Molecular Database and Conversion¶

Update: May 10/2022, Hajime Kawahara, Yui Kawashima

exojax uses a specific mdb (molecular database) class for each molecular/atom database, moldb.MdbExomol is for ExoMol, moldb.MdbExoHit is for HITRAN/HITEMP. Here, we use MdbExomol for explanation because most instances are common in mdb classes.

Click below for the details for mdb class for each database.

>>> from exojax.spec import moldb
>>> from exojax.utils.grids import wavenumber_grid
>>> nus,wav,res=nugrid(22880.,23000.,1000,unit="AA")
>>> mdbCO=moldb.MdbExomol('.database/CO/12C-16O/Li2015',nus)
default broadening parameters are used for  71  J lower states in  152  states

Basic Quantities¶

In mdb, the line centers in the unit of cm-1, for instance, are stored as

>>> mdbCO.nu_lines

Examples of the other quantities in mdb are listed in the table below.

quantity	instance	unit	np/jnp
line center	nu_lines	cm-1	np
line center	dev_nu_lines	cm-1	jnp
lower state energy	elower	cm-1	jnp
natural broadening	gamma_natural	cm-1	jnp
Einstein coefficient	A	s-1	jnp
reference line strength	Sij0	cm	np
log_e Sij0	logsij0		jnp

The fourth column indicates the data type of the array; np means the array is numpy nd array (float64). jnp is jax.numpy array on device. Remember that the jnp array is float32. Why do we have both np and jnp versions of the line center? This is because the float64 is needed to keep precision for some conversions. See the last section of ” Computing CO cross section using HITRAN (opacity calculator = LPF) ” for more details. Because the lien strength is small number in general, we have np version of S0 and jnp version of logarithm of S0. In fact, logsij0 is used to compute the line strength.

Line Strength¶

The line strength is a function of temperature, expressed as

\(S (T) = S_0 \frac{Q(T_\mathrm{ref})}{Q(T)} \frac{e^{- h c E_\mathrm{low} /k_B T}}{e^{- h c E_\mathrm{low} /k_B T_\mathrm{ref}}} \frac{1- e^{- h c \hat{\nu} /k_B T}}{1-e^{- h c \hat{\nu} /k_B T_\mathrm{ref}}}\)

The reference line strength S_0 is the line strength at \(T_\mathrm{ref}=296\) K (Sij0). exojax can compute S(T) in jax based. As I said, s0=logsij0 is used to compute S(T) as

\(S (T) = q_t^{-1} e^{ s_0 - c_2 E_\mathrm{low} (T^{-1} - T_\mathrm{ref}^{-1}) } \frac{1- e^{- c_2 \hat{\nu}/ T}}{1-e^{- c_2 \hat{\nu}/T_\mathrm{ref}}}\)

where \(c_2 = h c/k_B\). In exojax, S(T) is computed using the normalized partition function \(q_t=Q(T)/Q(T_\mathrm{ref})\) as

>>> from exojax.spec import SijT
>>> qt=mdbCO.qr_interp(Tfix)
>>> Sij=SijT(Tfix,mdbCO.logsij0,mdbCO.nu_lines,mdbCO.elower,qt)

Masking Weak Lines¶

exojax has the capability to mask the weak lines to reduce the computational cost. You can do this by providing two parameters, line strength criterion crit and typical temperature of the system Ttyp, to moldb.MdbExomol and moldb.MdbExoHit such as

>>> mdbCO=moldb.MdbExomol('.database/CO/12C-16O/Li2015',nus,crit=1.e-40,Ttyp=2000.)

In this example, lines are ignored if their strengths at 2,000 K are below 1.e-40 [cm]. When calculating the emission spectrum, we recommend setting Ttyp as the highest temperature of the atmospheric region of interest. This is because the number of the lines whose strengths are above a certain criterion usually increases as the temperature increases. Note that the default value of Ttyp is set to be 1,000 K, while for exojax<1.1.0, masking is only possible based on the line strengths at the reference temperature 296 K (i.e., Ttyp is not available).

The following figure shows the calculated CO cross sections using the ExoMol line list in the same way as this tutorial, but for a higher temperature of 2,000 K. Different values for crit and Ttyp are adopted for the four cases (Ttyp=296 K case is calculated with exojax v1.0.0, while the other three cases are calculated with exojax v1.1.0). You can realize that adopting a proper Ttyp is essential for a high-temperature case.