Sky & Telescope - July 2022 - 32

Relative intensity
Energy
SORCE SATELLITE: NASA; GRAPHS: GREGG DINDERMAN / S&T; SOURCE:
DOUGLAS MACDOUGAL (2)
Understanding the Sun
at the Sun's photosphere to be about 63
million watts per square meter. That's a
difficult number to grasp! It's the equivalent
of a million 60-watt bulbs crammed
into a one-meter-square frame.
Taking the Sun's Temperature
After calculating the total energy output
at the Sun's surface, Abbot next had to
convert the solar flux into temperature.
This required understanding the relationship
between thermal radiation and temperature.
In other words, if we record the
heat from a candle at a distance of one
foot, how do we determine the temperature of the candle?
For much of the 19th century, the relationship between
heat and temperature was unknown. Fortunately, in 1879
Slovenian physicist (and poet) Jožef Štefan showed that for
an ideal blackbody radiator - one that emits and absorbs
radiation in equal amounts in perfect equilibrium - radiation
is proportional to the fourth power of the temperature.
We know this today as the Stefan-Boltzmann law.
However, the solar spectrum has areas of absorption
where the Sun's radiation curve deviates from the ideal
blackbody, especially at shorter wavelengths. Abbot was
concerned about this effect and about the uneven transmissivity
of the Sun's photosphere. Today, though, we
know that for the wavelength range Abbot was working
with (ignoring the bites taken out of it by the absorption
lines), the Sun's smoothed spectrum approximates a
blackbody radiation curve corresponding to an effective
temperature of 5,700 kelvin. Abbot used his 1908 value for
WORKHORSE INSTRUMENT The Solar
Radiation and Climate Experiment (SORCE) was
a satellite mission designed to measure incoming
X-ray, ultraviolet, visible, near-infrared, and total
solar radiation. Its mission ended in 2020 but
overlapping data collection continues with the Total
and Spectral Solar Irradiance Sensor (TSIS-1)
instrument aboard the International Space Station
and with TSIS-2 set for launch in 2024.
the solar constant and found the Sun's
effective temperature to be 5,962K. At the
time, this was the closest match to the
currently accepted value of 5,772K.
Abbot also tried to compute the Sun's
surface temperature using Wien's Law,
named after German physicist Wilhelm Wien. The idea is
simple: The temperature of a blackbody radiator is betrayed
by its color. Each radiator has a unique radiation curve
(described by fellow German physicist Max Planck and called
the Planck curve) that's strictly determined by its temperature.
It's the peak radiation intensity that chiefly determines the
colors of stars (and other hot objects) as they appear to us.
A hot star will peak in the blue end of the spectrum, while
cooler ones peak more toward the red - just as red charcoals
are cooler than the blue flame of a welder's torch. The Wien
relation between the peak wavelength (λmax, in microns) of
the curve and temperature (T) of a blackbody radiator is given
by a simple relation:
T = 2,898/λmax
This may be one of the simplest equations in physics, so
savor it! What it says is that if you can identify the wave10,000K
2,000
1,500
1,000
500
Solar
spectrum at
zero air mass
Solar Spectra Compared
Mount Wilson 1906 and 1907 data
Solar spectrum
at Earth's surface
0.5
1.0
1.5
Wavelength (microns)
SOLAR CURVES Abbot's Mount Wilson 1906-1907 data show
solar radiation intensity versus wavelength. The purple curve depicts
measured intensities from Mount Wilson in California, while the blue line
extrapolates the data to zero air mass, outside the Earth's atmosphere.
The pronounced gap between the two graphs at the shorter wavelengths
is due to increased atmospheric absorption at those wavelengths. The
sharp dips are due to so-called telluric absorption lines of molecules in
Earth's atmosphere.
32 JULY 2022 * SKY & TELESCOPE
2.0
2.5
6,000K
8,000K
500
1000
4,000K
1500
2000
Wavelength (nanometers)
READING THE CURVES The four curves in this diagram show blackbody
radiation at different temperatures. By measuring a star's peak
spectral output, astronomers can determine its temperature. The peak
of the curve shifts to shorter wavelengths at higher temperatures, while
the area under the curve is proportional to the total amount of energy
radiated.
2500
3000
Sky & Telescope - July 2022

Table of Contents for the Digital Edition of Sky & Telescope - July 2022
