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A star’s color, temperature, size, brightness and distance
are all related!
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The Beginnings
• Late 1800’s, early 1900’s – how light is produced by atoms is being intensely studied by… – Gustav Kirchoff & Robert Bunsen – Max Planck…Josef Stefan... – Ludwig Boltzmann…Albert Einstein
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Black Bodies
• In 1862, 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.
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• a perfect absorber of light would also be a perfect emitter
• amount of light energy given off each second (its brightness or luminosity) and the color of its light are related to the object’s temperature.
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• Molten lava and hot iron are two good examples of black bodies, but…
• a star is an excellent black body emitter.
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• 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.
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• 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.
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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) • Cooler stars should emit more of their light
at longer wavelengths (redder light). • All stars emit some energy at all
wavelengths!
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• 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.
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Stefan-Boltzmann Law • Today, we honor both scientists by naming
the equation after them…the Stefan-Boltzmann 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
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• 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.
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• 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
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• 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.
• This “main” color is the peak wavelength,
called λmax , at the top of the Planck Curve.
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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 = 2.9 x 106
T λmax • T must be in Kelvin, and λmax in
nanometers.
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• What is the peak wavelength of our sun, with a T = 5750 K?
• What is the peak wavelength of a star with
a surface temperature of 3500 K?
2.9 x 106 = 504 nm (yellowish-green) 5750 K
2.9 x 106 = 829 nm (this star emits the 3500 K majority of its light as infrared, IR).
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• A reddish star has a peak wavelength of 650 nm. What is the star’s temperature?
A star has a peak wavelength in the ultra-
violet of 300 nm. What is the star’s temperature?
2.9 x 106 = 4462 K (cooler than the sun) 650 nm
2.9 x 106 = 9667 K 300 nm
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• 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.
• We know that different classes of objects
are at different temperatures and give off different peak wavelengths.
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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
• Where would the peak wavelength be for
– your body – a lightning bolt – the coals from a campfire
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A star’s spectrum is also influenced by its temperature. •In 1872, Henry Draper obtained the first spectrum of a star, Vega, in the constellation Lyra.
photojournal.jpl.nasa.gov/jpeg/PIA04204.jpg Credit: Lick Observatory Archives
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•In 1885, Edward Pickering began a project at Harvard University to determine the spectra of many stars. Draper’s widow funded the work. •The first 10,000 spectra obtained were classified by Williamnia Fleming, using the letters A through Q.
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•From 1901 to 1919, Pickering & his assistant Annie Jump Cannon classified and published the spectra of 225,000 stars (at the rate of about 5000 per month!) •When Pickering died in 1919, Cannon continued the work, eventually classifying and publishing the spectra of 275,000 stars.
Credit: amazing-space.stsci.edu
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Hotter stars have simpler spectra. Cooler stars have more complex spectra, since most atoms are not ionized.
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Class O >30,000 K bluish He lines in spectrum. (These stars are so hot that H is mostly ionized & doesn’t shows lines.) Pleiades
Class B 11,000-30,000 K bluish He lines, weaker H lines
Rigel, Regulus, Spica
Class A 8,000-11,000 K blue-white H lines (Balmer Series)
Sirius, Vega
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Class F 6,000-8,000 K white H, Ca lines, weaker H lines Procyon
Class G 5,000-6,000 K yellow Ca, Na lines, + other metals
Sun, Capella, α-Centauri
Class K 3,500-5,000 K orange Ca & other metals
Arcturus, Aldebaran
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Class M <3,500 K red metal oxides (TiO2), molecules
Betelgeuse, Antares
Oh, Be A Fine Girl, Kiss Me!
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The stellar classes (OBAFGKM) are further subdivided with a number 0 to 9 following the letter. Our sun, a G2 star, is slightly cooler than the F range. A G9 star would be just a bit warmer than the K range.
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•1910-1913, Henry Russell, a professor at Princeton, and Ejnar Hertzsprung, an astronomer at Leiden Observatory in the Netherlands, used the data from the Draper catalog to plot the temperature of the stars vs. their brightness or luminosity. •What kind of result would you expect, a random scatter, or a pattern?
univ
erse
-rev
iew.
ca/I0
8-01
-HR
diag
ram
.jpg
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Betelgeuse and Antares show on the diagram as being red stars, and red stars should be faint. Both stars are also hundreds of light years distant, so why do they appear so bright in our sky?
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Red Dwarfs
‘Red’
‘Red’
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The H-R Diagram makes a lot more sense when you realize that the different regions don’t show different kinds of stars… …but stars at different stages of their lives.
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Determining distance using the HR Diagram •From a star’s color-temperature, determine its absolute magnitude (M). •Observe the star’s apparent magnitude (m) through a telescope. •Use the distance modulus equation to calculate the distance.
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How far away is an F1 star that has a surface temperature of 8000 K, if its apparent magnitude is +9.6?
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distance in parsecs = 10^[(9.6 - 3.0 +5) 5] = 10^[11.6 5] = 10^2.32 = 209 parsecs (or 681 light years)
Where might this method run into trouble? Red & Orange star come in 2 varieties: giants & dwarfs. The spectrum of the star must be used to determine if the star is large or small. The presence of what element(s) in higher than normal percentages might indicate that the star is a giant, not a dwarf?
