Atmospheres of Cool Stars

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Atmospheres of Cool Stars

• Radiative Equilibrium ModelsExtended
  AtmospheresHeating Theories

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Radiative Equilibrium Models

• Gustafson et al. (2005) MARCS codedifficult
  because of UV line haze(millions of b-b
  transitions of Fe I in 300-400 nm range, and Fe
  II in 200-300 nm range)
• Convection important at depth
• Metallicity and line blanketing causes surface
  cooling and back warming

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Dwarfs Giants

• Solid line Solar abundancesFe/H0
• Dashed line Metal poorFe/H-2
• Dot-dashed Kurucz LTE-RE model

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Semi-empirical Models Based on Observations of
I?(µ1,t1)

• Solar spectrum shows non-thermal components at
  very long and short wavelengths that indicate
  importance of other energy transport mechanisms

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• Major b-b and b-f transitions for solar opacity
  changes

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• Determine central specific intensity across
  spectrum
• Get brightness temperaturefrom Planck curve for
  I?
• From opacity get optical depth on standard depth
  scale
• T(h) for hheight

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Reality Structured and Heated
Opticalphotosphere
EUV higher
X-ray higher yet
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Extended Atmospheres

• Photosphere
• Chromosphere
• Transition region
• Corona
• Wind

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Corona

• Observed during solar eclipses or by coronagraph
  (electron scattering in optical)
• Nearly symmetric at sunspot maximum,
  equatorially elongated at sunspot minimum
• Structure seen in X-rays (no X-ray emission from
  cooler, lower layers)
• Coronal lines identified by Grotrian, Edlén
  (1939) Fe XIV 5303, Fe X 6374, Ca XV 5694
• High ionization level and X-rays indicate T106 K

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X-ray image of Suns hot coronal gas
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Chromosphere

• Named for bright colors (flash spectrum)
  observed just before and after total eclipse
• H Balmer, Fe II, Cr II, Si II lines present
  indicates T 6000 10000 K
• Lines from chromosphere appear in UV (em. for
  ?lt1700 Å absorption for ?gt1700 Å)
• Large continuous opacity in UV, but lines have
  even higher opacity appear in emission when
  temperature increases with height

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Transition Region

• Seen in high energy transitions which generally
  require large energies (usually in lines with
  ?lt2000 Å)
• Examples in solar spectrumSi IV 1400, C IV 1550
  (resonance or ground state transitions)

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Stellar Observations

• Chromospheric and transition region lines seen in
  UV spectra of many F, G, K-type stars
  (International Ultraviolet Explorer)
• O I 1304, C I 1657, Mg II 2800
• Ca II 3968, 3933 (H, K) lines observed as
  emission in center of broad absorption (related
  to sunspot number in Sun useful for starspots
  and rotation in other stars)
• Emission declines with age (rotation)

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Chromospheres in H-R Diagram

• Emission lines appear in stars found cooler than
  Cepheid instability strip
• Red edge of strip formed by onset of significant
  convection that dampens pulsations
• Suggests heating is related to mechanical motions
  in convection

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Coronae in H-R Diagram

• Upper luminosity limit for stars with transition
  region lines and X-ray coronal emission
• Heating not effective in supergiants (but mass
  loss seen)

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Theory of Atmospheric Heating

• Increase in temperature cannot be due to
  radiative or thermal processes
• Need heating by mechanical or magneto-electrical
  processes

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Acoustic Heating

• Large turbulent velocities in solar granulation
  are sources of acoustic (sound) waves
• Lightman (1951), Proudman (1952) show that energy
  flux associated with waves iswhere v
  turbulent velocity and cs speed of sound

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Acoustic Heating

• Acoustic waves travel upwards with energy flux
  (energy density) x (propagation speed) ½ ? v2
  cs
• If they do not lose energy, then speed must
  increase as density decreases? form shock waves
  that transfer energy into the surrounding gas

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Wave Heating

• In presence of magnetic fields, sound and shock
  waves are modified into magneto-hydrodynamic
  (MHD) waves of different kinds
• Damping (energy loss) of acoustic modes depends
  on wave periodex. 5 minute oscillations of Sun
  in chromosphere with T 10000 K yields a damping
  length of ? 1500 km

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Wave Heating

• Change in shock flux with height is
• Energy deposited (dissipated into heat) at height
  h is where

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Wave Heating

• Energy also injected by Alfvén waves (through
  Joule heating caused by current through a
  resistive medium)
• Observations show spatial correlation between
  sites of enhanced chromospheric emission and
  magnetic flux tube structures emerging from
  surface magnetic processes cause much of energy
  dissipation

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Balance Heating and Cooling

• Energy loss by radiation through H b-f
  recombination in Lyman continuum (? lt 912 Å) and
  collisional excitation of H
• In chromosphere, H mainly ionized, primary source
  of electrons
• for H recombination for H collisional
  excitation
• Similar relations exist for other ions

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Radiative Loss Function

• Below T 15000 K, f(T) is a steep function of T
  because of increasing H ionization
• Above T 15000 K, H mostly ionized so it no
  longer contributes much to cooling
• He ionization becomes a cooling source for T gt
  20000 K
• Above T105 K, most abundant species are totally
  ionized ? slow decline in f(T)

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Radiative Loss Function
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Energy Balance

• In lower transition region (hot) Pg 2
  PeElectron densityRadiation loss
  rate(almost independent of T since f(T)T 2.0)
• Set T(h) by Einput Erad
• Suppose Einput Fmech(h) / ?

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(1) Einput constantT(h) increases with h
Increasing height in outer atmosphere
Each line down corresponds to a 12 drop in Pg or
a 26 drop in Pg2
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(2) Einput declines slowly with hT(h) still
increases with h
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(3) Einput declines quickly with h T(h) may not
increase with h
No T increase for damping length ? and pressure
scale height H if? lt H/2H is large in
supergiants so heating in outer atmosphere does
not occur.
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Temperature Relation for Dwarfs

• Suppose ? gtgt H in lower transition region so that
  Fmech(h) / ? constant

Constant temperature gradient
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Heating in the Outer Layers

• Tgt105 K, rad. losses cannot match heating
• T increases until loss by conductive flux
  downwards takes over ( wind, rad. loss)
• Conductive flux (from hot to cool regions by
  faster speeds of hotter particles)
• Find T(h) from (? 10-6 c.g.s.)

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