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Stars
Thursday, February 28
Thu, Feb 28: Stars
Tue, Mar 4: Planets
Problem Set #7 due
Thu, Mar 6: Past & Future
Problem Set #7 returned
Tue, Mar 11, 1:30 pm
Exam
Final
What is a star?
Examples of stars:
Sun
Betelgeuse
Pleiades: known traditionally as the
“seven sisters” (6 bright stars, 1 fainter)
With his telescope,
Galileo saw many more stars.
Average density of ordinary matter
in the universe =
-28
3
0.04 ρcrit = 3.6 × 10 kg/m
3
kg/m =
Density of Sun = 1400
4 quadrillion quadrillion × average
Stars are lumps of ordinary
matter compressed to small size
and high density.
What is a star?
A luminous ball of gas
powered by nuclear fusion
in its interior.
“Why do stars shine?”
Stars are dense (Sun is 40%
denser than liquid water).
Stars are opaque (because
they’re made of ionized gas).
Stars are hot (surface
temperatures > 2000 Kelvin).
Flashback slide!
Hot, dense, opaque objects
emit light!
Today, we call hot,
dense, opaque objects
that emit light “stars”.
Question:
Why do stars shine?
Short answer:
Stars shine because they are hot.
Follow-up question:
Why don’t stars cool down?
There’s a continuous fossil record of life
on Earth for over 3 billion years.
Sun’s luminosity can’t have been
wildly variable – if it had, life would
have scorched or frozen.
Sun must have an interior power
source to replace the energy
carried away by photons.
What’s the power source?
The Sun’s mostly hydrogen –
what about burning hydrogen?
2 H + O → H2O + energy
Burning 1 kg of hydrogen releases
1.4 × 108 joules of energy.
Sun’s mass = 2 × 1030 kg.
(1.4 ×
× (2 ×
= 2.8 × 1038 joules
8
10 joules/kg)
30
10
kg)
The Sun throws away energy at a rate
Lsun = 3.9 × 1026 watts
= 3.9 × 1026 joules/sec.
Time to “burn up” the Sun =
2.8 × 1038 joules / 3.9 × 1026 joules/sec
= 7.2 × 1011 seconds
= 23,000 years
We need a power source that
gives us more bang for the buck
(more joules for the kilogram…)
The Sun’s mostly hydrogen –
what about nuclear fusion,
converting hydrogen into helium?
4 H → He + a lot of energy
Fusing 1 kg of hydrogen into helium
releases 6.3 × 1014 joules of energy.
That’s 4.5 million times what you’d
get by burning the hydrogen.
Sun’s hydrogen supply adequate for
billions, not thousands, of years.
If nuclear fusion is
such a great
energy source, why
don’t we all have
“Mr. Fusion” units?
proton
positron
neutron
proton
neutrino
photon
Helium
Fusion
inside
the Sun
The fusion chain
starts with combining
two protons.
Protons are positively charged;
overcoming their electrostatic
repulsion requires high speeds.
T > 10 million Kelvin.
Fusion occurs only
in the hot, dense
central regions.
Energy is generated in
the Sun’s hot core.
Energy is radiated from the
Sun’s surface, 700,000 km away.
How does the energy get from
the core to the surface?
Photons are good at carrying
energy from point A to point B.
A
B
If the Sun were transparent,
photons could travel from its center
to its surface in 2.3 seconds.
The Sun is not transparent.
Photons travel only an inch before
being scattered in a random direction.
It takes 200,000 years (on average) for
light to stumble its way to the surface.
Galaxies form because ordinary matter
can cool down (by emitting photons)
and fall to the center of dark halos.
Why do galaxies curdle into tiny
stars, instead of remaining as
homogenous gas clouds?
Look at where stars are forming
now.
In the Whirlpool Galaxy,
we see newly formed
stars in dense, cold
molecular clouds.
In regions where the gas is cooler
and denser than elsewhere,
hydrogen forms molecules (H2).
These cool, dense
regions are thus called
“molecular clouds”.
Consider a
small, dense
molecular cloud.
Mass = 1 Msun
Radius = 0.1 pc = 4,000,000 Rsun
Temperature = 10 Kelvin = Tsun/580
Molecular clouds are usually stable;
but if you hit them with a shock wave,
they start to collapse gravitationally.
shock waves
Once the
collapse is
triggered, it
“snowballs”.
Once gravity has reduced the radius
of the cloud by a factor of 4,000,000,
it’s the size of a star.
1

4,000,000
Why doesn’t the molecular cloud
collapse all the way to a black hole?
Escape speed from
molecular cloud ≈ 0.3 km/sec
Escape speed from
star ≈ 600 km/sec
Escape speed from
black hole = 300,000 km/sec
As the gas of the molecular cloud is
compressed, it becomes denser.
As the gas is compressed,
it also becomes hotter.
When the gas temperature is high
enough (T ≈ 10 million Kelvin),
nuclear fusion begins!
Nuclear fusion keeps the
central temperature and
pressure of the star at a
constant level.
The star is static (not
contracting or expanding)
because it’s in
hydrostatic equilibrium.
Hydrostatic equilibrium = a balance
between gravity and pressure.
Pressure increases as you
dive deeper into the ocean:
pressure increases as you
dive deeper into the Sun.
Gas flows from regions of high
pressure to regions of low pressure.
For a fish in the ocean,
pressure creates a net upward force,
gravity creates a downward force.
The fish is in hydrostatic equilibrium.
For gas in the Sun,
pressure creates a net outward force,
gravity creates a inward force.
The Sun is in hydrostatic equilibrium.
The Sun is like a fat guy
on an inflatable chair.
fusion
energy
pressure
gravity
Hydrostatic equilibrium tends
to be very stable.
Put a six-pack on fat guy’s lap.
Gravitational force increases.
Gas in chair is compressed.
Upward pressure force increases.
Hydrostatic equilibrium is common
throughout the universe.
Sun is in hydrostatic equilibrium.
Oceans are.
Earth’s atmosphere is.
Earth’s interior is.
Fat guys in inflatable chairs are.
Tuesday’s Lecture:
Formation and
Evolution of Planets
Reading:
none