Substellar Atmospheres II. Dust, Clouds, Meteorology PHY 688, Lecture 19 Mar 11, 2009
Outline Review of previous lecture substellar atmospheres: opacity, LTE, chemical species, metallicity Dust, Clouds, Meteorology Mar 11, 2009 PHY 688, Lecture 19 2
Previously in PHY 688 Mar 11, 2009 PHY 688, Lecture 19 3
Opacity of M/L/T Dwarfs is Non-Grey (VB10, M8) Mar 11, 2009 PHY 688, Lecture 19 4 (Allard & Hausschildt 1995)
Neutral Atoms and Molecules Are Strong Wavelength-Dependent Absorbers Mar 11, 2009 PHY 688, Lecture 19 5
From Lecture 3: Radiative Transfer The optical depth τ λ accounts for interaction between photospheric matter and radiation field. Mar 11, 2009 PHY 688, Lecture 19 6
Non-Grey Opacities Exact interaction between radiation field and matter is complicated and often intractable vast number of excitable atomic and molecular transitions Assume local thermodynamic equilibrium (LTE) radiation and matter characterized by the same temperature T gas: Maxwell-Boltzmann, radiation: Planck Mar 11, 2009 PHY 688, Lecture 19 7
Non-Grey Opacities, LTE In LTE, level populations completely determined by T from the Boltzmann and Saha equations Need only find all important transitions in dominant atoms and molecules also a formidable problem H 2 O alone has hundreds millions of lines(!) # i Z i = g i e "E i kt Mar 11, 2009 PHY 688, Lecture 19 8
Infrared Opacities at Late-L: Dominated by Molecules Mar 11, 2009 PHY 688, Lecture 19 9 (Burrows et al. 2001)
Chemical Abundances and Species Mar 11, 2009 PHY 688, Lecture 19 10 (Burrows et al. 2001)
Solar Metallicity vs. Metal-Poor Spectra the depletion of metals changes the ingredients for atmospheric chemistry thin condensate clouds, strong metal hydrides, strong H 2 O (Burgasser et al. 2006) Mar 11, 2009 PHY 688, Lecture 19 11
With Decreasing Metallicity double-metal species (e.g., TiO) disappear metal-hydrides survive preferentially H continuum dominant at <1.1 micron CIA H 2 dominant over 1.1 4 micron deeper layers revealed stronger metal-hydrides pressure-broadened atomic absorbers T eff = 3000 K (Allard et al 1997) Mar 11, 2009 PHY 688, Lecture 19 12
Validity of LTE Assumption Depends on Fate of Excited Atom/Molecule bound-bound case: if excited state is collisionally de-excited photon energy is absorbed by the gas absorption couples radiation to matter through collisions if absorption dominates opacity, LTE approximation is valid if excited state is radiatively de-excited original photon is scattered; its energy radiated away no collisions, weak dependence on temperature of matter transitions have finite energy width; re-emission at a low absorption probability wavelength can lead to further decoupling of radiation and matter if scattering dominates opacity, LTE approximation is not valid bound-free and free-free (continuum) cases, Thomson, Rayleigh scattering unimportant at low T, high P Mar 11, 2009 PHY 688, Lecture 19 13
Complications with Atmospheric Modeling departure from LTE due to: pressure broadening (Na I, K I; van der Waals), interaction potentials (H 2 ) micro-turbulent velocity broadening generally small; 1 2 km s 1 formation of large grains; condensation of grains into clouds grain sedimentation rate cloud distribution and variations ( weather ) chemistry, especially non-equilibrium mixing depth of convection zone (10 3 < τ < 1) Mar 11, 2009 PHY 688, Lecture 19 14
Outline Review of previous lecture substellar atmospheres: opacity, LTE, chemical species, metallicity Dust, Clouds, Meteorology Mar 11, 2009 PHY 688, Lecture 19 15
The Optical to IR SEDs of UCDs (Cushing Mar 11, 2009 et al. 2006; Marley & Leggett 2008) PHY 688, Lecture 19 16
UCD Spectral Classification largely based on strengths of atomic or molecular absorbers e.g.: CaH and TiO indices for M dwarfs CrH, Rb I, Cs I for L dwarfs, among others CaH TiO M9 (latest M dwarf) L0 (earliest L dwarf) Rb L2 dwarf (like GD 165B) L8 (latest L dwarf) T6.5 dwarf (Gl 229B) TiO CrH Cs Mar 11, 2009 (Kirkpatrick PHY 688, et al. Lecture 1999) 19 17
But Atoms and Simple Molecules Do Not Make Up the Whole Picture forsterite (Mg 2 SiO 4 ) ruby corundum (Al 2 O 3 ) Mar 11, 2009 PHY 688, Lecture 19 18 (Burrows et al. 2001)
Simplified Chemical Picture As gas temperature of a (brown) dwarf drops, atoms: first favor an ionized state e.g., Ca II, Fe II in Sun then favor a neutral state e.g., Na I, K I in M/L/T dwarfs then form molecules e.g, H 2 O, TiO, FeH, CH 4 in M/L/T dwarfs then condense into a solid or liquid e.g., Mg 2 SiO 4, Al 2 O 3 in L/T dwarfs dust clouds More refractory elements tend to condense first Exact sequence of molecule and condensate formation depends on gas pressure metallicity turbulent mixing from warmer or colder layers, etc Mar 11, 2009 PHY 688, Lecture 19 19
Preview of Dust Cloud Chemistry (Burrows et al. 2001) Mar 11, 2009 PHY 688, Lecture 19 20
Example: the M/L Dwarf Transition Teff ~ 2300 K first TiO and then VO weaken at early L and then disappear by mid-l TiO converts into TiO2 or condenses into CaTiO3 (pervoskite) or into other Ti-bearing molecules VO, less refractory, then converts into VO2 or into solid VO/Ti-bearing condensate Al, Ca, Si similarly removed no directly observable effect however, if present would have bound and removed K I from atmosphere K I, Na I left as dominant absorbers over 4000 10000 Å by mid-l Mar 11, 2009 PHY 688, Lecture 19 KI (Kirkpatrick 2005) Wavelength (Å) 21
Dust in Substellar Atmospheres Once dust condenses, it may: remain suspended at level of formation sediment to deeper, optically thick layers Either can occur, depending on temperature, surface gravity Presence of suspended dust (clouds) is required to explain very red colors of L dwarfs Mar 11, 2009 PHY 688, Lecture 19 22
From Lecture 8: Near-IR CMD of Stars and Brown Dwarfs F K T M L Mar 11, 2009 PHY 688, Lecture 19 (Kirkpatrick 2005) 23
From Lecture 3: Extinction and Optical Depth Light passing through a medium can be: transmitted, absorbed, scattered dl ν (s) = κ ν ρ L ν ds = L dτ ν medium opacity κ ν [cm 2 g 1 ] optical depth τ ν = κ ν ρs [unitless] L ν = L ν,0 e τ = L ν,0 e κρs =L ν,0 e s/l photon mean free path: l ν = (κ ν ρ) 1 = s/τ ν [cm] If there is extinction along the line of sight, apparent magnitude m ν is attenuated by A ν = 2.5 lg (F ν,0 /F ν ) = 2.5 lg(e)τ ν = 0.43τ ν mag reddening between two frequencies (ν1, ν2) or wavelengths is defined as E ν1,ν2 = m ν1 m ν2 (m ν1 m ν2 ) 0 [mag] (m ν1 m ν2 ) 0 is the intrinsic color of the star A V / E(B V) 3.0 Mar 11, 2009 PHY 688, Lecture 19 24
From Lecture 3: Interstellar Extinction Law extinction is highest at ~100 nm = 0.1 µm decreases at longer wavelengths Mar 11, 2009 PHY 688, Lecture 19 25
L Dwarfs Are M Dusty Objects models that incorporate suspended dust (DUSTY) can reproduce L dwarf colors but these same models do not work for T dwarfs late T s better fit by COND models (dust removed upon formation) T COND models (dust is removed) L DUSTY models (dust remains suspended) Mar 11, 2009 PHY 688, Lecture 19 26 (Baraffe et al. 2003)
Detailed Dust Cloud Chemistry (Burrows et al. 2001) Mar 11, 2009 PHY 688, Lecture 19 27
Cloud Formation: Meteorology 101 A cloud appears where adiabatic cooling of an air parcel in an upward draft results in saturation Further cooling condenses vapor in excess of saturation onto cloud particles The particles grow through condensation and coalescence until their sedimentation velocities exceed the updraft speed and then fall out of the parcel Why is there convection in a supposedly radiative region (the atmosphere)??? Mar 11, 2009 PHY 688, Lecture 19 28
Radiation, Convection, and Conduction in Earth s Atmosphere Mar 11, 2009 PHY 688, Lecture 19 29
Cloud Formation: Meteorology 102 Mar 11, 2009 PHY 688, Lecture 19 30
Sedimentation Cloud condensates will settle under gravity to a level where there is enough upward convective (turbulent) motion to keep them afloat. Level and vertical extent of clouds depend on droplet size (i.e., mass) convective velocity, mixing efficiency K: eddy diffusion coefficient; q t : mixing ratio; w * : convecitve velocity scale, f rain : sedimentation efficiency Mar 11, 2009 PHY 688, Lecture 19 31
Condensate Clouds (AM01 Baseline Models) L dwarf T dwarf giant planet Mar 11, 2009 PHY 688, Lecture 19 32 (Ackerman & Marley 2001)