Download L = σAT 4

E2 Stellar radiation and stellar types
Fusion
http://www.youtube.com/watch?v=gS1dpow
PlE8&feature=relmfu
Life-cycle of a star
Video on life of a star
Birth of a Star
All stars start life as a nebula of gas and dust.
Over millions of years gravity pulls these
closer together.
Birth of a star
Pressure builds up and the
core starts to heat up giving
out infra red radiation.
Gravitational force
Nebula
Birth of a star
The dust and gas from
the nebula is added to
the protostar, it gains
mass. As mass is gained
gravity increases and
the temperature within
the protostar increases
Protostar
Star
The gravity eventually gets
so big and the temperature
gets so high that nuclear
fusion starts, it becomes a
star
Life of a star
A Stable Star like our Sun
Gravitational force
From the mass of the material
The force of the
radiation pressure
from nuclear
fusion is balanced
with the
gravitational force
in a stable star.
(Grade B)
Radiation Pressure
From the energy of fusion
Nuclear fusion
4 Hydrogen
(Grade A)
1Helium + ENERGY
Death of a Star
Star like our Sun
A large Star
White
Red
Black
Star
Giant
Dwarf
dwarf
Eventually a star the size of
our sun becomes a Red
Giant.
This cools down to become
a black dwarf.
The star keeps increasing in
size until the gravitational
force causes it to collapse
into itself creating a White
Dwarf
Red
Pulsar
Large
Star
Supernova
Neutron
Black
Hole
Star
Supergiant
A larger star eventually
becomes a super Red
Giant.
The small core becomes a
neutron star.
This then collapses, heats
up and explodes in a
supernova.
This can turn into a
pulsar
If a star is large enough it’ll
become a black hole.
Equilibrium between radiation
pressure and gravity
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 radiation
Need to “learn” this!
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)
Example
• The sun (radius R = 7.0 x 108 m) has a
luminosity of 3.9 x 1026 W. Find its surface
temperature.
• From L = σAT4 and A = 4πR2 we find
T = (L/σ 4πR2)¼ = 5800 K
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
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)
Intensity at a distance from a light
source (Apparent brightness)
b = L/4πd2
d
Apparent brightness - CCD
Apparent brightness is measured using a
charge-coupled device (used also in digital
cameras) Read the final paragraph of page
495.
Apparent brightness and Luminosity
Note that the apparent brightness b and
luminosity L are proportional
b=
2
L/4πd
bαL α
4
T
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
How will you do this?
Spectral classes
Oh be a fine girl….kiss me!
Let’s try some
luminosity/brightness questions!
Bummer.
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 star
Niels Bohr
In 1913, a Danish
physicist called Niels
Bohr realised that the
secret of atomic
structure lay in its
discreteness, that
energy could only be
absorbed or emitted at
certain values.
At school they
called me
“Bohr the
Bore”!
The Bohr Model
Bohr realised that the
electrons could only be
at specific energy levels
(or states) around the
atom.
The Bohr Model
We say that the energy
of the electron (and
thus the atom) can exist
in a number of states
n=1, n=2, n=3 etc.
(Similar to the “shells”
or electron orbitals that
chemists talk about!)
n=1
n=2
n=3
The Bohr Model
The energy level diagram of the hydrogen
atom according to the Bohr model
Energy
eV
0
High energy n levels are very
close to each other
n=5
n=4
n=3
n=2
Electron can’t have less
energy than this
-13.6
n = 1 (the ground state)
The Bohr Model
An electron in a higher state than the ground state is
called an excited electron.
Energy
eV
0
High energy n levels are very
close to each other
n=5
n=4
n=3
electron
n=2
-13.6
n = 1 (the ground state)
Atomic transitions
If a hydrogen atom is in an excited state, it can make a transition to a
lower state. Thus an atom in state n = 2 can go to n = 1 (an electron jumps
from orbit n = 2 to n = 1)
Energy
eV
0
n=5
n=4
Wheeee!
n=3
electron
n=2
-13.6
n = 1 (the ground state)
Atomic transitions
Every time an atom (electron in the atom) makes a transition, a single
photon of light is emitted.
Energy
eV
0
n=5
n=4
n=3
electron
n=2
-13.6
n = 1 (the ground state)
Atomic transitions
The energy of the photon is equal to the difference in energy (ΔE)
between the two states. It is equal to hf. ΔE = hf
Energy
eV
0
n=5
n=4
n=3
electron
n=2
ΔE = hf
-13.6
n = 1 (the ground state)
Atomic transitions
An electron can also absorb a photon of the same energy and jump to a
hjgher level.
Energy
eV
0
n=5
n=4
n=3
electron
n=2
ΔE = hf
-13.6
n = 1 (the ground state)
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.
Doppler effect on spectra
Radial velocity
Rotation
Different types of stars
Binary stars
Spectroscopic binaries
Eclipsing binaries
Eclipsing binaries
Cepheids
• A type of variable start whose luminosity
changes with time (more later!)
Red giants and red supergiants
• Large in size and red in colour.
• Large luminosity
• Since they are red, they are comparatively
cool.
• The source of energy is the fusion of some
elements other than hydrogen.
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.
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
Cepheids!
Hertzsprung – Russell diagram
• A large number of stars the 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.
Questions
• Page 504 Questions 1, 2, 3, 4, 5, 6, 7, 9.