Deducing Temperatures and Luminosities of Stars (and other objects

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Deducing Temperatures and Luminosities of
Stars(and other objects)
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Review Electromagnetic Radiation
Increasing energy
10-15 m
103 m
10-6 m
10-2 m
10-9 m
10-4 m
Increasing wavelength

• EM radiation consists of regularly varying
  electric magnetic fields which can transport
  energy over vast distances.
• Physicists often speak of the particle-wave
  duality of EM radiation.
• Light can be considered as either particles
  (photons) or as waves, depending on how it is
  measured
• Includes all of the above varieties -- the only
  distinction between (for example) X-rays and
  radio waves is the wavelength.

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Wavelength
?

• Wavelength is the distance between two identical
  points on a wave. (It is referred to by the
  Greek letter ? lambda)

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Frequency
time
unit of time

• Frequency is the number of wave cycles per unit
  of time that are registered at a given point in
  space. (referred to by Greek letter ? nu)
• It is inversely proportional to wavelength.

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Wavelength andFrequency Relation
? v/?

• Wavelength is proportional to the wave velocity,
  v.
• Wavelength is inversely proportional to
  frequency.
• eg. AM radio wave has a long wavelength (200 m),
  therefore it has a low frequency (KHz range).
• In the case of EM radiation in a vacuum, the
  equation becomes

????c??
Where c is the speed of light (3 x 108 m/s)
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Light as a Particle Photons

• Photons are little packets of energy.
• Each photons energy is proportional to its
  frequency.
• Specifically, each photons energy is

E h?
Energy (Plancks constant) x (frequency of
photon)
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The Planck function

• Every opaque object (a human, a planet, a star)
  radiates a characteristic spectrum of EM
  radiation
• spectrum (intensity of radiation as a function of
  wavelength) depends only on the objects
  temperature
• This type of spectrum is called blackbody
  radiation

visible
infrared
radio
ultraviolet
Intensity (W/m2)
0.1
1.0
10
100
1000
10000
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Temperature dependence of blackbody radiation

• As temperature of an object increases
• Peak of black body spectrum (Planck function)
  moves to shorter wavelengths (higher energies)
• Each unit area of object emits more energy (more
  photons) at all wavelengths

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Wiens Displacement Law

• Can calculate where the peak of the blackbody
  spectrum will lie for a given temperature from
  Wiens Law

????5000/T
Where ? is in microns (10-6 m) and T is in
degrees Kelvin (recall that human vision ranges
from 400 to 700 nm, or 0.4 to 0.7 microns)
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Colors of Stars

• The color of a star provides a strong indication
  of its temperature
• If a star is much cooler than 5,000 K, its
  spectrum peaks in the IR and it looks reddish
• It gives off more red light than blue light
• If a star is much hotter than 15,000 K, its
  spectrum peaks in the UV, and it looks blueish
• It gives off more blue light than red light

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Betelguese and Rigel in Orion
Betelgeuse 3,000 K (a red supergiant)
Rigel 30,000 K (a blue supergiant)
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Blackbody curves for stars at temperatures of
Betelgeuse and Rigel
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Luminosities of stars

• The sum of all the light emitted over all
  wavelengths is called a stars luminosity
• luminosity can be measured in watts
• measure of stars intrinsic brightness, as
  opposed to what we happen to see from Earth
• The hotter the star, the more light it gives off
  at all wavelengths, through each unit area of its
  surface
• luminosity is proportional to T4 so even a small
  increase in temperature makes a big increase in
  luminosity

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Consider 2 stars of different Ts but with the
same diameter
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What about large small stars of the same
temperature?

• Luminosity goes like R2 where R is the radius of
  the star
• If two stars are at the same temperature but
  have different luminosities, then the more
  luminous star must be larger

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How do we know that Betelgeuse is much, much
bigger than Rigel?

• Rigel is about 10 times hotter than Betelgeuse
• Rigel gives off 104 (10,000) times more energy
  per unit surface area than Betelgeuse
• But the two stars have about the same total
  luminosity
• therefore Betelguese must be about 102 (100)
  times larger in radius than Rigel

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So far we havent considered stellar distances...

• Two otherwise identical stars (same radius, same
  temperature gt same luminosity) will still appear
  vastly different in brightness if their distances
  from Earth are different
• Reason intensity of light inversely proportional
  to the square of the distance the light has to
  travel
• Light wave fronts from point sources are like the
  surfaces of expanding spheres

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Stellar brightness differences as a tool rather
than as a liability

• If one can somehow determine that 2 stars are
  identical, then their relative brightnesses
  translate to relative distances
• Example the Sun and alpha Centauri
• spectra look very similar gt temperatures, radii
  almost identical (T follows from Planck function,
  radius can be deduced by other means) gt
  luminosities about the same
• difference in apparent magnitudes translates to
  relative distances
• Can check using the parallax distance to alpha Cen

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The Hertsprung-Russell Diagram