Our Star and Other Stars
Lots of material to cover in this one week!
A Closer Look at the Sun
Our Goals for Learning:
• Why does the Sun
shine?
• What is the Sun’s
structure?
Our star
LUMINOSITY = TOTAL ENERGY EMITTED PER SECOND
Is it on FIRE? … NO!
Chemical Energy Content
Luminosity
~ 10,000 years
Is it CONTRACTING? … NO!
Gravitational Potential Energy
Luminosity
~ 25 million years
E=
2
mc
- Einstein, 1905
Is it powered by NUCLEAR ENERGY? … YES!
Nuclear Potential Energy (core)
Luminosity
~ 10 billion years
Note: Any gaseous cloud
that is a little bit denser
in the inside will pull in
the outer particles.
Gravitational
equilibrium:
The Sun is a huge
ball of hydrogen
and helium gas held
together by gravity.
The outward push or
pressure from very
hot expanding gases
is balanced by the
strong inward pull of
gravity.
Like a stack of pillows, the
weight of the upper layers
compresses lower layers.
This is exactly what happens
to the layers of hydrogen gas.
Compressed gas becomes hot
The Role of Gravity in the Sun
Gravitational
contraction:
Gravitational
equilibrium:
Provided the energy that
heated the core as the
Sun was forming and
thus slowed contraction.
Energy provided by
nuclear fusion of
hydrogen to helium in
the Sun’s hot core
maintains the very high
temperature and creates
a pressure balance
against gravity.
Contraction stopped
when fusion began.
This was the moment
that the proto-Sun
became a “star”.
The Solar
wind:
A flow of charged
particles, protons
and electrons, from
the opaque
“surface” of the
Sun. (This “wind”
causes the aurora
when it hits Earth.)
Corona:
Outermost gaseous
layer of the solar
“atmosphere”.
Very thin; fast moving
particles. Temperature
~1 million K.
Chromosphere:
Middle layer of the
solar atmosphere;
can be seen as
pinkish in eclipse
due to hydrogen
emission – hence
the “chromo” in
the name.
~ 104 - 105 K
Photosphere:
Visible “surface” of
Sun.
Not really a surface
in the normal sense.
This is just as far
into the Sun as we
can see. The gas
becomes dense and
opaque below this
level.
~ 6,000 K
Convection Zone:
Hot, dense, very
turbulent gas.
Energy transported
upward by rising
hot gas.
Breaks through
photosphere to
cause a granulation
appearance that
reminds one of
boiling water.
Radiation Zone:
A much hotter and
denser region.
Energy transported
upward by photons,
not by the mass
motion of gas.
Core:
Extremely dense
region, but still
gaseous!!
Energy generated
by nuclear fusion.
Temperature:
~ 15 million K
Nuclear Fusion in the Sun
Our Goals for Learning:
• How does nuclear fusion occur in the Sun?
• How does the energy from fusion get out of
the Sun?
• How do we know what is happening inside
the Sun?
Two kinds of nuclear reactions
Fission
Fusion
Big nucleus (e.g. uranium)
splits into smaller pieces
Small nuclei stick together
to make a bigger one
(Nuclear power plants)
(Sun, stars)
TWO POWERFULL FORCES
The very high
temperature enables
nuclear fusion to
happen in the core.
Electrostatic repulsion
between positively
charged protons can be
overcome if the nuclei
get close enough for the
STRONG force – a
nuclear binding force – to
take over.
THE BASIC NUCLEAR FUSION PROCESS
The Sun releases energy by fusing four hydrogen nuclei
(protons) into one helium nucleus (2 protons and 2 neutrons).
Let’s look at details.
Proton-proton chain is how hydrogen fuses into helium in Sun
The process may seem complicated at first, but it is in fact very
simple, and it can be reproduced by Man in a Hydrogen bomb!
IN
4 protons
OUT
4He
nucleus
2 gamma rays
2 positrons
2 neutrinos
Total mass is
0.7% lower!
This mass goes to
ENERGY because
of E = mc2
HOW DOES THE
ENERGY GET OUT?
Energy gradually leaks out of the radiation zone in the form of randomly bouncing
photons. The photons bounce off electrons and make a “random walk”. It can take over
100,000 years for a photon to reach the surface.
At the top of the radiation zone the temperature has dropped to ~2 million K.
Here, photons are absorbed, not scattered. This creates rising plumes of hot gas
(convection) that takes energy to the surface.
Granulation
Bright blobs on the photosphere are where hot gas is reaching the surface.
We learn about the inside of the Sun
by
• Making mathematical models
– To predict the radius, temperature, luminosity
and age of the Sun from its mass and chemical
composition
• Observing “sun quakes”
• Observing solar neutrinos
Patterns of
vibration on the
surface tell us
about what the Sun
is like inside. This
is a mathematical
model predicting
one such pattern.
Helio-seismology uses “quaking” of the Sun.
Doppler shifts in
the spectrum from
different parts of
the surface can be
measured. Results
agree very well
with mathematical
models of the solar
interior.
NEUTRINOS
Neutrinos are very tiny
nuclear particles with no
electric charge created
during fusion. They fly
directly through the
Sun and escape!
Observations of these
solar neutrinos can tell us
what’s happening in the
core.
Neutrinos are remarkable!
They are exceedingly
small and have almost no
interaction with anything.
The Solar neutrino problem:
Sudbury Mine, Canada
Homestake Mine,
South Dakota
Early searches for solar
neutrinos failed to find
the predicted number but,
More recent observations find the
right number of neutrinos, but some
have changed form  new physics!
These pictures show 2 huge underground neutrino “observatories”
What have we learned?
• How does nuclear fusion occur in
the Sun?
• Fusion of hydrogen into helium, which
occurs via the proton–proton chain.
Gravitational equilibrium acts as a
thermostat that keeps the fusion rate
steady.
Surveying
the
Stars
Properties of
Stars
Our Goals for Learning
• How luminous are stars?
• How hot are stars?
• How massive are stars?
Not all stars are exactly like the Sun!
Everything we know is deduced from the light we receive
Luminosity:
Amount of power a star radiates
(energy per second)
The units of power is:
1 Joule per second = 1 Watt
Apparent brightness:
Amount of starlight that reaches
Earth - the energy per second per
square meter.
So, apparent brightness of a star
depends on LUMINOSITY &
DISTANCE
How are Luminosity and Brightness related?
Luminosity (energy
per second) passing
through each sphere
in the diagram is the
same – this is conservation
of energy.
Area of sphere:
= 4π (radius)2
So, divide Luminosity
by Area to get
Brightness.
The relationship between apparent brightness and luminosity
depends on distance:
Brightness =
Luminosity
4π (distance)2
We can determine a star’s luminosity if we can measure its distance
and apparent brightness:
Luminosity = 4π (distance)2 x (Brightness)
Brightness is easy to measure with a photo-meter.
How do we measure distance?
PARALLAX
This works
out to 100pc
or 326 ly
d (parsecs) =1/p (arcsec)
1 parsec is the distance that gives
a parallax angle of 1 second of arc
= 3.26 light years = 206265 AU
p can be as
small as
0.01 arcsec
How hot are stars?
Laws of Thermal Radiation
Shape of curve
depends only
on T
1) Hotter objects emit more light at all wavelengths (~σT4)
2) Hotter objects emit light at shorter wavelengths (~3000/T)
If we measure the spectrum we can get the temperature.
STELLAR
SPECTRA
Hottest stars
50,000 K
Letters (A-O)
assigned over 100
years ago before
temperatures were
known. Had to be
re-ordered to
make sense. Still
a useful aid to
memory.
Coolest stars
3,500 K
Dark lines in a star’s spectrum correspond to a spectral type that
reveals its temperature. Spectral type (letter/number) is shorthand for T
(Hottest)
O B A F G K M
(Coolest)
Remembering Spectral Types
(Hottest)
O B A F G K M
(Coolest)
• Oh, Be A Fine Girl/Guy, Kiss Me
We have distance, luminosity and temperature. What else can we get?
GRAVITATIONALLY BOUND STARS
Two stars orbiting each other = BINARY
Binary Stars yield Stellar Masses
Types of Binary Star Systems
• Visual Binary
• Eclipsing Binary
• Spectroscopic Binary
NOTE: About half of all stars are in binary systems
Visual Binary
We can directly observe the orbital motions of
these stars.
We can determine the orbital period and projected
size of the orbit (on the sky) directly.
We don’t know the inclination of the plane of the
orbit (so the orbital size is the “projected” size).
Eclipsing Binary
This Light Curve is observed even if the two stars are blended together by distance.
Inclination of the orbit is essentially zero (edge-on), causing eclipses.
Periodic eclipses implies orbital period. Duration gives RADIUS.
Spectroscopic Binary
Again, seen as one object because of large distance but,
We find the orbit (period and velocity) by measuring Doppler shifts
We measure mass
using gravity
Newton’s Form of Kepler’s 3rd
Law
Direct mass measurements are
possible only for stars in binary
star systems 4π2
p2 =
a3
G (M1 + M2)
Isaac Newton
If you only have p and a then you
get M1+M2, but if you have the
separate orbits then you can get M1
and M2 separately.
p = period
a = average separation
How massive are stars?
• The overall range of stellar masses runs
from 0.08 times the mass of the Sun to
about 150 times the mass of the Sun.
• Masses are only known for stars that form
binary systems, but about half of all stars
are in fact in binary systems!
– 0.08 MSun is approximately 80 MJupiter
• Objects less massive than 0.08 MSun exist;
discovered 1995 – called Brown Dwarfs
What have we learned?
How luminous are stars?
• The apparent brightness
of a star in our sky depends
on both its luminosity —
the total amount of light it
emits into space—and its
distance from Earth, as
expressed by the inverse
square law for light.
What have we learned?
• How hot are stars?
• The surface temperatures of
the hottest stars exceed
40,000 K and those of the
coolest stars are less than
3,000 K. We measure a star’s
surface temperature from its
COLOR or SPECTRUM, and
we classify spectra according
to the sequence of spectral
types OBAFGKM, which
runs from hottest (O) to the
coolest (M).
Classifying Stars
Our Goals for Learning
• How do we classify stars?
• Why is a star’s mass its most
important property?
• What is a Hertzsprung–Russell
diagram?
Mass & Lifetime
Sun’s life expectancy: 10 billion years
Until core hydrogen
(10% of total) is
used up.
Life expectancy of 10 MSun star:
10 times as much fuel, but uses it 104 times as fast
10 million years ~ 10 billion years x 10 / 104
Life expectancy of 0.1 MSun star:
0.1 times as much fuel, uses it 0.01 times as fast
100 billion years ~ 10 billion years x 0.1 / 0.01
Normal Star Summary
High Mass:
High Luminosity
Short-Lived
Large Radius
Blue
Low Mass:
Low Luminosity
Long-Lived
Small Radius
Red
The Sun is “low mass”.
Luminosity
This diagram
plots the
Luminosity (y)
as a function of
Temperature (x)
of many different
kinds of stars.
It is called a
HertzsprungRussell
Diagram.
It tells us everything
in one picture!
Temperature
Normal
hydrogenburning stars
reside on the
main sequence
of the H-R
diagram.
Mass increases
from lower right
to upper left.
Gravitational
equilibrium for
each mass.
A
Luminosity
D
B
D
C
Temperature
Which of these
stars must be
physically larger
in radius than
main sequence
stars of the same
temperature?
Relative to the
size of the Sun,
stars in the
upper right are
“giants”, those
in the lower left
are “dwarfs”
Two types of star clusters
• Open clusters contain up
to several thousand stars
and are found in the disk
of the Milky Way galaxy.
• Globular clusters
contain hundreds of
thousands of stars, all
closely packed together.
They are found mainly in a
“halo” around our galaxy.
Measuring the age of a star cluster
• Because all of a cluster’s
stars we born at the same
time, we can measure a
cluster’s age by finding the
main sequence turnoff
point on an H–R diagram of
its stars.
• The cluster’s age is equal to
the hydrogen-burning
lifetime of the hottest, most
luminous stars that remain
on the main sequence. That
is, those that have not
“evolved” in red giants.
What have we learned?
• How do we classify stars? • Why is a star’s mass its
most important
• We classify stars according
property?
to their spectral type and
• A star’s mass at birth
luminosity class.
determines virtually
• The spectral type tells us
everything
that
the star’s surface
happens to it
temperature
throughout its life.
• The luminosity class tells
us how much light it puts
out (surface area).