StarsStars

Thursday, February 28Thursday, 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 pm1:30 pm Final ExamFinal Exam

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 =

0.04 ρcrit = 3.6 × 10-28 kg/m3

Density of Sun = 1400 kg/m3 = 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 fusionnuclear 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).

Hot, dense, opaque objects emit light!

Today, we call hot, dense, opaque objects that emit light “starsstars”.

Flashback slide!

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 × 108 joules/kg) × (2 × 1030 kg) = 2.8 × 1038 joules

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= 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 fusionnuclear fusion,

converting hydrogen into helium?

4 H → He + a lotlot 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 billionsbillions, not thousands, of years.

If nuclear fusion is such a great

energy source, why don’t we all have

“Mr. Fusion” units?

positron

neutron

neutrino

proton

proton

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 onlyonly 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?

PhotonsPhotons are good at carrying energy from point A to point B.

IfIf the Sun were transparent, photons could travel from its center

to its surface in 2.3 seconds.

A B

The Sun is notnot 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 nownow.

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 cloudsmolecular 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 wavesshock 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.

000,000,4

1

Why doesn’t the molecular cloud collapse all the way to a black holeblack 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

When the gas temperature is high enough (T ≈ 10 million Kelvin),

nuclear fusion begins!

As the gas of the molecular cloud is compressed, it becomes denser.

As the gas is compressed, it also becomes hotter.

Nuclear fusion keeps the central temperaturetemperature and pressurepressure of the star at a

constant level.

The star is static (not contracting or expanding)

because it’s in hydrostatic equilibriumhydrostatic 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 equilibriumhydrostatic equilibrium.

For gas in the Sun, pressure creates a net outward force,

gravity creates a inward force.

The Sun is in hydrostatic equilibriumhydrostatic equilibrium.

The Sun is like a fat guy on an inflatable chair.

pressure gravity

fusion energy

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:

Reading:

none

Formation and Evolution of PlanetsPlanets