A Star’s Color, Temperature,
and Brightness are Related!
The Beginnings
• Late 1800’s, early 1900’s – how light is
produced by atoms is being intensely
studied by…
– Gustav Kirchoff (remember Mr. Spectroscopy?)
– Max Planck…Josef Stefan...
– Ludwig Boltzmann…Albert Einstein
– All these guys don’t sound familiar? (Take
more chemistry and they will!)
Black Bodies
• During the same time as our Civil War, in
1862, Gustav Kirchoff coins the phrase
“black body” to describe an imaginary
object that would perfectly absorb any light
(of any wavelength) that hit it.
– No light transmitted through, no light
reflected off, just totally absorbed.
More Kirchoff
• Kirchoff realized that any object that would
be a perfect absorber of light would also
be a perfect emitter…but the amount of
light energy it would give off each second
(its brightness or luminosity) and the color
of the light would be related to the object’s
temperature.
Examples
• Molten lava and hot iron are two good
examples of black bodies, but…
• a star is an excellent black body emitter.
Moving Right Along
• Max Planck, a German physicist, was able
to make theoretical predictions of how
much light of each color or wavelength
would be given off by a perfect black body
at any given temperature.
• These predictions or models are today
called Planck Curves.
What do you notice?
• What 2 characteristics of the curves
change as the temperature increases?
(1) The size of the curve increases.
(2) The peak of the curves shift to the
left, to shorter wavelengths & higher
energies.
Can we draw some conclusions?
• Hotter stars should be brighter than cooler
stars.
• Hotter stars should emit more of their light
at shorter wavelengths (bluer light) while
cooler stars should emit more of their light
at longer wavelengths (redder light).
• Notice however that all stars emit some
energy at all wavelengths!
Stick with me!
• In 1879, Josef Stefan discovered that the
luminosity of a star was proportional to the
temperature raised to the 4th power.
• In 1884, Stefan’s observations were
confirmed when Ludwig Boltzmann
derived Stefan’s equation from simpler
thermodynamic equations.
Stefan-Boltzmann Law
• Today, we honor both scientists by naming
the equation after them…the StefanBoltzmann Law:
• At the surface of the star, the energy that’s
given off per square meter (Watts / m2)
called the luminous flux is...
W / m2 = 5.67 x 10-8 T4
An Example
• At 100 K (cold enough to freeze you solid
in just seconds), a black body would emit
only 5.67 W/m2.
• At 10x hotter, 1000 K, the same black
body would emit 104 times as much light
energy, or 56,700 W/m2.
You Try…
• If the temperature of a star were to
suddenly double, how much brighter would
the star become?
• If the temperature of a star somehow fell
to 1/3 of what it was, how much fainter
would the star become?
24 = 16 times brighter
(1/3)4 = 1/81, or 81 times dimmer
The Other Half of the Puzzle
• In 1893, Wilhelm Wien (pronounce “vine”)
discovered by experiment the relationship
between the “main” color of light given off
by a hot object and its temperature.
• By “main” color, I mean the peak
wavelength, called λmax , at the top of the
Planck Curve.
For each curve, the
top of the curve is the
peak wavelength.
Wien’s Law
• Wien’s Law says that the peak wavelength
is proportional to the inverse of the
temperature:
λmax = 2.9 x 106
T
T = 2.9 x 106
λmax
• T must be in Kelvin, and λmax in
nanometers.
Examples
• What is the peak wavelength of our sun,
with a T = 5750 K?
2.9 x 106 = 504 nm (yellowish-green)
5750 K
• What is the peak wavelength of a star with
a surface temperature of 3500 K?
2.9 x 106 = 829 nm (this star emits the
3500 K
majority of its light as
infrared, IR).
Examples
• A reddish star has a peak wavelength of
650 nm. What is the star’s temperature?
2.9 x 106 = 4462 K (cooler than the sun)
650 nm
A star has a peak wavelength in the ultraviolet of 300 nm. What is the star’s
temperature?
2.9 x 106 = 9667 K
300 nm
Uses
• We now have a “color thermometer” that
we can use to determine the temperature
of any astronomical object, just by
examining the light the object gives off.
• Astronomers have found that different
classes of objects are at different
temperatures and give off different peak
wavelengths.
What kinds of objects?
• Clouds of
cold
hydrogen
gas
(nebulae)
emit radio
waves
http://www.narrowbandimaging.com/images/vdb142_small.jpg
Warmer clouds of molecules where
stars form emit microwaves and IR.
Protostars emit IR.
http://www.antonine-education.co.uk/Physics_GCSE/Unit_3/Topic_10/protostar.jpg
Sun-like stars emit mostly visible light,
while hotter stars peak in the UV.
http://www.nasa.gov/images/content/138952main_whywe16full.jpg
Neutron stars and black holes peak in
the X-ray.
Star cores emit gamma rays.
http://aspire.cosmic-ray.org/labs/star_life/images/star_pic.jpg
How about these?
• Where would the peak wavelength be for
– your body
– a lightning bolt
– the coals from a campfire