Stellar evolution 2015

ASTROPHYSICS
Stellar
characteristics and
stellar evolution
Astronomyonline.org

Black body radiation
 A black body is a perfect emitter. A good model for
a black body is a filament light bulb: the light bulb
emits in a very large region of the electromagnetic
spectrum.
 There is a clear relationship between the
temperature of an object and the wavelength for
which the emission is maximum. That relationship
is known as Wien’s law:
Km2.9x10T
constantT
3-
max
max





Commons wikipedia
Wien Displacement law
By analysing a star’s spectrum,
we can know in what wavelength
the star emits more energy.
The Sun emits more energy at
λ=500 nm.
According to Wien’s law, the
temperature at the Sun’s surface
is inversely proportional to the
maximum wavelength.
So:
K5800
500x10
2.9x102.9x10
T 9-
-3
max
-3



Black body radiation and Wien Law

Star’s Colour and Temperature
Blackbody Applet

Black body radiation
Apart from temperature, a radiation spectrum can also give
information about luminosity.
The area under a black body radiation curve is equal to the
total energy emitted per second per unit of area of the black
body. Stefan showed that this area was proportional to the
fourth power of the absolute temperature of the body.
The total power emitted by a black body is its luminosity.
According to the Stefan-Boltzmann law, a body of surface area
A and absolute temperature T has a luminosity given by:
4
σATL 
where, σ = 5.67x108 W m-2 K-4 , A = 4πr2

Why is this important?
The spectrum of stars is similar to the
spectrum emitted by a black body.
We can therefore use Wien Law to find
the temperature of a star from its
spectrum.
If we know its temperature and its
luminosity then its radius can be found
from Stephan-Boltzmann law.

Real spectra are more
complicated than this (remember
emission and absorption lines?)
Blackbody
Spectrum
Emission and
Absorption
Lines

Example 1
The apparent brightness of our Sun is
1,393 Wm-2. This can be determined using light
sensors on Earth.
We know that the Earth is 1AU from the Sun.
The Sun has an approximate black body
spectrum with most of the energy radiated at a
wavelength of 5.0 X 10-7 m. This is done using
a spectrometer on Earth.

Example 1
 Use the above information to find out
the
 1. Luminosity of the Sun
 2. Surface temperature of the Sun
 3. Radius of the Sun
 USE YOUR DATA BOOKLET!

Atomic Spectra
The spectrum of atomic hydrogen was
discussed and accounted for using the Bohr
model of the atom.
Remember that the electron shells of a given
atom can absorb a specific frequency of
energy.
E = hf
Lets look at Hydrogen as an example.

http://crab0.astr.nthu.edu.tw/~hchang/ga1/f0503-H_Levels.JPG

Atomic Spectra
An electron transition downwards leads to an
emission of a specific frequency of light.
This produces an emission spectrum
if observed through a spectrometer.

Atomic Spectra
Another good example of line emission
spectra is the burning of sodium.
The gaseous sodium’s electrons produce
two distinct spectral lines in the yellow
region of the E-M spectrum.

Atomic Spectra
A particular gas, like Hydrogen can also
ABSORB specific frequencies of light.
This removes particular frequencies from
a continuous spectrum.
This is called an ABSORPTION
SPECTRUM.

www.scienceinschool.org
Atomic Spectra
In all cases the absorption and the
emission spectra will match perfectly.

Atomic Spectra
The spectrum seen from a star is due to
the presence of a particular chemical
element in the outer atmosphere of the
star.
The sun produces absorption lines of
Hydrogen, iron, calcium and sodium.

Atomic Spectra
The absorption spectrum also tells us the
outer temperature of the sun’s surface.
For every element there is a temperature
range which will produce strong
absorption lines.

Atomic Spectra
Examples would be…
 Hydrogen absorption lines occur at
temperatures of 4000 to 12 000 K.
 Helium lines require temperatures of
between 15 000 and 30 000 K in order to
get their electrons to absorb energy.

Atomic Spectra
Different atoms are sensitive to different
temperatures.
It is possible to determine a star’s
temperature by the absorption spectra
that the star is producing.

Atomic Spectra
The chemical composition of stars due to
their line absorption spectra are found to
be remarkably similar.
The average composition of stars is 74%
Hydrogen, 25% Helium and only 1%
other elements.

Atomic Spectra
In summary, line absorption spectra tell
us more about a star’s temperature
rather than its chemical composition (as
most stars have the same composition).

Stars can be arranged into
categories based on the
features in their spectra…
This is called
“Spectral Classification”
1. by the “strength” (depth) of the absorption lines in their
spectra
2. by their color as determined by their blackbody curve
3. by their temperature and luminosity
How do we categorise stars?
A few options:

First attempts to classify stars
used the strength of their
absorption lines…
Williamina Fleming
They also used
the strength of
the Harvard
“computers”!
Stars were labeled “A, B, C…”
in order of increasing strength
of Hydrogen lines.

OBAFGKM(LT)!
Later, these categories were
reordered according to
temperature/color…
Annie Jump Cannon

OBAFGKM - Mnemonics
Only Boring Astronomers Find Gratification in
Knowing Mnemonics!
O Be A Fine Girl Kiss Me

Eventually, the connection
was made between the
observables and the theory.
Observable:
• Strength of Hydrogen Absorption Lines
• Blackbody Curve (Color)
Theoretical:
• Using observables to determine things
we can’t measure:
Temperature and Luminosity
Cecilia Payne

The Spectral Sequence
Class Spectrum Color Temperature
O
ionized and neutral helium,
weakened hydrogen
bluish 31,000-49,000 K
B
neutral helium, stronger
hydrogen
blue-white 10,000-31,000 K
A
strong hydrogen, ionized
metals
white 7400-10,000 K
F
weaker hydrogen, ionized
metals
yellowish white 6000-7400 K
G
still weaker hydrogen, ionized
and neutral metals
yellowish 5300-6000 K
K
weak hydrogen, neutral
metals
orange 3900-5300 K
M
little or no hydrogen, neutral
metals, molecules
reddish 2200-3900 K
L
no hydrogen, metallic
hydrides, alkalai metals
red-infrared 1200-2200 K
T
methane bands infrared under 1200 K

“If a picture is worth a 1000
words, a spectrum is worth
1000 pictures.”
 Spectra tell us about the physics of the star
and how those physics affect the atoms in it

The Hertzsprung-Russell diagram
This diagram shows a
correlation between the
luminosity of a star and
its temperature.
The scale on the axes is
not linear as the
temperature varies from
3000 to 25000 K
whereas the luminosity
varies from 10-4 to 106,
10 orders of magnitude.

H-R diagram
 The stars are not randomly distributed on
the diagram.
 There are 3 features that emerge from
the H-R diagram:
 Most stars fall on a strip extending
diagonally across the diagram from
top left to bottom right. This is called
the MAIN SEQUENCE.
 Some large stars, reddish in colour
occupy the top right – these are red
giants (large, cool stars).
 The bottom left is a region of small
stars known as white dwarfs (small
and hot)

H-R Diagram
 H-R Diagram animation

What is the role of
interpretation in the sciences?
 Go to https://www.zooniverse.org/ and
participate in real science now!

Types of Stars
 Red Giants
Very large, cool stars with a reddish appearance. All main
sequence stars evolve into a red giant. In red giants there
are nuclear reactions involving the fusion of helium into
heavier elements.

Red Giants
 The fuel is expended much faster than
in stars like our sun.
 Within a red giant is a core still
increasing in temperature.
 When the temperature rises to 100
million degrees Kelvin helium fusion
takes place.

Red Giants
 There are now two layers of energy
production;
 the hydrogen burning shell,
 the helium-burning core.
 This process eventually yields a carbon
and oxygen core,that may eventually
produce an iron core,in the most
massive stars.

Red Giants
 The fusion process stops with iron;
 Iron represents the most stable form, in
which protons and neutrons can exist.
 Once the Iron core is formed energy
production comes to an end.
 The pressure forcing the star to expand
no longer is present, gravity takes over.

Red Giants
 Within seconds, iron core collapses with
such a force,not even the space within
the orbital structure of the atom is
preserved.
 The layers within the iron core fall into
the centre,at different rates,an outward
shock wave is produced.

Red Giants
 This shock wave is capable of driving
off most of the mass of the star.
 For a star of size 10 solar masses;
 85% of the mass is lost,
 the star goes supernova.

Types of Stars
 White dwarfs
A red giant at the end stage of its
evolution will throw off mass and
leave behind a very small size
(the size of the Earth), very
dense star in which no nuclear
reactions take place. It is very
hot but its small size gives it a
very small luminosity.
As white dwarfs have mass
comparable to the Sun's and
their volume is comparable to the
Earth's, they are very dense.
A comparison between the
white dwarf IK Pegasi B
(center), its A-class
companion IK Pegasi A (left)
and the Sun (right). This
white dwarf has a surface
temperature of 35,500 K.

Types of Stars
 Neutron stars
A neutron star is formed from
the collapsed remnant of a
massive star (usually
supergiant stars – very big red
stars). Models predict that
neutron stars consist mostly of
neutrons, hence the name.
Such stars are very hot. A
neutron star is one of the few
possible conclusions of stellar
evolution.
The first direct observation
of a neutron star in visible
light. The neutron star
being RX J185635-3754.

Types of Stars
 Supernovae
A supernova is a stellar
explosion that creates an
extremely luminous object.
The explosion expels much or all
of a star's material at a velocity
of up to a tenth the speed of
light, driving a shock wave into
the surrounding interstellar
medium. This shock wave
sweeps up an expanding shell of
gas and dust called a supernova
remnant.
Crab Nebula

Types of Stars
 Supernovae
A supernova causes a
burst of radiation that
may briefly outshine its
entire host galaxy before
fading from view over
several weeks or months.
During this short interval,
a supernova can radiate
as much energy as the
Sun would emit over 10
billion years.
Supernova remnant N 63A lies
within a clumpy region of gas
and dust in the Large Magellanic
Cloud. NASA image.

Types of Stars
 Pulsars
Pulsars are highly
magnetized rotating
neutron stars which emit
a beam of detectable
electromagnetic radiation
in the form of radio
waves. Periods of
rotation vary from a few
milliseconds to seconds.
Schematic view of a pulsar. The
sphere in the middle represents
the neutron star, the curves
indicate the magnetic field lines
and the protruding cones
represent the emission beams.

Types of Stars
 Black Holes
A black hole is a region of space in which the
gravitational field is so powerful that nothing can escape
after having fallen past the event horizon. The name
comes from the fact that even electromagnetic radiation
is unable to escape, rendering the interior invisible.
However, black holes can be detected if they interact
with matter outside the event horizon, for example by
drawing in gas from an orbiting star. The gas spirals
inward, heating up to very high temperatures and
emitting large amounts of radiation in the process.

Types of Stars
 Cepheid variables
Cepheid variables are stars of variable luminosity. The
luminosity increases sharply and falls of gently with a
well-defined period.
The period is related to the absolute luminosity of the
star and so can be used to estimate the distance to the
star.
A Cepheid is usually a giant yellow star, pulsing
regularly by expanding and contracting, resulting in a
regular oscillation of its luminosity. The luminosity of
Cepheid stars range from 103 to 104 times that of the
Sun.
Cepheid Variable Sim Real Data used by Astronomers

Types of Stars
 Binary stars
A binary star is a stellar system consisting
of two stars orbiting around their centre
of mass. For each star, the other is its
companion star. A large percentage of
stars are part of systems with at least two
stars.
Binary star systems are very important in
astrophysics, because observing their
mutual orbits allows their mass to be
determined. The masses of many single
stars can then be determined by
extrapolations made from the observation
of binaries.
Hubble image of
the Sirius binary
system, in which
Sirius B can be
clearly
distinguished
(lower left).

Binary stars
There are three types of binary stars
 Visual binaries – these appear as two separate stars
when viewed through a telescope and consist of two stars
orbiting about common centre. The common rotation period
is given by the formula:
)(
4
21
32
2
MMG
d
T



where d is the distance between the stars.
Because the rotation period can be measured directly, the
sum of the masses can be determined as well as the
individual masses. This is useful as it allows us to determine
the mass of singles stars just by knowing their luminosities.

Binary stars
 Eclipsing binaries – some binaries are two far to be
resolved visually as two separate stars (at big distances two
stars may seem to be one).
But if the plane of the
orbit of the two stars is
suitably oriented relative
to that of the Earth, the
light of one of the stars in
the binary may be
blocked by the other,
resulting in an eclipse of
the star, which may be
total or partial
Eclipsing Binary Simulation

Binary stars
 Spectroscopic
binaries – this
system is detected
by analysing the
light from one or
both of its
members and
observing that
there is a periodic
Doppler shifting of
the lines in the
spectrum.

Binary stars
A blue shift is expected as the star
approaches the Earth and a red shift as it
moves away from the Earth in its orbit
around its companion.
If λ0 is the wavelength of a spectral line
and λ the wavelength received on earth,
the shift, z, is defined as:
0
0

 
z
If the speed of the source is small compared with the speed
of light, it can be shown that:
c
v
z  The speed is proportional to the shift

TOK
 Stars are a long way away. How can we
claim we know anything about them?
 Do stars die?
 Are we stardust?

H-R diagram
 The stars are not randomly
distributed on the diagram.
 There are 3 features that emerge
from the H-R diagram:
 Most stars fall on a strip
extending diagonally across
the diagram from top left to
bottom right. This is called the
MAIN SEQUENCE.
 Some large stars, reddish in
colour occupy the top right –
these are red giants (large,
cool stars).
 The bottom left is a region of
small stars known as white
dwarfs (small and hot)

Star Formation
 Protostar
 High temperature leads to ionisation of
elements.
 E-M energy is emitted.
 The star can have considerable Luminosity.
 5000 times the surface area and 100 times
as Luminous as our Sun.

Star Formation
 Protostar-
 Temperature continues to increase…
 Electrons stripped from the atoms in the
core.
 A plasma is formed.

Star Formation
 Main Sequence Star-
 Nuclear Fusion starts up.
 Temperatures now high enough to
fuse Hydrogen into Helium.
 Gravitational contraction will now stop
as the Fusion process will offset the
contraction.
 “Hydrostatic Equilibrium”

You are not
Required to
Memorize these
Reactions

Main Sequence Stars
 Where a star lands on the Main Sequence depends
on its mass.
 A star will
stay at this
place on the
main sequence
for its lifetime
as a Main Sequence
Star.
QuickTime™ and a
Photo - JPEG decompressor
are needed to see this picture.

Main Sequence Stars
 The life of a Main Sequence star is determined by its
mass.
 High Mass =
Short Lifespan.
 Sun (1M) - 10 Billion
Years.
 15 M - 10,000
Years.
QuickTime™ and a
Photo - JPEG decompressor
are needed to see this picture.

Main Sequence Stars
 Once hydrostatic equilibrium is
reached… the star will remain stable for
as long as it is a Main Sequence Star
(thousands to up to billions of years).

The Future of our Sun
 There is enough Hydrogen in our Sun’s
core to produce fusion for another 5
billion years.
 Eventually the core will be mostly
Helium.
 Hydrogen Fusion will then begin outside
the core.

 No fusion happening in the core to
counteract the gravitational contraction.
 The core will begin to collapse.
 This raises the cores temperature.
 Sun will start to expand.
 Surface temperature will drop.
 Sun enters RED GIANT STAGE.

 Luminosity increases due to massive
size.
 Out to the orbit of Venus.
 Core temperature now so high that
Helium can be fused.
 Higher temperature required to fuse
Helium as it has two positive charges.

 Helium fused into Carbon and Oxygen.
 This is where our carbon comes from.
 Once the Helium is used up in the core, the
star collapses due to the high mass core
even more… this raises the temperature
even higher!
 Burning of Hydrogen in the outer layers
causes further expansion.

 At this point the Sun’s surface will reach
out to the Earth’s Orbit!
 10,000 times as luminous as today.
 The sun will start to shed layers… these
layers are called planetary nebula.

 The core will now be exposed.
 The core is called a White Dwarf.
 About the size of the Earth.
 Very hot, very small.
 Not luminous.
 Will eventually cool into a cold, “dead” star
called a brown dwarf.

Types of Stars (review)
 Cepheid variables
Cepheid variables are stars of
variable luminosity. The luminosity
increases sharply and falls of
gently with a well-defined period.
The period is related to the
absolute luminosity of the star and
so can be used to estimate the
distance to the star.
A Cepheid is usually a giant yellow star, pulsing regularly
by expanding and contracting, resulting in a regular
oscillation of its luminosity. The luminosity of Cepheid
stars range from 103 to 104 times that of the Sun.

Cepheid variables
The relationship between a Cepheid
variable's luminosity and variability period is
quite precise, and has been used as a
standard candle (astronomical object that has
a known luminosity) for almost a century.
This connection was
discovered in 1912 by
Henrietta Swan Leavitt.
She measured the
brightness of hundreds
of Cepheid variables
and discovered a
distinct period-
luminosity relationship.

A three-day period Cepheid has a luminosity of about 800
times that of the Sun.
A thirty-day period Cepheid is 10,000 times as bright as the
Sun.
The scale has been calibrated using nearby Cepheid stars, for
which the distance was already known.
This high luminosity, and the precision with which their
distance can be estimated, makes Cepheid stars the ideal
standard candle to measure the distance of clusters and
external galaxies.
Cepheid variables

Mass – Luminosity
Relationship
 There is a relationship between the
luminosity of a star and its mass
 L = M3.5
 Where L is luminosity, M is mass in
solar units and applies to all main
sequence stars
 The power (3.5) can be any value
between 3 and 4 as it is itself mass
dependant.

The Chandrasekhar Limit
 If the initial solar mass of a star is
greater than 4 solar masses… then the
star will become a…
 Supergiant Star and eventually collapse to
a…
 Neutron Star or a Black Hole.

 A star greater than 4 solar masses (1
solar mass is the mass of our Sun)…
will collapse to a core…
 With a mass of greater than 1.4 Solar
Masses.
 A neutron star or a black hole
 If the core is less than 1.4 solar masses
the star will become a White Dwarf.

 This 1.4 solar mass of the core
boundary is called the Chandrasekhar
limit.
 Famous Indian astronomer.
 Less than 1.4 solar mass for the core…
electron degeneracy prevents further
collapse.
 Electrons cannot be packed together any
further.

THE OPPENHEIMER-VOLKOFF
LIMIT
 is the equivalent to Chandrasekhar
but applies to neutron stars.

The Supergiants
 Stars with masses greater than 4 solar
masses initially will evolve into a
Supergiant star…
 Eventually collapse to a core greater than
1.4 solar masses.
 Become a Neutron Star or a Black Hole.

The Supergiants
 The star will undergo the same process
as a Red Giant…
 Fusion of Helium in the inner core.
 Fusion of Hydrogen in the outer layers.
 Expansion.
 Cooling at the surface of the star.
 Subsequent fusion of Oxygen and Carbon
in the core.

The Supergiants
 The difference is that the star is
massive enough to continue to…
 Collapse after the Oxygen and Carbon
fusion.
 Further gravitational collapse leads to
further temperature rises.
 Capable of beginning the fusion of silicon.

The Supergiants
 The fusion of silicon makes iron.
 Supergiants are the brightest stars
visible due to their enormous size.
 Betelgeuse in the constellation Orion.

The Supergiants
 Iron cannot undergo fusion due to its
very high coulombic repulsion (26
protons).
 It would need astronomical
temperatures.
 The star has reached a critical state.

The Supergiants
 The star will once again begin to
collapse into the core.
 But no more fusion will take place to
counteract the gravitational collapse.
 Incredibly high temperatures lead to
the combining of electrons and protons.

The Supergiants
 Neutrons and neutrinos are formed in
large quantities.
 High energy neutrinos form an outward
pressure wave.
 This wave hurtles outward.

The Supergiants
 This shock wave rips the outer layers
off of the star.
 The inner core is now exposed.
 Huge amount of radiation floods into
space.

Stellar evolution 2015

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