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Things to remember about the Sun
Radius 695,510 km (109 radii)Mass 1.989 x 1030 kg (332,946 ’s) Volume 1.412 x 1027 m3 (1.3 million ‘s)Density 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 kmTSI (@1 AU) 1,361 W/m2 Composition 92.1% hydrogen
7.8% helium 0.1% argon
Wavelength Dependence of Sun Images
Yohkoh Soft X-rayTelescope (SXT)
Extreme UltravioletImaging Telescope(EIT)Fe XII 195 Å
Ca II KspectroheliogramsNSOSacramento Peak
He I 10830 Åspectroheliograms NSO Kitt Peak
Radiometric Terminology
Name Symbol Description Units Radiant Energy U J Radiant Power (flux) P Rate of transfer of energy W (or J s-1) Radiant Intensity J Power per solid angle from source W ster-1
Radiance N Power per solid angle per unit area from a source
W ster-1cm-2
Irradiance H Power per unit area incident on a surface
W m-2
Physical Constants Symbol Value Units Planck’s Constant h 0.66262×10-33 J sec Boltzman’s Constant k 1.3806×10-23 J deg-1
Speed of Light c 2.997925×108 m sec-1
Solid angle subtended by the Sun at 1 AU
6.79994×10-5 steradians
Advice: PAY ATTENTION TO YOUR UNITS!!!
Definition of Solid Angle ( )
Solid angle subtended by sphere (from an ‘interior’point):
=4• For an area seen from a point of observation:
• Approximation for a distant point ( small):
2
dA
s
2 1 cos
The inverse square law: Intensity
• Consider a point source of energy radiating isotropically– If the emission rate is P watts, it will have a radiant
intensity (J) of:
– If a surface is S cm from the source and of area x cm2, the surface subtends x2/S2 steradians.
– The irradiance (H) on this surface is the incident radiant power per unit area:
-1(W ster )4
PJ
2-2
2 2 (W cm )
4
x PH J
S S
Point source illuminating a plane
23
2
coscos
cos
o
xH J H
S
2
2o
xH J
S
Extended sources must be treated differently than point sources
• Radiance (N): power per unit solid angle per unit area
• Has units of W m-2 ster-1
• Lambert’s Law: J = Jo cos
• Surface that obeys Lambert’s is known as a Lambertian surface
Brightness independent of angle for a Lambertian surface
Lambertian source radiating into a hemisphere
-1 -2
-10
Source has radiance (W ster cm ) and area
At some angle , the intensity is :
cos cos (W ster )
The incremental ring area on the hemisphere :
2 sin
and subtends a solid angle :
2 sin
N A
J J NA
da R d
R dd
2
0
/ 22/ 2
00
2 sin
The radiation intercepted by this ring is then :
2 sin 2 sin cos
Integrate over hemisphere :
sin2 sin cos 2 (watts)
2
dR
dP J d NA d
P NA d NA NA
{P/A is ½ of what you would expect from a point source}
History of Absolute Radiometry
• Ferdinand Kurlbaum (1857-1927)– Radiometric developments for the
measurement and verification of the Stefan-Boltzmann radiation law.
• Knut Ångström (1857-1910)– Observations of the ‘Solar
Constant’ and atmospheric absorption
Absolute Radiometry
Basic process for electrical substitution radiometry
Remember:Joule Heating:P = I2R = V2/R
Implementation for SORCE (SIM)
Total Irradiance Monitor (TIM)
Major Advances• Phase sensitive detection at the shutter fundamental
frequency eliminates DC calibrations• Nickel-Phosphide (NiP) black absorber provides
high absorptivity and radiation stability
Goals• Measure TSI for >5 yrs
• Report 4 TSI measurements per day
• Absolute accuracy <100 ppm (1 s)
• Relative accuracy 10 ppm/yr (1 s)
• Sensitivity 1 ppm (1 s)
Radiometer Cones
Glory Prototype Cone Interior
Glory Prototype Cone
Post-Soldered Cone
TIM Baffle DesignGlint FOV46.6 degrees
Vacuum DoorBase Plate
Shutter
PrecisionAperture
ShutterHousing
Baffle 1,2,3 FOV Baffle
ConeHousing
Rear Housing
Cone
TSI Record
Planck’s equation
2
2
5
Planck's distribution law for the density of radiation
in a cavity :
First radiation const = 2 = 3.7418e-016 (mks)2 1
hcexp 1 Second radiation const = 0.014388 (k
hchc
WhckT
2
5
4
mks)
(radiation emitted into a hemisphere)
Two important limits :
Wein's approximation
2When 5 then exp
Rayleigh - Jeans approximation
2When 1 then
hc hc hcW
kT kT
hc c kTW
kT
?
=
Properties of the Planck distribution
max
max
max
15 5
On differentiation of the Planck equation and setting = 0
an equation for the peak wavelength can be found :
2897.8 (micron - degree)4.965
Peak power at :
1.288 10
The equation
hcT
k
W T
4 -2Total 0
5 48
2 3
of Stefan - Boltzmann relates the total thermal
radiation density with temperature
W (W m )
25.6697 10 {the Stefan - Boltzmann Constant mks}
15
W d T
k
c h
Spectral Irradiance Monitor SIM
• Measure 2 absolute solar irradiance spectra per day
• Broad spectral coverage
– 200-2400 nm
• High measurement accuracy
– Goal of 0.1% (1)• High measurement precision
– SNR 500 @ 300 nm
– SNR 20000 @ 800 nm
• High wavelength precision
– 1.3 m knowledge in the focal plane
– (or < 150 ppm)
• In-flight re-calibration
– Prism transmission calibration
– Duty cycling 2 independent spectrometers
SORCE SIM: ESR-based spectral radiometry
SIM Measures the Full Solar Spectrum
Solar Stellar Irradiance Comparison Experiment (SOLSTICE)
Science Objectives:
• Measure solar irradiance from 115 to 320 nm with 0.1 nm spectral resolution and 5% or better accuracy.
• Monitor solar irradiance variation with 0.5% per year accuracy during the SORCE mission.
• Establish the ratio of solar irradiance to the average flux from an ensemble of bright early-type stars with 0.5% accuracy for future studies of long-term solar variability.
•The optical configuration matches illumination areas on the detector•Interchanging entrance slits and exit slits provides ~ 2x105 dynamic range•Different stellar/solar integration times provide ~ 103 dynamic range•A optical attenuator (neutral density filter), which can be measured in flight, provides additional ~ 102 dynamic range in the MUV wavelength range for >220 nm
SOLSTICE: Experiment Concept
Photomultiplier Detector
Interference Filter Out DiffractionGrating
Photomultiplier Detector
Interference Filter In DiffractionGrating
Camera Mirror
Camera Mirror
Stellar Observation: Objective Grating Spectrometer
Solar Observation: Modified Monk-Gilleison Spectrometer
Solar Exit Slit
Stellar Exit Slit
Entrance Aperture
Entrance Slit
SORCE SOLSTICE FUV & MUV Spectra
The Sun as a blackbody
Brightness Temperature
4
21
1
2 1ln 1
brightness
au
hT
k hc I
Sources of opacity in the solar atmosphere
Solar Emissions (VAL, 1992)
SIM Time Series at Fixed Wavelengths
Model Solar Atmosphere (FAL99)
-500 0 500 1000 1500 2000 2500Height (km)
4000
6000
8000
10000
27 Day Variability Depends on the Formation Region
Wavelength Dependence of Sun Images #2
Identification of solar active regions
Solar Radiation Physical Model (SRPM) employs solar images from HAO's PSPT (left panel) to identify and locate 7 solar activity features (R=sunspot penumbra; S=sunspot umbra; P,H=facula and plage; F=active network; E,C=quiet sun) to produce a mask image of the solar features (center panel). The SRPM combines solar feature information with physics-based solar atmospheric spectral models at high spectral resolution to compute the emergent intensity spectrum.
Recent quiet and active solar scenes
11 Feb 2006 27 Oct 200415 Jan 2005
Instantaneous Heating Rates
References
• “Modern Optical Engineering”, Warren J. Smith, McGraw Hill, 1990.
• ‘Quantitative Molecular Spectroscopy and Gas Emissivities”, S. S. Penner, Addison-Wesley, 1959.
• “Statistical Mechanics”, J. E. Mayer and M. G. Mayer, Wiley & Sons, 1940.
• “Absolute Radiometry”, F. Hengstberger, Academic Press, 1989.