1

Atmospheres of Cool Stars

Radiative Equilibrium ModelsExtended Atmospheres

Heating Theories

2

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

3

Dwarfs Giants

• Solid line = Solar abundances[Fe/H]=0

• Dashed line =Metal poor[Fe/H]=-2

• Dot-dashed =Kurucz LTE-RE model

4

Semi-empirical Models Based on Observations of Iλ(μ=1,τ=1)

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

5

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

6

• Determine central specific intensity across spectrum

• Get brightness temperaturefrom Planck curve for Iλ

• From opacity get optical depth on standard depth scale

• T(h) for h=height

7

8

9

Optical:photosphere

EUV: higher

X-ray: higher yet

Reality: Structured and Heated

10

Extended Atmospheres

• Photosphere• Chromosphere• Transition region• Corona• Wind

11

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 T~106 K

12

X-ray image of Sun’s hot coronal gas

13

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 λ<1700 Å; absorption for λ>1700 Å)

• Large continuous opacity in UV, but lines have even higher opacity: appear in emission when temperature increases with height

14

Transition Region

• Seen in high energy transitions which generally require large energies (usually in lines with λ<2000 Å)

• Examples in solar spectrum:Si IV 1400, C IV 1550 (resonance or ground state transitions)

15

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)

16

17

18

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

19

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)

20

Theory of Atmospheric Heating

• Increase in temperature cannot be due to radiative or thermal processes

• Need heating by mechanical or magneto-electrical processes

T T T ateff e ff4 4 43

4

2

3

1

20

21

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 is

where v = turbulent velocity and cs = speed of sound

F v cac s 8 5/

22

Acoustic Heating

• Acoustic waves travel upwards with energy flux = (energy density) x (propagation speed)= ½ ρ 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

23

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 period:ex. 5 minute oscillations of Sun in chromosphere with T = 10000 K yields a damping length of λ = 1500 km

24

Wave Heating

• Change in shock flux with height is

• Energy deposited (dissipated into heat) at height h is

where

dF

dhFmechm ech

1

F h F emech mh

0/

F hmech /

25

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

26

Balance Heating and Cooling

• Energy loss by radiation through H b-f recombination in Lyman continuum (λ < 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

E n f T

n n f Trad e

e H H

2 ( )

27

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 > 20000 K:

• Above T=105 K, most abundant species are totally ionized → slow decline in f(T)

f TT

10

300002 022

, .

28

Radiative Loss Function

29

Energy Balance

• In lower transition region (hot) Pg = 2 Pe

Electron density:

Radiation loss rate:

(almost independent of T since f(T)~T 2.0)• Set T(h) by Einput = Erad

• Suppose Einput = Fmech(h) / λ

nP

kTe

g2

E f TP

kTrad

g

2

22

30

(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 Pg

2

31

(2) Einput declines slowly with hT(h) still increases with h

32

(3) Einput declines quickly with h T(h) may not increase with h

No T increase for damping length λ and pressure scale height H ifλ < H/2

H is large in supergiants so heating in outer atmosphere does not occur.

33

Temperature Relation for Dwarfs• Suppose λ >> H in lower transition region

so that Fmech(h) / λ ≈ constant

f T n B T n BTP

kconst

d T

dh

d P

dh

d T

dh

d P

dh

d P

dh HgP

g m

kT

d T

dh

g m

kT

A

T

dT

dhA

e e

g

g

g g H

H

2 2 2

2

2

2 2 0

2

2

1

2

2

( ) .

ln ln

ln ln,

ln

ln

Constant temperature gradient

34

Heating in the Outer Layers

• T>105 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 (η ~ 10-6 c.g.s.)

| | /F TdT

dhF h F F hc m ech wind rad 5 2

35