Transcript The Milky Way - UNT Department of Political Science

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Chapter 7
Starlight and Atoms
Guidepost
Some chapters in textbooks do little more than present
facts. The chapters in this book attempt to present
astronomy as organized understanding. But this chapter
is special. It presents us with a tool. The interaction of
light with matter gives astronomers clues about the
nature of the heavens, but the clues are meaningless
unless astronomers understand how atoms leave their
traces on starlight. Thus, we dedicate an entire chapter
to understanding how atoms interact with light.
This chapter marks a transition in the way we look at
nature. Earlier chapters described what we see with our
eyes and explained those observations using models
and theories. With this chapter, we turn to modern
astrophysics, the application of physics to the study of
Guidepost (continued)
the sky. Now we can search out secrets of the stars that
lie beyond the grasp of our eyes.
If this chapter presents us with a tool, then we should
use it immediately. The next chapter will apply our new
tool to understanding the sun.
Outline
I. Starlight
A. Temperature and Heat
B. The Origin of Starlight
C. Two Radiation Laws
D. The Color Index
II. Atoms
A. A Model Atom
B. Different Kinds of Atoms
C. Electron Shells
III. The Interaction of Light and Matter
A. The Excitation of Atoms
B. The Formation of a Spectrum
Outline (continued)
IV. Stellar Spectra
A. The Balmer Thermometer
B. Spectral Classification
C. The Composition of the Stars
D. The Doppler Effect
E. Calculating the Doppler Velocity
F. The Shapes of Spectral Lines
The Amazing Power of Starlight
Just by analyzing the light received from a
star, astronomers can retrieve information
about a star’s
1. Total energy output
2. Surface temperature
3. Radius
4. Chemical composition
5. Velocity relative to Earth
6. Rotation period
Color and Temperature
Stars appear in
different colors,
from blue (like Rigel)
Orion
Betelgeuse
via green / yellow (like
our sun)
to red (like Betelgeuse).
These colors tell us
about the star’s
temperature.
Rigel
Black Body Radiation (1)
The light from a star is usually
concentrated in a rather
narrow range of wavelengths.
The spectrum of a star’s light
is approximately a thermal
spectrum called a black body
spectrum.
A perfect black body emitter
would not reflect any radiation.
Thus the name “black body”.
Two Laws of Black Body Radiation
1. The hotter an object is, the more luminous it is:
L = A*s*T4
where A = surface area;
s = Stefan-Boltzmann constant
2. The peak of the black body spectrum shifts
towards shorter wavelengths when the
temperature increases.
 Wien’s displacement law:
lmax ≈ 3,000,000 nm / TK
(where TK is the temperature in Kelvin).
The Color Index (1)
The color of a star is
measured by comparing its
brightness in two different
wavelength bands:
The blue (B) band and the
visual (V) band.
We define B-band and V-band
magnitudes just as we did
before for total magnitudes
(remember: a larger number
indicates a fainter star).
B band
V band
The Color Index (2)
We define the Color Index
B–V
(i.e., B magnitude – V magnitude).
The bluer a star appears, the
smaller the color index B – V.
The hotter a star is, the smaller its
color index B – V.
Light and Matter
Spectra of stars are
more complicated than
pure blackbody spectra.
 characteristic
lines,
called absorption lines.
To understand
those lines, we
need to
understand atomic
structure and the
interactions
between light and
atoms.
Atomic Structure
• An atom consists of
an atomic nucleus
(protons and
neutrons) and a
cloud of electrons
surrounding it.
• Almost all of the
mass is contained
in the nucleus,
while almost all of
the space is
occupied by the
electron cloud.
Atomic Density
If you could fill a teaspoon
just with material as dense as
the matter in an atomic
nucleus, it would weigh
~ 2 billion tons!!
Different Kinds of Atoms
• The kind of atom
depends on the
number of protons
in the nucleus.
• Most abundant:
Hydrogen (H),
with one proton
(+ 1 electron).
• Next: Helium (He),
with 2 protons (and
2 neutrons + 2 el.).
Helium 4
Different
numbers of
neutrons ↔
different
isotopes
Electron Orbits
• Electron orbits in the electron cloud are
restricted to very specific radii and energies.
r3, E3
r2, E2
r1, E1
• These characteristic electron energies are
different for each individual element.
Atomic Transitions
• An electron can
be kicked into a
higher orbit
when it absorbs
a photon with
exactly the right
energy.
Eph = E3 – E1
Eph = E4 – E1
Wrong energy
• The photon is
absorbed, and
the electron is in
an excited state.
(Remember that Eph = h*f)
• All other photons pass by the atom unabsorbed.
Kirchhoff’s Laws of Radiation (1)
1. A solid, liquid, or dense gas excited to emit
light will radiate at all wavelengths and thus
produce a continuous spectrum.
Kirchhoff’s Laws of Radiation (2)
2. A low-density gas excited to emit light will
do so at specific wavelengths and thus
produce an emission spectrum.
Light excites electrons in
atoms to higher energy states
Transition back to lower states
emits light at specific frequencies
Kirchhoff’s Laws of Radiation (3)
3. If light comprising a continuous spectrum
passes through a cool, low-density gas,
the result will be an absorption spectrum.
Light excites electrons in
atoms to higher energy states
Frequencies corresponding to the
transition energies are absorbed
from the continuous spectrum.
The Spectra of Stars
Inner, dense layers of a
star produce a continuous
(blackbody) spectrum.
Cooler surface layers absorb light at specific frequencies.
=> Spectra of stars are absorption spectra.
Kirchhoff’s Laws
(SLIDESHOW MODE ONLY)
Analyzing Absorption Spectra
• Each element produces a specific set of
absorption (and emission) lines.
• Comparing the relative strengths of these sets of
lines, we can study the composition of gases.
By far the
most
abundant
elements
in the
Universe
Lines of Hydrogen
Most prominent lines
in many astronomical
objects: Balmer
lines of hydrogen
The Balmer Lines
n=1
Transitions
from 2nd to
higher levels
of hydrogen
Ha
Hb
Hg
The only hydrogen
lines in the visible
wavelength range.
2nd to 3rd level = Ha (Balmer alpha line)
2nd to 4th level = Hb (Balmer beta line)
…
Observations of the H-Alpha Line
Emission nebula, dominated
by the red Ha line.
Absorption Spectrum Dominated
by Balmer Lines
Modern spectra are usually
recorded digitally and
represented as plots of intensity
vs. wavelength
The Balmer Thermometer
Balmer line strength is sensitive to temperature:
Most hydrogen
atoms are ionized
=> weak Balmer
lines
Almost all hydrogen atoms in
the ground state (electrons in
the n = 1 orbit) => few
transitions from n = 2 => weak
Balmer lines
Measuring the Temperatures of Stars
Comparing line strengths, we can
measure a star’s surface temperature!
Spectral Classification of Stars (1)
Temperature
Different types of stars show different
characteristic sets of absorption lines.
Spectral Classification of Stars (2)
Mnemonics to
remember the
spectral
sequence:
Oh
Oh
Only
Be
Boy,
Bad
A
An
Astronomers
Fine
F
Forget
Girl/Guy
Grade
Generally
Kiss
Kills
Known
Me
Me
Mnemonics
Stellar Spectra
F
G
K
M
Surface temperature
O
B
A
The Composition of Stars
From the relative strength of absorption lines (carefully
accounting for their temperature dependence), one can
infer the composition of stars.
The Doppler Effect
The light of a
moving source is
blue/red shifted by
Dl/l0 = vr/c
l0 = actual
wavelength
emitted by the
source
Blue Shift (to higher
frequencies)
vr
Red Shift (to lower
frequencies)
Dl = Wavelength
change due to
Doppler effect
vr = radial
velocity
The Doppler Effect (2)
The Doppler effect allows us to
measure the source’s radial velocity.
vr
The Doppler Effect (3)
Take l0 of the Ha (Balmer alpha) line:
l0 = 656 nm
Assume, we observe a star’s spectrum
with the Ha line at l = 658 nm. Then,
Dl = 2 nm.
We find Dl/l0 = 0.003 = 3*10-3
Thus,
vr/c = 0.003,
or
vr = 0.003*300,000 km/s = 900 km/s.
The line is red shifted, so the star is receding from
us with a radial velocity of 900 km/s.
Doppler Broadening
In principle, line absorption
should only affect a very
unique wavelength.
In reality, also slightly
different wavelengths are
absorbed.
↔ Lines have a finite width;
we say:
Blue shifted
abs.
Red shifted
abs.
vr
vr
Atoms in random thermal motion
they are broadened.
One reason for
broadening:
The Doppler effect!
Observer
Line Broadening
Higher Temperatures
Higher thermal velocities
 broader lines
Doppler Broadening is usually the most
important broadening mechanism.
New Terms
temperature
Kelvin temperature scale
absolute zero
thermal energy
electron
black body radiation
wavelength of maximum
intensity (λmax)
color index
nucleus
proton
neutron
isotope
ionization
ion
molecule
Coulomb force
binding energy
quantum mechanics
permitted orbit
energy level
excited atom
ground state
continuous spectrum
absorption spectrum
(dark-line spectrum)
absorption line
emission spectrum (brightline spectrum)
emission line
Kirchhoff’s laws
transition
Lyman series
Balmer series
Paschen series
spectral class or type
New Terms (continued)
spectral sequence
L dwarf
T dwarf
Doppler effect
blue shift
red shift
radial velocity (Vr)
transverse velocity
line profile
Doppler broadening
collisional broadening
density
Discussion Questions
1. In what ways is our model of an atom a scientific
model? How can we use it when it is not a completely
correct description of an atom?
2. Can you think of classification systems we commonly
use to simplify what would otherwise be very complex
measurements? Consider foods, movies, cars, grades,
clothes, and so on.
Quiz Questions
1. Which of the following statements is true about the Celsius
and Kelvin (Absolute) temperature scales?
a. Zero is at the same temperature on both scales.
b. The size of one degree is the same on both scales.
c. Zero degrees Celsius is the same temperature as -273 K.
d. The size of one Celsius degree is 5/9 that of a Kelvin.
e. The size of one Kelvin is 5/9 that of a Celsius degree.
Quiz Questions
2. The temperature of a gas is a measure of the
a. total amount of internal energy in the gas.
b. amount of heat that flows out of the gas.
c. total number of atoms in the gas.
d. density of the gas.
e. average motion of its atoms.
Quiz Questions
3. Which subatomic particle has a negative charge?
a. The electron.
b. The proton.
c. The neutron.
d. Both a and b above.
e. Both a and c above.
Quiz Questions
4. The wavelength of maximum intensity that is emitted by a
black body is
a. proportional to temperature.
b. inversely proportional to temperature.
c. proportional to temperature to the fourth power.
d. inversely proportional to temperature to the fourth power.
e. Both a and c above.
Quiz Questions
5. Of the following, which color represents the lowest surface
temperature star?
a. Yellow.
b. Blue.
c. Orange.
d. Red.
e. White.
Quiz Questions
6. The amount of electromagnetic energy radiated from every
square meter of the surface of a blackbody each second is
a. proportional to temperature.
b. inversely proportional to temperature.
c. proportional to temperature to the fourth power.
d. inversely proportional to temperature to the fourth power.
e. Both a and c above.
Quiz Questions
7. The B - V color index of a star indicates its
a. density.
b. total mass.
c. radius.
d. chemical composition.
e. surface temperature.
Quiz Questions
8. If a star appears brighter through a B filter than it does
through a V filter, its B - V color index is
a. negative.
b. zero.
c. positive.
d. greater than or equal to zero.
e. less than or equal to zero.
Quiz Questions
9. An atom that is ionized must have
a. more neutrons than protons.
b. more protons than neutrons.
c. more electrons than protons.
d. more protons than electrons.
e. Either c or d above.
Quiz Questions
10. Which of the following is true of an atomic nucleus?
a. It contains more than 99.9% of an atom’s mass.
b. It contains all of an atom's positive charge.
c. It contains no electrons.
d. Both a and b above.
e. All of the above.
Quiz Questions
11. At what energy level are the electrons in hydrogen gas at a
temperature of 25,000 K?
a. Most are in energy level 1 (also known as the ground state).
b. Most are in energy level 2.
c. Most are in levels higher than energy level 2.
d. Half are in energy level 1, and half are in level 2.
e. None of the above.
Quiz Questions
12. What conditions produce a dark (absorption line)
spectrum?
a. A hot solid, liquid, or high-density gas.
b. A hot low-density gas.
c. Light from a continuous spectrum source passing through a
cooler low-density gas.
d. Both a and b above.
e. All of the above.
Quiz Questions
13. Where is the location of the cooler low-density gas that
yields the dark (absorption) line stellar spectra that were
studied by Annie Jump Cannon?
a. In the interior of the star.
b. In the star's lower atmosphere.
c. In Earth's atmosphere.
d. Both a and b above.
e. Both b and c above.
Quiz Questions
14. Which electron energy level transition corresponds to a
hydrogen atom absorbing a visible-light photon that has a
wavelength of 656 nanometers?
a. The electron makes the transition from energy level 1 to
energy level 2.
b. The electron makes the transition from energy level 2 to
energy level 1.
c. The electron makes the transition from energy level 2 to
energy level 3.
d. The electron makes the transition from energy level 3 to
energy level 2.
e. The electron makes the transition from energy level 3 to
energy level 4.
Quiz Questions
15. What does the presence of molecular bands in the
spectrum of a star indicate?
a. The star has a low surface temperature.
b. The star has a high surface temperature.
c. The star is about to go supernova.
d. The star is spectral type G.
e. The star is spectral type TiO.
Quiz Questions
16. Of the following spectral types, which one represents a star
with the highest surface temperature?
a. A
b. B
c. F
d. K
e. G
Quiz Questions
17. All stars are composed of mostly hydrogen and helium, yet
many stars have no lines for hydrogen or helium in their
spectrum. What causes this apparent contradiction?
a. Spectral lines are created in the lower atmospheres of stars,
and for many stars hydrogen and helium are hidden below the
atmosphere.
b. The upper layers of a star contain hot low-density gases that
produce bright lines at precisely the same wavelengths as the
dark lines, thus making them invisible.
c. Hot hydrogen and helium gas in the interstellar medium
produces bright lines to fill in the dark lines.
d. The resolution of many spectrographs is too poor to show the
extremely thin spectral lines for hydrogen and helium.
e. The surface temperature is such that the electrons are not at
the proper energy levels to produce spectral lines at visible
wavelengths.
Quiz Questions
18. You research the star Sirius and find that its spectral lines
are blue shifted. What does this tell you about Sirius?
a. Its surface temperature is higher than that of the Sun.
b. It has a transverse velocity that is away from us.
c. It has a transverse velocity that is toward us.
d. It has a radial velocity that is away from us.
e. It has a radial velocity that is toward us.
Quiz Questions
19. Suppose that you take the spectrum of several stars and
identify the 656-nanometer line of hydrogen. You then
measure against the reference spectrum on the same image
and find that some of the 656-nm lines are shifted due to the
Doppler Effect. Of the following shifted locations of this line,
which one signals a star that is moving away from us at the
highest speed?
a. Star A @ 655 nm.
b. Star B @ 657 nm.
c. Star C @ 658 nm.
d. Star E @ 659 nm.
e. Star D @ 654 nm.
Quiz Questions
20. What property of a star can broaden the width of its spectral
lines?
a. Rapid rotation of the star.
b. High-density atmosphere.
c. High-temperature atmosphere.
d. Both b and c above.
e. All of the above.
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
b
e
a
b
d
c
e
a
e
e
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
c
c
e
c
a
b
e
e
d
e