Lecture 17 - The solar surface and atmosphere
o Topics to be covered:
o Photosphere
o Chromosphere
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o Transition region
o Corona
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The solar atmosphere
o
Photosphere
o T ~ 5,800 K
o d ~ 100 km
o
Chromosphere
o T ~ 105 K
o d <2000 km.
o
Transition Region
o T ~ 105.5 K
o d ~2500 km
o
Corona
o T >106 K
o d >10,000 km
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The photosphere
o
T ~ 5,800 K
o
r ~ RSun
o
Photosphere is the visible surface of the Sun.
o
At the photosphere, the density drops off
abruptly, and gas becomes less opaque.
o
Energy can again be transported via
radiation. Photons can escape from Sun.
o
Photosphere contains many features:
o Sunspots
o Granules

PG
2nkT
 2
PB B /8
 >>1 in photosphere

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The photosphere
(cont.)
o
o
Sunspots are dark areas in
the photosphere.
o Formed
by
the
concentration of large
magnetic
fields
(B>1000 G).
o Sunspots appear dark
because they are cooler
(~4,300 K).
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Granulation is a small scale
pattern of convective cells
o Results
from
temperature
gradients
close to the solar
surface.
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Photospheric granulation
o
o
Assume mass element in photosphere moves slowly
and adiabatically (no energy exchange)
a, Ta
i, Ti
Ambient density and pressure decrease:   a
o
Mass element expands and   i and T  Ti
o
o
If i > a => cell falls back (stable)
If i < a => cell rises (unstable)
o
Now replace internal parameters with adiabatic:
x
, T
, T
i  ad, Ti  Tad and a  rad
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Photospheric granulation
o
o
Now, pressure inside cell must balance with outside pressure:
Prad = Pad
=> radTrad = adTad
Stable if |ad| < |rad| or over x if
or equivalently if
o
o
dT
dT

dx ad dx rad
a, Ta
d
d

dx ad dx rad
i, Ti
x
, T
, T
From equation of hydrostaticequilibrium (dP/dx =- g) and
the ideal gas law:

dT dT dP dT
dT P d ln T


g ~

dx dP dx
dP
dP T d ln P
Therefore, stable if
d ln T
d ln T

Schwartzchild criterion
d ln P ad d ln P rad

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Determining the photospheric temperature.
o
The Sun emits a blackbody spectrum with peak ~ 5100 Å
peak
o
Using Wein’s Law:
and

T
2.8978  103
 peak
K
 peak = 5100  10 10 m
2.8978  10 3
Tsun 
5100  10 10
~ 5700 K
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The solar constant
o
We know from Stephan-Boltzman Law that
L = AT4 W
o
A is area of Sun’s surface, T is temperature, and  is Stephan-Boltzman constant
(5.67  10-8 W m-2 K-4).
o
The flux reaching the Earth is therefore:
F = L / 4πd2 = 4πR2T4 / 4πd2 Wm-2 [d = 1AU, R = solar radius]
= T4 (R/d)2
= 1396 W m-2
o
This is relatively close to the measured value of 1366 W m-2.
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The solar constant
o
The “solar constant”
actually has a tiny
variation (<1%)
with the solar cycle.
o
Represents the
driver for Earth and
planet climate
modelling.
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The chromosphere
o
Above the photosphere is a
layer of less dense but higher
temperature gases called the
chromosphere.
o
First observed at the edge of
the Moon during solar
eclipses.
o
Characterised by “spicules”,
“plage”, “filaments”, etc.
o
Spicules extend upward from
the photosphere into the
chromosphere.
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The chromosphere (cont.)
o
Prominence and filaments
are cool volumes of gas
suspended above the
chromosphere
by
magnetic fields.
o
Plage is hot plasma
(relative
to
the
chromosphere),
usually
located near sunspots.
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Model solar atmosphere
 1

 1

 ~ 1?


PG
PB

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The corona
o
Hot (T >1MK), low density
plasma (i.e. an ionized gas).
o
There are currently two coronal
heating theories:
o Magnetic waves (AC).
o Magnetic reconnection
(DC).
o
Coronal dynamics and
properties are dominated by the
solar magnetic field.


Yohkoh X-ray image
PG
2nkT
 2
1
PB B /8
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Static model of the corona
o
Assuming hydrostatic equilibrium:
dP
 g
dr
Eqn. 3
where the plasma density is  =n (me+mp) ≈ nmp (mp= proton mass) and both
electrons and protons contribute
 to pressure: P = 2 nkT = 2kT/mp
o
Substituting into Eqn.3,
and integrating =>
2kT d
 g
m p dr
 mgr 

 kT 
  0 exp

where 0 is the density at r ~ R.
o

OK in low coronae of Sun and solar-type stars (and planetary atmospheres).
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Static model of the corona
o
Chapman (1957) attempted to model a static corona with thermal conduction.
o
Coronal heat flux is
q =  T
where thermal conductivity is  = 0T5/2,
o
In absence of heat sources/sinks, q = 0 => (0T5/2T) = 0
o
In spherical polar coordinates,
1 d  2
5 / 2 dT 
r

T

 0
0
r 2 dr 
dr 
Eqn. 1

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Static model of the corona
r 2 0T 5 / 2
dT
C
dr
o
Eqn. 1 =>
o
Separating variables and integrating:

o
5/2
dT 
C
r
dr
2
0
2
C1
 T 7 / 2  
7
0 r
To ensure T = T0 at r = r0 and T ~ 
0 as r  ∞ set

o
T
r0 2 / 7
T  T0 
 r 

r0T07 / 2  
C 7
0 2
Eqn. 2
For T = 2 x 106 K at base of corona, ro = 1.05 R => T ~ 4 x 105 K at Earth (1AU = 214R).
Close to measured value.

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Static model of the corona
o
Subing for T from Eqn. 2, and inserting for P into Eqn. 3 (i.e., including
conduction),
2 / 7 

r0 
d

GM
2
kT
 2

0   


 r  
dr  m p
r
o
Using multiplication rule,

GMm p 
1 d


2
/7


r 2 / 7 dr
r9/ 7
2kT0 r02 / 7 r 2



0
d

dr GMm p

0 r
2kT0 r02 / 7
 2 /7  r
r

dr
r0 r12/ 7
r
7 GMm p r05 / 7
ln(  /  0 )  2 /7ln( r /r0 ) 
5 2kT0 r0 r 5 / 7

2/7
7 GMm r 5 / 7 
 r 
p
(r)  0   exp
 0  1


r0 

5 2kT0 r0  r 


Eqn. 4
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Static model of the corona
o
Both electrons and protons contribute to pressure: P = 2 nkT = 2kT/mp
o
Substituting into Eqn. 4 =>
7 GMm r 5 / 7 
p
0
P(r)  P0 exp
 1
5 2kT r 



r

0 0 

Eqn. 5
o As r  ∞, Eqn.4 => ∞ and Eqn. 5 => P  const >> PISM.
o
PISM ~ 10-15 P0. Eqn. 5 => P ~ 10-4 P0
=> There must be something wrong with the static model.
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