D.2 Stellar characteristics and stellar
evolution
D.2 Life cycle of stars
• A Nebula is a stellar
nursery - a region of
dust and gas where
new stars are born.
• The Orion Nebula
(M42) is the nearest
nebula and can be
seen with the naked
eye.
Collapsing gas cloud
• Dense regions in the clouds collapse due to
gravity
• Gravitational potential energy changes to
kinetic energy
• As it gets smaller the protostar(s) at its centre
gets hotter
• Once the star contracts enough that its central
core can fuse hydrogen to helium, it becomes
a "main sequence" star.
• The Sun formed 4.5
billion years ago, as the
Solar System coalesced
from a cloud of gas and
dust.
• The sun is a main
sequence star.
• This is the longest, most
stable period of a star’s
life.
• It converts hydrogen to
helium in its core,
generating heat and
light.
D.2 How the sun works
http://www.youtube.com/watch?v=gS1dpow
PlE8&feature=relmfu
Equilibrium between radiation
pressure and gravity
When the hydrogen runs out
• After the star has used up about 12% of its
hydrogen, its core will contract increasing its
temperature. This heats the outer layers
where fusion continues. The star leaves the
main sequence and moves over to the Red
Giant branch
• A planetary nebula occurs
at the end of a red giant’s
life.
• The outer layers of the red
giant start to drift off into
space.
• This is The Eskimo Nebula
The Cat’s Eye Nebula
What remains is
white dwarf (a
very hot, dense
star).
This white dwarf
is Shapley 1
about 1000 light
years away from
Earth.
White dwarfs
• The white dwarf can’t contract more because
electrons in the core cannot occupy the same
orbits at the same time (this is called electron
degeneracy and is due to the Pauli exclusion
principle)
• CHANDRASEKHAR LIMIT – The mass of the
white dwarf cannot exceed 1.4 solar masses
White dwarfs
• Small and white in colour.
• Since they are white they are comparatively
hot.
• Fusion is no longer taking place, and a white
dwarf is just a hot remnant that is cooling
down.
• Eventually a white dwarf will cool to become a black
dwarf.
• Since the time required for a white dwarf to become a
black dwarf is longer than the age of the universe (13.7
billion years), no black dwarfs exist yet.
• A giant star is much larger
and brighter than a normal
main-sequence star.
• Giant stars can be up to 100
times larger up to 1,000
times brighter than our the
Sun.
• After the hydrogen in a
giant star's core has been
used up, they become red
supergiants - the largest
stars in the universe in
terms of volume.
• These stars have very cool
surface temperatures
(3500–4500 K).
Anatomy of a RED SUPERGIANT
and neon
Death of a large star
• In the core of a red super
giant, lighter elements fuse
until they form iron.
• Iron nuclei absorb energy
when they fuse and so the
process slows down.
• Decreased pressure in the
core, means the outer
layers are not held up and
so they collapse inwards.
• As the core is so dense, the
outer material collides and
bounces off, resulting in a
huge explosion.
Supernovae
• The dying star explodes
violently, producing an
extremely bright object
for weeks or months.
• Temperatures rise to 10
billion K.
• Enough energy to cause
medium weight
elements to fuse,
forming heavy elements
(up to Uranium in the
Periodic Table).
Supernovae are rare – once every century in a typical galaxy.
The remnants of a
supernova in the
constellation Cassiopeia,
all that can be seen by
astronomers.
But the core remains…
If the mass of the remnant of a supernova is less
than 3 solar masses (the Oppenheimer-Volkoff
limit), it becomes a neutron star.
Calvera, the
closest neutron
star found in the
constellation
Ursa Minor
It is made almost entirely from neutrons, compressed
like a giant atomic nucleus.
Evolution of stars > 8Msun
After the supernova the remnant has a mass
above the Chandrasekhar limit (1.4Msun).
Degeneracy pressure is not enough to support
the star so electrons combine with protons to
form neutrons.
• A neutron star is formed
Evolution of stars > 8Msun
• The neutron star left over after the supernova
remains stable provided its has a mass of no
more than 3 solar masses (the OppenheimerVolkoff limit)
• A star with a mass greater than 20 times the mass of our
Sun may produce a black hole at the end of its life.
• Black holes are objects so dense that not even light can
escape their gravity and since nothing can travel faster
than light, nothing can escape.
Evolution of stars > 20Msun
• Neutron stars with masses substantially more
than the Oppenheimer-Volkoff limit (3 solar
masses) continue to collapse as the neutron
pressure is insufficient. They become Black
holes
• At the centre of the black hole is a singularity
• The boundary around the singularity where
even light does not have sufficient escape
velocity to escape is called the event horizon
or gravitational radius.
D.2 Life cycle of a star worksheet
D.2 Measuring the sun’s diameter
Measuring the diameter of the sun
Luminosity (symbol L)
Luminosity is defined as the amount of energy
radiated by the star per second (The power
radiated by the star)
Measured in Watts (J.s-1)
Black-body radiation
• Black Body - any object that is a perfect
emitter and a perfect absorber of radiation
• object does not have to appear "black"
• Stars behave approximately as black bodies
Black-body radiation
The amount of energy per second (power)
radiated from a star (its luminosity) depends
on its surface area and absolute temperature
according to
L = σAT4
where σ is the Stefan-Boltzmann constant
(5.67 x 10-8 W.m-2.K-4)
Wien’s law – Finding the temp of a star
• λmaxT = constant (2.9 x 10-3 mK)
Example
• The sun has an approximate black-body
spectrum and most of its energy is radiated at
a wavelength of 5.0 x 10-7 m. Find the surface
temperature of the sun.
• From Wien’s law
5.0 x 10-7 x T = 2.9 x 10-3
T = 5800 K
Spectral Class
Colour
Temperature/K
O
Blue
25 000 – 50 000
B
Blue - white
12 000 – 25 000
A
White
7 500 – 12 000
F
Yellow - white
6 000 – 7 500
G
Yellow
4 500 – 6 000
K
Yellow - red
3 000 – 4 500
M
Red
2 000 – 3 000
You need to remember the classes and their order
and approximate temperatures.
How will you do this?
Spectral classes
Oh be a fine girl….kiss me!
Apparent brightness (symbol b)
Apparent brightness is defined as the amount
of energy per second per unit area of detector
b=
where
2
L/4πd
d is the distance from the star (in m)
L is the luminosity (in W)
Apparent brightness and Luminosity
b=
d=
2
L/4πd
½
(L/4πb)
More information from spectra
The spectrum of a star can have dark
absorption lines across it. Each dark line
represents the absorption of light at a specific
frequency by a chemical element in the outer
layers of the star
More information from spectra
The absorption spectrum thus gives us
information about a star’s chemical
composition
Very hot stars
Very hot stars do not show an absorption
spectrum as all the gas is ionised so there are
no bound electrons orbiting around the nuclei
in the star. Thus absorption spectrums can
also tell us something about the temperature
of a star.
Hertzsprung – Russell diagram
Hertzsprung – Russell diagram
• The point of classifying the various types of stars is to
see is any patterns exists. A useful way of making the
comparison is the H-R diagram. Each dot on the
diagram represents a different star.
• The vertical axis is the luminosity of the star. It should
be noted that the scale is not a linear one.
• The horizontal axis is the spectral class of the star in the
order OBAFGKM. This is the same as a scale of
decreasing temperature. Once again the scale is not a
linear one.
• The result of such a plot is shown on the next slide
Hertzsprung – Russell diagram
• A large number of stars fall on the line that goes from
the top left to bottom right. This line is known as the
MAIN SEQUENCE and stars that are on it are known
as the main sequence stars. Our sun is a main
sequence star. These stars are ‘normal’ stable starsthe only difference between them is their mass. They
are fusing hydrogen to helium. The stars that are not
on the main sequence can also be put into
categories.
Cepheids!
Mass v luminosity relation
(Main sequence)
Lα
3.5
M
Mass v luminosity relation
Since the luminosity could be the total energy
given out by the star (E) divided by the
lifetime of the star T we get
E/T α M3.5
Since E = Mc2 from Einstein’s formula
Mc2/T α M3.5
T α M1-3.5
T α M-2.5
Lifetime of a star
Tα
-2.5
M
The bigger the mass of a star, the shorter
its life (it “burns” out quicker)
A star with a mass 10x greater than the sun will
have a life time a factor 10-2.5 (1/1000) less
than the sun
Example question
Example question
D.2 Using cepheids to measure
distance
• http://www.youtube.com/watch?v=E9gvk_Ok
rPw
Cepheid variables
• At distances greater than Mpc, neither parallax nor
spectroscopic parallax can be relied upon to measure
the distance to a star.
• When we observe another galaxy, all of the stars in
that galaxy are approximately the same distance
away from the earth. What we really need is a light
source of known luminosity in the galaxy. If we had
this then we could make comparisons with the other
stars and judge their luminosities. In other words we
need a ‘standard candle’ –that is a star of known
luminosity.
• The outer layers of Cepheid variable stars undergo
periodic expansion and contraction, producing a
periodic variation in its luminosity.
Cepheid variable stars are useful to
astronomers because of the period of their
change in brightness turns out to be related to
the average luminosity of the Cepheid. Thus
the luminosity of the Cepheid can be
calculated by observing the variation in
brightness.
•
•
•
•
The process of estimating the distance to a galaxy (in which the
individual stars can be imagined) might be as follows:
Locate a Cepheid variable in the galaxy
Measure the variation in brightness over a given period of
time.
Use the luminosity-period relationship for Cepheids to
estimate the average luminosity.
Use the average luminosity, the average brightness and the
inverse square law to estimate the distance to the star.
Cepheid calculation - Example
• From the left-hand graph we can see that the
period of the cepheid is 5.4 days. From the
second graph we can see that this
corresponds to a luminosity of about 103 suns
(3.9 x 1029 W).
• With a telescope the brightness of the star is
measured to be b = 9.15 x 10-10 W.m-2
• Now using the relationship between apparent
brightness, luminosity and distance
• d = (L/(4πb))½
• d = (3.9 x 1029/(4 x π x 9.15 x 10-10))½
• d = 5.8 x 1018 m = 615 ly = 189 pc
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