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…
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PHY 688, Lecture 19
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Opacity of M/L/T Dwarfs is Non-Grey
(VB10, M8)
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PHY 688, Lecture 19
(Allard & Hausschildt 1995)
4
Neutral Atoms and Molecules Are Strong
Wavelength-Dependent Absorbers
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PHY 688, Lecture 19
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From Lecture 3: Radiative Transfer
The optical depth τλ accounts for interaction between
photospheric matter and radiation field.
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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
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Non-Grey Opacities, LTE
• In LTE, level populations completely determined by T
from the Boltzmann and Saha equations
Z i = # gie"E i
kT
i
• Need “only” find all important transitions in dominant
atoms and molecules
– also a formidable problem
!
– H2O alone has hundreds millions of lines(!)
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PHY 688, Lecture 19
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Infrared Opacities at Late-L:
Dominated by Molecules
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PHY 688, Lecture 19
(Burrows et al. 2001)
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Chemical Abundances and Species
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PHY 688, Lecture 19
(Burrows et al. 2001)
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Solar Metallicity vs. Metal-Poor Spectra
• the depletion of
metals changes
the ingredients
for atmospheric
chemistry
• thin condensate
clouds, strong
metal hydrides,
strong H2O
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PHY 688, Lecture 19
11
(Burgasser et al. 2006)
With Decreasing Metallicity
•
•
•
•
•
double-metal species
(e.g., TiO) disappear
metal-hydrides survive
preferentially
H– continuum dominant
at <1.1 micron
CIA H2 dominant over
1.1–4 micron
deeper layers revealed
Teff = 3000 K
– stronger metal-hydrides
– pressure-broadened
atomic absorbers
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PHY 688, Lecture 19
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(Allard et al 1997)
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
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Complications with Atmospheric
Modeling
• departure from LTE due to:
– pressure broadening (Na I, K I; van der Waals), interaction
potentials (H2)
– 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)
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Outline
• Review of previous lecture
– substellar atmospheres: opacity, LTE, chemical species,
metallicity
• Dust, Clouds, Meteorology
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PHY 688, Lecture 19
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The Optical to IR SEDs of UCDs
Mar 11, 2009
(Cushing
et al. 2006; Marley & Leggett 2008)
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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
TiO
M9 (latest M dwarf)
L0 (earliest L dwarf)
CrH
Rb
L2 dwarf (like GD 165B)
Cs
L8 (latest L dwarf)
T6.5 dwarf (Gl 229B)
Mar 11, 2009
(Kirkpatrick
et al.
1999)19
PHY 688,
Lecture
17
But Atoms and Simple Molecules
Do Not Make Up the Whole Picture
forsterite
(Mg2SiO4)
ruby corundum
(Al2O3)
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PHY 688, Lecture 19
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(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, H2O, TiO, FeH, CH4 in M/L/T dwarfs
– then condense into a solid or liquid
• e.g., Mg2SiO4, Al2O3 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
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PHY 688, Lecture 19
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Preview of
Dust Cloud
Chemistry
(Burrows et al. 2001)
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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
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PHY 688, Lecture 19
KI
(Kirkpatrick 2005)
Wavelength (Å)
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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
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PHY 688, Lecture 19
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From Lecture 8:
Near-IR CMD of Stars and Brown Dwarfs
F–K
M
L
T
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(Kirkpatrick 2005)
From Lecture 3:
Extinction and Optical Depth
• Light passing through a medium can be:
– transmitted, absorbed, scattered
• dLν(s) = –κν ρ Lν ds = –L dτν
– medium opacity κν [cm2 g–1]
– optical depth τν = κν ρs [unitless]
• Lν = Lν,0e–τ = Lν,0e–κρs =Lν,0e–s/l
– photon mean free path: lν = (κν ρ)–1 = s/τν [cm]
• If there is extinction along the line of sight, apparent magnitude mν
is attenuated by
Aν = 2.5 lg (Fν,0/Fν) = 2.5 lg(e)τν = 0.43τν mag
– reddening between two frequencies (ν1, ν2) or wavelengths is defined as
Eν1,ν2 = mν1 – mν2 – (mν1 – mν2)0 [mag]
– (mν1 – mν2)0 is the intrinsic color of the star
AV / E(B–V) ≈ 3.0
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PHY 688, Lecture 19
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From Lecture 3:
Interstellar Extinction Law
extinction is highest at ~100 nm = 0.1 µm
decreases at longer wavelengths
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PHY 688, Lecture 19
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L Dwarfs Are
Dusty Objects
M
L
• models that incorporate
suspended dust
(DUSTY) can
reproduce L dwarf
colors
T
DUSTY models
(dust remains
suspended)
• but these same models
do not work for T
dwarfs
COND models
(dust is removed)
– late T’s better fit by
COND models (dust
removed upon
formation)
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PHY 688, Lecture 19
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(Baraffe et al. 2003)
Detailed
Dust Cloud
Chemistry
(Burrows et al. 2001)
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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)???
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Radiation, Convection, and Conduction in
Earth’s Atmosphere
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Cloud Formation: Meteorology 102
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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; qt: mixing ratio; w*: convecitve
velocity scale, frain: sedimentation efficiency
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Condensate Clouds
(AM01 Baseline Models)
L dwarf
Mar 11, 2009
T dwarf
PHY 688, Lecture 19
giant
planet
(Ackerman & Marley 2001)
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