A hybrid line list for CH4 and hot methane continuum

Abstract

Aims: Molecular line lists (a catalogue of transition frequencies and line strengths) are important for modelling absorption and emission processes in atmospheres of different astronomical objects, such as cool stars and exoplanets. In order to be applicable for high temperatures, line lists for molecules like methane must contain billions of transitions, which makes their direct (line-by-line usage) application in radiative transfer calculations impracticable. Here we suggest a new, hybrid line list format to mitigate this problem, based on the idea of temperature-dependent absorption continuum.

Methods: The line list is partitioned into a large set of relatively weak lines and a small set of important, stronger lines. The weaker lines are then used either to construct a temperature-dependent (but pressure-independent) set of intensity cross sections or are blended into a greatly reduced set of 'super-lines'. The strong lines are kept in the form of temperature-independent Einstein A coefficients.

Results: A line list for methane (CH₄) is constructed as a combination of 17 million strong absorption lines relative to the reference absorption spectra and a background methane continuum in two temperature-dependent forms of cross sections and super-lines. This approach significantly eases the use of large high temperature line lists as the computationally expensive calculation of pressure- dependent profiles (e.g. Voigt) only need to be performed for a relatively small number of lines. Both the line list and cross sections were generated using a new 34 billion methane line list (known as 34to10), which extends the 10to10 line list to higher temperatures (up to 2000 K). The new hybrid scheme can be applied to any large line lists containing billions of transitions. We recommend using super-lines generated on a high resolution grid based on a resolving power of R = 1,000,000 to model the molecular continuum as a more flexible alternative to the temperature-dependent cross sections.

Keywords: infrared: planetary systems; infrared: stars; line:profiles; methods: numerical; molecular data; opacity.

Fig. 1.

Reference cross sections obtained using the Doppler profile at T = 300 K and T = 2000 K on the uniform Δṽ = 10 wavenumber grid. The green line (T = 2000 K and P = 0 bar) is almost identical to the blue line (T = 2000 K and P = 50 bar) at this region and for this scale, and thus can be barely seen.

Fig. 2.

Dynamic scaling factor used in Eq. 3.

Fig. 3.

Intensity partitioning for I_thr = 10⁻²⁵ cm/molecule and C_scale = 10⁻⁵. The dashed line indicates the I_thr threshold; the blue (T = 300 K) and red ( T = 2000 K) areas are the regions of the strong lines; the grey area at the bottom indicates all transitions which were excluded from the line list to form the weak lines of the continuum. Here all cross sections were obtained using the Doppler profile on a grid of 10 cm^-1.

Fig. 4.

Number of strong lines for different partitionings.

Fig. 5.

Upper panel: Methane continuum at 2000 K, P = 10 bar (blue) and the total absorption (red). Lower panel: Relative differences of the P = 0 and P = 10 bar continuum cross sections for the three wavenum- ber grids of Δṽ = 0.01 cm⁻¹ (red), 0.1 cm⁻¹ (blue), and 1 cm⁻¹ (grey).

Fig. 6.

Comparison of the P = 0 and P = 10 bar cross sections for 300 K (left) and 2000 K (right): black (total P = 0), blue (continuum P = 0), and red (continuum P = 10). The middle panels are a zoom-in of the continuum, also for P = 0 and P = 10 bar, which are almost indistinguishable in the upper panels. The lower panels show the relative difference between the P = 0 and P = 10 bar continuum cross sections as defined in Eq. (4). The integrated area of the relative difference is 0.06 % over the region 6700 - 6750 cm^-1. A wavenumber grid of Δṽ = 0.01 cm⁻¹ was used.

Fig. 7.

Comparison of the P = 0 and P = 10 bar line profiles used to generate cross sections at 2000 K in the region of 1.615 μm. The a₀ model with the J-independent line broadening was used. The wavenumber grid Δṽ is 0.01 cm⁻¹.

Fig. 8.

Relative error from using J-independent line broadening to describe methane continuum at high temperature (T = 2000 K) and pressure (P = 10 bar) as the difference between two cross sections (J-dependent a₀ model vs J-independent model) relative to the total cross sections. The wavenumber grid of Δṽ = 0.1 cm⁻¹ is used.

Fig. 9.

Relative errors using the histogram model R = 1, 000, 000 to describe the methane continuum at T = 2000 K and P = 10 bar as the difference with the 34to10 cross sections (Voigt model) relative to the total 34to10 cross sections. The wavenumber grid of Δṽ = 0.01 cm⁻¹ is used.

Fig. 10.

Relative error from the histogram model for three different grids to describe the methane continuum at T = 2000 K and P = 0 bar as the difference with the 34to10 cross sections (pure Doppler model) relative to the total 34to10 cross sections at P = 0 bar. The wavenumber grid of Δṽ = 0.01 cm⁻¹ is used.

Fig. 11.

Inappropriate use of the super-line approach when the grid is too coarse. The super-lines use a resolution of R = 100,000, which is not sufficient, due to the narrow Doppler profiles at zero pressure, T = 2000 K. The cross section was computed on a Δṽ = 0.01 cm⁻¹ grid.

Fig. 12.

Transmissions computed using the Doppler model (upper panel) and histogram continuum models (R = 1, 000, 000, middle and lower panels) with relative errors for the column amounts 10¹⁹, 10²⁰, 10²¹, 10²², 10²³, and 10²⁴ molecule/cm2 at T = 2000 K, P = 0 and P = 10 bar. The upper part of each panel shows the total transmission obtained from both the strong and weak lines at this temperature, while the lower part shows the relative error compared to the direct lineby- line evaluation from the 34to10 line list using the a₀ Voigt model (Barton et al. 2017). The error in regions with very low transmissions (< 10⁻⁴) are removed as the medium is optically thick.