Analyzing Starlight

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Analyzing Starlight
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Image of stars in the direction of the center of
the Milky Way Galaxy, taken by the Hubble Space
Telescope How do the stars appear different?
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Not All Stars are Alike

• Stars appear different in
• brightness, from very bright to very faint
• color, from red to blue-white
• size
• A good constellation for seeing star colors in
  the winter sky is Orion (the
  hunter)
• Betelgeuse, a red super-
  giant star
• Rigel, a blue super-giant
  star

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Betelgeuse
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Brightness of Stars (1)

• The total amount of energy at all wavelengths
  that a star emits is called its luminosity
• Note this is how much energy the star gives off
  each second, NOT how much energy ultimately
  reaches our eyes or telescope
• The luminosity of a star is perhaps its most
  important characteristic
• The amount of a stars energy that actually
  reaches a given area each second here on Earth is
  called the stars apparent brightness
• If all stars had the same
  luminosity, their apparent
  brightnesses would tell us
  how far they
  are from us
• The inverse-square law of
  light propagation the apparent
  brightness of a light source decreases as the
  square of the distance from it

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Brightness of Stars (2)

• The inverse-square law
  implies that
• a star will appear 4 times
  fainter if an observers
  
  distance from it is
  doubled, 9 times fainter
  if the
  distance is tripled,
  etc.
• In reality, stars generally
  do not have the same
  luminosity
• In other words, they are
  not standard bulbs
• Consequently, distance
  is the among the most
  difficult quantities to measure in astronomy

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Stars Apparent Magnitudes (1)

• A stars apparent brightness is described using
  the magnitude system
• The system was devised by the Greek astronomer
  Hipparchus around 150 B.C.
• He put the brightest stars into the
  first-magnitude class, the next brightest stars
  into second-magnitude class, and so on, until he
  had all of the visible stars grouped into six
  magnitude classes
• Examples a star of the 1st magnitude appears 2.5
  times brighter than a star of the 2nd magnitude,
  whereas a star of the 2nd magnitude appears 40
  times brighter than a star of the 6th magnitude

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Stars Apparent Magnitudes (2)

• Thus, the smaller the magnitude, the brighter the
  object being observed!
• The old magnitude-system was based on how bright
  a star appeared to the unaided eye
• Todays magnitude system (based on more accurate
  measurements) goes beyond Hipparchus' original
  range of magnitudes 1 through 6
• Very bright objects can have a magnitude of 0, or
  even a negative number
• Very faint objects have magnitudes greater than
  10

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Stars Colors and Temperatures

• A star is a ball of dense, hot gas that emits a
  continuous spectrum of radiation
• The spectrum is very similar to that of radiation
  emitted by a blackbody
• The most intense color of a star is related to
  its surface temperature by Wiens law
• The higher the temperature, the shorter the
  wavelength of the most intense color
• Thus
• Blue colors dominate the light output of very hot
  stars
• Cool stars emit most of their visible radiation
  at red wavelengths
• Our Suns surface temperature is about 6,000 K,
  with the dominant color being a slightly greenish
  yellow
• Hottest stars can have surface temperatures of
  100,000 K, whereas coolest stars have surface
  temperatures of about 2,000 K

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Stars Color ? Temperature
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Determining Stars Temperature

• To determine the exact color of a star,
  astronomers usually observe its brightness
  through filters
• A filter allows only a
  narrow range of
  
  wavelengths (colors)
  to pass through
• Two commonly used
  filters are
• a blue (B) filter that
  lets through
  only a
  narrow band of blue
  
  wavelengths
• a visual (V) filter
  that lets
  through only colors around the green-yellow band
• The colored light transmitted by each filter has
  its own brightness, usually expressed in
  magnitudes
• The relative brightness of the transmitted colors
  can tell if the star is hot, warm, or cool

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B-V Color Index

• A B-V color index is defined as the difference
  in
  magnitude between the B and V bands
• A hot star has an
  index of around 0
  or a negative
  number, while a
  
  cool star has an
  index close to 2.0
• Other stars are
  somewhere in
  between

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Spectra of Stars

• To analyze starlight, one can also use
  spectroscopy, instead of filters
• In general, the spectra of different stars look
  different
• The primary reason is that stars have different
  temperatures
• Most stars are very similar in composition to the
  Sun
• Hydrogen is the most abundant element in stars
• In the hottest stars, the hydrogen atoms are
  completely ionized (no longer have their
  electrons attached) due to the high temperature
  and, consequently, they cannot produce hydrogen
  absorption lines in the spectra
• In the coolest stars, the hydrogen atoms are all
  in lowest state and, consequently, hydrogen
  transitions that can occur do not produce
  absorption lines in the visible spectrum
• Only stars with intermediate surface temperatures
  (not too hot, not too cool about 10,000 K) have
  spectra with hydrogen lines

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How Absorption Line is Produced
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Spectral Classes

• Astronomers sort stars according to the patterns
  of lines seen in their spectra into seven
  principal spectral classes
• From hottest to coldest, the classes are
  designated O, B, A, F, G, K, and M

G
K
M
O
B
A
F
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Spectral Classes L and T

• Since 1995, astronomers have discovered objects
  cooler than those in class M, but they are not
  considered true stars because they are not
  massive enough
• Objects with masses less than 7.2 of or our
  Suns mass (0.072 MSun) are not expected to
  become hot enough for the nuclear fusion to take
  place
• Those objects are called brown dwarfs
• They are very faint and cool, emitting radiation
  in the infrared part of the spectrum
• The warmer brown dwarfs are assign to spectral
  class L, and the cooler ones to spectral class T

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Spectra of Stars in Different Spectral Classes
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Doppler Effect in Sound Waves

• Case (a)
• The source is moving towards observer A
• Observer A sees a compressed wave, and hence a
  shorter wavelength (or a higher frequency)
• Observer B sees a stretched wave, and hence a
  longer wavelength (or a lower frequency)
• Case (b)
• The source is stationary
• Observers A and B both see same wavelength

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Doppler Effect in Starlight

• The motion of a star causes its spectral lines to
  shift positions
• The shift depends on its speed and direction of
  motion
• If the star is moving toward us, the wavelengths
  of its light get shorter
• Its spectral lines are shifted toward the
  shorter-wavelength (bluer) end of the spectrum
• This is, therefore, called a blueshift
• If the star is moving away
  from us, the wavelengths of
  its light get
  longer
• Its spectral lines are shifted
  toward the
  longer-wavelength
  (redder) end of the visible
  spectrum
• This is, thus, called a redshift

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Doppler Effect in Stellar Spectra

• The Doppler effect doesnt affect the overall
  color of an object, unless it is moving at a
  significant fraction of the speed of light (VERY
  fast!)
• For an object moving toward us, the red colors
  will be shifted to the orange and the
  near-infrared will be shifted to the red, etc.
• All of the colors shift
• The overall color of the object depends on the
  combined intensities of all of the wavelengths
  (colors)

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The Suns Spectral Shifts

• The Suns spectra at 3 speeds (0, 0.01c, 0.1c)
• The hydrogen-alpha line (at 656.3nm) is shown
• The Doppler-shifted continuous spectrum of the
  Sun moving at 0.01c is almost indistinguishable
  from that of the Sun
  being at rest

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Doppler Shift of Spectral Lines

• The Doppler shift of spectral lines is measurable
  even for slow speed
• Astronomers can detect spectral-line Doppler
  shifts for speeds as small
  as 1 km/sec or
  
  lower (less than
  3.3?10-6 c)

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Doppler Effect in Stellar Rotation The
broadening of spectral lines indicates that the
star is rotating The greater the broadening, the
greater the speed of rotation