1. Molecular Line Absorption Coefficients:
Kari Ehrmann
Wichita State University Physics Department
Schall Fellowship

2. Outline Equations Stellar Structure Data Sources Opacity
Types of Absorption
Monochromatic Opacity
Equations
Data Sources
Results of Computations
Computation of Kappa
Future Plans

3. Stellar Structure

4. Stellar Structure Equations
Hydrostatic Equilibrium
Mass Continuity
Radiative Transfer
Conservation of Energy

5. Stellar Structure Equations

6. Rosseland Mean Opacity
Harmonic mean
Includes the weighting function for the average opacity
This incorporates all the weak lines for the contribution to the calculation
Good for the inner layers of the star
Mean free path is very short

7. Planck Mean Opacity Straight Mean
Good for the outermost layers of the star
Mean free path of the photon is very long

8. Monochromatic Opacity

9. What is Opacity? Interaction of light with matter
Measure of absorption, emission and scattering of light passing through a medium
Mean free path of a photon
Absorption and emission by atoms, molecules and grains interfere with the photon
Alters its path and redistributes its energy

10. What is Opacity?
Atoms
Molecules
Grains
Ferguson et al. 2005

11. Atoms ( T > 5000 K) Types of Absorption Bound-Free Free-Free
Bound-Bound

12. Bound-Free Absorption
Photoionization
A photon is absorbed by an atom in a bound state and ionizes the bound electron which then escapes.
When this happens, the photon is destroyed and the extra energy feeds into the electron's kinetic energy and thermal pool

13. Free-Free Absorption Scattering process
A photon is absorbed by a free electron in the same field as an ion which affects the electron's kinetic energy.
Emission process known as bremsstrahlung
The electron loses energy by emitting a photon near an ion.

14. Bound-Bound Absorption
Photoexcitation
The photon is absorbed by an atom causing an electron to be excited and transition to a higher state
Normally responsible for absorption lines in stellar spectra

15. Molecules (1500-5000 K) Rotation Vibration
Millions of lines representing the transitions of states
based on a figure 1a in Lictman & Cochello, 1995 (DOI: /nmeth817)

16. Molecules
( K)

17. Bands of C2

18. Grains
(T < 1500 K)
Opacity is dominated by dust grains, such as silicate and carbon particles found in the atmospheres of red giants

19. Research Goal
Create program that calculates sigma for a range of temperatures
Create a table of these sigmas to be used in an opacity calculator
Focus on one molecule, C2

20. Monochromatic Opacity

21. Monochromatic Absorption Coefficient

22. Monochromatic Absorption Coefficient
Constants:
Pi, charge of the electron, mass of the electron and the speed of light

23. Statistical Weight g - Statistical weight f - Oscillator strength
Relation Einstein A to the oscillator strengths
Probability of transition

24. Partition Function Q(T) - Total Partition function
Probability relating to the Boltzmann distribution
The statistical weight, partition function and energy levels were part of the data set that was analyzed

25. Exponentials
Boltzmann Factor
Stimulated Emission Correction Factor

26. Normalized Doppler Broadening

27. Doppler Profile

28. Computations
Created a program that calculated a table Sigma for the bound-bound absorption lines of C2 for temperatures ranging from 631 K to 10,000K
Draw comparisons of Log(Sigma) between three data sets from Atop, Phoenix and Yueqi
Use our new Sigma calculation in an Opacity program using our new C2 tables

29. Data Sources Transition states ExoMol.com Brooke et al. (2013) Yueqi
Phoenix
Huber & Herzberg 1979
Atop
Sharp 1984
Partition Function
ExoMol.com
Brooke et al. (2013)
Yueqi
Temperatures Range
(0-3000K)
vizier.u-strasbg.fr
Barklem & Collet 2016
Temperature Range
(0 - 10,000K)

30. Partition Function Data

31. Results of the Sigma Computation

32. Results of the Sigma Computation

33. Results of the Sigma Computation

34. Testing the Results
Using our results we were able to test the opacity and compare our results to previous calculations

35. Results of the Kappa Computation

36. Results of the Kappa Computation

37. Results of the Kappa Computation

38. Results of the Kappa Computation Without the Contribution of C2

39. Future Expanding the number of molecules analyzed
CO, CN, H2O, C2H2, TiO, OH
Including other data sources, like HiTran

40. Image credit: NASA, ESA, and G.Bacon (STScI).
Many Thanks
The Schall Fellowship
Dr. Jason Ferguson
Image credit: NASA, ESA, and G.Bacon (STScI).