REU Training
The Solar Atmosphere
Jerry Harder
jerry.harder@lasp.colorado.edu
303 492 1891
Topic Outline
• What we will talk about
– The solar irradiance problem – it’s all about the Earth…
– Rudimentary radiative transfer
• Planck’s law
• Role of quantum mechanics
– Atomic and molecular processes that determine the
structure of the solar atmosphere
• Formation of Fraunhofer lines
– Solar structures (biased toward photosphere and
chromosphere)
– SRPM modeling of solar irradiance from solar images
• What we won’t talk about
– Plasma and electromagnetic processes
– Convection and magnetohydrodynamics
Things to remember about the Sun
695,510 km (109  radii)
1.989 x 1030 kg (332,946 ’s)
1.412 x 1027 m3 (1.3 million  ‘s)
151,300 kg/m3 (center)
1,409 kg/m3 (mean)
Temperature 15,557,000° K (center)
5,780° K (photosphere)
2 - 3×106 ° K (corona)
1 AU
1.49495×108 km
TSI (@1 AU) 1,361 W/m2
Composition 92.1% hydrogen
7.8% helium
0.1% argon
Radius
Mass
Volume
Density
Fourth Assessment Report of the IPCC, 2007
There is uncertainty in
solar forcing since the
start of the industrial
era but climate
response is even more
uncertain:
Where Does the Earth Atmosphere Get Its Energy?
Large-scale energy sources that act continuously or quasicontinuously in the
Heat Flux*
atmosphere and at its boundaries.
[W/m 2 ]
Solar Irradiance
340.25
Heat Flux from Earth's Interior
0.0612
Radioactive Decay
0.0480
Solar Cycle Variability alone, ~ 0.1% of TSI,
Geothermal
0.0132
Infrared Radiation from the Full Moon
0.0102
is
~
10X
larger
than
the
second
largest
energy
Sun's Radiation Reflected from Moon
0.0034
Energy Generated by Solar Tidal Forces in the Atmosphere
0.0034
Combustion of Coal, Oil, and Gas in US (1965)
0.0024
Energy Dissipated in Lightning Discharges
0.0002
Dissipation of Magnetic Storm Energy
6.8E-05
Radiation from Bright Aurora
4.8E-05
Energy of Cosmic Radiation
3.1E-05
Dissipation of Mechanical Energy of Micrometeorites
2.0E-05
Total Radiation from Stars
1.4E-05
Energy Generated by Lunar Tidal Forces in the Atmosphere
1.0E-05
Radiation from Zodiacal Light
3.4E-06
Total of All Non-Solar Energy Sources
0.0810
* global average
Heat Source
Physical Climatology, W.D. Sellers, Univ. of Chicago Press, 1965
Table 2 on p. 12 is from unpublished notes from
H.H. Lettau, Dept. of Meteorology, Univ. of Wisconsin.
Relative Input
1.000
1.8E-04
1.4E-04
3.9E-05
3.0E-05
source
1.0E-05
1.0E-05
7.0E-06
6.0E-07
2.0E-07
1.4E-07
9.0E-08
6.0E-08
4.0E-08
3.0E-08
1.0E-08
2.4E-04
T  30 K without Sun
340.25 W m-2
340.25
Energy budget within the atmosphere after Kiehl and Trenberth [1997]. The numbers give the globally and
annually averaged solar (left side of the figure) and longwave (right side) irradiances [W m-2].
Solar Forcing on Long-term Climate Change
-0.6 K
-3.0 W/m2
-2.5 W/m2
Modern Maximum
Maunder
Minimum
Dalton
Minimum
-1.2 W/m2
[figures from Scafetta and West, GRL, 2006]
Solar Forcing Causes Natural Climate Variability
The complex climate system has
many components that drive long
term changes.
Solar variations are one of the
crucial climate components.
[Figure from J. Lean, Solar Physics, 2005]
The TSI Climate Record
• TSI climate record is a combination of multiple data sets to obtain
composite time series of the total solar irradiance (TSI)
• The VIRGO-based and ACRIM-based composite time series indicate
similar downward trend for current for solar minimum
– A 0.02% decrease is observed for both sets, but both are very preliminary results
VIRGO Composite
ACRIM Composite
-0.02%
-0.02%
Why measure solar spectral irradiance?
Solar Forcing and Response Mechanisms are Wavelength Dependent
Chemistry Climate Models Need SSI
GISS GCM [Rind et al., 2004; Shindell et al., 2006]
Near UV, visible, near infrared radiation
NCAR WACCM [Marsh et al., 2007]
affect surface and ocean processes
HAMMONIA [Schmidt and Brasseur, 2006]
CMAM [Beagley et al., 1997]
Ultraviolet (UV) radiation drives
many atmospheric processes
Altitude contour for attenuation
by a factor of 1/e
[Adapted from P. Pilewskie, Solar Physics, 2005]
Wavelength Dependence of Sun Images
Yohkoh Soft X-ray
Telescope (SXT)
Ca II K
spectroheliograms
NSO
Sacramento Peak
Extreme Ultraviolet
Imaging Telescope
(EIT)
Fe XII 195 Å
He I 10830 Å
spectroheliograms
NSO Kitt Peak
Solar Radiative Transfer in the Lowest
Denomination
Planck’s equation
Planck's distribution law for the density of radiation
in a cavity :
First radiation const = 2 hc 2 = 3.7418e-016 (mks)



2 hc 2 
1


W 
5 
 hc  
hc
Second radiation const =
 0.014388 (mks)
 exp   kT   1 

 

k
(radiation emitted into a hemisphere)
Two important limits :
Wein's approximation
hc
2 hc 2
 hc 
When
? 5 then W 
exp


5
 kT

  kT 
Rayleigh - Jeans approximation
When
hc
2 c kT
= 1 then W 
 kT
4
Properties of the Planck distribution
On differentiation of the Planck equation and setting
 
=0

an equation for the peak wavelength can be found :
hc
maxT 
 2897.8 (micron - degree)
4.965 k
Peak power at max :
Wmax  1.288 1015 T 5
The equation of Stefan - Boltzmann relates the total thermal
radiation density with temperature

WTotal   W d    T 4 (W m -2 )
0
2 5 k 4
8


5.6697

10
{the Stefan - Boltzmann Constant mks}
2 3
15c h
The Sun as a blackbody
Brightness Temperature
Tbrightness


h 
1

k   2h 4 1
 ln  2
  c  I1au



 
  1 
 
Sources of opacity in the solar atmosphere
The Spectrum of the Sun: Role of Quantum
Physics
• The presence of trace atoms and molecules in the sun
greatly complicates its spectrum.
• These trace components can be determined from
atomic and molecular quantum theory - both in line
position and intensity.
• Trace component absorption and emission properties
determine the radiative output of the ‘star’ (radiative
transfer).
• Trace components act as a temperature probe for the
solar atmosphere.
Hydrogen
• sdfa
In the Bohr Approximation:
 1
1 
  RZ  2  2 
 n2 n1 
The Rydberg Constant :
2
2 2  e 4
-1
R

109,
677.581
cm
ch3
Extension to Other Atoms and Molecules
• Heavy atoms and their ions add an enormous number of
transitions to the spectrum.
• Simple molecules (CN, CH, LiH, CO,H2O…) add structure
and important information to the spectrum
• >1,000,000 atomic and molecular transitions needed to
describe the spectrum
Atomic and Collisional Processes That Determine
Atmospheric Structure
Process
Incoming
Absorption
A + h
Spontaneous Emission
A*
Induced Emission
A* + h
Free-Free Emission (Bremsstrahlung) e- + A+
Free-Free Absorption
e- + A+ + h
Photoionization
A + h
2-Body Recombination
e- + A+
Collisional Excitation
e- + A
Collisional De-excitation
e- + A*
Collisional Ionization
e- + A
3-Body Recombination
2e- + A+
Dielectric Recombination
e- + A
Dielectric Absorption (Autoionization) A* + h
 = decrease, increase in electron energy
*
= excited state
+
= ionized state
Outgoing
A*
A + h
A +2 h
e- + A+ + h
e- + A+
e- + A+
A* + h or A + h
e- + A*
e- + A
2e- + A+
e- + A
A* + h
e- + A+
RT Summary
• As expected, radiant emissions arise from
different portions of the solar atmosphere.
• Atomic and molecular processes are apparent
in the emission spectra and follow the welldefined quantum mechanical rules. Therefore
identification is very certain.
• Spectral inversion techniques are then possible
to determine the structure of the solar
atmosphere.
Formation of Solar Fraunhofer Lines
•
Caused by a selective process of line scattering or line absorption followed by continuum
absorption.
– A two level atom through absorption and spontaneous emission emits light of wavelength 0 into
a sphere reducing the intensity of the original beam.
– Absorption of the emitted light by H- over a long optical path followed by the production of a free
electron that is rapidly thermalized. The thermalized electron will recombine to form H - with a
different kinetic energy and emit at a different wavelength.
•
The flux of photons of wavelength 0 is depleted and the energy emerges at a wavelengths
distributed smoothly throughout the photospheric continuum.
SRPM Modeling of Solar Spectrum
CN Spectrum in the violet
portion of the spectrum
(in brightness temperature)
H in the red part of the spectrum
(done in radiance)
RT Example
• MUV portion of spectrum shows a case:
– Nominally follows Planck Continuum
– Absorption edges apparent
– Mg II shows broad Fraunhofer structure and h & k lines show upper
photospheric/chromospheric emissions
The Solar Atmosphere
SRPM Solar Atmosphere Models/Image Processing
Wavelength Dependence of Sun Images
•
•
•
•
•
Observations of Photospheric and
Chromospheric Active Regions
Center-to-limb brightness curves
Granulation, super granulation
Sunspots
Ultra-high resolution images
Facular Regions
SRPM/PSPT modeling of solar images
}
Center-to-Limb Brightness #1
PSPT
Blue Image
Center-to-Limb Brightness #2
• The sun’s brightness changes as a function of position from disk
center and wavelength (From P. Foukal, Solar Astrophysics)
Granulation and Super Granulation #1
• Long slit spectrum
Granulation and Super Granulation
• Doppler imaging shows the appearance of
supergranulation, characteristic of 30 km
(larger than granulation shown in image)
Sunspot and Facular Regions
Active Region as seen by TRACE spacecraft
What are Facula ?
• Faculae = plural of facula-Latin for “small torch”
• History of observations:
– Originally discovered near the limb in full-disk images of the Sun, faculae
are the small, bright, patterns around dark sunspots and in the
“photospheric network”.
• Facular brightness is difficult to model
– Depends sensitively on wavelength, size, and disk position.
– Small-scale magnetic flux ranges in angular size from 1-to-2 arc-seconds
(micropores) down to less than 0.1 arc-seconds (“flux tubes”) –very hard to
observe.
– Hardest thing to measure/model: the Center-to-Limb Variation (CLV) in
brightness of faculae as a function of size and/or magnetic field strength.
CLV as a function of magnetic field
Measures how bright the facula
is relative to the local continuum.
Concurrent measurements of
magnetic field from magnetograms complete the plot
Swedish 1-m Solar Telescope, G-Band Image
Tick marks
= 1 Mm
= 1.4 arc-sec
Images from Tom Berger, 2004 SORCE meeting
Hot Wall Model for Facula
• D is the tube diameter, Zw is the Wilson depression, and  is the
angle between the local vertical and the line of sight (equal to the
heliocentric angle).
What are Sunspots?
Sunspot Geometry
Umbra
Penumbra
• Umbra dark center region, can be
as large as 20 Mm.
• Sometimes have light bridges (see
SST image).
• Penumbral regions can extend the
spot size to ~50 Mm. Outer edges
is always sharp.
• Some images will show
granulation within the umbral
core.
• Sunspots tend to come in pairs to
conserve div B=0
Spots Are Cool regions
• Typical spot temperature ~3700K
• Possesses an intense, extended, and relatively
long-lived magnetic field.
– Intense vertical magnetic fields inhibit
convection:3000-4000 Gauss
– Convective heat flux is blocked below the spot,
and heat flux flows around it
• Penumbra exhibit complex flow patterns (both
spectrally and spatially) – Evershed flow
SRPM Solar Atmosphere Models/Image Processing
References
• “Solar Astrophysics”, Peter Foukal, Wiley
Interscience, 1990.
• “The Solar Atmosphere”, Harold Zirin,
Blaisdell Publishing Co, 1966.
• ‘Quantitative Molecular Spectroscopy and Gas
Emissivities”, S. S. Penner, Addison-Wesley,
1959.
• “The Quiet Sun”, Edward Gibson, NASA SP303, 1972