1. Introduction As temperatures below approximately 1800 K (depending upon the density and composition) are encountered in an astrophysical environments, dust grains become important sources of opacity. Because these small grains are very efficient absorbers and scatterers of light, they increase the opacity from one to several orders of magnitude wherever they exist. Dust opacity is important in modeling the radiative transfer in such diverse objects as cool stellar atmospheres (both dwarfs and giants), brown dwarf atmospheres, extrasolar planet atmospheres, star forming clouds, protoplanetary disks, white dwarf atmospheres, pulsating stars, supernovae ejecta, among others.

2. Grain condensation is very temperature sensitive Solid MgSiO 3 H2OH2OH2OH2O

5. Shown to the right, is the partial pressure versus temperature for several species. The gas pressure corresponds to the log R=-3 shown in the previous slide. Al 2 O 3 forms at the highest T, then CaTiO 3, which is not an important opacity source, but does deplete gaseous TiO Solid Fe, the black line, forms and is most abundant until the emergence of FeS. Enstatite and Forsterite are also very abundant.

6. Number density of grains N g = N p / N p/g = N p / (4/3  a g 3  g /m p ) Where: g refers to grains p refers to condensate particles p refers to condensate particles a g is the grain size a g is the grain size  g is the mass density of the grain  g is the mass density of the grain (4 to 8 g/cm 3 ) (4 to 8 g/cm 3 ) m p is the condensate particle’s mass m p is the condensate particle’s mass

7. Computation of Dust Opacity Where Q ext depends on the complex index of refraction Where Q ext depends on the complex index of bbbbbbbbbbbbrefraction n i depends on the size distribution and the abundance of species i computed by the equation of state n i depends on the size distribution and the abundance of species i computed by the equation of state  a 2 is the geometrical cross section  a 2 is the geometrical cross section

9. Grain size

10. Grain particle extinction cross-sections (Mie). Monoatomic condensates such as Fe, Ni, Cu, contribute essentially scattering (dotted lines) in the UV, while corrundum, magnesium spinel, CaTiO 3, and the silicates Absorb also in the infrared.

11. Extinction profiles for a grain size distribution going from 1, 2, 10, to 100 times that of the ISM, for conditions prevailing in photospheric layers (T  1300K) of our AMES-Dusty model at 1800K. The structures above 8.5  m are due to absorption by Mg 2 SiO 3 at 10 and 15.5  m, and MgAl 2 O 4 at 13  m.

12. Dust particles dominate the opacity at low temperatures

13. Frequency Averaged Opacity It is often useful to average the opacity of a gas over wavelength. It is often useful to average the opacity of a gas over wavelength. There are, in general 2 techniques for averaging There are, in general 2 techniques for averaging Rosseland mean opacity Rosseland mean opacity Planck mean opacity Planck mean opacity

14. Rosseland mean opacity The diffusion equation is useful in stellar interiors where the gas is optically thick Rosseland Mean Opacity

15. Planck mean opacity In optically thin situations the radiative transfer equation is approximately Planck Mean Opacity

16. Density Parameter All results presented here are computed with a density parameter of log R = - 3.0. The density parameter is defined as R =  /T 6 3, where  is the mass density and T 6 is the temperature expressed in millions of K. The table below gives representative values of the density and pressure for this value of R. All results presented here are computed with a density parameter of log R = - 3.0. The density parameter is defined as R =  /T 6 3, where  is the mass density and T 6 is the temperature expressed in millions of K. The table below gives representative values of the density and pressure for this value of R. log T [K]log P g [dyn cm -2 ] log ρ [cm gm -3 ] 3.30 -0.06 -11.10 3.15 -0.85 -11.55 3.00 -1.46 -12.00 2.85 -2.06 -12.45 2.70 -2.66 -12.90 log T [K]log P g [dyn cm -2 ] log ρ [cm gm -3 ] 3.30 -0.06 -11.10 3.15 -0.85 -11.55 3.00 -1.46 -12.00 2.85 -2.06 -12.45 2.70 -2.66 -12.90 -2.66 2.70 -12.45 -2.06 2.85 -12.00 -1.46 3.00 -11.55 -0.85 3.15 -11.10 -0.06 3.30 log ρ [cm gm -3 ] log P g [dyn cm -2 ]log T [K] Log T [K] Log P [dyn cm -2 ] Log  [cm gm -3 ] 3.30-0.06-11.10 3.15-0.85-11.55 3.00-1.46-12.00 2.85-2.06-12.45 2.70-2.66-12.90

17. Rosseland Opacities Log R = -3.0

18. A number of differences can be seen between the Alexander & Ferguson results of 1994 and the current results. The first grain to condense here is Al 2 O 3, at log T~ 3.2, was not included in AF94. Silicate grains condensed at a higher temperature in the more approximate equation of state of AF94. The CDE approximation for the opacity of grains used by AF94 produced a greater opacity.

19. The distribution of particle sizes can significantly affect the opacity due to grains, as shown on the left above. The corresponding size distribution is shown to the right, where each size distribution has been normalized to a constant total grain volume. The Weingartner & Draine (ApJ, 548, 296, 2001) distribution produces a grain opacity similar to that produced by the Mathis, Rumple & Nordsieck (ApJ, 217, 425, 1977; MRN) distribution. The Kim, Martin & Hendry (ApJ, 422, 164, 1994) distribution produces less opacity due to the larger number of small particles, which are less efficient absorbers. The log normal distribution has a mean particle size of 0.15  m and a sigma of 2.5. The distribution of particle sizes can significantly affect the opacity due to grains, as shown on the left above. The corresponding size distribution is shown to the right, where each size distribution has been normalized to a constant total grain volume. The Weingartner & Draine (ApJ, 548, 296, 2001) distribution produces a grain opacity similar to that produced by the Mathis, Rumple & Nordsieck (ApJ, 217, 425, 1977; MRN) distribution. The Kim, Martin & Hendry (ApJ, 422, 164, 1994) distribution produces less opacity due to the larger number of small particles, which are less efficient absorbers. The log normal distribution has a mean particle size of 0.15  m and a sigma of 2.5.

20. Rosseland mean opacities computed with all but one source illustrate the importance of the ‘missing’ source. Al 2 O 3 grains condense at relatively high temperatures and increase the opacity by about an order of magnitude. A variety of silicates (principally MgSiO 3 and Mg 2 SiO 4 ) and iron condense at log T ~ 3.05, and produce another order of magnitude increase in the opacity. Metallic iron is gradually replaced by iron sulfide at still lower temperatures.

21. We have adopted a standard wavelength range for our calculations of 0.1  m to 500  m. Optical constants for condensed species are often not available over this entire range. Because the Rosseland mean (and photons) favor wavelengths with low opacity, missing data produces huge changes in the opacity. For this plot, all optical constants at long or short wavelengths were eliminated to illustrate the effect of missing data. We have adopted a standard wavelength range for our calculations of 0.1  m to 500  m. Optical constants for condensed species are often not available over this entire range. Because the Rosseland mean (and photons) favor wavelengths with low opacity, missing data produces huge changes in the opacity. For this plot, all optical constants at long or short wavelengths were eliminated to illustrate the effect of missing data.

22. Grains can have a profound effect on the spectra of cool dwarf stars.

23. Refractory Elements Quasi-Static cloud model

24. Microphysical and convective characteristic timescales as a function of the grains’ mean radius Grain growth: Radial condensable matter transport by convective turbulence Radial condensable matter transport by convective turbulence (rain) of dust particles Sédimentation (rain) of dust particles increases the nuclei's radius Condensation increases the nuclei's radius of particles produces larger grains Coalescence of particles produces larger grains Rossow (Icarus 36, 1,1978) Rossow (Icarus 36, 1,1978)

25. Surface Convection Ludwig, Allard, Hauschildt, A&A 2002 HRD Simulation T eff =2800K, logg=5.0 Vertically:  =100 sec  =240 m/s Horizontally: cell = 80 km Contrast= 1.1%

26. Mass exchange frequency as a function of Pressure for various degrees of subsonic filtering

27. Considered Options Phenomenological model Phenomenological model without adjustable parameter  mix   conv H p /   mix   conv H p /  in the convective zone in the convective zone  mix  parabola  mix  parabola of same opening as in the convective zone of same opening as in the convective zone

28. Tsuji et al. (1999, 2002)  T cr Ackerman & Marley (2001)  f rain

29. Settl vs Cond/Dusty

31. Settl vs a T2 dwarf

32. Cond/Dusty vs Settl 2002 Allard, Guillot & Ludwig (2003)

33. What’s left to do? Explore properties of grain opacities Explore properties of grain opacities Different size distributions Different size distributions Inhomogeneous grains Inhomogeneous grains Porous grains Porous grains Non-spherical grains Non-spherical grains Thermal history of condensation sequence Thermal history of condensation sequence Obtain optical constants for missing but abundant grain species Obtain optical constants for missing but abundant grain species