Modeling Cosmic Dust:

1. Modeling Cosmic Dust: How to Use Optical "Constants"

2. The life-cycle of stardust

3. Dust and energy flow Global average temperature From climatecrocks.com

4. Diamonds&Graphite

5. Rubies and sapphires

6. How light interacts with matter • Reflection • Propagation • Transmission Incident light Transmitted light Propagation through the medium Reflected light

7. What phenomena can occur during propagation of light through a medium? • Refraction • Absorption • Luminescence • Scattering • Refraction: reduction in propagation speed; causes light to bend • Absorption: occurs if the frequency of the light is at a resonant frequency of the medium. Transmission is related to absorption, only unabsorbed light is transmitted • Luminescence: spontaneous production of light, due to excitation by absorption of incident light • Scattering: light changes direction Refraction Absorption & luminescence Scattering

8. Reflectivity and Transmittance • Reflectivity = ratio of reflected flux to incident flux • Transmittivity* = ratio of transmitted flux to incident flux • Both quantities are wavelength dependent • If there is no absorption, R + T = 1 *Transmittivity is not a real word! However, the correct term is Transmittance, which is confusing because reflectance  reflectivity; absorbance absorptivity.

9. dx F Fʹ  Opacity k is the opacity ρis the density dx is the thickness of the slab Flux diminishes exponentially with penetration

10. dx F Fʹ  Absorption Coefficient absis the absorption coefficient This is Beer’s Law This assume no reflection

11. Refraction and absorption • In a real medium light is both refracted and absorbed. • So transmittance is not just T = 1 – R Incident light Transmitted light Propagation through the medium Reflected light • T = (1-R1)e-L(1-R2) • AssumingR1andR2are identical:T = (1-R)2e-L

12. Terminology AbsorptivityA = Fabs/Finc Absorbance a = absL = kρL A = e-a • T = (1-R)2e-L= (1-R)2A

13. But this doesn’t account for back reflections

14. Refractive index and absorption • For a transparent medium (no absorption), the refractive index is given by: n = c/v. • This is usually wavelength dependent

15. Complex refractive index • This combines both refraction and absorption into a single physical “quantity” (it is wavelength dependent) • Be careful of notation!! • The real part of m (i.e. n) is just the regular refractive index • The imaginary part, k, is sometime called the absorption coefficient (sometimes the extinction coefficient) • Note that this k abs kλ(opacity)

16. Optical “constants” • There are two sets of optical functions that are closely interrelated. • the real and imaginary parts of the complex refractive index • the real and imaginary parts of the complex dielectric function (relative permittivity)

17. What effect does the complex refractive index have? • Once the radiation enters the medium, the velocity of light becomes v = c / m, so that: • The intensity (flux) of the light wave is proportional to H2, and will exponentially decrease with a decay constant of 2k = 4k/. • Assume we have light as an idealized, sinusoidal wave. The incident radiation can be written as: where H0 is the amplitude,  is the angular frequency, and  is the wavenumber (=2/)

18. Beer’s Law • Where abs is the absorption coefficient. • T = (1-R)2e-L We can measure T and get k!

19. Derive n,k from lab spectra (n.b., several alternate methods, depending on spectral & sample type) • Measure absorbance a, specular reflectance R, and sample thickness d. • Solve for ideal absorption coefficient A Solve for imaginary index of refraction (same in every method): OR Back out real index of refraction from k and R 2. Measure absorbance of samples: one thick and one thin. Solve for A and R. For thin films or polished slabs Hofmeister, Pitman, Goncharov, & Speck (2009)

21. OHM and DL From Draine & Lee (1984)

22. Calculating interactions of light with small particles… • The total energy depleted from the original beam can be put equal to the incident energy on the area Cext, the extinction cross-section. Cext = Csca + Cabs • Small particles do not behave like blackbodies; how their behaviour deviates from blackbody behave can be defined by efficiency factors – Q-factors. • From the cross sections it is easy to see that the efficiencies of a particle to absorb, scatter and extinguish light are given by: • The Q-factors can be calculated from the complex refractive index (or complex dielectric function)

23. Emissivity and Q-factors • Q-factors essential describe how a real solid deviates from blackbody behaviour • The flux emitted by a particle is given by: where B(,T) is the Planck blackbody curve. • Emissivity is the ratio of energy radiated by a particular material to energy radiated by a black body at the same temperature = Q! • For metals and covalently bonded solid Q is generally a simple trend with wavelength such that •  is sometimes referred to as the emissivity law

24. How does Q relate to lab data? AbsorptivityA = Iabs/Iinc A = e-a Absorbance a = absL • τλis more or less ≡a • Qabs is more or less equivalent to A

25. What are we seeing when we look at the spectrum of a dust cloud? the sum of the contributions of particles of different compositions, sizes, crystal structures etc.

26. From Marra et al. (2011)

27. From Corman (2010)

28. OHM and DL

29. Cosmic Silicate New Stuff Black = new!. Blue = Draine (2003) Green = Draine & Lee (1984). Red, yellow = Ossenkopf et al. (1992) Same sample at all l Careful sample prep & analysis to eliminate contributions to n,k from back reflections Cross-checked by comparing many overlapping spectral segments Not grain size dependent Derived from combo of transmission & reflectivity spectra

30. Absorption Cross Sections UV-VIS-NIR particularly affected New Stuff

32. Olivine Melilite Pyroxene

33. Olivine From Pitman et al. (2010)

34. Speck et al 2011 Dorschner et al. (1995) http://www.astro.uni-jena.de/Laboratory/Database/databases.html • NBO/T vs. Fe/Mg

35. Conclusions • Beware of vocabulary • Read the paper! • If optical constants are derived from particulates, particle shape effects are embedded in the data. • If optical constants are derived from observations they cannot tell you anything about mineralogy

37. Temperature Effects

38. Case Study: HD 161796 (IRAS 17436+5003) • Simple test environment to model using DUSTY • - Post AGB star + dust BB w/ • twin peaked spectrum • Optically thin • Insignificant photoionization • Typically modeled with • amorphous silicates, • crystalline silicates (Fo, En), • crystalline H2O ice dust Assumptions = central star T = 6750±150 K (Hoozgaad et al. 2002) 1/r2 radial dust density distribution (constant mass loss) MRN size distribution 1 dust species

39. DUSTY Models: HD 161796 l (mm)

40. New models τV ≈2.3, Tin ≈ 125 τV ≈1.3, Tin ≈ 120 70-80% Cosmic Silicate 20-30% Metallic Iron

41. Crystalline Amorphous

43. History From Gillett et al (1968)

44. Crystalline olivine Elias 16 Trapezium Amorphous olivine DI Cep Cep

45. Crystalline olivine Comet Halley Amorphous olivine Comet Hale-Bopp HAe/Be star HD163296

47. Olivine [M2SiO4] Melilite [M2Si2O7] Pyroxene [M2Si2O6]

48. Crystalline Amorphous

49. Crystalline olivine Amorphous olivine

50. Crystalline olivine Crystalline Amorphous olivine Amorphous