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DEVIL PHYSICS
THE BADDEST CLASS ON CAMPUS
IB PHYSICS
TSOKOS LESSON E-2
STELLAR RADIATION
IB Assessment Statements
Topic E-2, Stellar Radiation and Stellar Types
Energy Source
E.2.1. State that fusion is the main energy source of
stars.
E.2.2. Explain that, in a stable star (for example our
Sun), there is an equilibrium between radiation
pressure and gravitational pressure.
Luminosity
E.2.3. Define the luminosity of a star.
E.2.4. Define apparent brightness and state how it is
measured.
IB Assessment Statements
Topic E-2, Stellar Radiation and Stellar Types
Wien’s Law and the Stefan-Boltzmann Law
E.2.5. Apply the Stefan-Boltzmann Law to compare
the luminosities of different stars.
E.2.6. State Wien’s (displacement) Law and apply it to
explain the connection between the colour and
temperature of stars.
Stellar Spectra
E.2.7. Explain how atomic spectra may be used to
deduce chemical and physical data for stars.
E.2.8. Describe the overall classification system of
spectral classes.
IB Assessment Statements
Topic E-2, Stellar Radiation and Stellar Types
Types of Stars
E.2.9. Describe the different types of stars.
E.2.10. Discuss the characteristics of
spectroscopic and eclipsing binary stars.
The Hertzsprung-Russell Diagram
E.2.11. Identify the general regions of star types
on a Hertzsprung-Russell (HR) diagram.
Objectives
 Understand that a star is in equilibrium
under the action of two opposing forces,
gravitation and radiation pressure of the
star
 Appreciate that nuclear fusion provides the
energy source of the star
Objectives
 Give the definition of luminosity as the
power radiated into space by a star and
apparent brightness as the power received
per unit area on the earth
L  AT
4
L
b
2
4d
Objectives
 State the Wien displacement law and solve
problems using it
0T  2.90 x10 K  m
3
 Appreciate the kind of information a stellar
spectrum can provide
Objectives
 State the main properties of main sequence
stars, red giants, white dwarfs, and binary
stars
 Describe the structure of an HR diagram
and place the main types of stars on the
diagram
Energy Source of Stars
 Stars are composed of a core and a dense
“atmosphere” of extremely hot gasses
 The core is a dense mass that creates
gravitational force that tries to draw the
atmosphere into the core
 In the atmosphere, nuclear fusion
reactions are taking place between
hydrogen atoms that release energy that
generates heat
Energy Source of Stars
 High temperatures overcome electrostatic
repulsion between hydrogen protons
 High pressure allow atoms to come close
enough to collide and fuse
Energy Source of Stars
 Each fusion cycle turns 4 hydrogen atoms
into 1 helium atom with the release of 2
electrons, 2 photons, and 2 neutrinos
1
1
H  H  H  e  e
1
1
H  H  He  
1
1
3
2
0 
1
2
1
2
1
3
2
0
0
0
0
He  He  He  2 H
3
2
4
2
1
1
Energy Source of Stars
 The heat creates a radiation pressure that
keeps the star from collapsing under the
gravitational pressure
 To remain stable, the gravitation and radiation
forces must be in equilibrium
Luminosity
 Luminosity is the amount of energy
radiated by a star per second, which is the
same as saying it is the amount of power
radiated by the star
4
L  AT
 σ is the Stefan-Bolzmann constant, equal
to 5.67x10-8 W/m2K4
Luminosity
 Luminosity depends on
2 things: the surface
temperature and the
surface area of the star
 Think of the star as a
sphere and consider
that it radiates power in
all directions from the
surface of the sphere
Apparent Brightness
 Imagine that you could put a detector
somewhere on the surface of the star
 The detector would measure the energy at that spot
 That spot represents a fraction of the total surface
area and the energy it measures would be the same
fraction of the total energy generated by the star
Apparent Brightness
 This is called the apparent brightness whose units are
W/m2
 If we can measure the apparent brightness, which is
the energy at a spot, we can then calculate the
Luminosity
L
b
2
4d
Apparent Brightness
 Measured using a charge-coupled device
or CCD
 It has a photosensitive silicon surface that releases
an electron when hit by a photon
 The number of electrons released is proportional
to the number of incident photons
 We then measure the charge released and that
becomes a direct measure of the brightness of the
object
Black Body Radiation
 Black-body Law - A body of surface area A
and absolute temperature T, radiates energy
in waves according to the Stefan-Bolzman
law (Section 7-2, pages 434-435)
Black Body Radiation
 Therefore, luminosity is the amount of
energy radiated per second by a star of
surface area A and absolute surface
temperature T, and is given by the equation,
L  AT
4
Black Body Radiation
L  AT
4
 A is the surface area of a sphere
 T is absolute surface temperature in Kelvin
 And σ is the Stefan-Bolzman constant 5.67 x
10-8 W/m2K4
 So the units for luminosity will be watts
Black Body Radiation
 Using the previous equation for apparent
brightness, we now find this equation,
L  AT
4
AT
b
2
4d
4
L
b
2
4d
Wavelength
 The energy radiated
by a star is in the form
of electromagnetic
radiation that covers
an infinite range of
wavelengths
 This figure gives the
radiation profiles for
different
temperatures
Wavelength
 This is also called the
spectrum of a black
body and is the energy
radiated per second
per wavelength
interval from a unit
area of the body
Wavelength
 The horizontal axis
represents the
wavelength in
micrometers
 The vertical scale is
relative intensity in
W/m3
Wavelength
 Majority of emitted
energy centers around
the peak wavelength,
λ0
 Colour of a star is
determined by this
wavelength
 Total power, L, is area
under the curve
4
L  AT
Wien Displacement Law
 Relates the wavelength to
surface temperature by,
0T  const  2.90 x10 Km
3
 Implies that the higher
the temperature, the
lower the peak
wavelength and vice versa
Stellar Spectra - Temperature
 Using Wien’s Law, stellar temperature
determined by peak wavelength
0T  const  2.90 x10 Km
3
Stellar Spectra –
Chemical Composition
 Chemical composition obtained from emission
spectra
 Typical composition is,
 70% hydrogen
 28% helium
 2% other heavier elements
Stellar Spectra – Chemical
Composition
 Most stars have the same composition, but
different spectra caused by temperature
 In hot stars the hydrogen is ionized. Atoms cannot
absorb and re-emit photons thus lines will not show
 Cooler stars will have most hydrogen electrons in state
n=2 and will show spectra for transitions to n=3 and
n=4
 ‘Cold’ stars will have most of its electrons in the ground
state and will only absorb and re-emit ultraviolet
photons
Stellar Spectra – Spectral
Classes
 Stars are divided into spectral classes based on
colour/temperature
 Oh Be A Fine Girl/Guy Kiss Me
Stellar Spectra – Rotation
 As a star rotates, one side is moving toward the
observer and one side is moving away from the
observer
 Side moving toward the observer will be blueshifted (shorter wavelength, higher frequency)
 Side moving away from the observer will be redshifted (longer wavelength, lower frequency)
Stellar Spectra –
Magnetic Fields
 In a magnetic field, a spectral line may split into
two or more lines (Zeeman effect)
 Measurement of the amount of splitting in the
spectra provides information about the magnetic
field of the star
Hertzsprung-Russell Diagram
 Correlations between
luminosity and
temperature
 Between temperature
and size
 Between absolute
magnitude and
spectral class
 Result was the HR
Diagram
Hertzsprung-Russell Diagram
 Important Notes:
 Luminosity along the left
vertical axis is in terms of
our sun’s luminosity
 Surface temperature
along lower horizontal
axis goes from right-toleft
 Scales on the axes are
not linear
Hertzsprung-Russell Diagram
 Features:
 Most stars fall along a
diagonal from upper left
to lower right – main
sequence stars
 Top right, large reddish
cool (in temp) stars – red
giants
 Bottom left, small,
bright, hot (in temp)
stars – white dwarfs
Hertzsprung-Russell Diagram
 Features:
 90% of all stars are main
sequence
 9% are white dwarfs
 1% are red giants
Hertzsprung-Russell Diagram
 Features:
 As you move from
bottom right to top left
on main sequence,
luminosity and mass
increase
 Bottom right = red
dwarfs
 Top left = blue giants
Types of Stars
 Main Sequence Stars
 Our sun is a main
sequence star
 Luminosity increases as
mass increases
 Produce enough energy
in the core to balance
gravitational force
Types of Stars
 Red Giants
 Very large, cool, reddish
appearance
 Luminosity much
greater than main
sequence stars of the
same temperature – up
to a billion times greater
 Mass as much as 1000
times our sun but low
density
 Hot core surrounded by
envelope of gas
Types of Stars
 White Dwarfs
 Sirius A and B most well
known
 Faint and hard to detect
 Mass similar to the sun
but size similar to earth
= density 106 times that
of earth
 Formed when collapsing
stars stabilize as a result
of electron degeneracy
pressure
Types of Stars
 White Dwarfs
 Electron degeneracy
pressure occurs when
forced into the same
quantum state
 Pauli exclusion principle
says they will acquire
large kinetic energy
which allows the star to
resist gravitational
pressure to collapse
Types of Stars
 Variable Stars
 Luminosity varies with
time – light curve
 Periodic or non-periodic
 Mainly due to changes
in internal structure of
the star
 As the core becomes
more dense, outer gas
envelope expands
 Mass ejected from outer
layers as nebula or
supernovas
Types of Stars
 Variable Stars
 When mass ejected,
luminosity increases by
a factor of a million
 Matter can also be
transferred from one
star to another which
will heat up and radiate
further increasing
luminosity
Types of Stars
 Variable Stars
 Cepheids
 Most prominent of the
periodic variables
 Periods of 1-50 days
 Relationship between
period of light curve and
peak luminosity
 Peak luminosity
compared to apparent
brightness yields
distance to stars
Types of Stars
 Variable Stars
 Cepheids
 Study of variable stars
provides information
about internal structure
of stars and testing
ground for theories
Types of Stars
 Binary Stars
 Two stars that orbit a
common center
 Important because they
allow determination of
stellar masses
Types of Stars
 Visual Binary
 Formula for common
period of rotation given
below
 Measurement of the
separation distance and
period gives the sum of
the two masses making
up the binary
4 d
T 
G M 1  M 2 
2
2
3
Types of Stars
 Eclipsing Binary
 Orbit plane in relation to
the earth such that the
light of one is
periodically blocked by
the other
Types of Stars
 Spectroscopic Binary
 Detected by analyzing
the Doppler shift of the
light from each
  0 v
z

0
c
Summary Review
 Do you understand that a star is in
equilibrium under the action of two
opposing forces, gravitation and radiation
pressure of the star?
 Do you appreciate that nuclear fusion
provides the energy source of the star?
Summary Review
 Can you give the definition of luminosity as
the power radiated into space by a star and
apparent brightness as the power received
per unit area on the earth?
L  AT
4
L
b
2
4d
Summary Review
 Can you state the Wien displacement law
and solve problems using it
0T  2.90 x10 K  m
3
 Do you appreciate the kind of information a
stellar spectrum can provide
Summary Review
 Can you state the main properties of main
sequence stars, red giants, white dwarfs,
and binary stars
 Can you describe the structure of an HR
diagram and place the main types of stars
on the diagram
IB Assessment Statements
Topic E-2, Stellar Radiation and Stellar Types
Energy Source
E.2.1. State that fusion is the main energy source of
stars.
E.2.2. Explain that, in a stable star (for example our
Sun), there is an equilibrium between radiation
pressure and gravitational pressure.
Luminosity
E.2.3. Define the luminosity of a star.
E.2.4. Define apparent brightness and state how it is
measured.
IB Assessment Statements
Topic E-2, Stellar Radiation and Stellar Types
Wien’s Law and the Stefan-Boltzmann Law
E.2.5. Apply the Stefan-Boltzmann Law to compare
the luminosities of different stars.
E.2.6. State Wien’s (displacement) Law and apply it to
explain the connection between the colour and
temperature of stars.
Stellar Spectra
E.2.7. Explain how atomic spectra may be used to
deduce chemical and physical data for stars.
E.2.8. Describe the overall classification system of
spectral classes.
IB Assessment Statements
Topic E-2, Stellar Radiation and Stellar Types
Types of Stars
E.2.9. Describe the different types of stars.
E.2.10. Discuss the characteristics of
spectroscopic and eclipsing binary stars.
The Hertzsprung-Russell Diagram
E.2.11. Identify the general regions of star types
on a Hertzsprung-Russell (HR) diagram.
QUESTIONS?
Homework
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