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Homework #9
1. A nearby star is found to have a parallax angle of 40
arcsec, How far away is it in meters?
2. The flux of radiation we detect here on Earth for this
star is 7x1010 W/m2 What is its Luminosity?
3.
Where would we have to put this star so that it would
have the same Luminosity as the Sun?
Homework #9 continued
• A star has a photosphere whose temperature is 5772 K,
what is the wavelength of the peak of its blackbody
spectrum? What color is it?
•
If the star has a measured brightness of f  1.57  10 W / m
What is the luminosity of this star which is found to be 20
light years away from us?
8
2
How does light tell us the speed
of a distant object?
The Doppler Effect
Explaining the Doppler Effect
Understanding the Cause of the Doppler Effect
Same for
light
The Doppler Effect for Visible Light
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.
The amount of blue or red shift tells
us an object’s speed toward or away
from us:
The Doppler Shift of an Emission-Line Spectrum
Doppler shift tells us ONLY about the part of an
object’s motion toward or away from us.
How a Star's Motion Causes the Doppler Effect
The Bizarre Stellar Graveyard
The objects depend on which force is
resisting the crush of gravity:
Thermal pressure – main sequence stars and red giants
Electron degeneracy pressure – white dwarfs
Neutron degeneracy pressure – neutron stars
Black holes – gravity wins!!!
Electron Degeneracy
• The central star collapses, heats up, and
ejects a Planetary Nebula.
• The star has insufficient mass to get hot
enough to fuse Carbon.
• Gravity is finally stopped by the force of
electron degeneracy pressure.
• The star is now stable…...
White Dwarfs
• They generate no new
energy.
• They slide down the HRdiagram as they radiate
their heat into space,
getting cooler and fainter.
• They are very dense; 0.5 1.4 M packed into a
sphere the size of the
Earth!
White Dwarfs
• Degenerate matter obeys different laws of physics.
• The more mass the star has, the smaller the star becomes!
• increased gravity makes the star denser
• greater density increases degeneracy pressure to balance gravity
1 M White Dwarf
1.3 M White Dwarf
White Dwarfs
Sirius B is the closest white dwarf to us
Sirius A + B in X-rays
A white dwarf is about the same size as Earth
The White Dwarf Limit
Einstein’s theory of relativity says that nothing can
move faster than light
When electron speeds in White
Dwarf approach speed of light,
electron degeneracy pressure
can no longer work since
electrons cannot go faster than
c – the speed of light
Chandrasekhar found that this
happens when a white dwarf’s
mass reaches 1.4 M
Calculated values for the limit will depend on the nuclear composition of the mass.
Chandrasekhar got his solution based on the equation of state for an ideal Fermi gas
An equation of state is a thermodynamic equation which describes the state of matter
under a given set of physical conditions. It provides a mathematical relationship
between two or more state functions such as its temperature, pressure, volume, or
internal energy
P  K1 

M limit 

0
3
3  hc 


2  2 G 
3/2
1
 e mH 
2
h
Planck’s constant
c
Speed of light
G
Gravitational constant
e
Average molecular weight per electron (depends on chemical
composition of star)
mH
Mass of Hydrogen atom

~ 2.018236 from the Lane Emden equation
0
3
This gives a value that’s a little high ~1.7M. A more accurate value of the limit than
that given by this simple model requires adjusting for various factors, including
electrostatic interactions between the electrons and nuclei and effects caused by nonzero
temperature. A rigorous derivation of the limit comes from a relativistic many-particle
Schrödinger equation.
We will learn a little about this later…
Two Types of Supernova
Massive star supernova:
Iron core of massive star reaches
white dwarf limit and collapses into a
neutron star, causing explosion. Contains
prominent hydrogen lines
White dwarf supernova:
Carbon fusion suddenly begins as white
dwarf in close binary system reaches
white dwarf limit, causing total explosion. No
prominent lines of hydrogen seen.
Supernova Light Curves
(Type II)
(Type I)
The Bizarre Stellar Graveyard
The objects depend on which force is
resisting the crush of gravity:
Thermal pressure – main sequence stars and red giants
Electron degeneracy pressure – white dwarfs
Neutron degeneracy pressure – neutron stars
Black holes – gravity wins!!!
Neutron Stars
• …are the leftover cores from supernova explosions.
• If the core < 3 M, it will stop collapsing and be held up by
neutron degeneracy pressure.
• Neutron stars are very dense (1012 g/cm3 )
– 1.5 M with a diameter of 10 to 20 km
• They rotate very rapidly: Period = 0.03 to 4 sec
• Their magnetic fields are 1013 times stronger than Earth’s.
Chandra X-ray image of the neutron star left
behind by a supernova observed in A.D. 386.
The remnant is known as G11.20.3.
Novae and Supernovae…
Hydrogen that accretes
onto a neutron star builds
up in a shell on the surface
When base of shell gets
hot enough, hydrogen
fusion suddenly begins
leading to a nova
Nova explosion generates a burst of light lasting a few weeks
and expels much of the accreted gas into space (H-bomb)
• While a nova may reach about 100,000 L…
• a white dwarf supernova attains 10,000,000,000 L
(10 billion L)
– runaway carbon fusion in core – causes explosion
– since they all attain the same peak luminosity white dwarf
supernovae make good distance indicators
– they are more luminous than Cepheid variable stars so they
can be used to measure out to greater distances than
Cepheid variables
The cores of many Type II
supernovae become neutron stars
• When stars between 4 and 9 times the mass of
the Sun explode as supernovae, their remnant
cores are highly compressed clumps of neutrons
called neutron stars.
– These tiny stars are much smaller than planet Earth in fact, are about the diameter of a large city (about
20 km)!!
– suggested in 1934
– max. mass of 3 solar masses (otherwise, collapse)
– LGM’s discovered
LGM
• In 1967, graduate student Jocelyn Bell and
her advisor Anthony Hewish accidentally
discovered a radio source in Vulpecula.
• It was a sharp pulse which recurred every
1.3 sec.
• They determined it was 300 pc away.
• What was it?
LGM 1
Jocelyn Bell
A part of the LGM puzzle was solved when a
pulsar was discovered in the heart of the Crab
Nebula.
The Crab pulsar also
pulses in visual light.
Pulsars
Some neutron stars in binary systems
emit powerful jets of gas
Pulsars and Neutron Stars
Pulsars are the lighthouses of Galaxy!
Lighthouse Model
Pulsars and Neutron Stars
• All pulsars are neutron stars, but all neutron stars are
not pulsars!!
• Synchotron emission --- non-thermal process where
light is emitted by charged particles moving close to
the speed of light around magnetic fields.
• Emission (mostly radio) is concentrated at the
magnetic poles and focused into a beam.
• Whether we see a pulsar depends on the geometry.
– if the polar beam sweeps by Earth’s direction once each
rotation, the neutron star appears to be a pulsar
– if the polar beam is always pointing toward or always
pointing away from Earth, we do not see a pulsar
Rotation Periods of Neutron Stars
• As a neutron star ages, it slows down.
• The youngest pulsars have the shortest periods.
• Sometimes a pulsar will suddenly speed up.
– This is called a glitch!
• There are some pulsars that have periods of several
milliseconds.
– they tend to be in binaries.
They are perhaps the most accurate clocks in the universe –
Neutron
Star