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 is the combination of time- and
  space- varying electric magnetic fields that
  convey energy.
• 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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Electromagnetic Fields
Direction of Travel
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Sinusoidal Fields

• BOTH the electric field E and the magnetic field
  B have sinusoidal shape

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Wavelength ? of Sinusoidal Function
?

• Wavelength ? is the distance between any two
  identical points on a sinusoidal wave.

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Frequency n of Sinusoidal Wave
time
1 unit of time (e.g., 1 second)

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

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Units of Frequency
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Wavelength and Frequency Relation

• Wavelength is proportional to the wave velocity
  v.
• Wavelength is inversely proportional to
  frequency.
• e.g., AM radio wave has long wavelength (200 m),
  therefore it has low frequency (1000 KHz
  range).
• If EM wave is not in vacuum, the equation becomes

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Light as a Particle Photons

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

E h?
Energy (Plancks constant) (frequency of
photon) h ? 6.625 10-34 Joule-seconds 6.625
10-27 Erg-seconds
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Plancks Radiation Law

• Every opaque object at temperature T gt 0-K (a
  human, a planet, a star) radiates a
  characteristic spectrum of EM radiation
• spectrum intensity of radiation as a function
  of wavelength
• spectrum depends only on temperature of the
  object
• This type of spectrum is called blackbody
  radiation

http//scienceworld.wolfram.com/physics/PlanckLaw.
html
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Plancks Radiation Law

• Wavelength of MAXIMUM emission ?max is
  characteristic of temperature T
• Wavelength ?max ? as T ?

?max
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Sidebar The Actual Equation

• Complicated!!!!
• h Plancks constant 6.63 10-34 Joule -
  seconds
• k Boltzmanns constant 1.38 10-23 Joules
  -K-1
• c velocity of light 3 108 meter - seconds-1

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Temperature dependence of blackbody radiation

• As temperature T of an object increases
• Peak of blackbody 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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Sidebar The Actual Equation

• Complicated!!!!
• h Plancks constant 6.63 10-34 Joule -
  seconds
• k Boltzmanns constant 1.38 10-23 Joules
  -K-1
• c velocity of light 3 108 meter - seconds-1
• T temperature K
• ? wavelength meters

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Shape of Planck Curve
http//csep10.phys.utk.edu/guidry/java/planck/plan
ck.html

• Normalized Planck curve for T 5700-K
• Maximum value set to 1
• Note that maximum intensity occurs in visible
  region of spectrum

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Planck Curve for T 7000-K
http//csep10.phys.utk.edu/guidry/java/planck/plan
ck.html

• This graph also normalized to 1 at maximum
• Maximum intensity occurs at shorter wavelength ?
• boundary of ultraviolet (UV) and visible

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Planck Functions Displayed on Logarithmic Scale
http//csep10.phys.utk.edu/guidry/java/planck/plan
ck.html

• Graphs for T 5700-K and 7000-K displayed on
  same logarithmic scale without normalizing
• Note that curve for T 7000-K is higher and
  peaks to the left

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Features of Graph of Planck Law T1 lt T2 (e.g.,
T1 5700-K, T2 7000-K)

• Maximum of curve for higher temperature occurs at
  SHORTER wavelength ?
• ?max(T T1) gt ?max(T T2) if T1 lt T2
• Curve for higher temperature is higher at ALL
  WAVELENGTHS ?
• ? More light emitted at all ? if T is larger
• Not apparent from normalized curves, must examine
  unnormalized curves, usually on logarithmic
  scale

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Wavelength of Maximum EmissionWiens
Displacement Law

• Obtained by evaluating derivative of Planck Law
  over T

(recall that human vision ranges from 400 to 700
nm, or 0.4 to 0.7 microns)
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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

(recall that human vision ranges from 400 to 700
nm, or 0.4 to 0.7 microns)
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?max for T 5700-K

• Wavelength of Maximum Emission is
• (in the visible region of the spectrum)

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?max for T 7000-K

• Wavelength of Maximum Emission is
• (very short blue wavelength, almost
  ultraviolet)

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Wavelength of Maximum Emission for Low
Temperatures

• If T ltlt 5000-K (say, 2000-K), the wavelength of
  the maximum of the spectrum is
• (in the near infrared region of the
  spectrum)
• The visible light from this star appears
  reddish

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Why are Cool Stars Red?
Less light in blue Star appears reddish
0.4 0.5 0.6 0.7
0.8 0.9 1.0 1.1 1.2
1.3
l (mm)
lmax
Visible Region
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Wavelength of Maximum Emission for High
Temperatures

• T gtgt 5000-K (say, 15,000-K), wavelength of
  maximum brightness is
• Ultraviolet region of the spectrum
• Star emits more blue light than red ?appears
  bluish

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Why are Hotter Stars Blue?
More light in blue Star appears bluish
0.1 0.2 0.3 0.4
0.5 0.6 0.7 0.8
0.9 1.0
l (mm)
lmax
Visible Region
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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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Stellar Luminosity

• Sum of all light emitted over all wavelengths is
  the luminosity
• brightness per unit surface area
• luminosity is proportional to T4 L ? T4
• L can be measured in watts
• often expressed in units of Suns luminosity LSun
• L measures stars intrinsic brightness, rather
  than apparent brightness seen from Earth

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Stellar Luminosity Hotter Stars

• Hotter stars emit more light per unit area of its
  surface at all wavelengths
• T4 -law means that small increase in temperature
  T produces BIG increase in luminosity L
• Slightly hotter stars are much brighter (per unit
  surface area)

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Two stars with Same Diameter but Different T

• Hotter Star emits MUCH more light per unit area ?
  much brighter

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Stars with Same Temperature and Different
Diameters

• Area of star increases with radius (? R2, where
  R is stars radius)
• Measured brightness increases with surface area
• If two stars have same T but different
  luminosities (per unit surface area), 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
• Measured from its color
• Rigel gives off 104 (10,000) times more energy
  per unit surface area than Betelgeuse
• But the two stars have equal total luminosities
• ? Betelguese must be about 102 (100) times
  larger in radius than Rigel
• to ensure that emits same amount of light over
  entire surface

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So far we havent considered stellar distances...

• Two otherwise identical stars (same radius, same
  temperature ? 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 waves from point sources are surfaces of
  expanding spheres

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Sidebar Absolute Magnitude

• Recall definition of stellar brightness as
  magnitude m
• F, F0 are the photon numbers received per second
  from object and reference, respectively.

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Sidebar Absolute Magnitude

• Absolute Magnitude M is the magnitude measured
  at a Standard Distance
• Standard Distance is 10 pc ? 33 light years
• Allows luminosities to be directly compared
• Absolute magnitude of sun ? 5 (pretty faint)

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Sidebar Absolute Magnitude Apply Inverse
Square Law

• Measured brightness decreases as square of
  distance

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Simpler Equation for Absolute Magnitude
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Stellar Brightness Differences are Tools, not
Problems

• If we can determine that 2 stars are identical,
  then their relative brightness translates to
  relative distances
• Example Sun vs. ? Cen
• spectra are very similar ? temperatures, radii
  almost identical (T follows from Planck function,
  radius R can be deduced by other means)
• ? luminosities about equal
• difference in apparent magnitudes translates to
  relative distances
• Can check using the parallax distance to ? Cen

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Plot Brightness and Temperature on
Hertzsprung-Russell Diagram
http//zebu.uoregon.edu/soper/Stars/hrdiagram.htm
l
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H-R Diagram

• 1911 E. Hertzsprung (Denmark) compared star
  luminosity with color for several clusters
• 1913 Henry Norris Russell (U.S.) did same for
  stars in solar neighborhood

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Hertzsprung-Russell Diagram
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Clusters on H-R Diagram

• n.b., NOT like open clusters or
• globular clusters
• Rather are groupings of stars
• with similar properties
• Similar to a histogram

?90 of stars on Main Sequence ?10 are White
Dwarfs lt1 are Giants
http//www.anzwers.org/free/universe/hr.html
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H-R Diagram

• Vertical Axis ? luminosity of star
• could be measured as power, e.g., watts
• or in absolute magnitude
• or in units of Sun's luminosity

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Hertzsprung-Russell Diagram
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H-R Diagram

• Horizontal Axis ? surface temperature
• Sometimes measured in Kelvins.
• T traditionally increases to the LEFT
• Normally T given as a ratio scale'
• Sometimes use Spectral Class
• OBAFGKM
• Oh, Be A Fine Girl, Kiss Me
• Could also use luminosities measured through
  color filters

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Standard Astronomical Filter Set

• 5 Bessel Filters with approximately equal
  passbands ??? 100 nm
• U ultraviolet, ?max ? 350 nm
• B blue, ?max ? 450 nm
• V visible ( green), ?max ? 550 nm
• R red, ?max ? 650 nm
• I infrared, ?max ? 750 nm
• sometimes II, farther infrared, ?max ? 850 nm

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Filter Transmittances
100
Visible Light
II
R
I
V
B
U
Transmittance ()
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0
200 300 400 500 600 700
800 900 1000 1100
Wavelength (nm)
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Measure of Color

• If image of a star is
• Bright when viewed through blue filter
• Fainter through visible
• Fainter yet in red

• Star is BLUISH
• and hotter

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Measure of Color

• If image of a star is
• Faintest when viewed through blue filter
• Somewhat brighter through visible
• Brightest in red

• Star is REDDISH
• and cooler

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How to Measure Color of Star

• Measure brightness of stellar images taken
  through colored filters
• used to be measured from photographic plates
• now done photoelectrically or from CCD images
• Compute Color Indices
• Blue Visible (B V)
• Ultraviolet Blue (U B)
• Plot (U V) vs. (B V)

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Why are Cool Stars Red?
Less light in blue Star appears reddish
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Plancks Radiation Law

• Every opaque object at a temperature gt 0-K (a
  human, a planet, a star) radiates a
  characteristic spectrum of EM radiation
• spectrum intensity of radiation as a function
  of wavelength
• spectrum depends only on temperature of the
  object
• This type of spectrum is called blackbody
  radiation

maximum
visible
infrared
radio
ultraviolet
Intensity (W/m2)
0.1
1.0
10
100
1000
10000
Spectrum for blackbody with T 273-K (0 C)