Download Luminosity

Stellar Radiation
Stellar Radiation
 Where do stars get their energy?
 Energy from stars can be understood using
Einstein’s famous equation E=mc2
 The product of the nuclear reaction has less
mass than the reactant.
 The missing mass is converted to energy.
Nuclear fusion in Stars (pg 496)
What is the most important
thing about a star?
MASS!
The mass of a normal star almost
completely determines its
LUMINOSITY and TEMPERATURE!
 Note: “normal” star means a star that’s
fusing Hydrogen into Helium in its center
(we say “hydrogen burning”).
The LUMINOSITY of a star is
how much ENERGY it gives off
per second:
This light bulb has a
luminosity of 60
Watts
The energy the Sun emits is generated
by the fusion in its core…
What does luminosity have to do
with mass?
The mass of a star determines
the pressure in its core:
Gravity pulls outer layers
in,
Gas Pressure pushes
them out.
Pressure
The core
supports the
weight of the
whole star!
The more mass the star has,
the higher the central pressure!
The core pressure determines
the rate of fusion…
MASS
PRESSURE &
TEMPERATURE
RATE OF
FUSION
…which in turn determines
the star’s
luminosity!
Luminosity is an intrinsic property…
it doesn’t depend on distance!
This light bulb has a luminosity
of 60 Watts…
…no matter where it is, or
where we view it from, it will
always be a 60 Watt light bulb.
Luminosity
The Luminosity of a star is the energy that it releases
per second. Sun has a luminosity of 3.90x1026 W
(often written as L): it emits 3.90x1026 joules per
second in all directions.
The energy that arrives
at the Earth is only a
very small amount
when compared will the
total energy released by
the Sun.
Luminosity
Exercise
The Sun is a distance d=1.5 x 1011 m from the Earth.
Estimate how much energy falls on a surface of 1m2
in a year.
L= 3.90x1026 W
d
Apparent brightness
 When the light from the Sun reaches the Earth it will
be spread out over a sphere of radius d. The energy
received per unit time per unit area is b, where:
d
L
b
2
4d
b is called the apparent
brightness of the star
At a distance of d=1.5 x 1011 m, the energy is “distributed”
along the surface of a sphere of radius 1.5 x 1011 m
The sphere’s surface area is given by:
A = 4πd2 = 4 π x (1.5 x 1011)2 =
d
=2.83 x 1023 m2
The energy that falls on a surface area of
1m2 on Earth per second will be equal to:
b = L/A = 3.90x1026 / 2.83 x 1023 =
= 1378.1 W/m2 or 1378.1 J/s m2
In a year there are: 365.25days x 24h/day x 60min/h x
60s/min = 3.16 x 107 s
So, the energy that falls in 1 m2 in 1 year will be:
1378.1 x 3.16 x 107 = 4.35 x 1010 joules
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. i.e. ultra violet, visual, and infrared.
 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:
max T  constant
max T  2.9x10 m K
-3
Star’s Color and Temperature
Black body radiation and Wien Law
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:
T
2.9x10 -3
max
2.9x10 -3

 5800 K
-9
500x10
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.
 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:
L  σAT
where, σ = 5.67x10-8 W m-2 K-4
4
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.
Emission of Light
 Emission Spectra: The actual wavelengths of light
emitted by a source. These are dependent on
transition states of the atom’s electrons. These can
be seen with a spectroscope.
 Here is Hydrogen’s Signature!
 Here is Iron’s Signature!
Absorption Spectra
 When a Light source passes by a cool gas the atomic
signature of the cloud is revealed as specific
wavelengths of light are absorbed.
Absorption and Emission Spectra
for Hydrogen
Real spectra are more
complicated than this (remember
emission and absorption lines?)
Blackbody
Spectrum
Emission and
Absorption
Lines
Stars can be arranged into
categories based on the
features in their spectra…
This is called
“Spectral Classification”
How do we categorize stars?
A few options:
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
First attempts to classify stars
used the strength of their
absorption lines…
Stars were labeled “A, B, C…”
in order of increasing strength
of Hydrogen lines.
They also used
the strength of
the Harvard
“computers”!
Williamina Fleming
Later, these categories were
reordered according to
temperature/color…
OBAFGKM(LT)!
Annie Jump Cannon
OBAFGKM - Mnemonics
O Be A Fine Girl/Guy Kiss Me
Only Boring Astronomers Find Gratification in
Knowing Mnemonics!
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
A
F
G
neutral helium, stronger
hydrogen
blue-white
10,000-31,000 K
strong hydrogen, ionized
metals
white
7400-10,000 K
weaker hydrogen, ionized
metals
yellowish white
6000-7400 K
still weaker hydrogen, ionized
and neutral metals
yellowish
5300-6000 K
K
M
weak hydrogen, neutral
metals
orange
3900-5300 K
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)