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Lecture 11
The Sun
University of Naples Federico II, Academic Year 2011-2012Istituzioni di Astrofisica, read by prof. Massimo Capaccioli
EIT - Extreme-ultraviolet Imaging Telescope of SOHO
Review: static stellar structure equations
2
2 2
4 4
Hydrostatic equilibrium: Equation of state:
Mass conservation: Energy generation:
Radiati o n:
r
H
r r
dP GM kTP
dr r m
dM dLr r
dr dr
ρ ρµ
π ρ π ρε
= − =
= =
2 3 2
3 1
pConvection (
olitr ) :op
e
164
r H r
P
dT L dT m GM
dr r T dr k r
γρκρ µπσ γ
∝
= − = −
The Solar modelBy solving the equations of the previous slide we can build up a model of the interior structure of the Sun.In general the differential equations are solved .
Instead of assuming a
numeric
polyt
ally
rope temperature gradient mode of energy transport
Boundary condition 0
, choose the depending on the
at :
.
......., ,: in the si
.........mplest case
at :
0 0
, , a
.
0 0 nd 0.s
r M L
r R P Tρ= = == = = =
⊙
Convection zones in the Sun
For the Solar model we can plot as a function of radius.
Where radiation most effecti this is , ve form is the o ener
ln ln
2.5 gy trans rf po t.
d P d T
>
The Solar interior
The interior can be divided into three regions:
1. Core: site of nuclear reactions
2. Radiative zone
3. Convective zone
Abundance distribution
32
H depleted in the core
He
He
pp chain
most abu
is ,
where is produced.
is an intermediate species
in the .
It is atndant top
H-burnin
the
of the ,
where
g region
Abundances
is lower.
a
T
⊳
⊳
i
i
i
i
i
⊳
within the ,
since
re homogeneou
the plasma is
s
convective zone
effectively
mi e .
x d
i
i
i
The solar model: evolutionAs the abundances in the corechange, the nuclear reaction rates change accordingly, and the luminosity L, temperature Te , and radiusR of the star are affected.
time
R R
L L⊙
⊙eT
Energy production
nuclear reaction rates higher temperature higher
is not
Although are where the is ,
most of the energy of produced center
amount of mass
the Sun because:
1. the in a
a
shell
radiu
at the
4s t is r dM π= 2 ;
. . there is more mass per unit
volume at
(assuming constant density);
2. the of
( ) at the center has b
large radius
mass fraction Hydrogen
depleteeen
due to
d
fusio , and the rat
X
n
i e
r drρ
2
e equations
depend o Xn .
rate of change of L
Recall: proton-proton chain
1 41 2
7 1 44 1 2
3 4 1 42 2 1 2
The net reactions are:
4 2 2 2
PPI
PPII
PP
2
2
In all cases,
III
neutr are produced ino w i hs h c
e
e
e
H He e
Be H He e
He He H e He
γ
γ
γ
υ
υ
υ
+
+
−
→ + + +
+ → + + +
+ + + → + +
have a .
So they leave the Sun , telling us what the physical conditi
negligig
ons are
le cross section
untouched
where they are produced.
Expected Solar neutrino flux
33 1bolometric Solar fluxHe n
3.864 10 erg s26.7
Given the , ,the energy produced by the production of a , ,and carried by
ucleusaverage energy neut
MeVq 0.6 the , ,
the rino
total Soa
lar nMe
uV
e trin
LQ
ν
−= ×=
=
( )( )33
38
2 1
6
13
102
is:
.
At the distance of the Earth, , the
o flux
flux per
3.864 102 1.851 10 neutrin
cm
osq 1.609 10 26
is:
, apparentl
.7 0.6
1.495 10 cm
6.588 10 neutrin y enorm
s
us!s oo4
L
Q
d
d
νν
ννφ
π
−
−
×Φ = × = = ×− × −
= ×
Φ= = ×
3717One type of neutrino detector on Earth uses an isotope of ( Cl), which
will (rarely) int
chlorine
radioactiveeract with a neutrino to produce a o isotope argon
f :
37 3717 18
This reaction requires the neutrino to have an energy
of or more, and can only detect
neutrinos from the "side-reactions" in the PP chain:
0.814 MeV
PPII
eCl Ar eυ −+ ⇔ +
3 4 7 7 1 82 2 4 4 1 5
7 7 8 84 3 5 4
7 1 4 8 43 1 2 4 2
The Homes
2
take (South
PP II
2
I
e e
He He Be Be H B
Be e Li B Be e
Li H He Be He
γ γυ υ− +
+ → + + → +
+ → + → + +
+ → →
3
2 430
Dakota) detector contains ~ 400,000 cm of perchloroethylene (C Cl ), a cleaning flu
id.
2 10 atoms of Cl isoto pe.
× o ne Arg on ato Det m eve ry ect 2 3 .s days÷
Direct observations of the core: neutrinos
Ray Davis
Direct observations of the core: neutrinos
7131
GALLEX SAGE natural
gallium aqueous gallium chloride solutio
More recently, the (also ) experiments uses of
in a to detect neutrinos via:
3
0
tons
100 to
n n 7132
1 1 21 1 1
2 1 31 1 2
3 3 4 12 2 2 1
This is sensitive to ( ) and can detect
neutrinos fro
lower neutrino energies
main branch PP chain
0.233 MeV
m the of the :
2
e
e
Ga Ge e
H H H e
H H He
He He He H
υ
υγ
−
+
+ ⇔ +
+ → + +
+ → +
+ → +
Both the and experiments detected (by a
factor 2 3) than were expected from the PP-chain reactions.
This problem exist 3
Homestake GALLEX fe
ed for .
The soluti
wer neutr
on was su
0
gg
i
e
nos
ste
y
d
ear
r
s
by
÷∼
esults from the in
Japan.
Results showed that
produced in the
can change into
Super-Kamiokande detector
electron neutrinos
upper atmosphere
t or .
This means neutrinos
au- muo
must h
n-neutrinos
so
ave
me mass
oscillate
and can t
between fl
heref
avo
ore
urs.
The Solar neutrino: problem and solution
The Solar neutrino problem: final solution
The Sudbury Neutrino Observatory (Ontario, Canada) uses heavy water, and was able to directly detect the flux of all types of neutrinos from the Sun.
The results are now completely consistent with the standard Solar model.
The Solar atmosphere
T ~ 106 K
T ~ 25000 K
T ~ 5770 K
The solar atmosphere extends thousands of km above the photosphere(from which the optical radiation is emitted)
It is of much lower density and higher temperature than the photosphere
T ~ 107 KCore
The extended solar spectrum
While the solar radiation is similar to a blackbody prediction at optical wavelengths, there is excess radiation at very short wavelengths. This light is also highly variable.
The radio Sun
Radio waves penetrate through the chromosphere and corona.
The image here shows the "transition region" between the chromosphere and the corona.
The infrared Sun
Infrared images show some features of the Sun's chromosphere, and some features in the corona.
Dark markings are caused by absorption of the infrared light by regions of high density.
The chromosphere
• UV (30.4 nm) images reveal the chromosphere.• Can sometimes see large prominences rising high above the surface of
the Sun. • At the north and south poles of the Sun, less EUV light is emitted -these
regions often end up looking dark in the pictures, giving rise to the term coronal holes.� These are low density regions extending above the surface where
the solar magnetic field opens up.
HeI emission
The X-ray Sun
The X-rays we see all come from the corona.
The corona is a very stormy place, constantly changing and erupting.
Movie from http://www.lmsal.com/SXT/sxt_movie.html
Sunspots
Dark (cool) regions of the photosphere.
Number of spots changes on a 11 year cycle.
Concentrations of magnetic field lines.
The Sun’s magnetic field
By studying sunspots we can learn about the nature of the Sun’s magnetic field.
Switches polarity every 11 years.
Recap: electromagnetic radiation
Region Wavelength [Å] Wavelength [cm] Frequency [Hz] Energy [eV]
Radio > 109 > 10 < 3×109 < 10−5
Microwave 109 ÷ 106 10 ÷ 0.01 3×109 ÷ 3×1012 10−5 ÷ 0.01
Infrared 106 ÷ 7000 0.01 ÷ 7×10−5 3×1012 ÷ 4.3×1014 0.01 ÷ 2
Visible 7000 ÷ 4000 7×10−5 ÷ 4×10−5 4.3×1014 ÷ 7.5×1014 2 ÷ 3
Ultraviolet 4000 ÷ 10 4×10−5 ÷ 10−7 7.5×1014 ÷ 3×1017 3 ÷ 103
X-Ray 10 ÷ 0.1 10−7 ÷ 10−9 3×1017 ÷ 3×1019 103 ÷ 105
Gamma Ray < 0.1 < 10−9 > 3×1019 > 105
h = 6.625×10−27 erg s k = 1.38×10-16 erg K−1
Thermal energy at ambient temperature 0.04 eV
Visible light photons 1.5 ÷ 3.5 eV
Dissociation energy of a molecule of NaCl in ions Na+ and Cl- 4.2 eV
Hydrogen atom dissociation energy 13.6 eV
Energy of an electron shooting the screen of a color TV ∼0.2 keV
X photons for medial diagnostics 0.2 MeV
Nuclear decay energies:
(1) gamma 0 ÷ 3 MeV
(2) beta 0 ÷ 3 MeV
(3) alpha 2 ÷ 10 MeV
Cosmic rays energy 1 MeV ÷ 1000 TeV
Recap: elettronVolt
1 eV/c² = 1.783×10−33 g1 keV/c² = 1.783×10−30 g1 MeV/c² = 1.783×10−27 g = 2×mel
1 GeV/c² = 1.783×10−24 g = mprot