Lecture 16 - The solar surface and atmosphere
o  Topics to be covered:
o  Photosphere
o  Chromosphere
o  Transition region
o  Corona
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
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
β=
PG
2nkT
= 2
PB B /8π
>>1 in photosphere
€
The photosphere
(cont.)
o  Sunspots are dark areas in
the photosphere.
o  F o r m e d b y t h e
concentration of large
magnetic fields
(B>1000 G).
o  Sunspots appear dark
because they are cooler
(~4,300 K).
o  Granulation is a small scale
pattern of convective cells
o  R e s u l t s f r o m
temperature gradients
close to the solar
surface.
Determining the photospheric temperature.
o  The Sun emits a blackbody spectrum with
peak
2.8978 × 10−3
T=
λ peak
o  Using Wein’s Law:
K
and
λ peak = 5100 × 10 −10 m
€
€
Tsun
2.8978 × 10 −3
=
5100 × 10 −10
~ 5700 K
peak ~
5100 Å
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
(5.67
10-8 W m-2 K-4).
is Stephan-Boltzman constant
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.
The solar constant
o  The “solar constant”
actually has a tiny
variation (~0.1%)
with the solar cycle.
o  Represents the
driver for Earth and
planet climate
modelling.
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.
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.
Model solar atmosphere
β >> 1
€
β << 1
€
β ~ 1?
€
β=
€
PG
PB
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.
β=
€
PG
2nkT
= 2
<< 1
PB B /8π
Yohkoh X-ray image
Static model of the corona
o  Assuming hydrostatic equilibrium:
dP
= −gρ
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 =>
where
2kT dρ
= −gρ
m p dr
$ mgr '
ρ = ρ 0 exp&−
)
% kT (
€
0
is the density at r ~ R. The scale height is H = kT / mg.
€
o  OK in low coronae of Sun and solar-type stars (and planetary atmospheres).
Static model of the corona
o  Chapman (1957) attempted to model a static corona with thermal conduction.
o  Coronal heat flux is
q=
where thermal conductivity is
o  In absence of heat sources/sinks,
T
=
0T
5/2,
q = 0 =>
(
0T
5/2
T) = 0
o  In spherical polar coordinates,
1 d# 2
5 / 2 dT &
r
κ
T
%
(=0
0
r 2 dr $
dr '
€
Eqn. 1
Static model of the corona
r 2κ 0T 5 / 2
dT
=C
dr
o 
Eqn. 1 =>
o 
Separating variables and integrating:
€
o 
5/2
dT =
C
κ0
dr
∫r
2
2
C1
=> T 7 / 2 = −
7
κ0 r
To ensure T = T0 at r = r0 and T ~ €
0 as r
€
o 
∫T
∞ set
# r0 & 2 / 7
∴T = T0 % (
$r'
€
r0T07 / 2 = −
C 7
κ0 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.
€
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&
#
#r &
d
ρ
kT0 % 0 (
%%2
$r'
dr $ m p
GMm p ρ
1 dρ
ρ
−
2
/7
=
−
r 2 / 7 dr
r9/7
2kT0 r02 / 7 r 2
o  Using multiplication rule,
€
∫
€
GMρ
(( = − 2
r
'
GMm p
r dr
dρ
=
2
/7
−
∫
ρ0 ρ
r0 r
2kT0 r02 / 7
ρ
∫
dr
r0 r12 / 7
r
7 GMm p r05 / 7
ln( ρ / ρ 0 ) = 2 /7ln(r /r0 ) +
5 2kT0 r0 r 5 / 7
€
# 7 GMm *# r & 5 / 7 -&
# r &2 / 7
p
ρ(r) = ρ 0 % ( exp%%
,% 0 ( −1/((
$ r0 '
.'
$ 5 2kT0 r0 +$ r '
€
€
Eqn. 4
Static model of the corona
o  Both electrons and protons contribute to pressure: P = 2 nkT = 2
o  Substituting into Eqn. 4 =>
o  As r
∞, Eqn.4 =>
" 7 GMm )" r % 5 / 7 ,%
p
P(r) = P0 exp$$
+$ 0 ' −1.''
-&
# 5 2kT0 r0 *# r &
€ ∞ 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.
kT/mp
Eqn. 5