An Overview of Molecular Opacities

Experimental Molecular Spectroscopy & Data Compilations An Overview of Molecular Opacities Peter Peter Bernath Old Dominion University Norfolk, VA

JWST Spectroscopy: mainly IR and low resolution

Spectra of Cool Stars and Brown Dwarfs T=3000 K electronic spectra of free radicals, e.g., TiO, FeH and CaOH; T=1500 K IR and near IR spectra of hot molecules: e.g., H 2 O, NH 3 and CH 4 ; T=1000 K Cushing et al. ApJ 648, 614 (2006)

Exoplanet Emission and Transit Spectra with JWST Hot super-earth around an M-type star: emission and transit spectra GJ 436b, hot Neptune around an M2.5 V star: transit spectra for different chemical compositions Beichman et al. PASP 126, 1134 (2014) Shabram et al. ApJ 727, 65 (2011)

Exoplanet Atmospheric Models Hot Jupiter HD 189733b Hot super-earth CoRoT-7b T eq =1800 K mbar Mole fraction Venot et al. A&A 546, A43 (2012) Schaefer et al. ApJ 755, 41 (2012)

Laboratory Astrophysics for Exoplanets Fortney et al., The Need for Laboratory Work to Aid in The Understanding of Exoplanetary Atmospheres, 2016 (https://arxiv.org/abs/1602.06305). In many cases, uncertainties in a path towards model advancement stems from insufficiencies in the laboratory data that serve as critical inputs to atmospheric physical and chemical tools. (1) Molecular opacity line lists with parameters for a diversity of broadening gases (2) Extended databases for collision-induced absorption and dimer opacities (3) High spectral resolution opacity data for a variety of relevant molecular species (4) Laboratory studies of haze and condensate formation and optical properties (5) Significantly expanded databases of chemical reaction rates (6) Measurements of gas UV photoabsorption cross sections at high temperatures Line lists and absorption cross sections for molecules and solids. (These data needs are not just for exoplanets.)

From Beer-Lambert law: Molecular Opacity Requirements: Line lists Molecular data at high spectral resolution for samples at low (10 K) and high temperatures (e.g., 4000 K). Although observations may be at low spectral resolution, underlying radiative transfer is at high resolution. [ S g( ν ) Nl] I = I0 exp ν10 Need a lineshape function g(ν-ν 10 ) (assumed to be Voigt; H 2, He and CO 2 pressure broadening parameters needed; non-voigt) and a line strength S in SI units, from Bernath, Spectra of Atoms and Molecules: S 2 10 J J low 10 = 2π ν S 3ε hcq 0 T exp E kt 1 exp Therefore need a line position, ν 10, partition function, Q T (calculated, Q(T)=Σg i exp(-e i /kt)), line intensity, S J J (or S ), and the lower state energy, E low. hν kt

Molecular Opacities: Line Lists Create line list and then compute opacity tables (absorption cross-section as a function of wavelength) suitable for a range of temperatures, pressures and compositions. Line lists (ν 10, S, E low ) can be created by: 1. Ab initio calculation. Solve the electronic Schrödinger equation (Hψ=Eψ) to obtain potential energy functions and (transition) dipole surfaces, then vibration-rotation Schrödinger equation for each electronic state to obtain energy levels (transitions) and wavefunctions (intensities). 2. Experimental measurement. 3. Combination of 1 and 2. Ab initio calculations provide the large number of transitions needed at high temperature, but line position accuracy is too low. Experimental measurement has required accuracy, but not the millions /billions of lines needed. However, calculated line intensities can be as good as experiment for small molecules. In fact, the billions of weak lines can be replaced by a quasi-continuum (i.e., final line list can consist of about 100,000 strong lines and an absorption cross-section to represent the billions of weak lines).

Laboratory Spectra NH Hollow cathode emission spectrum of NH radical Fourier Transform Spectrometer NH ACE solar absorption spectrum Microwave discharge NH ATMOS solar absorption spectrum

Semi-empirical Method for Diatomics (J. Brooke) Start Spectrum Line assignment and fit Molecular constants fit Einstein As and f-values line list with positions and intensities PGOPHER Case (a) matrix elements Hund s case (b) to (a) Case (b) vibrational wavefunctions and transition dipole moment matrix elements End Equilibrium constants RKR1 Potential energy curve LEVEL + Start Ab initio Electronic (transition) dipole moment function

Miscellaneous Diatomics (Bernath) MOLLIST (Molecular Line Lists, Intensities and Spectra): http://bernath.uwaterloo.ca/molecularlists.php 1. A. Burrows, et al., New CrH Opacities for the Study of L and Brown Dwarf Atmospheres, Astrophys. J. 577, 986-992 (2002) 2. M. Dulick, et al., Line Intensities and Molecular Opacities of the FeH F 4 i -X 4 i Transition, Astrophys. J. 594, 651-663 (2003) 3. A. Burrows, et al., Spectroscopic Constants, Abundances and Opacities of the TiH Molecule, Astrophys. J. 624, 988-1002 (2005). 4. K. H. Hinkle, et al., The magnesium isotopologues of MgH in the A 2 Π-X 2 Σ + system, Astrophys. J. Suppl. 207, 26 (7pp) (2013). 5. J. S. A. Brooke, et al., Line strengths and updated molecular constants for the C 2 Swan system, J. Quant. Spectrosc. Rad. Trans. 124, 11-20 (2013). 6. R. S. Ram, et al., Improved Line Data for the Swan System 12 C 13 C Isotopologue, Astrophys. J. Suppl. 211, 5 (7pp) (2014). 7. J. S. A. Brooke, et al., Einstein A Coefficients and Oscillator Strengths for the A 2 П-X 2 Σ + (red) and B 2 Σ + -X 2 Σ + (violet) Systems and Rovibrational Transitions in the X 2 Σ + state of CN, Astrophys. J. Suppl. 210, 23 (15pp) (2014). 8. C. Sneden, et al., Line lists for the A 2 П-X 2 Σ + (red) and B 2 Σ + -X 2 Σ + (violet) Systems of CN, 13 CN, and C 15 N, and Application to Astronomical Spectra, Astrophys. J. Suppl. 214, 26 (10pp) (2014). 9. R. S. Ram, et al., Einstein A-values and oscillator strengths of the A 2 П-X 2 Σ + system of CP, J. Quant. Spectrosc. Rad. Transfer 138, 107-115 (2014). 10. T. Masseron, et al., CH in stellar atmospheres: an extensive linelist, AA 571, A47 (29pp) (2014). 11. J. S. A. Brooke, et al., Improved line strengths of rovibrational and rotational transitions within the X 3 Σ - ground state of NH, J. Chem. Phys. 143, 026101 (3 pp) (2015) 12. J. S. A. Brooke, et al., Line Strengths of Rovibrational and Rotational Transitions in the X 2 Π Ground State of OH, J. Quant. Spectrosc. Rad. Transfer 168, 142-157 (2016). 13. J. N. Hodges, et al., Improved Ultraviolet and Infrared Oscillator strengths for OH +, Astrophys. J. 855, 21(4pp) (2018). 45 total data sets to date

ExoMol: http://exomol.com/ Patrascu et al., IX. The spectrum of AlO, MNRAS, 449, 3613 (2015) Yurchenko et al., XIII. The spectrum of CaO, MNRAS 456, 4524 (2016) McKemmish et al., XVIII. The high-temperature spectrum of VO, MNRAS 463, 771 (2016) Wong et al., XXI. Nitric Oxide (NO), MNRAS 470, 882 (2017) Prajapat et al., XXIII. Spectra of PO and PS, MNRAS 472, 3648 (2017) Yurchenko et al., XXIV. a new hot line list for silicon monohydride, SiH, MNRAS 473, 5324 (2018)

Polyatomics: H 2 O, CH 4 and NH 3 1400 K 3000 K 1500 K 1800 K 1000 K 1000 K 1500 K

Experimental Absorption Spectroscopy with a Fourier Transform Spectrometer

CH 4 Transmission Spectrum (700 C) 1: Hot CH 4 + Lamp 3: No sample + Lamp 2: Hot CH 4 + no lamp Notice the quasicontinuum from millions of weak lines. 4: No sample + no lamp Transmission = (1-3)/(2-4) Hargreaves et al. ApJ 813, 12 (2015) Notice quasi-continuum due to millions of lines.

150 billion lines, divided into a few million strong lines and a quasi-continuum of super-lines, which are histograms of all the weak lines.

Y Hargreaves et al. ApJ 813, 12 (2015). Experimental spectrum. Rey et al. ApJ 847, 105 (2017). 150 billion lines calculated, experimental band origins Rey et al. ApJ 789, 2 (2014) 12 billion lines calculated, experimental band origins Yurchenko & Tennyson, MNRAS 440, 1649 (2014). 10 billion lines, potential adjusted to experiment

Experimental Absorption Cross-sections C 2 H 6, ethane Hot ethane absorption cross-sections in 3.3 μm region (C-H stretching modes) Hargreaves et al., Mol. Astrophys. 1, 20 (2015)

Data Distribution: UV, Visible, IR Molecular Databases 1. HITRAN: http://hitran.org/; aimed mainly at Earth s atmosphere 2. GEISA: http://cds-espri.ipsl.upmc.fr/ethertypo/?id=950&l=0; aimed mainly at Earth s atmosphere 3. ExoMol: http://exomol.com/; calculated line lists numerous molecules 4. VAMDC: http://portal.vamdc.eu/; web portal to 33 databases 5. NASA Ames: http://huang.seti.org/ (CO 2, NH 3, CO 2 ); http://www.astrochem.org/pahdb/; PAHs 6. Reims-Tomsk, TheoReTS: http://theorets.tsu.ru/home; CH 4, PH 3, C 2 H 4, etc. 7. Bernath (MOLLIST): http://bernath.uwaterloo.ca/molecularlists.php 8. Kurucz: http://kurucz.harvard.edu/ 9. Sneden: http://www.as.utexas.edu/~chris/lab.html 10. Perevalov: ftp://ftp.iao.ru/pub/ CDSD-296,-1000,-4000; NDSC; ASD-1000; CO 2, NO 2 and C 2 H 2 11. Boudon (Dijon): http://vamdc.icb.cnrs.fr/php/methane.php; CH 4, C 2 H 4, etc. 12. And many others

HITRAN Database Old HITRAN: ftp site to download an ascii data file (.par) for each molecule; each line in the file (fixed-format 160 characters) was a transition assuming a Voigt profile for air. HITRANonline uses an SQL database that accommodates non- Voigt lineshapes and pressure broadeners other than air such as H 2, N 2, He, H 2 O, etc. HITRANonline has the interfaces needed to distribute astrophysics data: vibrationrotation line parameters, IR absorption cross sections (no UV), collision-induced absorption, optical constants for aerosols, HITEMP (ftp site for hot H 2 O, CO 2, CO, NO, and OH; needs updating) HAPI: set of tools in Python to work with HITRAN data

Choose molecules to work with, then isotopologues, then spectral range of interest, then output options

Select different parameters as needed from the menu to make the file. HT: Hartmann-Tran lineshape