Download The Luminosity

Podcasts:
http://blogs.uci.edu/cosmoforthepeople/
- Navigate to “Class lectures” on the right panel
Tweets: http://twitter.com/#!/james_s_bullock
Lecture
9
Energy Sources in Stars
•  Most stars generate their energy via
nuclear fusion
–  Fusing 4 protons (Hydrogen nuclei)
into one helium nucleus
–  The mass of the He nucleus is 0.007
= 0.7% smaller than the sum of the 4
Hydrogen nuclei that formed it.
–  The mass difference that
“disappears” is the source of the
energy via Einstein’s:
E=mc2
Stars live most of their lives in a balance, between two powerful
forces -- outward pressure from their heat and the inward pull
of gravity.
- Stars spend most of their lives in this equilibrium state, on the main sequence.
- During this time, there is a tight relationship between a star’s temperature and its luminosity
Death of the Sun (low mass star)
-10 billiion yrs: the Sun runs out of hydrogen fuel in its core.
- Core is pure helium, shrinks.
- Hydrogen farther out in the star gets hot enough to fuse “hydrogen shell burning”
- Overall luminosity of star goes up and becomes a red giant.
- 300million yrs later: Core gets hot enough to fuse helium.
-  Helium Flash! Burns helium for about another billion years. (back on main sequence
- Eventually the core contains only inert carbon, and a shell around the core starts burning
helium. This time the star may become a Red Supergiant,
- Carbon core doesn’t get hot enough to fuse (600 million K!)
- Instead, the outer layers of the star are ejected into space in a planetary nebula.
What is left? A White Dwarf star!
- A carbon core, with the mass of the sun but as
small as the Earth!
Hot at first and then cools.
See:
http://web.njit.edu/~gary/202/Lecture18.html
Stars that are not on the main sequence.
Red giants: stars smaller than 8
times the sun’s mass become
much larger and slightly cooler
when fusion exhausts the
hydrogen in their centers.
Pressure goes down in the
center, matter falls in, and
fusion again “turns on” but now
in a shell around the core.
The new energy causes the
star to swell. (e.g., we expect
the Sun to swell to 60 times its
current diameter, ~30% the
radius of the earth).
Stars not on the main sequence.
supergiants: stars > 10 times the
sun’s mass use up hydrogen
>1000 times faster than the sun.
Outer layers expand as helium
core contracts… Helium fuses to
form carbon, carbon fuses with
helum to make oxygen, and
heavier and heavier nuclei get built
until Iron (Fe) is made.
Betelgeuse shoulder of constelation Orion
Stars not on the main sequence.
The last days of massive stars:
Outer layers expand as helium
core contracts… Helium fuses to
form carbon, carbon fuses with
helum to make oxygen, and
heavier and heavier nuclei get built
until Iron (Fe) is made.
Iron does not fuse (because it
takes energy to fuse Fe to
heavier elements).
Whole thing stops…
Equilibrium breaks down and
something bad is about to happen
Last Days of a Massive Star
Star burns through a succession of nuclear fusion fuels:
Hydrogen burning: 10 Myr
Helium burning: 1 Myr
Carbon burning: 1000 years
Neon burning: ~10 years
Oxygen burning: ~1 year
Silicon burning: ~1 day
Finally builds up an inert Iron core in the center.e in the center.
Iron Core Collapse
Iron core grows until its mas is about 1.2-1.4 Msun, and then pressure and temperatures cause the
core to shrink and disintegrate in less than 1 second.
At the start of Iron Core collapse, the core properties are:
･Radius ~ 6000 km (~Rearth)･
Density ~ 108 g/cc
A second later, the properties are:
･Radius ~50 km･
Density ~1014 g/cc･
http://www.astronomy.ohio-state.edu/~pogge/Ast162/
Supernova
•  Core collapses until its density hits ~2.4x1014 g/cc,
which is about density of an atomic nucleus!
•  Infall in the center stops, and bounces back.
•  BOOM!
As bright as
An entire galaxy
Of 10 billion stars.
“Crab Nebula” remnant of
Supernova noted by Chinese, Japanese,
and Korean astrologers in 1054
Supernovae
Remnant of Supernova noted by
Kepler in 1604. (Chandra x-ray
image)
Massive stars die and
turn into black holes.
•  After some massive stars (> 10 suns) explode as supernovae,
they will retain a mass of 2 to 3 solar masses in their cores.
•  Nothing in the universe is strong enough to hold up the
remaining mass against the force of gravity, so it collapses into
a black hole.
•  Matter that falls into a black hole disappears from contact with
the rest of the Universe. Not even light can escape the
gravitational pull of a black hole.
•  The “escape velocity” exceeds the speed of light.
•  Black holes are a consequence of Einstein’s theory of gravity
which is called General Relativity.
Fusion: Big nucleus is less
massive than the sum of its
parts. Can gain energy by
building heavier nuclei.
Fission: Big nucleus is more
massive than the sum of its parts.
Can gain energy by splitting nuclei
apart.
(<- smaller) Type of atomic nucleus (bigger->)
Fusion vs. Fission
Fission
Used in power plants
Fusion
Also used in
modern
“thermonuclear”
bombs
Fission reactors
Under 1% of the uranium found in nature is the easily
fissionable U-235 isotope. The uranium must be enriched
to about 4% U-235, usually by means of gaseous diffusion
or gas centrifuge. "
The U-235 absorbs a neutron, and then becomes an
unstable U-236 isotope and then splits into two or more
lighter nuclei along with neutrons that go on to produce
more fissions."
The process generates entergy (in the form of heat) and
this is used to turn a steam turbine (and is one million
times more efficient than coal per unit mass)."
Fission reactors
Under 1% of the uranium found in nature is the easily
fissionable U-235 isotope. The uranium must be enriched
to about 4% U-235, usually by means of gaseous diffusion
or gas centrifuge. "
The U-235 absorbs a neutron, and then becomes an
unstable U-236 isotope and then splits into two or more
lighter nuclei along with neutrons that go on to produce
more fissions."
The process generates entery (in the form of heat) and this
is used to turn a steam turbine (and is one million times
more efficient than coal per unit mass)."
Nuclear power produces this “spent fuel”, a unique
solid waste problem. In volume spent fuels from
nuclear power plants are roughly a million times
smaller than fossil fuel solid wastes. However,
because spent nuclear fuels are radioactive, they
are pound for pound a more substantial problem. "
Fusion
Fusion is a lot harder to achieve than fission, because like charges repel. If you try to
shove two hydrogen nuclei together--each consisting of a single positively charged
proton--they're not going to like it.
The sun overcomes this by cramming everything together to a density 100 times that of
water, then heating it up to 15 or 20 million degrees. Even in the centre of the sun, it's
estimated that a proton will exist on the average for 10 billion years before it's finally
fused with another. Slow!
Why a Fusion reactor on earth is hard:
In order to create the high temperatures required for fusion, physicists must turn the
deuterium and tritium into a plasma. Trouble is, this plasma is at a temperature of 100
million degrees Kelvin. Obviously you can't let this touch the walls of the container
you're trying to keep it in.
The promise of a fusion reactor
The half-lives of the radioactive material produced by fusion tend to be
shorter than those from fission. They also tend to be less biologically
dangerous."
Unlike fission reactors, whose waste remains dangerous for thousands of
years, most of the radioactive material in a fusion reactor would would be
dangerous for about 50 years. By 300 years the material would have the
same radioactivity coal ash. "
⇒ many benefits (e.g. no greenhouse gases, virtually infinite supply)"
⇒  Much less dangerous than fusion waste."
Luminosity and Brightness of
Stars
Luminosity is the same as Power
Power = Energy per unit time
Unit of Energy: Joules
Unit of Power: Watt= Joules/s
Light bulb: 100 watts (uses 100 Joules/s of energy)
If you leave a 100W light bulb on for 100 seconds you
use 100*100 = 10,000 Joules of energy.
Your energy bill: typically charged per kiloWatt * hr (kWhr)
-- that’s 1000 Watts * hr = 1000 (Joules/s) *(3600 s)
= 3,600,000 Joules = 3.6 Million Joules
A typical household in California uses about 8,000 kWhr per
year or ~ 25 million joules per year.
Luminosity:
•  Luminosity = Energy given off per time = power
•  The sun:
Think of a 100 watt light bulb…
Luminosity: How “bright” are stars?
•  Luminosity = Energy given off per time = power
•  The sun:
You can figure out how far away a star is by
comparing how bright it looks with its intrinsic
luminosity.
This is like knowing that one light bulb is
further away than another one based on
how bright it looks to your eye.
Inverse square law:
dimming with distance
•  A star’s apparent
brightness depends
on its distance
•  The light spreads out uniformly in all
directions over a sphere whose radius
is the distance.
•  Surface area of a sphere = 4 π R2
•  The star’s apparent brightness will
depend on intrinsic luminosity L, and
distance from the star R, as:
Distance between lights in
the sky…
•  If two stars have the same luminosity but one
appears 100 times dimmer to the eye, how much
farther away is the dim star?
•  You are 1m away from a candle and 5m away
from a 100 watt light bulb, but both the candle
and the bulb look to be the same brightness to
you. How many watts of luminosity (or power) is
the candle producing?
Distance between lights in
the sky…
•  If two stars have the same luminosity but one appears
100 times dimmer to the eye, how much farther away is
the dim star? A: 10 times farther away.
•  You are 1m away from a candle and 5m away
from a 100 watt light bulb, but both the candle
and the bulb look to be the same brightness to
you. How many watts of luminosity (or power) is
the candle producing? A: 4 watts.
The Luminosity - Temperature relation for stars
More massive
stars are also
hotter.
Luminosity
How do we know the overall luminosities of stars?
Normal stars on
the longest-lasting
phase of their
lifetime sit in this
band.
90% of sun’s life will
be “spent” here.
Hottest stars
Hotter stars
Temperature
cool stars
The Luminosity - Temperature relation for stars
•  Recall that we can determine a
star’s temperature by measuring
the wavelength of its peak
brightness. Wien’s law:
•  Astronomers can also
determine the
distance to the
nearest stars using
the method of
“parallax”.
•  Distance + Apparent
brightness
Allows us to determine
the underlying luminosity
of a star!
Apparent Brightness
•  The sun has an apparent
brightness of
•  b = 1370 Joules/s/m2
= 1370 watts/m2.
• 
That is, if you had a perfectly efficient solar panel one
meter on a side, if you held it perpendicular to the
Sun's rays, it would generate 1370 watts of electricity
Problem: A typical household needs about 1000 watts of
power continuously averaged over a year to operate its lights,
heating, cooling etc.
How big of a solar panel would you need to power your house
if the solar panel could convert 100% of the sun’s energy into
usable energy?
Apparent Brightness
•  bsun =
• 
1370 watts/m2.
=> If you had a perfectly efficient solar panel one
meter on a side, if you held it perpendicular to the
Sun's rays, it would generate 1370 watts of electricity
Assume it’s dark half of the time. If you had
a 2m2 perfect solar panel, you could collect
~2x1370 = 2740 Watts of power during the
day, and store half of it to use at night!
Problem: solar panels are far from perfect!
But you can see that the potential is awesome.
Apparent Brightness
•  The sun has an apparent
brightness of
•  b = 1370 Joules/s/m2
= 1370 watts/m2.
• 
That is, if you had a perfectly efficient solar panel one
meter on a side, if you held it perpendicular to the
Sun's rays, it would generate 1370 watts of electricity
Problem: What is the apparent brightness of a
nearby star with the same intrinsic luminosity
L, of the sun, but which is 3 lt yrs away?
Use: dsun = 1.5 x 1011 m
1 lt yr = 9.5 x 1015 m
(1.5/(3*9.5))^2 =2.77x10-3
Show:
bstar = 3.8 x 10-8 watts/m2