Download lec1_2008 - Stanford Solar Physics

Solar and Solar-Terrestrial Physics
Physics 363
Time: 3:15-4:45, Tuesday, Thursday
Place: Hewlett , room 103
Instructor: Alexander Kosovichev
e-mail: [email protected]
Phone: 723-7667
Office: Physics and Astrophysics, room 128
URL: http://sun.stanford.edu/~sasha/PHYS363
Grades: bi- weekly assessments + presentations
Lecture Plan
1. Jan. 8, Tuesday. Introduction: The Sun as a star. General properties,
place in the Hertzsprung-Russell diagram. Distance, mass, radius,
luminosity, composition, age, evolution, spectral energy distribution. "Big
problems": solar neutrinos, rotation, dynamo, magnetic energy release,
coronal heating.
2. Jan. 10, Thursday. Internal structure I. Stellar Scaling Laws. Standard
model. Evolution. Nuclear reactions. Equation of state. Radiative transfer.
3. Jan. 15, Tuesday. Internal structure II. Stability. Convective transfer. Nonstandard models. Solar neutrinos, neutrino transitions, MSW effect.
4. Jan. 17, Thursday. Solar oscillations. Observations. Theory of p-, g-, and
r-modes. Excitation mechanisms.
5. Jan. 22, Tuesday. Helioseismology I. Variational principle, perturbation
theory. Inversions, sound speed and rotation inferences.
6. Jan. 24, Thursday. Helioseismology II. Local-area helioseismology, ringdiagrams, acoustic imaging, time-distance tomography.
7. Jan. 29, Tuesday. Convection. Granulation, supergranulation, giant cells.
Blue shift, models. Energy balance. Superadiabatic layer. Rotational and
magnetic effects. Numerical simulations.
8. Jan. 31, Thursday. Differential rotation. Observations. Heliographic
coordinates. Oblateness, quadrupole moment, test of the general relativity.
Rotational history. Models of differential rotation.
9. Feb. 5, Tuesday. Solar MHD. MHD equations, Alfven and magnetoacoustic waves. Instabilities. Shocks.
10.
11.
12.
13.
14.
15.
16.
Feb. 7, Thursday. Dynamo The solar cycle, global magnetism. "Magnetic
carpet". Mean-field electrodynamics, dynamo models.
Feb. 12, Tuesday. Magnetic energy release. Reconnection. Particle
acceleration. Observations. Theories of reconnection, current sheets, MHD
and plasma instabilities. Acceleration mechanisms.
Feb. 14, Thursday. Solar atmosphere. The structure of the solar
atmosphere, photosphere, chromosphere, corona. Transition region.
Chromospheric network, filaments, prominences, spicules.
Feb. 19, Tuesday. Sunspots. Active regions. Flux tubes. Observations.
Static models. Flows, Evershed effect. Formation and decay. Theories of
emerging flux tubes, magnetic buoyancy.
Feb. 21, Thursday. Flares. Observations. Radiation, radio-, X-, and
gamma-rays. Energetic particles. Thin- and thick-target models,
evaporation, heat conduction. Radiative and MHD shocks. Moreton waves,
"sunquakes".
Feb. 26, Tuesday. Corona. CME. Observations, eclipses. White light
corona, Thompson scattering. Coronal heating, heat conduction. Largescale structure, change with the solar cycle. Coronal mass ejections,
shocks.
Feb. 28, Thursday. Solar wind. Observations. Expansion, Parker’s model,
high- and low-speed wind. Composition, first-ionization potential effect.
Sector structure, current sheet. Geomagnetic effects. Space weather.
17.
18.
19.
20.
March 4, Tuesday. Space weather. Interaction of solar wind with the
Earth's magnetosphere and planets. Geomagnetic effects. Space weather
March 6, Thursday. Tools for solar observations I. Solar telescopes.
Resolution, MTF, seeing. High resolution telescopes. Spectrographs.
March 11, Tuesday. Tools for solar observations II. Measurements of
the line shift. Magnetic fields and polarimetry.
March 13, Thursday. Tools for solar observations III. Solar space
missions: SOHO, TRACE, STEREO, Hinode, SDO. Neutrino telescopes.
Books
1.
2.
3.
4.
5.
6.
7.
8.
9.
Stix, M. 2002, The Sun: An Introduction, (Berlin: Springer)
Cox, A.N., Lingston, W.C., Matthews, M.S., 1991, Solar Interior
and Atmosphere (Tucson, University of Arizona)
Zirin, H. 1988, Astrophysics of the Sun (Cambridge Univ. Press)
Bahcall J.N. 1989, Neutrino Astrophysics (Cambridge Univ. Press)
Foukal, P. 1990, Solar Astrophysics (New York: Wiley)
Priest, E.R. 1982, Solar Magnetohydrodynamics (Dordrecht:
Reidel)
Golub, L., and Pasachoff, J.M. 1997, The Solar Corona
(Cambridge Univ. Press)
Sturrock, P. (ed.) 1986, Physics of the Sun, (Kluwer).
Aschwanden, M. J., Physics of the Solar Corona, Springer, 2006
Essay Topics.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Solar diameter, oblateness and gravitational quadrupole moment
Solar neutrino problem.
Predictions of the solar cycle.
Helioseismic inverse problem for structure.
Helioseismic inverse problem for rotation
Excitation of solar oscillations.
Solar convection and turbulence.
Mechanism of differential rotation.
Solar tachocline.
Magnetic reconnection.
MHD shocks and Moreton waves.
Dynamo models.
Acceleration mechanisms in solar flares.
Coronal mass ejections.
Mechanisms of coronal heating.
Coronal seismology.
Acceleration of solar wind.
Waves in magnetosphere
General Properties of the Sun.
Hertzsprung-Russel Diagram.
Sun
Hertzsprung-Russel Diagram. Numbers in the mainsequence
band are
stellar
masses
in units ofcatalog
the solar mass.
22,000
stars
from
Hipparcos
Dotted lines correspond to constant radius in units of the
solar radius.RW - radiatively driven wind.
•1911-13, Ejnar Hertzsprung and
Henry Norris Russell independently
developed H-R diagram
•Horizontal axis - spectral type
(or, equivalently, color index or
surface temperature)
•Vertical axis - absolute
magnitude (or luminosity)
•Data points define definite regions,
suggesting common relationship
exists for stars composing region.
Each region represents stage in
evolution of stars.
•The place of a star on the H-R
diagram also tells us about its
radius, energy generation and
transport, periods and growth rates
of pulsations, rotation rate, stellar
activity, X-ray coronas, etc.
•Sun is G2 main-sequence star.
Lies roughly in middle of diagram
among what are referred to as
yellow dwarfs.
Overall properties
Age
45  109 years
101065 years
Mass ( M )
199  1033 g
103330 g
696  1010 cm
101084 cm
Radius ( R )
Mean density
1.4 g cm 3
10015 g cm 3
Mean distance from Earth (AU) 15  1013 cm
101384 cm
274  104 cm s 2 10444 cm s 2
Surface gravity ( g )
Escape velocity
617  107 cm s 1 10779 cm s 1
386  1033 erg s 1 103359 erg s 1
Luminosity ( L )
Equatorial rotation period
26 days
10635 s
Angular momentum
17  1048 g cm 2 s 1 104823 g cm 2 s 1
Mass loss rate
1012 g s 1
5785 K
Effective temperature ( Te )
10376 K
1 arc sec
726 km
10786 cm
Distance
Until recently distances in the solar system were measured by triangulation.
More accurate results are obtained by measuring radar echos.
In principle, a single measurement of a linear distance between two bodies of the solar
system is sufficient to derive all distances between the planets and the Sun.
This is because of Kepler’s third law which relates semi-major axes ai and periods Ti
for a body m :
a 3 GM

(1  mM )
2
2
T
4
The ratios of the semi-major axes of two bodies is:
3
2
 a1   T1  1  m1M

   
a
T
1

m

M
2
 2  2
Masses m1 and m2 are determined from the mutual perturbations of planetary orbits.
The Sun is not used directly to determine the distance to the Sun, the astronomical
unit (AU).
Distance - II
Kepler’s law
Triangulation
The light time for 1 AU is:
 A  499004782  0000006 s
The speed of light by definition (since 1983) is
c  299792458 m s 1 .
1AU  149597880  2 km
Then,
The major semi-axis for the Earth is
a  1000000036 AU  1496  1013 cm.
Linear distances on the Sun are measured in arc sec:
1  726 km at the disk center.
The Sun's angular size varies from 31' 27.7" to 32' 31.9" during the
course of a year.
Sun’s rotation axis is inclined by 7.25 degrees to
the ecliptic
January 5
February 8
March 7
April 8
May 5
June 5
July 7
August 13
September 8
October 11
November 9
December 7
Figure : Due to the Earth revolution and axis inclination, the position angle of the Sun’s axis is varying
all along the sidereal year. The value of this angle is near zero around Earth perihelion and aphelion.
The distance of the Sun’s rotational poles from the limb has been exaggerated: at maximum the shift
reaches 7°. We can only see the sunspots’ paths as straight lines in early June and December.
Mass
Once distances are known the Sun’s mass is determined from Kepler’s law.
Only the product, GM , is determined with high precision:
GM  (132712438  000000005)  1026 cm3s2 
The gravitation constant is determined in laboratory measurements:
G  (6672  0004)  108 cm3g 1s2 
Therefore,
M  (19891  00012)  1033 g
Mass loss due to the energy radiated into space:
1
dM dt  L c2  4 1012 g s 
Mass loss due to the solar wind: 1012 g s 1 .
The total loss during the Sun’s life of 15  1017 s:
75  1029 g (0.04%).
Radius
The angular diameter is defined as the angular distance between the
inflection points of the intensity profile at two opposite limbs.
It is measured photoelectrically.
Results for the solar radius:
apparent angular
apparent linear
photospheric(   1 )
1
960"01  0"1
6960  1010 cm
(6.9626  0.0007) 1010 cm
2
959"68  0"01 (6.9602  0.00007) 1010 cm 6955  1010 cm
1
Wittman, A. 1977, Astron. Astrophys., 61, 255
2
Brown, T.M. & Christensen-Dalsgaard, J. 1998, ApJ, 500, L195.
The current reference
69599  007 Mm.
value
is:
(69599  00007)  1010
cm
=
Helioseismic estimate of the solar radius from f-mode frequencies:
(69568  00003)  1010 cm (Schou, J. et al., 1997, ApJ, 489, L197).
The frequencies of the f mode (surface gravity wave) depend only on the
horizontal wavenumber k  l (l  1)R ( l is the mode angular degree)
and surface gravity g  GM R 2 :
  gk  GM [l (l  1)]1 2 R3 
This allows us to estimate R from the wave dispersion relation,  (l ) ,
and GM .
The discrepancies may be related to the poor understanding the upper
convective boundary layer of the Sun.
The evolutionary change of the solar radius: dR dt 24 cm/year.
There is controversial evidence that the solar radius changes with the
solar activity cycle.
The Sun’s mean density:   1408 g/cm 3 .
The gravitational acceleration:
g  GM R 2 274  104 cm/s 2 .
Oblateness
Oblateness is defined as
( Requator  Rpole ) R  RR
Origin: rotation + magnetic fields (?).
Measurements:
 even n

Rsurf ( )  R 1   rn Pn (cos )  
n 2


where Pn are Legendre polynomials.
r2
Solar Disk
Sextant 1
SOHO/MDI 2
1
2
( 5810  0400)  106
(5329  0452)  106
r4
( 417  459)  107
( 553  040)  107 (1996)
( 141  055)  107 (1997)
Lydon, T.J. & Sofia, S. 1996, Phys.Rev.Lett., 76, 177.
Kuhn, J. et al. 1998, Nature, 392, 155.
Quadrupole moment
The gravitational potential:
2

GM 
R


 ( r  )  
P2 ( )  
1  J 2 

r 
 r 

where J 2 is the quadrupole moment.
From the equation of hydrostatic equilibrium:
2 R
J2 
 r2 
3g
where  is the Sun’s angular velocity.
The first term is almost equal to r2 :
2 R
3g
 5625  10
6
.
7
Therefore, J 2  (184  40)  10 .
If general relativity describes the advance of perihelion of Mercury, then
4298  004 acrsec/century corresponds to a quadrupole moment
(23  31)  107 .
Composition
The approximate fraction of the mass of the plasma near the surface of
the Sun:
Element
abundance
H (hydrogen)
He (helium)
Li (lithium)
Be (beryllium)
B (boron)
C (carbon)
N (nitrogen)
O (oxygen)
0735  075
0248  025
155  109
141  1011
200  1010
372  10 4
115  104
676  10 4
Luminosity
The solar luminosity, L , is the the total output of electromagnetic
energy per unit time. It is measured from space because the Earth’s
atmosphere attenuates the solar radiation.
L  (3845  0006)  1033 erg s
The absolute magnitude of the Sun is M  474 (at 10 parsec distance).
The Sun’s luminosity increased by 28% over the Sun’s life of about
46  109 years.
The total irradiance at 1 AU ("solar constant"): S  L  4 A2  1367  2
W/m 2 .
Absorption in the Earth’s
atmosphere.
The edge of the shaded area
marks the height where the
radiation is reduced to 1/2 of its
original strength.
UV - ultraviolet; V- visible; IR infrared.
Irradiance
The total irradiance at 1 AU ("solar constant"):
S  L  4 A2  1367  2 W/m 2 .
The composite total irradiance
from 1977 to 1999.
Note the variation with the
solar activity cycle of order
0.1%
Effective temperature
The effective temperature is determined by:
L  4 R  T 
2
4
eff
where   567032  1011 erg/cm 2 K 4 is the
Stefan-Boltzmann constant.
Teff  5777  25 K
Spectral energy distribution
The energy flux, F (  ) , is the emitted energy per unit area, time and
wavelength interval.
The spectral irradiance:
S ( )  F ( ) R 2  (1 AU) 2 
Intensity, I (   ) , is the energy emitted per unit area, time, wavelength
interval, and sterad. It depends on angular distance  from the normal to
the surface.

F ( )  2  I (   )cos sin  d 
0
(check this).
The limb-darkening function is I (   ) I (0  )
Solar irradiance spectrum
1 Angstrom = 10-10 m = 10-8 cm = 0.1 nm
1 nm = 10 A
3 million K
1 million K
60,000 K
6,000 K
Temperature (K)
10 7
Corona
nH
10 6
T
10 5
10
10 14
Transition Region
Chromosphere
104
1012
10 10
10 8
3
10
10 16
2
Total Hydrogen Density (cm-3)
Temperature & Density Structure
of the “Solar Atmosphere”
10 3
10 4
10 5
Height Above Photosphere (km)
Visible spectrum
The visible spectrum. The upper curve - I (0  ) ; the lower curve F (  )  (intensity averaged over the disk); The smooth curve is a
black-body spectrum at T  Teff  5557 K. Note the hydrogen H 
absorption line at   6563 nm.
Infrared spectrum
About 44% of the energy is emitted above 08  m. The spectrum is
approximated by the Reileigh-Jeans relation:
S ( )
2ckT  2 ( R 1 AU) 2 
The brightness temperature, TB , is defined by I   B (TB ) , where I  is
the observed absolute intensity,
2h 3
1
B (T )  2
c exp(hkT )  1
is the Kirchhoff-Plank function. TB
5000 K at   10  m.
The infrared spectral
irradiance.
Radio spectrum
The radio spectrum begins at   1 nm. The energy is often given
per unit frequency rather than per unit wavelength. For quiet Sun it
continues smoothly from the infrared. Discovered in 1942.
Solar radio emission.
Dots and solid curve - quiet Sun;
dashed - slowly varying component
( s  component ); dotted curves - rapid
events ( bursts ). Note the transition
between   1 cm and   1 m. There
is a transition in TB from 104 K to 106
K - transition from the solar
chromosphere to corona.
UV spectrum
UV irradiance. The solid and dashed smooth curves are black-body spectra.
Note the sharp decrease at   210 nm due to the ionization of Al I. Absorption
lines are mostly above 200 nm. Below 150 nm emission lines dominate the
spectrum. The most prominent is the Lyman  line at 121.57 nm. The spectrum
is highly variable.
EUV and X-ray spectrum
EUV is below 120 nm. It is highly variable, and characterized by a large number
of emission lines from highly ionized atom, e.g. Fe XVI. The range of TB is
6
from 8000 K to 4  10 K. The main source of EUV radiation is the transition
region between the chromosphere and corona.
Soft X-ray emission is between 0.1 nm and 10 nm.
Hard X-rays are below 1 nm.
Soft X-ray from GOES satellite
Black body radiation
Black body spectrum depends only on temperature
3 million K
1 million K
60,000 K
6,000 K
Temperature (K)
10 7
Corona
nH
10 6
T
10 5
10
10 14
Transition Region
Chromosphere
104
1012
10 10
10 8
3
10
10 16
2
Total Hydrogen Density (cm-3)
Temperature & Density Structure
of the “Solar Atmosphere”
10 3
10 4
10 5
Height Above Photosphere (km)
Visible solar spectrum with absorption (Fraunhofer) lines
Color indices
Color indices are rough characteristics of the spectral energy distribution.



0
0

U  B  25 log  S (  ) EU (  )d   log  S (  ) EB (  )d   CUB



0
0

B  V  25 log  S ( ) EB ( )d   log  S ( ) EV ( )d   CBV
where EU  EV  EB are ultraviolet, blue and visible filter functions about 100
nm wide, centered at 365, 440, and 548 nm respectively. Constants CUB and
CBV are chosen that both U  B and B  V are zero for A0-type stars.
The Sun has U  B  020 and B  V  066 .
Real-time solar images
http://sohowww.nascom.nasa.gov/
http://www.bbso.njit.edu/cgi-bin/LatestImages
http://www.raben.com/maps/
White-light
Image
SOHO/MDI
Continuum 6768 A
Magnetogram
magnetogram
H-alpha
H-alpha 6563 A
Ca II K line
Chromosphere
Ca II K 3933 A
EUV
He II
304 Å
SOHO
EIT
He II 304A
EUV
Fe IX/X
171 Å
SOHO
EIT
Fe IX/X 171 A
Fe XII 195 A
Fe XV 284 A
“Big” problems in solar physics
•
•
•
•
•
•
Solar neutrino problem
Solar cycle and dynamo
Magnetic energy storage and release
Particle acceleration
Coronal heating
Source of solar wind
Solar Neutrino Problem
Solar cycle and dynamo
Magnetic energy storage and
release
Particle acceleration
RHESSI observations of
July 23, 2002, flare
00:20-00:40 UT (RED: 12-20 keV,
BLUE: 100-150 keV)
Coronal heating
Source of solar wind
"The sun, with all the planets revolving
around it, and depending on it, can still
ripen a bunch of grapes as though it had
nothing else in the universe to do“
Galileo Galilei