.spec.dit.xsvector(cnu, indexnu, pmarray, sigmaD, gammaL, S, nu_grid, sigmaD_grid, gammaL_grid)

Cross section vector (DIT/2D+ version; default)

The original code is rundit in [addit package](https://github.com/HajimeKawahara/addit)

Parameters

• cnu – contribution by npgetix for wavenumber

• indexnu – index by npgetix for wavenumber

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• sigmaD – Gaussian STD (Nlines)

• gammaL – Lorentzian half width (Nlines)

• S – line strength (Nlines)

• nu_grid – linear wavenumber grid

• sigmaD_grid – sigmaD grid

• gammaL_grid – gammaL grid

Returns

Cross section in the linear nu grid

Note

This function uses the precomputed neibouring contribution function for wavenumber (nu_ncf). Use npnc1D to compute nu_ncf in float64 precision.

exojax.spec.ditkernel module

Kernels for Discrete Integral Transform.

• Fourier kernels for the Voigt are given in this module

• For coarsed wavenumber grids, folded one is needed to avoid negative values, See discussion by Dirk van den Bekerom at https://github.com/radis/radis/issues/186#issuecomment-764465580 for details.

exojax.spec.ditkernel.fold_voigt_kernel(k, beta, gammaL, vmax, pmarray)

Fourier Kernel of the Voigt Profile.

Parameters

• k – conjugated of wavenumber

• beta – Gaussian standard deviation

• gammaL – Lorentian Half Width

• vmax – Nnu x dq

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

Returns

kernel (N_x,N_beta,N_gammaL)

Note

Conversions to the (full) width, wG and wL are as follows: wG=2*sqrt(2*ln2) beta wL=2*gamma

exojax.spec.ditkernel.fold_voigt_kernel_logst(k, log_nstbeta, log_ngammaL, vmax, pmarray)

Folded Fourier Kernel of the Voigt Profile for a common normalized beta. See https://github.com/dcmvdbekerom/discrete-integral- transform/blob/master/demo/discrete_integral_transform_log.py for the alias correction.

Parameters

• k – conjugate wavenumber

• log_nstbeta – log normalized Gaussian standard deviation (scalar)

• log_ngammaL – log normalized Lorentian Half Width (Nlines)

• vmax – vmax

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

Returns

kernel (N_x,N_gammaL)

Note

Conversions to the (full) width, wG and wL are as follows: wG=2*sqrt(2*ln2) beta wL=2*gamma

exojax.spec.ditkernel.voigt_kernel(k, beta, gammaL)

Fourier Kernel of the Voigt Profile.

Parameters

• k – conjugated of wavenumber

• beta – Gaussian standard deviation

• gammaL – Lorentzian Half Width

Returns

kernel (N_x,N_beta,N_gammaL)

Note

Conversions to the (full) width, wG and wL are as follows: wG=2*sqrt(2*ln2) beta wL=2*gamma

exojax.spec.ditkernel.voigt_kernel_logst(k, log_nstbeta, log_ngammaL)

Fourier Kernel of the Voigt Profile for a common normalized beta.

Parameters

• k – conjugate wavenumber

• log_nstbeta – log normalized Gaussian standard deviation (scalar)

• log_ngammaL – log normalized Lorentian Half Width (Nlines)

Returns

kernel (N_x,N_gammaL)

Note

Conversions to the (full) width, wG and wL are as follows: wG=2*sqrt(2*ln2) beta wL=2*gamma

exojax.spec.evalline module

Evaluation of molecular lines (center)

• This module evaluates the contibution of molecular lines to an emission spectrum.

• This module only consider the line center to reduces computation complexity.

exojax.spec.evalline.contfunc(dtau, nu, Parr, dParr, Tarr)

contribution function.

Parameters

• dtau – delta tau array [N_layer, N_lines]

• nu – wavenumber array [N_lines]

• Parr – pressure array [N_layer]

• dParr – delta pressure array [N_layer]

• Tarr – temperature array [N_layer]

Returns

contribution function

exojax.spec.evalline.mask_weakline(mdb_mol, Parr, dParr, Tarr, SijM, gammaLM, sigmaDM, MMR_mol, molmass_mol, mmw, g, vmrH2, cdbH2H2, margin=2, mask=None, Nlim=1000)

masking weak lines compared to CIA H2-H2 continuum.

Parameters

• mdb_mol – mdb

• Parr – pressure layer (bar)

• dParr – delta pressure layer (bar)

• Tarr – temperature layer (K)

• SijM – Sij matrix

• gammaLM – gamma coefficient matrix

• sigmaDM – Doppler broadening matrix

• MMR_mol – Mass Mixing Ratio of the molecule

• molmass_mol – molecualr mass of the molecule

• mmw – mean molecular weight of the atmosphere

• gravity – gravity (cm/s2)

• vmrH2 – volume mixing ratio of H2

• cdbH2H2 – cdb

Returns

mask (weak line mask), maxcf (P at max contribution function for the molecule), maxcia (P at max contribution function for CIA)

exojax.spec.evalline.reduceline_exomol(mdb, Parr, dParr, mmw, gravity, vmrH2, cdb, maxMMR, molmass, Tmodel, *Tparams)

Reduce lines for Exomol.

Parameters

• mdb – mdb (exomol)

• Parr – pressure layer (bar)

• dParr – delta pressure layer (bar)

• mmw – mean molecular weight of the atmosphere

• gravity – gravity (cm/s2)

• vmrH2 – volume mixing ratio of H2

• cdb – cdb for continuum

• maxMMR – max Mass Mixing Ratio

• molmass_mol – molecualr mass of the molecule

• Tmodel – Tmodel function

• *Tparams – parameter sets

Returns

mask for exomol mdb maxcf: max contribution function,but for the last value of parameter set. maxcia: max cia level but for the last value of parameter set.

Return type

mask

exojax.spec.evalline.voigt0(sigmaD, gammaL)

Voigt-Hjerting function at nu=nu0.

Parameters

• nu – wavenumber

• sigmaD – sigma parameter in Doppler profile

• gammaL – broadening coefficient in Lorentz profile

Returns

Voigt profile at nu=nu0

Return type

v

exojax.spec.evalline.xsmatrix0(sigmaDM, gammaLM, SijM)

cross section matrix at nu=nu0.

Parameters

• sigmaDM – doppler sigma matrix in R^(Nlayer x Nline)

• gammaLM – gamma factor matrix in R^(Nlayer x Nline)

• SijM – line strength matrix in R^(Nlayer x Nline)

Returns

cross section matrix in R^(Nlayer x Nwav)

exojax.spec.evalline.xsvector0(sigmaD, gammaL, Sij)

cross section at nu=nu0.

Parameters

• sigmaD – doppler sigma vector in R^Nline

• gammaL – gamma factor vector in R^Nline

• Sij – line strength vector in R^Nline

Returns

cross section vector in R^Nwav

exojax.spec.exomol module

exojax.spec.exomol.Sij0(A, g, nu_lines, elower, QTref)

Reference Line Strength in Tref=296K, S0.

Note

Tref=296K

Parameters

• A – Einstein coefficient (s-1)

• g – the upper state statistical weight

• nu_lines – line center wavenumber (cm-1)

• elower – elower

• QTref – partition function Q(Tref)

• Mmol – molecular mass (normalized by m_u)

Returns

Line strength (cm)

Return type

Sij(T)

exojax.spec.exomol.gamma_exomol(P, T, n_air, alpha_ref)

gamma factor by a pressure broadening.

Parameters

• P – pressure (bar)

• T – temperature (K)

• n_air – coefficient of the temperature dependence of the air-broadened halfwidth

• alpha_ref – broadening parameter

Returns

pressure gamma factor (cm-1)

Return type

gamma

exojax.spec.exomol.gamma_natural(A)

gamma factor by natural broadning.

1/(4 pi c) = 2.6544188e-12 (cm-1 s)

Parameters

A – Einstein A-factor (1/s)

Returns

natural width (cm-1)

Return type

gamma_natural

exojax.spec.exomolapi module

API for Exomol molecular database.

exojax.spec.exomolapi.check_bdat(bdat)

cheking codes in .broad.

Parameters

bdat – exomol .broad data given by exomolapi.read_broad

Returns

None, a0, a1, other codes unavailable currently,

Return type

code level

exojax.spec.exomolapi.make_j2b(bdat, alpha_ref_default=0.07, n_Texp_default=0.5, jlower_max=None)

compute j2b (code a0, map from jlower to alpha_ref)

Parameters

• bdat – exomol .broad data given by exomolapi.read_broad

• alpha_ref_default – default value

• n_Texp_default – default value

• jlower_max – maximum number of jlower

Returns

j2alpha_ref[jlower] provides alpha_ref for jlower j2n_Texp[jlower] provides nT_exp for jlower

exojax.spec.exomolapi.make_jj2b(bdat, j2alpha_ref_def, j2n_Texp_def, jupper_max=None)

compute jj2b (code a1, map from (jlower, jupper) to alpha_ref and n_Texp)

Parameters

• bdat – exomol .broad data given by exomolapi.read_broad

• j2alpha_ref_def – default value from a0

• j2n_Texp_def – default value from a0

• jupper_max – maximum number of jupper

Returns

jj2alpha_ref[jlower,jupper] provides alpha_ref for (jlower, jupper) jj2n_Texp[jlower,jupper] provides nT_exp for (jlower, jupper)

Note

The pair of (jlower, jupper) for which broadening parameters are not given, jj2XXX contains None.

exojax.spec.exomolapi.make_numtag(numinf, maxnu)

making numtag from numinf.

Parameters

• numinf – nu minimum for trans

• maxnu – maximum nu

Returns

tag for wavelength range

Return type

numtag

exojax.spec.exomolapi.pickup_gE(ndstates, ndtrans, trans_file, trans_lines=False)

extract g_upper (gup), E_lower (elower), and J_lower and J_upper from states DataFrame and insert them to transition DataFrame.

Parameters

• ndstates – states numpy array

• ndtrans – transition numpy array

• trans_file – name of the transition file

• trans_lines – By default (False) we use nu_lines computed using the state file, i.e. E_upper - E_lower. If trans_nuline=True, we use the nu_lines in the transition file. Note that some trans files do not this info.

Returns

A, nu_lines, elower, gup, jlower, jupper

Note

We first convert pandas DataFrame to ndarray. The state counting numbers in states DataFrame is used as indices of the new array for states (newstates). We remove the state count numbers as the column of newstate, i.e. newstates[:,k] k=0: E, 1: g, 2: J. Then, we can directly use the state counting numbers as mask.

exojax.spec.exomolapi.pickup_gEslow(states, trans)

Slow version to extract g_upper (gup) and E_lower (elower) from states DataFrame and insert them to transition DataFrame.

Parameters

• states – states pandas DataFrame

• trans – transition pandas DataFrame

Returns

A, nu_lines, elower, gup

Warning

This code is the (thousands times) slower version of pickup_gE. However, we did not remove this one just because this version is much easier to understand.

exojax.spec.exomolapi.read_broad(broadf)

Reading braodening file (.broad)

Parameters

broadf – .broad file

Returns

broadening info in bdat form (pandas), defined by this instance.

Note

See Table 16 in https://arxiv.org/pdf/1603.05890.pdf

exojax.spec.exomolapi.read_def(deff)

Exomol IO for a definition file.

Parameters

deff – definition file

Returns

temperature exponent n_Texp broadening parameter alpha_ref molecular mass numinf: nu minimum for trans numtag: tag for wavelength range

Note

For some molecules, ExoMol provides multiple trans files. numinf and numtag are the ranges and identifiers for the multiple trans files.

exojax.spec.exomolapi.read_pf(pff)

Exomol IO for partition file.

Parameters

pff – partition file

Returns

partition data in pandas DataFrame

Note

T=temperature QT=partition function

exojax.spec.exomolapi.read_states(statesf)

Exomol IO for a state file.

Parameters

statesf – state file

Returns

states data in pandas DataFrame

Note

i=state counting number E=state energy g=state degeneracy J=total angular momentum See Table 11 in https://arxiv.org/pdf/1603.05890.pdf

exojax.spec.exomolapi.read_trans(transf)

Exomol IO for a transition file.

Parameters

transf – transition file

Returns

transition data in vaex DataFrame

Note

i_upper=Upper state counting number i_lower=Lower state counting number A=Einstein coefficient in s-1 nu_lines=transition wavenumber in cm-1 See Table 12 in https://arxiv.org/pdf/1603.05890.pdf

exojax.spec.hitran module

exojax.spec.hitran.SijT(T, logsij0, nu_lines, elower, qT)

(alias, deprecated) use hitran.line_strength, will be removed.

exojax.spec.hitran.doppler_sigma(nu_lines, T, M)

Dopper width (sigmaD)

Note

c3 is sqrt(kB/m_u)/c

Parameters

• nu_lines – line center wavenumber (cm-1)

• T – temperature (K)

• M – atom/molecular mass

Returns

doppler width (standard deviation) (cm-1)

Return type

sigma

exojax.spec.hitran.gamma_hitran(P, T, Pself, n_air, gamma_air_ref, gamma_self_ref)

gamma factor by a pressure broadening.

Parameters

• P – pressure (bar)

• T – temperature (K)

• Pself – partial pressure (bar)

• n_air – coefficient of the temperature dependence of the air-broadened halfwidth

• gamma_air_ref – gamma air

• gamma_self_ref – gamma self

Returns

pressure gamma factor (cm-1)

Return type

gamma

exojax.spec.hitran.gamma_natural(A)

gamma factor by natural broadning.

1/(4 pi c) = 2.6544188e-12 (cm-1 s)

Parameters

A – Einstein A-factor (1/s)

Returns

natural width (cm-1)

Return type

gamma_natural

exojax.spec.hitran.line_strength(T, logsij0, nu_lines, elower, qr)

Line strength as a function of temperature, JAX/XLA compatible

Parameters

• T – temperature (K)

• logsij0 – log(Sij(Tref)) (Tref=296K)

• nu_lines – line center wavenumber (cm-1)

• elower – elower

• qr – partition function ratio qr(T) = Q(T)/Q(Tref)

Returns

Line strength (cm)

Return type

Sij(T)

exojax.spec.hitran.line_strength_numpy(T, Sij0, nu_lines, elower, qr)

Line strength as a function of temperature, numpy version

Parameters

• T – temperature (K)

• Sij0 – line strength at Tref=296K

• elower – elower

• nu_lines – line center wavenumber

• qr – partition function ratio qr(T) = Q(T)/Q(Tref)

Returns

line strength at Ttyp

exojax.spec.hitran.normalized_doppler_sigma(T, M, R)

Normalized Dopper width (nsigmaD) by wavenumber difference at line centers.

Note

This quantity is used in MODIT. c3 is sqrt(kB/m_u)/c

Parameters

• T – temperature (K)

• M – atom/molecular mass

• R – spectral resolution

Returns

normalized Doppler width (standard deviation)

Return type

nsigma

exojax.spec.hitranapi module

API for HITRAN and HITEMP outside HAPI.

exojax.spec.hitranapi.extract_hitemp(parbz2, nurange, margin, tag)

extract .par between nurange[0] and nurange[-1]

Parameters

• parbz2 – .par.bz2 HITRAN/HITEMP file (str)

• nurange – wavenumber range list (cm-1) [min,max] or wavenumber grid

• margin – margin for nurange (cm-1)

• tag – tag for directory and output file

Returns

path of output file (pathlib)

exojax.spec.hitranapi.get_pf(M, I_list)

HITRAN/HITEMP IO for partition function

Parameters

• M – HITRAN molecule number

• I_list – HITRAN isotopologue number list

Returns

jnp array of partition function grid T_gQT: jnp array of temperature grid for gQT

Return type

gQT

exojax.spec.hitranapi.make_numtag(numinf, maxnu)

making numtag from numinf.

Parameters

• numinf – nu minimum for multiple file cases of HITEMP (H2O and CO2)

• maxnu – maximum nu

Returns

tag for wavelength range

Return type

numtag

exojax.spec.hitranapi.read_path(path)

HITRAN IO for a HITRAN/HITEMP par file.

Parameters

path – HITRAN/HITEMP par file

Returns

nu minimum for multiple file cases of HITEMP (H2O and CO2) numtag: tag for wavelength range

Return type

numinf

Note

For H2O and CO2, HITEMP provides multiple par files. numinf and numtag are the ranges and identifiers for the multiple par files.

exojax.spec.hitranapi.search_molecid(molec)

molec id from Hitran/Hitemp filename or molecule name or moleid itself.

Parameters

molec – Hitran/Hitemp filename or molecule name or molec id itself.

Returns

molecid (HITRAN molecular id)

Return type

int

exojax.spec.hitrancia module

exojax.spec.hitrancia.logacia(Tarr, nus, nucia, tcia, logac)

interpolated function of log10(alpha_CIA)

Parameters

• Tarr – temperature array

• nus – wavenumber array

• nucia – CIA wavenumber (cm-1)

• tcia – CIA temperature (K)

• logac – log10 cia coefficient

Returns

logac(Tarr, nus)

Example

>>> nucia,tcia,ac=read_cia("../../data/CIA/H2-H2_2011.cia",nus[0]-1.0,nus[-1]+1.0)
>>> logac=jnp.array(np.log10(ac))
>>> logacia(Tarr,nus,nucia,tcia,logac)

exojax.spec.hitrancia.read_cia(filename, nus, nue)

READ HITRAN CIA data.

Parameters

• filename – HITRAN CIA file name (_2011.cia)

• nus – wavenumber min (cm-1)

• nue – wavenumber max (cm-1)

Returns

wavenumber (cm-1) tcia: temperature (K) ac: cia coefficient

Return type

nucia

exojax.spec.hminus module

H minus opacity by John (1988)

exojax.spec.hminus.bound_free_absorption(wavelength_um, temperature)

bound free absorption of H-

Note

alpha has a value of 1.439e4 micron-1 K-1, the value stated in John (1988) is wrong

Parameters

• wavelength_um – wavelength in the unit of micron

• temperature – temperature in the unit of Kelvin

Returns

absorption coefficient [cm4/dyne]

exojax.spec.hminus.free_free_absorption(wavelength_um, temperature)

free free absorption of H- (coefficients from John (1988))

Note

to follow his notation (which starts at an index of 1), the 0-index components are 0 for wavelengths larger than 0.3645 micron

Parameters

• wavelength_um – wavelength in the unit of micron

• temperature – temperature in the unit of Kelvin

Returns

absorption coefficient [cm4/dyne]

exojax.spec.hminus.log_hminus_continuum(nus, temperature, number_density_e, number_density_h)

John (1988) H- continuum opacity.

Parameters

• nus – wavenumber grid (cm-1) [Nnu]

• temperature – gas temperature array [K] [Nlayer]

• number_density_e – electron number density array [Nlayer]

• number_density_h – H atom number density array [Nlayer]

Returns

log10(absorption coefficient) [Nlayer,Nnu]

exojax.spec.initspec module

Initialization for opacity computation.

The functions in this module are a wrapper for initialization processes for opacity computation.

exojax.spec.initspec.init_dit(nu_lines, nu_grid, warning=False)

Initialization for DIT. i.e. Generate nu contribution and index for the

line shape density (actually, this is a numpy version of getix)

Parameters

• nu_lines – wavenumber list of lines [Nline] (should be numpy F64)

• nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

Returns

cont (contribution) jnp.array index (index) jnp.array pmarray: (+1.,-1.) array whose length of len(nu_grid)+1

Note

cont is the contribution for i=index+1. 1 - cont is the contribution for i=index. For other i, the contribution should be zero.

exojax.spec.initspec.init_lpf(nu_lines, nu_grid)

Initialization for LPF.

Parameters

• nu_lines – wavenumber list of lines [Nline] (should be numpy F64)

• nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

Returns

numatrix [Nline,Nnu]

exojax.spec.initspec.init_modit(nu_lines, nu_grid, warning=False)

Initialization for MODIT. i.e. Generate nu contribution and index for the line shape density (actually, this is a numpy version of getix)

Parameters

• nu_lines – wavenumber list of lines [Nline] (should be numpy F64)

• nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

Returns

(contribution for q) jnp.array index: (index for q) jnp.array spectral_resolution: spectral resolution (R) pmarray: (+1.,-1.) array whose length of len(nu_grid)+1

Return type

cont

Note

cont is the contribution for i=index+1. 1 - cont is the contribution for i=index. For other i, the contribution should be zero. dq is computed using numpy not jnp.numpy. If you use jnp, you might observe a significant residual because of the float32 truncation error.

exojax.spec.initspec.init_modit_vald(nu_linesM, nus, N_usp)

Initialization for MODIT for asdb from VALD

Parameters

• nu_linesM – wavenumbers of lines for each species [N_species x N_line] (should be numpy F64)

• nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

• N_usp – number of species

Returns

(contribution) jnp.array [N_species x N_line] indexS: (index) jnp.array [N_species x N_line] R: spectral resolution

pmarray: (+1,-1) array whose length of len(nu_grid)+1

Return type

contS

exojax.spec.initspec.init_premodit(nu_lines, nu_grid, elower, gamma_ref, n_Texp, line_strength_ref, Ttyp, interval_contrast=0.1, dit_grid_resolution=0.2, warning=False)

Initialization for PreMODIT. i.e. Generate nu contribution and index for the line shape density (actually, this is a numpy version of getix)

Parameters

• nu_lines – wavenumber list of lines [Nline] (should be numpy F64)

• nu_grid – wavenumenr grid [Nnugrid] (should be numpy F64)

• elower – elower of lines

• gamma_ref – half-width at reference (alpha_ref for ExoMol, gamma_air for HITRAN/HITEMP etc)

• n_Texp – temperature exponent (n_Texp for ExoMol, n_air for HITRAN/HITEMP)

• line_strength_ref – line strength at reference temperature 296K, Sij0

• Ttyp – typical temperature in Kelvin

• interval_contrast – putting c = grid_interval_line_strength, then, the contrast of line strength between the upper and lower of the grid becomes c-order of magnitude.

• dit_grid_resolution – DIT grid resolution

Returns

contribution for wavenumber jnp.array index_nu: index for wavenumber jnp.array elower_grid: elower grid cont_broadpar: contribution for broadening parmaeters index_broadpar: index for broadening parmaeters R: spectral resolution pmarray: (+1,-1) array whose length of len(nu_grid)+1

Return type

cont_nu

Note

cont is the contribution for i=index+1. 1 - cont is the contribution for i=index. For other i, the contribution should be zero. dq is computed using numpy not jnp.numpy. If you use jnp, you might observe a significant residual because of the float32 truncation error.

exojax.spec.initspec.warn_dtype64(arr, warning, tag='')

check arr’s dtype.

Parameters

• arr – input array

• warning – True/False

• tag –

exojax.spec.initspec.warn_outside_wavenumber_grid(nu_lines, nu_grid)

Check if all the line centers are in the wavenumber grid.

Parameters

• nu_lines – line center

• nu_grid – wavenumber grid

Note

For MODIT/DIT, if the lines whose center are outside of the wavenumber grid, they contribute the edges of the wavenumber grid. This function is to check it. This warning often occurs when you set non-negative value to margin in MdbExomol, MdbHit, AdbVALD, and AdbKurucz in moldb. See #190 for the details.

exojax.spec.limb_darkening module

Limb darkening functions.

exojax.spec.limb_darkening.ld_kipping(q1, q2)

Uninformative prior conversion of the limb darkening by Kipping (arxiv:1308.0009)

Parameters

• q1 – U(0,1)

• q2 – U(0,1)

Returns

quadratic LD coefficient u1 u2: quadratic LD coefficient u2

Return type

u1

exojax.spec.lpf module

Custom JVP version of the line profile functions used in exospectral analysis.

exojax.spec.lpf.auto_xsection(nu, nu_lines, sigmaD, gammaL, Sij, memory_size=15.0)

compute cross section.

Warning

This is NOT auto-differentiable function.

Parameters

• nu – wavenumber array

• nu_lines – line center

• sigmaD – sigma parameter in Doppler profile

• gammaL – broadening coefficient in Lorentz profile

• Sij – line strength

• memory_size – memory size for numatrix0 (MB)

Returns

cross section (xsv)

Return type

numpy.array

Example

>>> from exojax.spec.lpf import auto_xsection
>>> from exojax.spec.hitran import SijT, doppler_sigma, gamma_hitran, gamma_natural
>>> from exojax.spec import moldb
>>> import numpy as np
>>> nus=np.linspace(1000.0,10000.0,900000,dtype=np.float64) #cm-1
>>> mdbCO=moldb.MdbHit('~/exojax/data/CO','05_hit12',nus)
>>> Mmol=28.010446441149536 # molecular weight
>>> Tfix=1000.0 # we assume T=1000K
>>> Pfix=1.e-3 # we compute P=1.e-3 bar
>>> Ppart=Pfix #partial pressure of CO. here we assume a 100% CO atmosphere.
>>> qt=mdbCO.qr_interp_lines(Tfix)
>>> Sij=SijT(Tfix,mdbCO.logsij0,mdbCO.nu_lines,mdbCO.elower,qt)
>>> gammaL = gamma_hitran(Pfix,Tfix, Ppart, mdbCO.n_air, mdbCO.gamma_air, mdbCO.gamma_self) + gamma_natural(mdbCO.A)
>>> sigmaD=doppler_sigma(mdbCO.nu_lines,Tfix,Mmol)
>>> nu_lines=mdbCO.nu_lines
>>> xsv=auto_xsection(nus,nu_lines,sigmaD,gammaL,Sij,memory_size=30)
 100%|████████████████████████████████████████████████████| 456/456 [00:03<00:00, 80.59it/s]

exojax.spec.lpf.exomol(mdb, Tarr, Parr, molmass)

compute molecular line information required for MODIT using Exomol mdb.

Parameters

• mdb – mdb instance

• Tarr – Temperature array

• Parr – Pressure array

• molmass – molecular mass

Returns

line intensity matrix, gammaL matrix, sigmaD matrix

exojax.spec.lpf.hjert_jvp(primals, tangents)

exojax.spec.lpf.ljert(x, a)

ljert function, consisting of a combination of imwofz and imag(asymptiotic wofz).

Parameters

• x –

• a –

Returns

L(x,a) or Imag(wofz(x+ia))

Note

ljert provides a L(x,a) function. This function accepts a scalar value as an input. Use jax.vmap to use a vector as an input.

exojax.spec.lpf.vald(adb, Tarr, PH, PHe, PHH)

Compute VALD line information required for LPF using VALD atomic database (adb)

Parameters

• adb – adb instance made by the AdbVald class in moldb.py

• Tarr – Temperature array

• PH – Partial pressure array of neutral hydrogen (H)

• PHe – Partial pressure array of neutral helium (He)

• PHH – Partial pressure array of molecular hydrogen (H2)

Returns

line intensity matrix gammaLM: gammaL matrix sigmaDM: sigmaD matrix

Return type

SijM

exojax.spec.lpf.vald_each(Tarr, PH, PHe, PHH, qt_284_T, QTmask, logsij0, nu_lines, ielem, iion, dev_nu_lines, elower, eupper, atomicmass, ionE, gamRad, gamSta, vdWdamp)

Compute VALD line information required for LPF for separated each species

Parameters

• Tarr – temperature array [N_layer]

• PH – partial pressure array of neutral hydrogen (H) [N_layer]

• PHe – partial pressure array of neutral helium (He) [N_layer]

• PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

• qt_284_T – partition function at the temperature T Q(T), for 284 species

• QTmask – array of index of Q(Tref) grid (gQT) for each line

• logsij0 – log line strength at T=Tref

• nu_lines – line center (cm-1) in np.array (float64)

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

• dev_nu_lines – line center (cm-1) in device (float32)

• elower – the lower state energy (cm-1)

• eupper – the upper state energy (cm-1)

• atomicmass – atomic mass (amu)

• ionE – ionization potential (eV)

• gamRad – log of gamma of radiation damping (s-1)

• gamSta – log of gamma of Stark damping (s-1)

• vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Returns

line intensity matrix [N_layer x N_line] gammaLM: gammaL matrix [N_layer x N_line] sigmaDM: sigmaD matrix [N_layer x N_line]

Return type

SijM

exojax.spec.lpf.voigt(nuvector, sigmaD, gammaL)

Custom JVP version of Voigt profile using Voigt-Hjerting function.

Parameters

• nu – wavenumber array

• sigmaD – sigma parameter in Doppler profile

• gammaL – broadening coefficient in Lorentz profile

Returns

Voigt profile

Return type

v

exojax.spec.lpf.voigtone(nu, sigmaD, gammaL)

Custom JVP version of (non-vmapped) Voigt function using Voigt-Hjerting function.

Parameters

• nu – wavenumber

• sigmaD – sigma parameter in Doppler profile

• gammaL – broadening coefficient in Lorentz profile

Returns

Voigt funtion

Return type

v

exojax.spec.lpf.vvoigt(numatrix, sigmaD, gammas)

Custom JVP version of vmaped voigt profile.

Parameters

• numatrix – wavenumber matrix in R^(Nline x Nwav)

• sigmaD – doppler sigma vector in R^Nline

• gammaL – gamma factor vector in R^Nline

Returns

Voigt profile vector in R^Nwav

exojax.spec.lpf.xsmatrix(numatrix, sigmaDM, gammaLM, SijM)

Custom JVP version of cross section matrix.

Parameters

• numatrix – wavenumber matrix in R^(Nline x Nwav)

• sigmaDM – doppler sigma matrix in R^(Nlayer x Nline)

• gammaLM – gamma factor matrix in R^(Nlayer x Nline)

• SijM – line strength matrix in R^(Nlayer x Nline)

Returns

cross section matrix in R^(Nlayer x Nwav)

exojax.spec.lpf.xsvector(numatrix, sigmaD, gammaL, Sij)

Custom JVP version of cross section vector.

Parameters

• numatrix – wavenumber matrix in R^(Nline x Nwav)

• sigmaD – doppler sigma vector in R^Nline

• gammaL – gamma factor vector in R^Nline

• Sij – line strength vector in R^Nline

Returns

cross section vector in R^Nwav

exojax.spec.lsd module

functions for computation of line shape density (LSD)

• there are both numpy and jnp versions. (np)*** is numpy version.

• (np)getix provides the contribution and index.

• (np)add(x)D constructs the (x)Dimensional LSD array given the contribution and index.

exojax.spec.lsd.add2D(a, w, cx, ix, cy, iy)

Add into an array when contirbutions and indices are given (2D).

Parameters

• a – lineshape density (LSD) array (np.array)

• w – weight (N)

• cx – given contribution for x

• ix – given index for x

• cy – given contribution for y

• iy – given index for y

Returns

a

exojax.spec.lsd.add3D(a, w, cx, ix, cy, iy, cz, iz)

Add into an array when contirbutions and indices are given (3D).

Parameters

• a – lineshape density (LSD) array (np.array)

• w – weight (N)

• cx – given contribution for x

• ix – given index for x

• cy – given contribution for y

• iy – given index for y

• cz – given contribution for z

• iz – given index for z

Returns

a

exojax.spec.lsd.getix(x, xv)

jnp version of getix.

Parameters

• x – x array

• xv – x grid, should be ascending order

Returns

cont (contribution) index (index)

Note

cont is the contribution for i=index+1. 1 - cont is the contribution for i=index. For other i, the contribution should be zero.

Example

>>> from exojax.spec.lsd import getix
>>> import jax.numpy as jnp
>>> y=jnp.array([1.1,4.3])
>>> yv=jnp.arange(6)
>>> getix(y,yv)
(DeviceArray([0.10000002, 0.3000002 ], dtype=float32), DeviceArray([1, 4], dtype=int32))

exojax.spec.lsd.inc2D_givenx(a, w, cx, ix, y, yv)

Compute integrated neighbouring contribution for 2D LSD (memory reduced sum) but using given contribution and index for x .

Parameters

• a – lineshape density (LSD) array (jnp.array)

• w – weight (N)

• cx – given contribution for x

• ix – given index for x

• y – y values (N)

• yv – y grid

Returns

lineshape distribution matrix (integrated neighbouring contribution for 2D)

Note

This function computes sum_n w_n fx_n otimes fy_n, where w_n is the weight, fx_n, fy_n, are the n-th NCFs for 1D. A direct sum uses huge RAM.

exojax.spec.lsd.inc3D_givenx(a, w, cx, ix, y, z, xv, yv, zv)

Compute integrated neighbouring contribution for the 3D lineshape distribution (LSD) matrix (memory reduced sum) but using given contribution and index for x .

Parameters

• a – lineshape density (LSD) array (jnp.array)

• w – weight (N)

• cx – given contribution for x

• ix – given index for x

• y – y values (N)

• z – z values (N)

• xv – x grid

• yv – y grid

• zv – z grid

Returns

lineshape distribution matrix (integrated neighbouring contribution for 3D)

Note

This function computes sum_n w_n fx_n otimes fy_n otimes fz_n, where w_n is the weight, fx_n, fy_n, and fz_n are the n-th NCFs for 1D. A direct sum uses huge RAM.

exojax.spec.lsd.npadd3D_direct1D(a, w, cx, ix, direct_cy, direct_iy, cz, iz)

numpy version: Add into an array when contirbutions and indices are given (2D+direct).

Parameters

• a – lineshape density (LSD) array (np.array)

• w – weight (N)

• cx – given contribution for x

• ix – given index for x

• direct_cy – direct contribution for y

• direct_iy – direct index for y

• cz – given contribution for z

• iz – given index for z

Returns

lineshape density a(nx,ny,nz)

exojax.spec.lsd.npadd3D_multi_index(a, w, cx, ix, cz, iz, uidx, multi_cont_lines, neighbor_uidx)

numpy version: Add into an array using multi_index system in y :param a: lineshape density (LSD) array (np.array) :param w: weight (N) :param cx: given contribution for x :param ix: given index for x :param cz: given contribution for z :param iz: given index for z

Returns

lineshape density a(nx,ny,nz)

exojax.spec.lsd.npgetix(x, xv)

numpy version of getix.

Parameters

• x – x array

• xv – x grid, should be ascending order

Returns

cont (contribution) index (index)

Note

cont is the contribution for i=index+1. 1 - cont is the contribution for i=index. For other i, the contribution should be zero.

exojax.spec.lsd.npgetix_exp(x, xv, Ttyp, conversion_dtype=<class 'numpy.float64'>)

numpy version of getix weigthed by exp(-hc/kT).

Parameters

• x – x array

• xv – x grid

• Ttyp – typical temperature for the temperature correction

• converted_dtype – data type for conversion. Needs enough large because this code uses exp.

Returns

cont (contribution) index (index)

Note

cont is the contribution for i=index+1. 1 - cont is the contribution for i=index. For other i, the contribution should be zero.

exojax.spec.make_numatrix module

exojax.spec.make_numatrix.add_nu(dd, fnu, fhatnu, Nz)

re-adding an interger part w/JIT.

Parameters

• dd – difference matrix

• fnu – integer part of wavenumber

• fhatnu – residual wavenumber

• Nz – boost factor

Returns

an integer part readded value

exojax.spec.make_numatrix.divwavnum(nu, Nz=1)

separate an integer part from a residual.

Parameters

• nu – wavenumber array

• Nz – boost factor (default=1)

Returns

integer part of wavenumber, residual wavenumber, boost factor

exojax.spec.make_numatrix.make_numatrix0(nu, hatnu, warning=True)

Generate numatrix0.

Note

Use float64 as inputs.

Parameters

• nu – wavenumber matrix (Nnu,)

• hatnu – line center wavenumber vector (Nline,), where Nm is the number of lines

• warning – True=warning on for nu.dtype=float32

Returns

numatrix (Nline,Nnu)

exojax.spec.make_numatrix.make_numatrix0_subtract(nu, hatnu, Nz=1, warning=True)

Generate numatrix0 using gpu.

Note

This function computes a wavenumber matrix using XLA. Because XLA does not support float64, a direct computation sometimes results in large uncertainity. For instace, let’s assume nu=2000.0396123 cm-1 and hatnu=2000.0396122 cm-1. If applying float32, we get np.float32(2000.0396123)-np.float32(2000.0396122) = 0.0. But, after subtracting 2000 from both nu and hatnu, we get np.float32(0.0396123)-np.float32(0.0396122)=1.0058284e-07. make_numatrix0 does such computation. Nz=1 means we subtract a integer part (i.e. 2000), Nz=10 means we subtract 2000.0, and Nz=10 means we subtract 2000.00.

Parameters

• nu – wavenumber matrix (Nnu,)

• hatnu – line center wavenumber vector (Nline,), where Nm is the number of lines

• Nz – boost factor (default=1)

• warning – True=warning on for nu.dtype=float32

Returns

wavenumber matrix w/ no shift

Return type

numatrix0

exojax.spec.make_numatrix.subtract_nu(dnu, dhatnu)

compute nu - hatnu by subtracting an integer part w/JIT

Parameters

• dnu – residual wavenumber array

• dhatnu – residual line center array

Returns

difference matrix

exojax.spec.modit module

Line profile computation using Discrete Integral Transform.

• MODIT is Modified version of the Discrete Integral Transform for rapid spectral synthesis, originally proposed by D.C.M van den Bekerom and E.Pannier. See Section 2.1.2 in Paper I.

• This module consists of selected functions in addit package.

• The concept of “folding” can be understood by reading the discussion by D.C.M van den Bekerom.

• See also DIT for non evenly-spaced linear grid by D.C.M van den Bekerom, as a reference of this code.

exojax.spec.modit.calc_xsection_from_lsd(Slsd, R, pmarray, nsigmaD, nu_grid, log_ngammaL_grid)

Compute cross section from LSD in MODIT algorithm

The original code is rundit_fold_logredst in addit package ). MODIT folded voigt for ESLOG for reduced wavenumebr inputs (against the truncation error) for a constant normalized beta

Parameters

• Slsd – line shape density

• R – spectral resolution

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• nsigmaD – normaized Gaussian STD

• nu_grid – linear wavenumber grid

• log_gammaL_grid – logarithm of gammaL grid

Note: When you have the error such as: “failed to initialize batched cufft plan with customized allocator: Allocating 8000000160 bytes exceeds the memory limit of 4294967296 bytes.” consider to use moditscanfft.calc_xsection_from_lsd, instead.

Returns

Cross section in the log nu grid

exojax.spec.modit.dgmatrix(x, dit_grid_resolution=0.1, adopt=True)

DIT GRID MATRIX (alias)

Parameters

• x – simgaD or gammaL matrix (Nlayer x Nline)

• dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns

grid for DIT (Nlayer x NDITgrid)

exojax.spec.modit.ditgrid(x, dit_grid_resolution=0.1, adopt=True)

DIT GRID (deprecated).

Parameters

• x – simgaD or gammaL array (Nline)

• dit_grid_resolution – grid resolution. res=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be res exactly.

Returns

grid for DIT

exojax.spec.modit.exomol(mdb, Tarr, Parr, R, molmass)

compute molecular line information required for MODIT using Exomol mdb.

Parameters

• mdb – mdb instance

• Tarr – Temperature array

• Parr – Pressure array

• R – spectral resolution

• molmass – molecular mass

Returns

line intensity matrix, normalized gammaL matrix, normalized sigmaD matrix

exojax.spec.modit.hitran(mdb, Tarr, Parr, Pself, R, molmass)

compute molecular line information required for MODIT using HITRAN/HITEMP mdb.

Parameters

• mdb – mdb instance

• Tarr – Temperature array

• Parr – Pressure array

• Pself – Partial pressure array

• R – spectral resolution

• molmass – molecular mass

Returns

line intensity matrix, normalized gammaL matrix, normalized sigmaD matrix

exojax.spec.modit.minmax_dgmatrix(x, dit_grid_resolution=0.1, adopt=True)

compute MIN and MAX DIT GRID MATRIX.

Parameters

• x – gammaL matrix (Nlayer x Nline)

• dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns

minimum and maximum for DIT (dgm_minmax)

exojax.spec.modit.precompute_dgmatrix(set_gm_minmax, dit_grid_resolution=0.1, adopt=True)

Precomputing MODIT GRID MATRIX for normalized GammaL.

Parameters

• set_gm_minmax – set of gm_minmax for different parameters [Nsample, Nlayers, 2], 2=min,max

• dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns

grid for DIT (Nlayer x NDITgrid)

exojax.spec.modit.set_ditgrid_matrix_exomol(mdb, fT, Parr, R, molmass, dit_grid_resolution, *kargs)

Easy Setting of DIT Grid Matrix (dgm) using Exomol.

Parameters

• mdb – mdb instance

• fT – function of temperature array

• Parr – pressure array

• R – spectral resolution

• molmass – molecular mass

• dit_grid_resolution – resolution of dgm

• *kargs – arguments for fT

Returns

DIT Grid Matrix (dgm) of normalized gammaL

Example

>>> fT = lambda T0,alpha: T0[:,None]*(Parr[None,:]/Pref)**alpha[:,None]
>>> T0_test=np.array([1100.0,1500.0,1100.0,1500.0])
>>> alpha_test=np.array([0.2,0.2,0.05,0.05])
>>> dit_grid_resolution=0.2
>>> dgm_ngammaL=setdgm_exomol(mdbCH4,fT,Parr,R,molmassCH4,dit_grid_resolution,T0_test,alpha_test)

exojax.spec.modit.set_ditgrid_matrix_hitran(mdb, fT, Parr, Pself_ref, R, molmass, dit_grid_resolution, *kargs)

Easy Setting of DIT Grid Matrix (dgm) using HITRAN/HITEMP.

Parameters

• mdb – mdb instance

• fT – function of temperature array

• Parr – pressure array

• Pself_ref – reference partial pressure array

• R – spectral resolution

• molmass – molecular mass

• dit_grid_resolution – resolution of dgm

• *kargs – arguments for fT

Returns

DIT Grid Matrix (dgm) of normalized gammaL

Example

>>> fT = lambda T0,alpha: T0[:,None]*(Parr[None,:]/Pref)**alpha[:,None]
>>> T0_test=np.array([1100.0,1500.0,1100.0,1500.0])
>>> alpha_test=np.array([0.2,0.2,0.05,0.05])
>>> dit_grid_resolution=0.2
>>> dgm_ngammaL=setdgm_hitran(mdbCH4,fT,Parr,Pself,R,molmassCH4,dit_grid_resolution,T0_test,alpha_test)

exojax.spec.modit.set_ditgrid_matrix_vald_all(asdb, PH, PHe, PHH, R, fT, dit_grid_resolution, *kargs)

Easy Setting of DIT Grid Matrix (dgm) using VALD.

Parameters

• asdb – asdb instance made by the AdbSepVald class in moldb.py

• PH – partial pressure array of neutral hydrogen (H) [N_layer]

• PHe – partial pressure array of neutral helium (He) [N_layer]

• PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

• R – spectral resolution

• fT – function of temperature array

• dit_grid_resolution – resolution of dgm

• *kargs – arguments for fT

Returns

DIT Grid Matrix (dgm) of normalized gammaL [N_species x N_layer x N_DITgrid]

Return type

dgm_ngammaLS

Example

>>> fT = lambda T0,alpha:  T0[:,None]*(Parr[None,:]/Pref)**alpha[:,None]
>>> T0_test=np.array([3000.0,4000.0,3000.0,4000.0])
>>> alpha_test=np.array([0.2,0.2,0.05,0.05])
>>> dit_grid_resolution=0.2
>>> dgm_ngammaLS = setdgm_vald_all(asdb, PH, PHe, PHH, R, fT, dit_grid_resolution, T0_test, alpha_test)

exojax.spec.modit.set_ditgrid_matrix_vald_each(ielem, iion, atomicmass, ionE, dev_nu_lines, logsij0, elower, eupper, gamRad, gamSta, vdWdamp, QTmask, T_gQT, gQT_284species, PH, PHe, PHH, R, fT, dit_grid_resolution, *kargs)

Easy Setting of DIT Grid Matrix (dgm) using VALD.

Parameters

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

• atomicmass – atomic mass (amu)

• ionE – ionization potential (eV)

• dev_nu_lines – line center (cm-1) in device

• logsij0 – log line strength at T=Tref

• elower – the lower state energy (cm-1)

• eupper – the upper state energy (cm-1)

• gamRad – log of gamma of radiation damping (s-1)

• gamSta – log of gamma of Stark damping (s-1)

• vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

• T_gQT – temperature in the grid obtained from the adb instance

• gQT_284species – partition function in the grid from the adb instance

• QTmask – array of index of Q(Tref) grid (gQT) for each line

• PH – partial pressure array of neutral hydrogen (H) [N_layer]

• PHe – partial pressure array of neutral helium (He) [N_layer]

• PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

• R – spectral resolution

• fT – function of temperature array

• dit_grid_resolution – resolution of dgm

• *kargs – arguments for fT

Returns

DIT Grid Matrix (dgm) of normalized gammaL [N_layer x N_DITgrid]

Return type

dgm_ngammaL

exojax.spec.modit.setdgm_exomol(mdb, fT, Parr, R, molmass, dit_grid_resolution, *kargs)

exojax.spec.modit.setdgm_hitran(mdb, fT, Parr, Pself_ref, R, molmass, dit_grid_resolution, *kargs)

exojax.spec.modit.setdgm_vald_all(asdb, PH, PHe, PHH, R, fT, dit_grid_resolution, *kargs)

exojax.spec.modit.setdgm_vald_each(ielem, iion, atomicmass, ionE, dev_nu_lines, logsij0, elower, eupper, gamRad, gamSta, vdWdamp, QTmask, T_gQT, gQT_284species, PH, PHe, PHH, R, fT, dit_grid_resolution, *kargs)

exojax.spec.modit.vald_all(asdb, Tarr, PH, PHe, PHH, R)

Compute atomic line information required for MODIT for separated ALL species, using VALD separated atomic database (asdb).

Parameters

• asdb – asdb instance made by the AdbSepVald class in moldb.py

• Tarr – temperature array [N_layer]

• PH – partial pressure array of neutral hydrogen (H) [N_layer]

• PHe – partial pressure array of neutral helium (He) [N_layer]

• PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

• R – spectral resolution [scalar]

Returns

line intensity matrix [N_species x N_layer x N_line] ngammaLMS: normalized gammaL matrix [N_species x N_layer x N_line] nsigmaDlS: normalized sigmaD matrix [N_species x N_layer x 1]

Return type

SijMS

exojax.spec.modit.vald_each(Tarr, PH, PHe, PHH, R, qt_284_T, QTmask, ielem, iion, atomicmass, ionE, dev_nu_lines, logsij0, elower, eupper, gamRad, gamSta, vdWdamp)

Compute atomic line information required for MODIT for separated EACH species, using parameters attributed in VALD separated atomic database (asdb).

Parameters

• Tarr – temperature array [N_layer]

• PH – partial pressure array of neutral hydrogen (H) [N_layer]

• PHe – partial pressure array of neutral helium (He) [N_layer]

• PHH – partial pressure array of molecular hydrogen (H2) [N_layer]

• R – spectral resolution [scalar]

• qt_284_T – partition function at the temperature T Q(T), for 284 species

• QTmask – array of index of Q(Tref) grid (gQT) for each line

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

• atomicmass – atomic mass (amu)

• ionE – ionization potential (eV)

• dev_nu_lines – line center (cm-1) in device

• logsij0 – log line strength at T=Tref

• elower – the lower state energy (cm-1)

• eupper – the upper state energy (cm-1)

• gamRad – log of gamma of radiation damping (s-1)

• gamSta – log of gamma of Stark damping (s-1)

• vdWdamp – log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Returns

line intensity matrix [N_layer x N_line] ngammaLM: normalized gammaL matrix [N_layer x N_line] nsigmaDl: normalized sigmaD matrix [N_layer x 1]

Return type

SijM

exojax.spec.modit.xsmatrix(cnu, indexnu, R, pmarray, nsigmaDl, ngammaLM, SijM, nu_grid, dgm_ngammaL)

Cross section matrix for xsvector (MODIT)

Parameters

• cnu – contribution by npgetix for wavenumber

• indexnu – index by npgetix for wavenumber

• R – spectral resolution

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• nu_lines – line center (Nlines)

• nsigmaDl – normalized doppler sigma in layers in R^(Nlayer x 1)

• ngammaLM – gamma factor matrix in R^(Nlayer x Nline)

• SijM – line strength matrix in R^(Nlayer x Nline)

• nu_grid – linear wavenumber grid

• dgm_ngammaL – DIT Grid Matrix for normalized gammaL R^(Nlayer, NDITgrid)

Returns

cross section matrix in R^(Nlayer x Nwav)

exojax.spec.modit.xsmatrix_vald(cnuS, indexnuS, R, pmarray, nsigmaDlS, ngammaLMS, SijMS, nu_grid, dgm_ngammaLS)

Cross section matrix for xsvector (MODIT) for VALD lines (asdb)

Parameters

• cnuS – contribution by npgetix for wavenumber [N_species x N_line]

• indexnuS – index by npgetix for wavenumber [N_species x N_line]

• R – spectral resolution

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• nsigmaDlS – normalized sigmaD matrix [N_species x N_layer x 1]

• ngammaLMS – normalized gammaL matrix [N_species x N_layer x N_line]

• SijMS – line intensity matrix [N_species x N_layer x N_line]

• nu_grid – linear wavenumber grid

• dgm_ngammaLS – DIT Grid Matrix (dgm) of normalized gammaL [N_species x N_layer x N_DITgrid]

Returns

cross section matrix [N_species x N_layer x N_wav]

Return type

xsmS

exojax.spec.modit.xsvector(cnu, indexnu, R, pmarray, nsigmaD, ngammaL, S, nu_grid, ngammaL_grid)

Cross section vector (MODIT)

Parameters

• cnu – contribution by npgetix for wavenumber

• indexnu – index by npgetix for wavenumber

• R – spectral resolution

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• nsigmaD – normaized Gaussian STD

• gammaL – Lorentzian half width (Nlines)

• S – line strength (Nlines)

• nu_grid – linear wavenumber grid

• gammaL_grid – gammaL grid

Returns

Cross section in the log nu grid

exojax.spec.modit_scanfft module

Line profile computation using Discrete Integral Transform using scan+fft (#277).

• MODIT using scan+fft allows > 4GB fft memory. but approximately 2 times slower than modit.

• When you use modit and get the error such as “failed to initialize batched cufft plan with customized allocator: Allocating 8000000160 bytes exceeds the memory limit of 4294967296 bytes.”,

you should consider to modit_scanfft

exojax.spec.modit_scanfft.calc_xsection_from_lsd_scanfft(Slsd, R, pmarray, nsigmaD, nu_grid, log_ngammaL_grid)

Compute cross section from LSD in MODIT algorithm using scan+fft to avoid 4GB memory limit in fft (see #277)

Parameters

• Slsd – line shape density

• R – spectral resolution

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• nsigmaD – normaized Gaussian STD

• nu_grid – linear wavenumber grid

• log_gammaL_grid – logarithm of gammaL grid

Returns

Cross section in the log nu grid

exojax.spec.modit_scanfft.xsmatrix_scanfft(cnu, indexnu, R, pmarray, nsigmaDl, ngammaLM, SijM, nu_grid, dgm_ngammaL)

Cross section matrix for xsvector (MODIT), scan+fft

Parameters

• cnu – contribution by npgetix for wavenumber

• indexnu – index by npgetix for wavenumber

• R – spectral resolution

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• nu_lines – line center (Nlines)

• nsigmaDl – normalized doppler sigma in layers in R^(Nlayer x 1)

• ngammaLM – gamma factor matrix in R^(Nlayer x Nline)

• SijM – line strength matrix in R^(Nlayer x Nline)

• nu_grid – linear wavenumber grid

• dgm_ngammaL – DIT Grid Matrix for normalized gammaL R^(Nlayer, NDITgrid)

Returns

cross section matrix in R^(Nlayer x Nwav)

exojax.spec.modit_scanfft.xsmatrix_vald_scanfft(cnuS, indexnuS, R, pmarray, nsigmaDlS, ngammaLMS, SijMS, nu_grid, dgm_ngammaLS)

Cross section matrix for xsvector (MODIT) with scan+fft, for VALD lines (asdb)

Parameters

• cnuS – contribution by npgetix for wavenumber [N_species x N_line]

• indexnuS – index by npgetix for wavenumber [N_species x N_line]

• R – spectral resolution

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• nsigmaDlS – normalized sigmaD matrix [N_species x N_layer x 1]

• ngammaLMS – normalized gammaL matrix [N_species x N_layer x N_line]

• SijMS – line intensity matrix [N_species x N_layer x N_line]

• nu_grid – linear wavenumber grid

• dgm_ngammaLS – DIT Grid Matrix (dgm) of normalized gammaL [N_species x N_layer x N_DITgrid]

Returns

cross section matrix [N_species x N_layer x N_wav]

Return type

xsmS

exojax.spec.modit_scanfft.xsvector_scanfft(cnu, indexnu, R, pmarray, nsigmaD, ngammaL, S, nu_grid, ngammaL_grid)

Cross section vector (MODIT scanfft)

Parameters

• cnu – contribution by npgetix for wavenumber

• indexnu – index by npgetix for wavenumber

• R – spectral resolution

• pmarray – (+1,-1) array whose length of len(nu_grid)+1

• nsigmaD – normaized Gaussian STD

• gammaL – Lorentzian half width (Nlines)

• S – line strength (Nlines)

• nu_grid – linear wavenumber grid

• gammaL_grid – gammaL grid

Returns

Cross section in the log nu grid

exojax.spec.moldb module

Molecular database (MDB) class.

class exojax.spec.moldb.AdbKurucz(path, nurange=[- inf, inf], margin=0.0, crit=0.0, Irwin=False, gpu_transfer=True)

Bases: object

atomic database from Kurucz (http://kurucz.harvard.edu/linelists/)

AdbKurucz is a class for Kurucz line list.

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1) (#NOT frequency in (s-1))

Type

nd array

dev_nu_lines

line center (cm-1) in device

Type

jnp array

Sij0

line strength at T=Tref (cm)

Type

nd array

logsij0

log line strength at T=Tref

Type

jnp array

A

Einstein A coeeficient in (s-1)

Type

jnp array

elower

the lower state energy (cm-1)

Type

jnp array

eupper

the upper state energy (cm-1)

Type

jnp array

gupper

(jnp array): upper statistical weight

jlower

lower J (rotational quantum number, total angular momentum)

Type

jnp array

jupper

upper J

Type

jnp array

QTmask

identifier of species for Q(T)

Type

jnp array

ielem

atomic number (e.g., Fe=26)

Type

jnp array

iion

ionized level (e.g., neutral=1, singly ionized=2, etc.)

Type

jnp array

gamRad

log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

Type

jnp array

gamSta

log of gamma of Stark damping (s-1)

Type

jnp array

vdWdamp

log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Type

jnp array

Atomic_gQT(atomspecies)

Select grid of partition function especially for the species of interest.

Parameters

atomspecies – species e.g., “Fe 1”, “Sr 2”, etc.

Returns

grid Q(T) for the species

Return type

gQT

QT_interp(atomspecies, T)

interpolated partition function The partition functions of Barklem & Collet (2016) are adopted.

Parameters

• atomspecies – species e.g., “Fe 1”

• T – temperature

Returns

interpolated in jnp.array for the Atomic Species

Return type

Q(T)

QT_interp_284(T)

interpolated partition function of all 284 species.

Parameters

T – temperature

Returns

interpolated in jnp.array for all 284 Atomic Species

Return type

Q(T)*284

QT_interp_Irwin_Fe(T, atomspecies='Fe 1')

interpolated partition function This function is for the exceptional case where you want to adopt partition functions of Irwin (1981) for Fe I (Other species are not yet implemented).

Parameters

• atomspecies – species e.g., “Fe 1”

• T – temperature

Returns

interpolated in jnp.array for the Atomic Species

Return type

Q(T)

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array.

make_QTmask(ielem, iion)

Convert the species identifier to the index for Q(Tref) grid (gQT) for each line.

Parameters

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly)

Returns

array of index of Q(Tref) grid (gQT) for each line

Return type

QTmask_sp

masking(mask)

applying mask

Parameters

mask – mask to be applied. self.mask is updated.

qr_interp(atomspecies, T)

interpolated partition function ratio The partition functions of Barklem & Collet (2016) are adopted.

Parameters

• T – temperature

• atomspecies – species e.g., “Fe 1”

Returns

interpolated in jnp.array

Return type

qr(T)=Q(T)/Q(Tref)

qr_interp_Irwin_Fe(T, atomspecies='Fe 1')

interpolated partition function ratio This function is for the exceptional case where you want to adopt partition functions of Irwin (1981) for Fe I (Other species are not yet implemented).

Parameters

• T – temperature

• atomspecies – species e.g., “Fe 1”

Returns

interpolated in jnp.array

Return type

qr(T)=Q(T)/Q(Tref)

class exojax.spec.moldb.AdbSepVald(adb)

Bases: object

atomic database from VALD3 with an additional axis for separating each species (atom or ion)

AdbSepVald is a class for VALD3.

nu_lines

line center (cm-1) (#NOT frequency in (s-1))

Type

nd array

dev_nu_lines

line center (cm-1) in device

Type

jnp array

logsij0

log line strength at T=Tref

Type

jnp array

elower

the lower state energy (cm-1)

Type

jnp array

eupper

the upper state energy (cm-1)

Type

jnp array

QTmask

identifier of species for Q(T)

Type

jnp array

ielem

atomic number (e.g., Fe=26)

Type

jnp array

iion

ionized level (e.g., neutral=1, singly ionized=2, etc.)

Type

jnp array

atomicmass

atomic mass (amu)

Type

jnp array

ionE

ionization potential (eV)

Type

jnp array

gamRad

log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

Type

jnp array

gamSta

log of gamma of Stark damping (s-1)

Type

jnp array

vdWdamp

log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Type

jnp array

uspecies

unique combinations of ielem and iion [N_species x 2(ielem and iion)]

Type

jnp array

N_usp

number of species (atoms and ions)

Type

int

L_max

maximum number of spectral lines for a single species

Type

int

gQT_284species

partition function grid of 284 species

Type

jnp array

T_gQT

temperatures in the partition function grid

Type

jnp array

class exojax.spec.moldb.AdbVald(path, nurange=[- inf, inf], margin=0.0, crit=0.0, Irwin=False, gpu_transfer=True)

Bases: object

atomic database from VALD3 (http://vald.astro.uu.se/)

AdbVald is a class for VALD3.

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1) (#NOT frequency in (s-1))

Type

nd array

dev_nu_lines

line center (cm-1) in device

Type

jnp array

Sij0

line strength at T=Tref (cm)

Type

nd array

logsij0

log line strength at T=Tref

Type

jnp array

A

Einstein A coeeficient in (s-1)

Type

jnp array

elower

the lower state energy (cm-1)

Type

jnp array

eupper

the upper state energy (cm-1)

Type

jnp array

gupper

(jnp array): upper statistical weight

jlower

lower J (rotational quantum number, total angular momentum)

Type

jnp array

jupper

upper J

Type

jnp array

QTmask

identifier of species for Q(T)

Type

jnp array

ielem

atomic number (e.g., Fe=26)

Type

jnp array

iion

ionized level (e.g., neutral=1, singly ionized=2, etc.)

Type

jnp array

solarA

solar abundance (log10 of number density in the Sun)

Type

jnp array

atomicmass

atomic mass (amu)

Type

jnp array

ionE

ionization potential (eV)

Type

jnp array

gamRad

log of gamma of radiation damping (s-1) #(https://www.astro.uu.se/valdwiki/Vald3Format)

Type

jnp array

gamSta

log of gamma of Stark damping (s-1)

Type

jnp array

vdWdamp

log of (van der Waals damping constant / neutral hydrogen number) (s-1)

Type

jnp array

Note

For the first time to read the VALD line list, it is converted to HDF/vaex. After the second-time, we use the HDF5 format with vaex instead.

Atomic_gQT(atomspecies)

Select grid of partition function especially for the species of interest.

Parameters

atomspecies – species e.g., “Fe 1”, “Sr 2”, etc.

Returns

grid Q(T) for the species

Return type

gQT

QT_interp(atomspecies, T)

interpolated partition function The partition functions of Barklem & Collet (2016) are adopted.

Parameters

• atomspecies – species e.g., “Fe 1”

• T – temperature

Returns

interpolated in jnp.array for the Atomic Species

Return type

Q(T)

QT_interp_284(T)

interpolated partition function of all 284 species.

Parameters

T – temperature

Returns

interpolated in jnp.array for all 284 Atomic Species

Return type

Q(T)*284

QT_interp_Irwin_Fe(T, atomspecies='Fe 1')

interpolated partition function This function is for the exceptional case where you want to adopt partition functions of Irwin (1981) for Fe I (Other species are not yet implemented).

Parameters

• atomspecies – species e.g., “Fe 1”

• T – temperature

Returns

interpolated in jnp.array for the Atomic Species

Return type

Q(T)

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array.

make_QTmask(ielem, iion)

Convert the species identifier to the index for Q(Tref) grid (gQT) for each line.

Parameters

• ielem – atomic number (e.g., Fe=26)

• iion – ionized level (e.g., neutral=1, singly ionized=2, etc.)

Returns

array of index of Q(Tref) grid (gQT) for each line

Return type

QTmask_sp

masking(mask)

applying mask.

Parameters

mask – mask to be applied. self.mask is updated.

qr_interp(atomspecies, T)

interpolated partition function ratio The partition functions of Barklem & Collet (2016) are adopted.

Parameters

• T – temperature

• atomspecies – species e.g., “Fe 1”

Returns

interpolated in jnp.array

Return type

qr(T)=Q(T)/Q(Tref)

qr_interp_Irwin_Fe(T, atomspecies='Fe 1')

interpolated partition function ratio This function is for the exceptional case where you want to adopt partition functions of Irwin (1981) for Fe I (Other species are not yet implemented).

Parameters

• T – temperature

• atomspecies – species e.g., “Fe 1”

Returns

interpolated in jnp.array

Return type

qr(T)=Q(T)/Q(Tref)

class exojax.spec.moldb.MdbExomol(path, nurange=[- inf, inf], margin=0.0, crit=0.0, Ttyp=1000.0, bkgdatm='H2', broadf=True, gpu_transfer=True, inherit_dataframe=False, local_databases='./')

Bases: radis.api.exomolapi.MdbExomol

molecular database of ExoMol.

MdbExomol is a class for ExoMol.

simple_molecule_name

simple molecule name

nurange

nu range [min,max] (cm-1)

nu_lines

line center (cm-1)

Type

nd array

Sij0

line strength at T=Tref (cm)

Type

nd array

logsij0

log line strength at T=Tref

Type

jnp array

A

Einstein A coeeficient

Type

jnp array

gamma_natural

gamma factor of the natural broadening

Type

DataFrame or jnp array

elower

the lower state energy (cm-1)

Type

DataFrame or jnp array

gpp

statistical weight

Type

DataFrame or jnp array

jlower

J_lower

Type

DataFrame or jnp array

jupper

J_upper

Type

DataFrame or jnp array

n_Texp

temperature exponent

Type

DataFrame or jnp array

dev_nu_lines

line center in device (cm-1)

Type

jnp array

alpha_ref

alpha_ref (gamma0), Lorentzian half-width at reference temperature and pressure in cm-1/bar

Type

jnp array

n_Texp_def

default temperature exponent in .def file, used for jlower not given in .broad

alpha_ref_def

default alpha_ref (gamma0) in .def file, used for jlower not given in .broad

A

QT_interp(T)

interpolated partition function.

Parameters

T – temperature

Returns

Q(T) interpolated in jnp.array

Sij0

compute_load_mask(df)

elower

eupper

generate_jnp_arrays()

(re)generate jnp.arrays.

Note

We have nd arrays and jnp arrays. We usually apply the mask to nd arrays and then generate jnp array from the corresponding nd array. For instance, self._A is nd array and self.A is jnp array.

gupper

instances_from_dataframes(df_load_mask)

generate instances from (usually masked) data farame

Parameters

df_load_mask (DataFrame) – (masked) data frame

Raises

ValueError – _description_

jlower

jupper

logsij0

nu_lines

qr_interp(T)

interpolated partition function ratio.

Parameters

T – temperature

Returns

qr(T)=Q(T)/Q(Tref) interpolated in jnp.array

exojax.spec.moldb.MdbHit

alias of exojax.spec.api.MdbHitemp

exojax.spec.molinfo module

exojax.spec.molinfo.molmass(molecule, db_HIT=False)

provide molecular mass from the molecular name.

Parameters

• molecule – molecular name e.g. CO2, He

• db_HIT – if True, use the molecular mass considering the natural terrestrial abundance and mass of each isotopologue provided by HITRAN (https://hitran.org/docs/iso-meta/)

Returns

molecular mass

Example

>>> from exojax.spec.moinfo import molmass
>>> print(molmass("H2"))
>>> 2.01588
>>> print(molmass("CO2"))
>>> 44.0095
>>> print(molmass("He"))
>>> 4.002602
>>> print(molmass("air"))
>>> 28.97

exojax.spec.opacitytools module

Extract tau=1 height pressure at different wavelengths

exojax.spec.opacitytools.pressure_at_given_opacity(dtau, Parr, tauextracted=1.0)

Extract pressure of tau=1(or a given value) at different wavelengths

Parameters

• dtau – delta tau for each layer [N_layer x N_nu]

• Parr – pressure at each layer [N_layer]

• tauextracted – the tau value at which pressure is extracted

Returns

[N_nu]

Return type

P_tauone

Note

Return 0 if tau is too optically thin and does not reach tauextracted.

exojax.spec.planck module

planck functions.

• The units are nu [1/cm], f [1/s], wav [cm]. In this module, the input variable is always wavenumber [cm].

• nu = f/c = 1/lambda.

• Recall nu B_nu = lambda B_lambda = f B_f.

• B_f (erg/s/cm2/Hz) = B_nu/c (erg/s/cm2/cm-1)

exojax.spec.planck.piBarr(T, nus)

pi B_nu (Planck Function)

Parameters

• T – temperature [K]

• nus – wavenumber [cm-1]

Returns

pi B_nu (erg/s/cm2/cm-1) [Nlayer x Nnu]

Note

hcperk = hc/k in cgs, fac = 2*h*c*c*pi in cgs

exojax.spec.plg module

Pseudo line generator

exojax.spec.plg.MdbExomol_plg(path_database, nus, Tgue, errTgue=500.0, Nelower=7, assess_width=1.0, threshold_persist_freezing=10000.0, crit=0.0, coefTgue=0.0)

Obtain molecular database (mdb) from the Exomol while reducing the number of weak lines by plg. (This function summarizes the plg procedure.)

Parameters

• path_database – path for Exomol data directory/tag. For instance, “/home/CO/12C-16O/Li2015”

• nus – wavenumber grid for model

• Tgue – rough guess on the typical atmospheric temperature

• errTgue – expected one-sided error of Tgue

• Nelower – The number of elower grid

• assess_width – To save computation time, let us use only this wavelength width in the middle of the whole range to optimize coefTgue. (Note that too narrow might cause a ValueError.)

• threshold_persist_freezing – How weak lines compared to the deepest one will you persist freezing (not retaken)?

• crit – line strength lower limit for extraction in exojax.spec.moldb.MdbExomol

• coefTgue – coefficient for Tgue to optimize elower_grid

Returns

molecular database instance cnu: contribution of wavenumber for LSD indexnu: nu index

Return type

mdb

exojax.spec.plg.diff_frozen_vs_pseudo(coefTgue_init, Tgue, errTgue, Mgue, Rgue, MMRgue, nus, mdb_orig, molmass, Nelower, verbose=False)

Evaluate difference between pseudo lines and the original lines

Parameters

• coefTgue_init – initial value of coefTgue (list/array with length=1)

• Tgue – rough guess on the typical atmospheric temperature

• errTgue – expected one-sided error of Tgue

• Mgue – rough guess on the mass

• Rgue – rough guess on the radius

• MMRgue – rough guess on the MMR of the molecule

• nus – wavenumber grid for model

• mdb_orig – original molecular database before compression (instance made by the MdbExomol/MdbHit class in moldb.py)

• molmass – mass of the molecule (amu)

• Nelower – # of elower grid

• verbose – vervose printing or not

Returns

abs(np.mean(mu_pseudo - mu_orig))

exojax.spec.plg.gather_lines(mdb, Na, Nnugrid, Nelower, nu_grid, cnu, indexnu, qlogsij0, qcnu, elower_grid, alpha_ref_grid, n_Texp_grid, frozen_mask, nonzeropl_mask)

gather pseudo lines and unfrozen lines into lines for exomol

Parameters

• mdb – molecular database (instance made by the MdbExomol/MdbHit class in moldb.py)

• Na – the number of the additional condition grid (gammaL set for Exomol)

• Nnugrid – # of nu_grid

• Nelower – # of elower grid

• nu_grid – nu grid

• cnu – contribution of wavenumber for LSD

• indexnu – index nu

• qlogsij0 – log line strength

• qcnu – cnu for pseudo line (contribution of wavenumber for LSD)

• elower_grid – elower_grid

• alpha_ref_grid – grid of alpha_ref

• n_Texp_grid – grid of n_Texp

• frozen_mask – mask for frozen lines into pseudo lines

• nonzeropl_mask – mask for pseudo-lines w/ non-zero

Returns

mdb for the gathered lines cnu for the gathered lines indexnu for the gathered lines

exojax.spec.plg.get_qlogsij0(cnu, indexnu, Nnugrid, logsij0, expme, expme_grid, Nelower=10, Ncrit=0)

gather (freeze) lines

Parameters

• cnu – contribution of wavenumber for LSD

• indexnu – index of wavenumber

• logsij0 – log line strength

• expme – exp(-elower/kT0)

• expme_grid – exp(-elower/kT0)_grid

• Nelower – # of division of elower between min to max values

exojax.spec.plg.get_qlogsij0_addcon(indexa, Na, cnu, indexnu, Nnugrid, mdb, expme, expme_grid, Ncrit=0, Tuplim=1000.0, Tmargin=0.0, threshold_persist_freezing=10000.0)

gather (freeze) lines w/ additional indexing

Parameters

• indexa – the indexing of the additional condition

• Na – the number of the additional condition grid

• cnu – contribution of wavenumber for LSD

• indexnu – index of wavenumber

• Nnugrid – number of nu grid

• mdb – molecular database (instance made by the MdbExomol/MdbHit class in moldb.py)

• expme – array of exponentials of functions of elower: exp(- hcperk*(elower/Tuplimc - elower/Tref) - preov)

• expme_grid – grid of expme

• Ncrit – frozen line number per bin

• Tuplim – rough guess on the typical atmospheric temperature

• Tmargin – margin even above Tuplim to prevent freeze of lines that become strong enough as temperature rises slightly. (more needed for cooler objects)

• threshold_persist_freezing – How weak lines compared to the deepest one will you persist freezing (not retaken)?

Returns

log line strength qcnu: cnu for pseudo line (contribution of wavenumber for LSD) num_unique: number of the lines in each bin of grid frozen_mask: mask for frozen lines into pseudo lines

Return type

qlogsij0

exojax.spec.plg.make_gamma_grid_exomol(mdb)

Make grids of parameters for Lorentzian width and an associated index.

Parameters

mdb – molecular database (instance made by the MdbExomol/MdbHit class in moldb.py)

Returns

grid of alpha_ref (gamma0) n_Texp_grid: grid of temperature exponent of gamma index_gamma: grid-index of the parameters above for each original line

Return type

alpha_ref_grid

exojax.spec.plg.optimize_coefTgue(Tgue, nus, mdb, molmass, Nelower, errTgue=500.0, Mgue=41.0, Rgue=1.0, MMRgue=0.001)

Optimize coefTgue for adjusting elower_grid

Parameters

• Tgue – rough guess on the typical atmospheric temperature

• nus – wavenumber grid for model

• mdb – molecular database (instance made by the MdbExomol/MdbHit class in moldb.py)

• molmass – mass of the molecule (amu)

• Nelower – # of elower grid

• errTgue – expected one-sided error of Tgue

• Mgue – rough guess on the mass

• Rgue – rough guess on the radius

• MMRgue – rough guess on the MMR of the molecule

Returns

optimized coefTgue

exojax.spec.plg.plg_elower(cnu, indexnu, Nnugrid, logsij0, elower, elower_grid=None, Nelower=10, Ncrit=0, reshape=True)

Pseudo Line Grid for elower

Parameters

• cnu – contribution of wavenumber for LSD

• indexnu – index of wavenumber

• Nnugrid – number of Ngrid

• logsij0 – log line strength

• elower – elower

• elower_grid – elower_grid (optional)

• Nelower – # of division of elower between min to max values when elower_grid is not given

• Ncrit – frozen line number per bin

Returns

qlogsij0 qcnu num_unique elower_grid

exojax.spec.plg.plg_elower_addcon(indexa, Na, cnu, indexnu, nu_grid, mdb, Tgue, errTgue=500.0, elower_grid=None, Nelower=10, Ncrit=0, reshape=False, weedout=False, Tmargin=0.0, coefTgue=1.0, verbose=True, threshold_persist_freezing=10000.0)

Pseudo Line Grid for elower w/ an additional condition

Parameters

• indexa – the indexing of the additional condition

• Na – the number of the additional condition grid

• cnu – contribution of wavenumber for LSD

• indexnu – nu index

• wavenumber_grid – nu grid

• mdb – molecular database (instance made by the MdbExomol/MdbHit class in moldb.py)

• Tgue – rough guess on the typical atmospheric temperature

• errTgue – expected one-sided error of Tgue

• elower_grid – elower_grid (optional)

• Nelower – # of division of elower between min to max values (when elower_grid is not given)

• Ncrit – frozen line number per bin

• reshape – reshaping output arrays

• weedout – Is it ok to remove weakest lines or not?

• Tmargin – margin even above Tuplim to prevent freeze of lines that become strong enough as temperature rises slightly. (more needed for cooler objects)

• coefTgue – coefficient for Tgue to optimize elower_grid

• verbose – vervose printing or not

• threshold_persist_freezing – How weak lines compared to the deepest one will you persist freezing (not retaken)?

Returns

pseudo logsij0 qcnu: pseudo cnu num_unique: number of the lines in each bin of grid elower_grid: elower of pl frozen_mask: mask for frozen lines into pseudo lines nonzeropl_mask: mask for pseudo-lines w/ non-zero

Return type

qlogsij0

exojax.spec.premodit module

Line profile computation using PremoDIT = Precomputation of LSD version of MODIT

exojax.spec.premodit.broadpar_getix(ngamma_ref, ngamma_ref_grid, n_Texp, n_Texp_grid)

get indices and contribution of broadpar

Parameters

• ngamma_ref – normalized half-width at reference

• ngamma_ref_grid – grid of normalized half-width at reference

• n_Texp – temperature exponent (n_Texp, n_air, etc)

• n_Texp_grid – grid of temperature exponent (n_Texp, n_air, etc)

Returns

multi_index_lines multi_cont_lines uidx_lines neighbor_uidx multi_index_uniqgrid number of broadpar gird

Examples

>>> multi_index_lines, multi_cont_lines, uidx_lines, neighbor_uidx, multi_index_uniqgrid, Ng = broadpar_getix(
>>> ngamma_ref, ngamma_ref_grid, n_Texp, n_Texp_grid)
>>> iline_interest = 1 # we wanna investiget this line
>>> print(multi_index_lines[iline_interest]) # multi index from a line
>>> print(multi_cont_lines[iline_interest]) # multi contribution from a line
>>> print(uidx_lines[iline_interest]) # uniq index of a line
>>> print(multi_index_uniqgrid[uniq_index]) # multi index from uniq_index
>>> ui,uj,uk=neighbor_uidx[uniq_index, :] # neighbour uniq index

exojax.spec.premodit.compute_dElower(T, interval_contrast=0.1)

compute a grid interval of Elower given the grid interval of line strength

Parameters

• T – temperature in Kelvin

• interval_contrast – putting c = grid_interval_line_strength, then, the contrast of line strength between the upper and lower of the grid becomes c-order of magnitude.

Returns

Required dElower

exojax.spec.premodit.g_bias(nu_in, T)

Parameters

• nu_in – wavenumber in cm-1

• T – txbemperature for unbiasing in Kelvin

Returns

bias g function

exojax.spec.premodit.generate_lbd(line_strength_ref, nu_lines, nu_grid, ngamma_ref, ngamma_ref_grid, n_Texp, n_Texp_grid, elower, elower_grid, Ttyp)

generate log-biased line shape density (LBD)

Parameters

• line_strength_ref – line strength at reference temperature 296K, Sij0

• nu_lines (_type_) – _description_

• nu_grid (_type_) – _description_

• ngamma_ref (_type_) – _description_

• ngamma_ref_grid (_type_) – _description_

• n_Texp (_type_) – _description_

• n_Texp_grid (_type_) – _description_

• elower (_type_) – _description_

• elower_grid (_type_) – _description_

• Ttyp (_type_) – _description_

Returns

log-biased line shape density (LBD) jnp.array: multi_index_uniqgrid (number of unique broadpar, 2)

Return type

jnp array

Examples

>>> lbd, multi_index_uniqgrid = generate_lbd(mdb.Sij0, mdb.nu_lines, nu_grid, ngamma_ref,
>>>               ngamma_ref_grid, mdb.n_Texp, n_Texp_grid, mdb.elower,
>>>               elower_grid, Ttyp)
>>> ngamma_ref = ngamma_ref_grid[multi_index_uniqgrid[:,0]] # ngamma ref for the unique broad par
>>> n_Texp = n_Texp_grid[multi_index_uniqgrid[:,0]] # temperature exponent for the unique broad par

exojax.spec.premodit.logf_bias(elower_in, T)

logarithm f bias function

Parameters

• elower_in – Elower in cm-1

• T – temperature for unbiasing in Kelvin

Returns

logarithm of bias f function

exojax.spec.premodit.make_broadpar_grid(ngamma_ref, n_Texp, Ttyp, dit_grid_resolution=0.2, adopt=True)

make grids of normalized half-width at reference and temperature exoponent

Parameters

• ngamma_ref (nd array) – n_Texp: temperature exponent (n_Texp, n_air, etc)

• n_Texp (nd array) – temperature exponent (n_Texp, n_air, etc)

• Ttyp – typical or maximum temperature

• dit_grid_resolution (float, optional) – DIT grid resolution. Defaults to 0.2.

• adopt (bool, optional) – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly. Defaults to True.

Returns

ngamma_ref_grid, grid of normalized half-width at reference nd array: n_Texp_grid, grid of temperature exponent (n_Texp, n_air, etc)

Return type

nd array

exojax.spec.premodit.make_elower_grid(Tmax, elower, interval_contrast)

compute E_lower grid given interval_contrast of line strength

Parameters

• Tmax – max temperature in Kelvin

• elower – E_lower

• interval_contrast – putting c = grid_interval_line_strength, then, the contrast of line strength between the upper and lower of the grid becomes c-order of magnitude.

Returns

grid of E_lower given interval_contrast

exojax.spec.premodit.parallel_merge_grids(grid1, grid2)

Merge two different grids into one grid in parallel, in a C-contiguous RAM mapping.

Parameters

• grid1 – grid 1

• grid2 – grid 2

Returns

merged grid (len(grid1),2)

exojax.spec.premodit.unbiased_lsd(lbd, T, nu_grid, elower_grid, qt)

unbias the biased LSD

Parameters

• lbd_biased – log biased LSD

• T – temperature for unbiasing in Kelvin

• nu_grid – wavenumber grid in cm-1

• elower_grid – Elower grid in cm-1

• qt – partition function ratio Q(T)/Q(Tref)

Returns

LSD, shape = (number_of_wavenumber_bin, number_of_broadening_parameters)

exojax.spec.premodit.unbiased_ngamma_grid(T, P, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid)

compute unbiased ngamma grid

Parameters

• T – temperature in Kelvin

• P – pressure in bar

• ngamma_ref_grid – pressure broadening half width at reference

• n_Texp_grid – temperature exponent at reference

• multi_index_uniqgrid – multi index of unique broadening parameter

Returns

pressure broadening half width at temperature T and pressure P

exojax.spec.premodit.xsmatrix(Tarr, Parr, R, pmarray, lbd, nu_grid, ngamma_ref_grid, n_Texp_grid, multi_index_uniqgrid, elower_grid, Mmol, qtarr)

compute cross section matrix given atmospheric layers, with scan+fft

Parameters

• Tarr (_type_) – temperature layers

• Parr (_type_) – pressure layers

• R (float) – spectral resolution

• pmarray (_type_) – pmarray

• lbd (_type_) – log biased line shape density

• nu_grid (_type_) – wavenumber grid

• ngamma_ref_grid (_type_) – normalized half-width grid

• n_Texp_grid (_type_) – temperature exponent grid

• multi_index_uniqgrid (_type_) – multi index for uniq broadpar grid

• elower_grid (_type_) – Elower grid

• Mmol (_type_) – molecular mass

• qtarr (_type_) – partition function ratio layers

Returns

cross section matrix (Nlayer, N_wavenumber)

Return type

jnp.array

exojax.spec.premodit.xsvector(T, P, nsigmaD, lbd, R, pmarray, nu_grid, elower_grid, multi_index_uniqgrid, ngamma_ref_grid, n_Texp_grid, qt)

compute cross section vector, with scan+fft

Parameters

• T (_type_) – temperature in Kelvin

• P (_type_) – pressure in bar

• nsigmaD – normalized doplar STD

• lbd (_type_) – log biased line shape density (LBD)

• R (_type_) – spectral resolution

• nu_grid (_type_) – wavenumber grid

• elower_grid (_type_) – E lower grid

• multi_index_uniqgrid (_type_) – multi index of unique broadening parameter grid

• ngamma_ref_grid (_type_) – normalized pressure broadening half-width

• n_Texp_grid (_type_) – temperature exponent grid

• qt (_type_) – partirion function ratio

Returns

cross section in cgs vector

Return type

jnp.array

exojax.spec.presolar module

PreSOLAR Precomputing Shape density and OverLap Add convolution Rxxxx

• LBD -> hat(LBD)

• shapefilter -> hat(shapefilter)

exojax.spec.presolar.lbd_olaform(lbd, ndiv, div_length, filter_length)

convert LBD to match the form of OLA, i.e. generate hat LBD

Parameters

• lbd (3D array) – line basis density (input length,:,:)

• ndiv (int) – number of mini batches

• div_length (int) – mini batch length

• filter_length (int) – filter length

Returns

hat(LBD) (ndiv, fft_length, :, :)

Return type

4D array

exojax.spec.presolar.optimal_mini_batch(input_length, filter_length)

compute the optimal number and length of the mini batches array

Parameters

• input_length (int) – input length i.e. the length of the wavenumber bin

• filter_length (int) – filter length

Returns

the optimal number, length of the mini batches.

Return type

int, int

exojax.spec.presolar.shapefilter_olaform(shapefilter, div_length, padding_value=0.0)

generate zero-padding shape filter

Parameters

• shapefilter (array) – shape filter

• div_length (int) – mini batch length

• padding_value – padding value (default = 0.0)

Returns

zero-padding shape filter, hat(V)

exojax.spec.response module

response.

• input nus/wav should be spaced evenly on a log scale (ESLOG).

• response is a response operation for the wavenumber grid spaced evenly on a log scale.

• ipgauss2 are faster than default when N >~ 10000, where N is the dimension of the wavenumber grid.

exojax.spec.response.ipgauss2(nus, F0, varr_kernel, beta)

Apply the Gaussian IP response to a spectrum F.

Parameters

• nus – input wavenumber, evenly log-spaced

• F0 – original spectrum (F0)

• varr_kernel – velocity array for the rotational kernel

• beta – STD of a Gaussian broadening (IP+microturbulence)

Returns

response-applied spectrum (F)

exojax.spec.response.ipgauss_sampling(nusd, nus, F0, beta, RV)

Apply the Gaussian IP response + sampling to a spectrum F.

Parameters

• nusd – sampling wavenumber

• nus – input wavenumber, evenly log-spaced

• F0 – original spectrum (F0)

• beta – STD of a Gaussian broadening (IP+microturbulence)

• RV – radial velocity (km/s)

Returns

response-applied spectrum (F)

exojax.spec.response.rigidrot(nus, F0, vsini, u1, u2, vsinimax=100.0)

(deprecated) rigid rotation. This will be removed.

exojax.spec.response.sampling(nusd, nus, F, RV)

Sampling w/ RV.

Parameters

• nusd – sampling wavenumber

• nus – input wavenumber

• F – input spectrum

• RV – radial velocity (km/s)

Returns

sampled spectrum

exojax.spec.rtransfer module

Radiative transfer module used in exospectral analysis.

exojax.spec.rtransfer.dtauCIA(nus, Tarr, Parr, dParr, vmr1, vmr2, mmw, g, nucia, tcia, logac)

dtau of the CIA continuum.

Parameters

• nus – wavenumber matrix (cm-1)

• Tarr – temperature array (K)

• Parr – temperature array (bar)

• dParr – delta temperature array (bar)

• vmr1 – volume mixing ratio (VMR) for molecules 1 [N_layer]

• vmr2 – volume mixing ratio (VMR) for molecules 2 [N_layer]

• mmw – mean molecular weight of atmosphere

• g – gravity (cm2/s)

• nucia – wavenumber array for CIA

• tcia – temperature array for CIA

• logac – log10(absorption coefficient of CIA)

Returns

optical depth matrix [N_layer, N_nus]

exojax.spec.rtransfer.dtauCIA_mmwl(nus, Tarr, Parr, dParr, vmr1, vmr2, mmw, g, nucia, tcia, logac)

dtau of the CIA continuum.

(for the case where mmw is given for each atmospheric layer)

Parameters

• nus – wavenumber matrix (cm-1)

• Tarr – temperature array (K)

• Parr – temperature array (bar)

• dParr – delta temperature array (bar)

• vmr1 – volume mixing ratio (VMR) for molecules 1 [N_layer]

• vmr2 – volume mixing ratio (VMR) for molecules 2 [N_layer]

• mmw – mean molecular weight of atmosphere [N_layer]

• g – gravity (cm2/s)

• nucia – wavenumber array for CIA

• tcia – temperature array for CIA

• logac – log10(absorption coefficient of CIA)

Returns

optical depth matrix [N_layer, N_nus]

exojax.spec.rtransfer.dtauHminus(nus, Tarr, Parr, dParr, vmre, vmrh, mmw, g)

dtau of the H- continuum.

Parameters

• nus – wavenumber matrix (cm-1)

• Tarr – temperature array (K)

• Parr – temperature array (bar)

• dParr – delta temperature array (bar)

• vmre – volume mixing ratio (VMR) for e- [N_layer]

• vmrH – volume mixing ratio (VMR) for H atoms [N_layer]

• mmw – mean molecular weight of atmosphere

• g – gravity (cm2/s)

Returns

optical depth matrix [N_layer, N_nus]

exojax.spec.rtransfer.dtauHminus_mmwl(nus, Tarr, Parr, dParr, vmre, vmrh, mmw, g)

dtau of the H- continuum.

(for the case where mmw is given for each atmospheric layer)

Parameters

• nus – wavenumber matrix (cm-1)

• Tarr – temperature array (K)

• Parr – temperature array (bar)

• dParr – delta temperature array (bar)

• vmre – volume mixing ratio (VMR) for e- [N_layer]

• vmrH – volume mixing ratio (VMR) for H atoms [N_layer]

• mmw – mean molecular weight of atmosphere [N_layer]

• g – gravity (cm2/s)

Returns

optical depth matrix [N_layer, N_nus]

exojax.spec.rtransfer.dtauM(dParr, xsm, MR, mass, g)

dtau of the molecular cross section.

Note

fac=bar_cgs/(m_u (g)). m_u: atomic mass unit. It can be obtained by fac=1.e3/m_u, where m_u = scipy.constants.m_u.

Parameters

• dParr – delta pressure profile (bar) [N_layer]

• xsm – cross section matrix (cm2) [N_layer, N_nus]

• MR – volume mixing ratio (VMR) or mass mixing ratio (MMR) [N_layer]

• mass – mean molecular weight for VMR or molecular mass for MMR

• g – gravity (cm/s2)

Returns

optical depth matrix [N_layer, N_nus]

exojax.spec.rtransfer.dtauM_mmwl(dParr, xsm, MR, mass, g)

dtau of the molecular cross section.

(for the case where mmw is given for each atmospheric layer)

Note

fac=bar_cgs/(m_u (g)). m_u: atomic mass unit. It can be obtained by fac=1.e3/m_u, where m_u = scipy.constants.m_u.

Parameters

• dParr – delta pressure profile (bar) [N_layer]

• xsm – cross section matrix (cm2) [N_layer, N_nus]

• MR – volume mixing ratio (VMR) or mass mixing ratio (MMR) [N_layer]

• mass – mean molecular weight for VMR or molecular mass for MMR [N_layer]

• g – gravity (cm/s2)

Returns

optical depth matrix [N_layer, N_nus]

exojax.spec.rtransfer.dtauVALD(dParr, xsm, VMR, mmw, g)

dtau of the atomic (+ionic) cross section from VALD.

Parameters

• dParr – delta pressure profile (bar) [N_layer]

• xsm – cross section matrix (cm2) [N_species x N_layer x N_wav]

• VMR – volume mixing ratio [N_species x N_layer]

• mmw – mean molecular weight [N_layer]

• g – gravity (cm/s2)

Returns

optical depth matrix [N_layer x N_nus]

Return type

dtau

exojax.spec.rtransfer.pressure_layer(logPtop=- 8.0, logPbtm=2.0, NP=20, mode='ascending')

generating the pressure layer.

Parameters

• logPtop – log10(P[bar]) at the top layer

• logPbtm – log10(P[bar]) at the bottom layer

• NP – the number of the layers

Returns

pressure layer dParr: delta pressure layer k: k-factor, P[i-1] = k*P[i]

Return type

Parr

Note

dParr[i] = Parr[i] - Parr[i-1], dParr[0] = (1-k) Parr[0] for ascending mode

exojax.spec.rtransfer.rtrun(dtau, S)

Radiative Transfer using two-stream approximaion + 2E3 (Helios-R1 type)

Parameters

• dtau – opacity matrix

• S – source matrix [N_layer, N_nus]

Returns

flux in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

exojax.spec.rtransfer.rtrun_direct(dtau, S)

Radiative Transfer using direct integration.

Note

Use dtau/mu instead of dtau when you want to use non-unity, where mu=cos(theta)

Parameters

• dtau – opacity matrix

• S – source matrix [N_layer, N_nus]

Returns

flux in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

exojax.spec.rtransfer.rtrun_surface(dtau, S, Sb)

Radiative Transfer using two-stream approximaion + 2E3 (Helios-R1 type) with a planetary surface.

Parameters

• dtau – opacity matrix

• S – source matrix [N_layer, N_nus]

• Sb – source from the surface [N_nus]

Returns

flux in the unit of [erg/cm2/s/cm-1] if using piBarr as a source function.

exojax.spec.rtransfer.trans2E3(x)

transmission function 2E3 (two-stream approximation with no scattering) expressed by 2 E3(x)

Note

The exponetial integral of the third order E3(x) is computed using Abramowitz Stegun (1970) approximation of E1 (exojax.special.E1).

Parameters

x – input variable

Returns

Transmission function T=2 E3(x)

exojax.spec.rtransfer.wavenumber_grid(x0, x1, N, unit='cm-1', xsmode='lpf')

exojax.spec.set_ditgrid module

set DIT

• This module provides functions to generate the grid used in DIT/MODIT/PreMODIT.

exojax.spec.set_ditgrid.ditgrid_linear_interval(input_variable, dit_grid_resolution=0.1, weight=None, adopt=True)

generate DIT GRID with constant interval in linear scale

Parameters

• input_variable – input array, e.g. n_Texp (temperature exponent) array (Nline)

• dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

• weight – weight, e.g. np.abs(ln(T)-ln(Tref))

• adopt – if True, min, max grid points are used at min and max values of x.

• this case (In) –

• grid width does not need to be dit_grid_resolution exactly. (the) –

Returns

grid for DIT

exojax.spec.set_ditgrid.ditgrid_log_interval(input_variable, dit_grid_resolution=0.1, adopt=True)

generate DIT GRID with constant interval in logarithm scale

Parameters

• input_variable – simgaD or gammaL array (Nline)

• dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x.

• this case (In) –

• grid width does not need to be dit_grid_resolution exactly. (the) –

Returns

grid for DIT

exojax.spec.set_ditgrid.ditgrid_matrix(x, res=0.1, adopt=True)

DIT GRID MATRIX.

Parameters

• x – simgaD or gammaL matrix (Nlayer x Nline)

• res – grid resolution. res=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be res exactly.

Returns

grid for DIT (Nlayer x NDITgrid)

exojax.spec.set_ditgrid.minmax_ditgrid_matrix(x, dit_grid_resolution=0.1, adopt=True)

compute MIN and MAX DIT GRID MATRIX.

Parameters

• x – gammaL matrix (Nlayer x Nline)

• dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns

minimum and maximum for DIT (dgm_minmax)

exojax.spec.set_ditgrid.precompute_modit_ditgrid_matrix(set_gm_minmax, dit_grid_resolution=0.1, adopt=True)

Precomputing MODIT GRID MATRIX for normalized GammaL.

Parameters

• set_gm_minmax – set of minmax of ditgrid matrix for different parameters [Nsample, Nlayers, 2], 2=min,max

• dit_grid_resolution – grid resolution. dit_grid_resolution=0.1 (defaut) means a grid point per digit

• adopt – if True, min, max grid points are used at min and max values of x. In this case, the grid width does not need to be dit_grid_resolution exactly.

Returns

grid for DIT (Nlayer x NDITgrid)

exojax.spec.shapefilter module

(line) shape filters used in PreSOLAR algorithm

exojax.spec.shapefilter.check_filter_condition(shape_filter)

_summary_

Parameters

shape_filter (_type_) – _description_

exojax.spec.shapefilter.compute_filter_length(wavenumber_halfwidth, representative_wavenumber, spectral_resolution)

compute the length of the FIR line shape filter

Parameters

• wavenumber_halfwidth (float) – half width at representative wavenumber (cm-1)

• representative_wavenumber (float) – representative wavenumber (cm-1)

• spectral_resolution (float) – spectral resolution R0

Returns

filter length

Return type

int

Examples

from exojax.utils.instfunc import resolution_eslog spectral_resolution = resolution_eslog(nu_grid) filter_length = compute_filter_length(50.0, 4000.0, spectral_resolution)

exojax.spec.shapefilter.generate_voigt_shape_filter(nsigmaD, ngammaL, filter_length)

generate a Voigt filter with a tail cut (naturally!)

Parameters

• nsigmaD (float) – normalized Dopper width

• ngammaL (float) – normalized Lorenz half width

• filter_length (int) – filter length

Returns

_description_

Return type

_type_

exojax.spec.spin_rotation module

exojax.spec.spin_rotation.convolve_rigid_rotation(F0, vr_array, vsini, u1=0.0, u2=0.0)

Apply the Rotation response to a spectrum F (No OLA and No cuDNN).

Parameters

• F0 – original spectrum (F0)

• vr_array – fix-sized vr array for kernel, see utils.dvgrid_rigid_rotation

• vsini – V sini for rotation (km/s)

• RV – radial velocity

• u1 – Limb-darkening coefficient 1

• u2 – Limb-darkening coefficient 2

Returns

response-applied spectrum (F)

exojax.spec.spin_rotation.rotkernel_jvp(primals, tangents)

exojax.spec.unitconvert module

unit conversion for spectrum.

exojax.spec.unitconvert.nu2wav(nus, unit='AA')

wavenumber to wavelength (AA)

Parameters

• nus – wavenumber (cm-1)

• unit – unit of wavelength

Returns

wavelength (AA)

exojax.spec.unitconvert.wav2nu(wav, unit)

wavelength to wavenumber.

Parameters

• wav – wavelength

• unit – unit of wavelength

Returns

wavenumber (cm-1)

Module contents