Download How are a star`s temperature, color, and brightness related?

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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 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
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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.
For each curve, the
top of the curve is the
peak wavelength.
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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.
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• What is the peak wavelength of our sun,
with a T = 5778 K?
2.9 x 106 = 502 nm (yellowish-green)
5778 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).
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• 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
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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.
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
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• 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.
Credit: Lick Observatory Archives
photojournal.jpl.nasa.gov/jpeg/PIA04204.jpg
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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 Williamina 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
He lines in spectrum.
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bluish
(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
bluewhite
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, -Centauri
Class K 3,500-5,000 K
Ca & other metals
Arcturus, Aldebaran
orange
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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?
universe-review.ca/I08-01-HRdiagram.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’
‘Red’
Red Dwarfs
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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?