Spectroscopy

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Spectroscopy
Astronomers can learn an immense amount from the
details of lines in the spectrum of light coming
from planets and stars.

• This tool is used by chemists, biologists,
  physicists and all of the other natural sciences.
• It is based on the quantum or particle (photon)
  nature of light.

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Spectral Lines

• By the mid 19th century chemists noticed specific
  colors of light coming from particular gases.
• Careful measurements indicated each element or
  compound produced a
  UNIQUE SET of EMISSION LINES
  
  equivalent to FINGERPRINTS identifying the
  element .
• Spectra of the SUN and other STARS showed
  emission at most frequencies, but distinct dark
  bands, or ABSORPTION LINES, were also detected.

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Stellar and Chemical Spectra
Introductory Spectroscopy Applet
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What are the three basic types of spectra?
Continuous Spectrum
Emission Line Spectrum
Absorption Line Spectrum
Spectra of astrophysical objects are usually
combinations of these three basic types how they
arise is described by Gustav Kirchhofs Laws.
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Continuous Spectrum

• Example The spectrum of a common (incandescent)
  light bulb spans all visible wavelengths, without
  interruption. (stars interior)
• A hot solid, liquid or dense gas produces a
  continuous thermal spectrum (Kirchhofs 1st Law)

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Emission Line Spectrum

• A thin or low-density cloud of gas emits light
  only at specific wavelengths that depend on its
  composition and temperature, producing a spectrum
  with bright emission lines (Kirchhofs 2nd Law).

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Absorption Line Spectrum

• A cloud of gas between us and a light bulb can
  absorb light of specific wavelengths, leaving
  dark absorption lines in the spectrum Kirchhofs
  3rd Law
• Kirchoff's Laws Applet Viewing Continuum and
  Lines

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What kind of spectrum does a hot solid produce?

1. Emission (bright lines)
2. Absorption (dark lines)
3. Continuous (all the colors of the rainbow)
4. Infrared
5. Ultraviolet

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What kind of spectrum does a hot solid produce?

1. Emission (bright lines)
2. Absorption (dark lines)
3. Continuous (all the colors of the rainbow)
4. Infrared
5. Ultraviolet

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By looking at the light of a hot, solid object,
you can tell

1. Its temperature
2. What it is made of
3. Both 1 and 2
4. Neither 1 nor 2, without some additional
   information

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By looking at the light of a hot, solid object,
you can tell

1. Its temperature
2. What it is made of
3. Both 1 and 2
4. Neither 1 nor 2, without some additional
   information

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Origin of Spectral Lines

• Those in the radio, mm, IR, visible, UV and most
  X-ray are due to
  QUANTUM TRANSITIONS BY ELECTRONS IN ATOMS
  and MOLECULES (Gamma-rays
  usually come from quantum transitions in the
  nuclei of atoms.)
• ABSORPTION LINES ARISE FROM PHOTONS BEING
  ABSORBED BY ATOMS AND EXCITING ELECTRONS TO
  HIGHER LEVELS.
• EMISSION LINES ARISE FROM ELECTRONS DROPPING
  DOWN TO LOWER ENERGY LEVELS, EMITTING PHOTONS.

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Atomic Structure
Helium 2 p 2 n Nuclei -- protons and neutrons
with essentially all the mass of the
atom. Electrons are in orbitals which define
atomic energy levels-- essentially fill the
volume. Carbon 6 p 6 n
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Atomic Energy Levels
Classical model -- not a very good approximation
Probabalistic electron cloud-- wave function
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Atomic Transitions
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Energy Level Transitions

• The only allowed changes in energy are those
  corresponding to a transition between energy
  levels (here, Hydrogen)
• Atomic Energy Levels

Allowed
Not Allowed
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Energy is Conserved in Atomic Transitions

• E2 - E1 hf
• Is the equation of CONSERVATION OF ENERGY FOR
  PHOTO-EXCITATION
  or PHOTOABSORPTION.
• In denser gases frequent collisions between
  atoms shift observed wavelengths (Doppler effect)
  and smear out (broaden) the lines.
• Once the density is high enough, the spectral
  lines blur into a CONTINUOUS SPECTRUM.

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Atomic Transitions
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Exciting Atoms

• ELECTRONS can be EXCITED THROUGH
  either
• PHOTO-EXCITATION (PHOTO-ABSORPTION), or
• COLLISIONAL EXCITATION (atom collides with
  another atom or electron)
• Here conservation of energy can be expressed
  as E1 KE1 E2 KE2,
  with E the
  electronic potential energy of the atom and KE
  the kinetic energy of the colliding atom or
  electron.

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De-exciting Atoms

• SPONTANEOUS (PHOTO-DE-EXCITATION) or
  PHOTO-EMISSION
• COLLISIONAL DE-EXCITATION (no photon out)
• STIMULATED PHOTOEMISSION, really requires 3
  energy levels
  a photon reminds an
  electron to drop to the middle level after
  another source of energy pumped many electrons
  the high level
• amplifying the original photon via a chain
  reaction these photons are in phase, or
  COHERENT (via constructive interference) yields
  LASERS and MASERS.
• Light or Microwave Amplification through
  Stimulated Emission of Radiation

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Peer Instruction QuestionWhat can cause an
electron to jump from a low-energy orbital to a
higher-energy one?

1. A photon of light is emitted
2. A photon of light is absorbed
3. The atom collides with an electron
4. Both 2 and 3
5. Both 1 and 3

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What can cause an electron to jump from a
low-energy orbital to a higher-energy one?

1. A photon of light is emitted
2. A photon of light is absorbed
3. The atom collides with an electron
4. Both 2 and 3
5. Both 1 and 3

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Results of First Exam

• Mean before curve 55.32
• Curve 19
• Mean after curve 74.32
• Standard deviation 11.54
• Distribution
• 90 17 (high 102)
• 80 15
• 70 34
• 60 22
• lt60 15 (low50 lt49 random guessing 0)

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Most Difficult Questions

• A6C3 False, sidereal day23h 56m 4s
• A15C10 False, p1/d1/500.02 NOT 0.05
• A21C18 B 1 AU 1.5x108km1.5x1013cm
• A25C29 B midnight, 4 min earlier/day 1 hr
  earlier/2 weeks 3 hours earlier in 6 weeks
• A34C38 C FGM1M2/d2 so if d0.25 AU then
  1/d216 times as much
• A37C41 Newton didnt determine distance between
  earth and sun he did everything else

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Rest of Most Difficult Questions

• A39C32 D, 20.00 AU because b2a2(1-e2) so b
  a(1-e2)1/2 30.00 (1-51/2/32)1/2
  b30.00 (1-5/9)1/230.00(4/9)1/230.00(2/3)
• A41C34 B 5.6km/s because
• VY/VE(2GMY/RY)1/2 / (2GME/RE)1/2
• VY/VE(MY/ME)1/2 / (RY/RE)1/2 (2/8)1/21/2
• So VYVE/211.2 km/s / 2 5.6 km/s

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Spectral Lines Sodium
Emission and absorption lines from Na gas Yellow
Doublet (two nearby wavelengths)
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Atomic Transitions Hydrogen

• Lyman series involve transitions to the ground
  state (all UV lines)
• Balmer series involve transitions to first
  excited state (visible and UV)

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• We should not expect to see an optical emission
  line spectrum from a very cold cloud of hydrogen
  gas because
• Hydrogen gas does not have any optical emission
  lines.
• The gas is too cold for collisions to bump
  electrons up from the ground state (lowest energy
  level).
• Hydrogen gas is transparent to optical light.
• Emission lines are only found in hot objects.
• Cold objects only produce absorption lines.

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• We should not expect to see an optical emission
  line spectrum from a very cold cloud of hydrogen
  gas because
• Hydrogen gas does not have any optical emission
  lines.
• The gas is too cold for collisions to bump
  electrons up from the ground state (lowest energy
  level).
• Hydrogen gas is transparent to optical light.
• Emission lines are only found in hot objects.
• Cold objects only produce absorption lines.

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Chemical Fingerprints

• Because those atoms can absorb photons with those
  same energies, upward transitions produce a
  pattern of absorption lines at the same
  wavelengths

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Molecular Lines
Hydrogen spectra on top, molecular H2 On
bottom simpler atomic H
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Molecular Transitions

• In molecules there are many more possible quantum
  states, so many more spectral lines
• Vibrational and rotational energy levels involve
  lower energies (longer wavelengths)

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Doppler Effect

• An observed wavelength or frequency will differ
  from the emitted one if there is a relative
  motion between the emitter and the observer.
• RECESSION ? the OBSERVED ? IS LONGER,
• or FREQUENCY IS LOWER --- REDSHIFT
• APPROACH ? the OBSERVED ? IS SHORTER,
• or FREQUENCY IS HIGHER --- BLUESHIFT

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Doppler Shift Illustration
Cause of Doppler Effect
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Measuring the Shift
Stationary
Moving Away
Away Faster
Moving Toward
Toward Faster

• We generally measure the Doppler Effect from
  shifts in the wavelengths of spectral lines
• Doppler effect for light

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Doppler shift tells us ONLY about the part of an
objects motion toward or away from us
Star Motion Doppler Applet
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Doppler Shift Formula

• Ex ?em 400.000 nm, ?obs400.005 nm
• What is the velocity of the star?
• ?? 400.005 nm - 400.000 nm 0.005 nm
• So, v c (??/ ?) 3.0x105 km/s (0.005 nm/400nm)
  3.0x105 km/s (1.25x10-5) 3.75 km/s
• Or the star is moving 3.8 km/s AWAY from us.
• Doppler shifts and velocities
• We can much more easily HEAR the Doppler effect
  than SEE it.
  WHY?

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Sound Speed vs Light Speed

• The speed of sound in air is a little more than
  300 m/s (or 1000 ft/s) while the speed of light
  in air is 300,000,000 m/s or nearly 1,000,000
  times more!
• A car traveling 62 mph (or 100 km/h) is moving
  roughly 30 m/s (really 27.8 m/s) or a little less
  than 10 of the speed of sound.
• You can hear a pitch change of 10 very easily.
• But the same car is traveling less than 10-7 of
  the speed of light -- that shift of a 500 nm
  visible spectral line would be only 0.00005 nm --
  
• way too small to see and extraordinarily hard to
  measure only a few instruments around the world
  can do this they are used to find planets around
  OTHER stars.

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Can the Doppler shift be measured with invisible
light?

1. No
2. Yes

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Can the Doppler shift be measured with invisible
light?

1. No
2. Yes, Thats how you get a speeding ticketpolice
   use radar (microwaves) to measure your cars
   Doppler shift.

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Thunder and Lightning

• You see lightning the thunderclap comes later.
• Lightning is seen at the speed of light
• Thunder is heard at the speed of sound.
• Since sound travels roughly 300 m/s or 1000 ft/s,
  if he sound arrives
• about 3 seconds later the bolt was about 1 km
  away
• 5 sec later, about a mile away
• 0 sec later -- you may be dead from a lightning
  strike!

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• If a distant galaxy has a substantial redshift
  (as viewed from our galaxy), then anyone living
  in that galaxy would see a substantial redshift
  in a spectrum of the Milky Way Galaxy.
• Yes, and the redshifts would be the same.
• Yes, but we would measure a higher redshift than
  they would.
• Yes, but we would measure a lower redshift than
  they would.
• No, they would not measure a redshift toward us.
• No, they would measure a blueshift.

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• If a distant galaxy has a substantial redshift
  (as viewed from our galaxy), then anyone living
  in that galaxy would see a substantial redshift
  in a spectrum of the Milky Way Galaxy.
• Yes, and the redshifts would be the same.
• Yes, but we would measure a higher redshift than
  they would.
• Yes, but we would measure a lower redshift than
  they would.
• No, they would not measure a redshift toward us.
• No, they would measure a blueshift.

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Spectral Line Shapes

• In reality, lines are not at exactly one
  frequency or wavelength
• All lines have widths, shown here for an emission
  line.
• Line shapes are an important tool in studying
  stars and gas in space

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Thermal and Rotational Broadening

• Higher pressure gas produces broader lines
• Rotation produces broadening of a different
  shape redshifts from receding side and
  blueshifts from approaching

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Spectrometers

• Most telescopes spend most of their time
  measuring spectra of stars, gas clouds and
  galaxies. WHY?
• Spectra tell us
• Compositions elements molecules (line
  positions)
• Temperatures (line strengths)
• Abundances (line strengths)
• Pressures (line widths pressure broadening)
• Radial velocities (Doppler shift)
• Rotation (Doppler broadening)
• Magnetic fields (Zeeman splitting)
• And, indirectly, masses, ages, distances, sizes
  and MORE!

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How do we interpret an actual spectrum?

• By carefully studying the features in a spectrum,
  we can learn a great deal about the object that
  created it.

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What is this object?
Reflected Sunlight Continuous spectrum of
visible light is like the Suns except that some
of the blue light has been absorbed - object must
look red
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What is this object?
Thermal Radiation Infrared spectrum peaks at a
wavelength corresponding to a temperature of 225 K
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What is this object?
Carbon Dioxide Absorption lines are the
fingerprint of CO2 in the atmosphere
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What is this object?
Ultraviolet Emission Lines Indicate a hot upper
atmosphere
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What is this object?
Mars!
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Peer Instruction QuestionSuppose you observed
the spectrum of sunlight reflected from Mars.
Compared to the spectrum of the sun observed
directly, it would

1. Have more emission (bright lines)
2. Have more absorption (dark lines)
3. Have more energy in the red part of the spectrum
4. 1 and 3
5. 2 and 3

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Suppose you observed the spectrum of sunlight
reflected from Mars. Compared to the spectrum of
the sun observed directly, it would

1. Have more emission (bright lines)
2. Have more absorption (dark lines)
3. Have more energy in the red part of the spectrum
4. 1 and 3
5. 2 and 3