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Properties of
Stars
Distances to Stars
The distance to a nearby star can be measured by
observing its parallax - the apparent shift of its
position on the sky relative to more distant stars.
Parallax is caused by Earth’s motion around the Sun.
A parsec is the distance at which 1 AU subtends an
angle of 1 arcsecond. 1 pc = 3.26 light years.
A star with a parallax p = 1 arcsec must be 1 pc away:
d (pc) = 1/p
Apparent vs. Intrinsic Brightness
The apparent brightness of a light source depends on:
(a) its intrinsic brightness (a.k.a. luminosity)
(b) its distance from us.
Inverse-Square Law
The apparent brightness of a
star decreases as the distance
to the star increases.
Brightness is proportional to
1/d 2.
F =
L
_____
4p d 2
L = intrinsic luminosity (energy emitted per second)
d = distance to light source
F = flux (i.e., apparent brightness)
Luminosities of Stars
• From the Stefan-Boltzmann Law, the hotter a star is, the more
energy it emits per square meter of surface area per second.
• The larger the radius of a star, the greater its surface area.
• So, we can express a star’s luminosity as:
L = 4p R2s T 4
• Thus, if we can measure the apparent brightness and distance
of a star and can estimate its temperature (from Wien’s Law)
we can determine:
 Luminosity (from apparent brightness and distance)
 Radius (from luminosity and temperature)
Stellar Spectra
Recall that the temperature
of a star determines:
• the overall shape of its
spectrum
• the spectral line features
it exhibits
Line Strength vs. Temperature
Stellar Spectra
What do the letters
O, B, A, F, G, K, M
mean?
Spectral Classification
So, the spectral class sequence is really a temperature sequence.
The H-R Diagram
Plotting the luminosities
of stars vs. their spectral
types (i.e., temperatures)
we find that stars follow
certain well-defined
patterns.
The H-R Diagram
Another H-R Diagram:
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
How can stars of the same spectral type
have different luminosities?
Recall that
L = 4p R2s T 4
Thus, stars that have the same spectral type
(i.e., temperature) but different luminosities
must have different radii.
Sizes of Stars
We can estimate the radii of stars. We call them “dwarfs,”
“giants,” or “supergiants” according to their sizes. 90% of
the stars we observe are dwarfs on the “Main Sequence.”
Luminosity Class
We divide dwarf, giant,
and supergiant stars into
various luminosity classes,
denoted I-V.
Stars that have the same
spectral type but different
luminosity classes are
distinguished by the
widths and strengths of
the absorption lines in
their spectra.
Stellar Demographics
There are many
more small, faint
red dwarf stars
on the main
sequence than
large, luminous
blue stars.
There are many
more main
sequence stars
than giant or
supergiant stars.
The Formation of Stars
Different types of nebulae:
The Horsehead Nebula in the constellation of Orion
Emission Nebulae
Hot, blue stars emit a lot of ionizing radiation,
which excites the gas that surrounds them.
Another example: the Eagle nebulae
Lifetimes of Hot, Luminous Stars
The big, hot, luminous, blue stars on the upper part of the main
sequence have relatively short lifetimes.
Star formation and gas clouds
These hot, blue stars are often found associated with gas
clouds in the Milky Way. Because of this association, we
believe all stars must be born in such gas clouds.
Star formation and gas clouds
The collapse of a gas cloud
Stars form from the rapid
collapse of a gas cloud due
to gravitational forces.
As the cloud collapses, it
converts gravitational
energy into thermal energy
and heats up.
The pressure in the gas increases as the particles in the gas move
faster and faster in random directions. This pressure will push
outwards against the gravitational forces.
At the same time the gas cloud will be losing thermal energy
through radiation so this increase in pressure is usually not
enough to halt the collapse.
Collapse of a gas cloud
Because of the conservation
of angular momentum, any
rotation of the cloud will be
amplified as it collapses. A
protostar will be surrounded
by a swirling disk of material.
Early stages of star formation
are hidden from our view by
the dense cloud of gas still
surrounding it.
Star formation and gas clouds
The Eagle Nebula
Protostar Evolution
The rapid collapse of the gas cloud will slow down as the
temperature and pressure increases in its center. The protostar
formed at the center of the cloud will then gradually contract
and heat up until...
A star is born…
...the gas at the center of the
star is hot and dense enough to
ignite nuclear fusion.
This will maintain the pressure
and temperature of the gas
sufficiently to balance the
immense gravitational forces
and halt the contraction of the
protostar.
Protostar Evolution
The more massive a star is, the more quickly it is born.
Stellar Energy Sources
In stars like the sun, most of the energy is produced via
the proton-proton chain, in which 4 H atoms are fused
into a single He atom, and energy is released.
Stellar Energy Sources
In higher mass stars,
some of the energy
produced in the stellar
core comes from a
different nuclear
reaction chain, called
the CNO cycle.
Stellar Mass Limits
Stellar Mass Limits
Young Stars
When a star is very young,
the outpouring of energy
from nuclear fusion can
drive away the remains of
the gas cloud surrounding
it, but it will usually still be
surrounded by a dark disk
of material which is in the
process of falling onto the
star (and may eventually
form planets!).
Young Stars
Stellar Structure & Evolution
Hydrostatic Equilibrium
In a stable star, the inward
pull of gravity is exactly
balanced by the outward
force of gas pressure at
each level within the star.
This is known as the law
of hydrostatic equilibrium.
When stars are not in
hydrostatic equilibrium,
they will either expand or
contract.
Stellar Energy Sources
One key piece of the puzzle is how stars produce
energy. Most of the energy is produced in their
cores via the fusion of 4 H atoms into a He atom.
Energy Transport in Stars
Another physical process that is important inside stars is
the way in which energy gets transported from the core to
the surface. For normal stars, this happens by convection,
radiation, or both.
Energy Transport in Stars
In the sun, energy is transported via radiation in the
central regions, but by convection in the outer regions.
Energy Transport in Stars
Cross sections of main sequence stars of different
masses, showing the modes of energy transport the
different stars use.
Modeling Stellar Structure
The structure and evolution of stars is accurately modeled with
only a few well understood laws of physics. Astronomers use
these laws and powerful computers to compute stellar models.
Main-Sequence Lifetime vs. Mass
• All stars, regardless of their mass, spend roughly 90% of
their total lifetimes as main sequence stars.
• Stars end their main sequence lives when their supply of
hydrogen fuel runs out in the core.
• The most massive stars (O and B types) have very short
lifetimes compared to low-mass stars (K and M types).
Main-Sequence Evolution
Stars begin their main
sequence lives when they
initiate hydrogen burning
in their cores. They are
located on the zero-age
main sequence (ZAMS)
at this time. As they age,
they evolve slowly away
from the ZAMS.
Post-MS Evolution
When stars evolve away from
the main sequence they become
red giants.
Recall that the equation
L = 4p R2s T 4
defines lines of constant radius
on an H-R diagram.
Red giants are… giant and red.
Post-MS Evolution
The sun today and the sun as a red giant star.
Post-MS Evolution
H-R diagram showing
the evolutionary paths
followed by stars that
are more massive than
the sun. Note how
these two tracks pass
through the regions
occupied by giant and
supergiant stars.
5
6
3
4
1
2
Post-MS evolutionary track for a 5 Msun star,
including the helium ignition stage, the helium
core-burning phase, and the asymptotic giant
branch phase.
Post-MS Evolution
A red giant star (cross
section), showing the
compact helium core,
H-burning shell, and
bloated outer envelope.
Note the size of the
present day sun, for
comparison.
How can we test stellar evolution models?
H-R diagram for a
group of stars all
born at the same
time: hot, massive
stars evolve the
most rapidly.
Over time, main
sequence stars of
progressively lower
temps/masses peel
away to the giant
regions on the
diagram.
“Open” Star Clusters
The Pleiades star cluster, a grouping of hundreds of stars
all born at roughly the same time and at the same distance
from Earth.
“Open” Star Clusters
The Jewel Box cluster. This cluster is somewhat older than
the Pleiades. Note the presence of at least one red giant star.
“Globular” Star Clusters
The globular cluster
47 Tuc, visible only
from the southern
hemisphere.
Globular clusters
contain several
hundred thousand
stars each!
Testing Stellar Evolution
Theoretical H-R diagram for a star cluster with an age
of 1 Myr. The red line is the ZAMS. Note that the
lower mass stars are still evolving toward the MS, while
some high-mass stars have already evolved off the MS.
Testing Stellar Evolution
Same as the previous panel, but for a cluster age of 10 Myr.
Testing Stellar Evolution
Cluster age = 100 Myr. All lower mass stars have
reached the MS, but the stars along the upper half of
the MS have all ended their lives.
Testing Stellar Evolution
Cluster age = 1 billion years.
Testing Stellar Evolution
Cluster age = 10 billion years.
Testing Stellar Evolution
A real H-R diagram
for NGC 2264, a
nearby cluster with
an age estimated at
1 million years.
ZAMS
Testing Stellar Evolution
A real H-R diagram
for the Pleiades
cluster, which has
an estimated age of
100 million years.
Testing Stellar Evolution
The H-R diagram
for M 67, a cluster
with an estimated
age of 4 billion
years.
Testing Stellar Evolution
H-R diagram for a
globular cluster.
The cluster age
estimated from
these data is over
10 billion years.
Testing Stellar Evolution
H-R diagrams of
star clusters verify
our models of
stellar evolution.
We can then use the
locations of cluster
turn-off points to
determine the ages
of clusters.
The Deaths of Stars
Deaths of the Least Massive Stars (M < 0.4 Msun)
• The least massive stars are fully convective: they will burn all of their hydrogen
• Once their hydrogen is gone they contract and heat up, but the contraction and
heating are halted by electron degeneracy pressure before helium fusion can ignite
• They will slowly cool as helium white dwarf stars
• The main-sequence lifetimes of these stars are longer than the age of the Universe,
so no such white dwarfs yet exist!
Deaths of Medium-Mass Stars (0.4-4 Msun)
• Medium-mass stars burn H  He in their cores while on the main sequence and
He  C and O while on the horizontal branch
• They are not massive enough to ignite C-burning once their He is gone. Their
cores contract and heat up until the contraction is stopped by electron degeneracy
pressure
• At the same time, their envelopes expand because of the energy generated by shell
H and He burning and they move up the asymptotic giant branch (AGB)
Deaths of Medium-Mass Stars (0.4-4 Msun)
• The envelope of a star on the AGB is thermally unstable; it pulsates as it expands
• Eventually, the entire envelope is ejected as a planetary nebula, leaving behind its
hot, degenerate core: a white dwarf
• The expanding envelope is ionized by UV photons from the hot white dwarf; it will
glow as an emission nebula for up to 50,000 years
Planetary Nebulae
Planetary Nebulae and White Dwarf Stars
Evolutionary track of a sun-like star from
red giant to white dwarf.
Observed Properties of White Dwarfs
• ~ 25% of nearby stars are white dwarfs
• masses range from ~ 0.4 - 1.0 Msun
• surface temperatures range from ~ 80,000 - 5,000 K
• radii range from ~ 0.007 – 0.02 times the sun’s radius
• their densities are very high: r > 106 g/cm3
• WDs cool as they age, eventually becoming black dwarfs
The sizes of white dwarfs…
• masses of white dwarfs fall
in narrow range
• R ~ 1 / M 1/3
• M’s about the same  R’s
about the same
Upper Mass Limit of White Dwarfs
Because it is supported by electron degeneracy pressure,
the more massive a white dwarf is, the smaller its radius is.
White dwarfs cannot exceed the Chandrasekhar Limit of
1.4 Msun.
Deaths of Very High-Mass Stars (M > 8 Msun)
When the core fuel source is exhausted in massive stars, they contract
and heat up to temperatures sufficient to ignite fusion in the “ash” left
over from the previous core-burning stage. The final burning stage is
silicon (Si) to iron (Fe) in the core. Fusion of lighter elements occurs
in shells surrounding the core.
Deaths of Very High-Mass Stars
• Iron has the most tightly bound
nucleus of all elements. It does not
produce energy when it is fused.
• Once the core of the star is all iron it
can’t produce energy and collapses.
• Electron degeneracy pressure is not
enough to halt the collapse because
the core mass exceeds the 1.4 Msun
Chandrasekhar limit.
• The core becomes extremely dense –
far denser than a white dwarf.
number of nuclear particles
Deaths of Massive Stars: Supernovae
At these immense densities
the electrons will smash into
the protons to form neutrons.
If the mass of the core is less
than ~3 Msun its collapse will
be suddenly halted by neutron
degeneracy pressure.
The outer layers of the star,
still collapsing onto the core,
bounce off in a violent
supernova explosion.
Supernovae in Galaxies beyond the Milky Way
SN 1999by
Observations of Supernovae
During a supernova explosion a star
will shine many billions of times
more brightly than the Sun.
Supernovae Type II result from the
deaths of massive stars.
Supernovae Type I are explosions
triggered when a white dwarf accretes
mass from a companion and suddenly
exceeds the Chandrasekhar limit.
Origin of Type Ia Supernovae
Accreted material from a companion star causes the mass of
a white dwarf to exceed the Chandrasekhar limit… kaboom!
Supernova Remnants
The Crab Nebula
Supernova Remnants
The Gum Nebula
Exploded high-mass stars: supernovae
Optical
X-ray
Neutron Stars
&
Black Holes
How big is a Neutron Star?
• Recall that RWD ≈ REarth (= 0.01 Rsun, or 7000 km)
• Neutron stars must be even smaller!
RNS ≈ 10 km!
M > 1.4 Msun
r ≈ 1014 g/cm3
Discovery of Pulsars
• first pulsar (source of pulsed
radio emission) discovered in
1967.
• “flashes” of radio waves
evenly spaced: periods of
first pulsars 0.033-3.75 sec
• pulse period increases very
gradually
• one of the first pulsars was
discovered at the center of
the Crab Nebula
Pulsars are Neutron Stars!
visible
visible (zoomed in)
X-ray (zoomed in more)
The Crab Nebula resulted from the supernova explosion of AD 1054.
How do pulsars work?
The “lighthouse” model attempts
to explains why pulsars:
• rotate rapidly
• have intense magnetic fields
• emit beams of radiation that
spew from their magnetic poles
Observations of the region near the Crab pulsar by…
QuickTime™ and a Sorenson Video 3 decompressor are needed to see this picture.
Chandra X-ray Observatory
Hubble Space Telescope
Black Holes
Black holes form when
matter collapses to a point
- a singularity.
Nothing – not even light
– can escape from within
the event horizon above a
black hole.
The event horizon is one
Schwarzschild radius (RS)
from the singularity.
As the gravitational field of an object increases, the
curvature of space-time near its surface increases to the
point (for black holes) where not even light can escape.
Light Bending Near a Black Hole
Black Holes
A probe falling into a black hole:
• would be distorted by the immense gravitational forces
• photons leaving the probe would lose more and more energy;
they would be “redshifted” to longer wavelengths.
• time on the probe would appear to move slower and slower
to the observer who sent it in.
Black Holes…
…are not cosmic vacuum cleaners!
Observing Black Holes
We can “see”
accreting black
holes in binary
star systems
via their X-ray
emission.
Black
Hole
X-rays from hot
accretion disk
X-ray Exotica
Compact objects give rise to
a wide variety of phenomena,
all of which have associated
X-ray emission.
The Black Widow Pulsar
X-ray Exotica
Jets from a black-hole binary
Summary of Stellar Evolution & Death
Initial mass < 0.4 Msun
 He white dwarf
0.4-4 Msun
 planetary nebula
 C-O white dwarf
4-8 Msun
 planetary nebula/
white dwarf likely
Mass 8-25 Msun
 supernova
 neutron star
> 25 Msun
 supernova
 black hole