STELLAR EVOLUTION

Stellar evolution is driven entirely by the never ending battle between pressure and gravity. As imbalances are reached, the star is driven to find a new energy source. Each stage in stellar evolution is marked by a different energy generation mechanism.

 HR Diagram at the end of this lecture, you'll not only understand this stellar evolution diagram, but will be able to make one of these yourself!

IDEAL GAS LAW

PV

= nR

T

(pressure) x (volume) = (particle density) x (constant) x (temp)

How

PV

= nR

T

works!

Increasing the temperature increases the volume and

decreases

the pressure.

Decreasing the volume increases the pressure (and the

increases

the temperature)

Why Doesn't a Star Burn all its Fuel Instantly?

If the fusion rate increases, the temperature and pressure go up...

Stars regulate their internal pressure and temperature via the ideal gas law PV = nRT. The rate at which atoms fuse together is a function of both pressure and temperature. So, if a star gets really hot and the pressure gets really high, the star will expand and cool down, thus lowering the fusion rate. ...the star will expand, and in the process lower its temperature and pressure, and thus its fusion rate.

Eventually, Hydrostatic Equilibrium will be reached. The pressure caused by the energy generation rate will balance the inward force of gravity

What is Light?

Light is a form of energy, called

radiative energy

. It is

both

a wave and a particle! It can be characterized by its wavelength and frequency:

c

= n speed of light in vacuum wavelength frequency

Color and Wavelength

The color of the light depends on its wavelength. Longer wavelengths correspond to “ redder ” light; shorter wavelengths correspond to “ bluer ” light.

Color and Temperature

Everything with a temperature emits light. Even as you sit there,

you

are emitting light in the infrared! The

peak wavelength

(or color) emitted by an object is a function of its temperature. Hotter objects emit more of their light at shorter wavelengths and are said to be “ bluer ”; cooler objects emit more of their light at longer wavelengths and are said to be “ redder ”. The relation between wavelength and temperature (in Kelvin) is given by

Wein's Law

, 

peak

T = 0.0029 meters

Wein's Law



peak

T = 0.0029 meters

Hotter objects emit more light

at all wavelengths

than cooler objects. Hotter objects also appear bluer than cooler objects.

Which Horseshoe Is the Hottest?

The Main Sequence

A star on the main sequence is one that is generating light and heat by the conversion of hydrogen to helium by nuclear fusion in its core.

brighter dimmer hotter cooler <---------------- temperature ---------------->

Stage 1: Protostar

Star formation begins with a dense cloud of gas. A disturbance in the gas triggers a collapse, and the cloud begins to condense under its own gravity to form a protostar. A

protostar

is a forming star that has not yet reached the point where sustained fusion can occur in its core.

The energy source for a protostar is

gravitational contraction

.

The star is cool, so its color is red, but it is very large so it has a high luminosity.

Sun's Age: 1-3 years old

Stage 2: Pre-Main Sequence

Once the star is close to hydrostatic equilibrium, the contraction slows down. However,

the star must continue to contract until the temperature in the core is high enough that nuclear fusion can

begin and support the star!

During the contraction the star's temperature stays about the same, but its luminosity decreases because of its shrinking size. Once nuclear reactions begin in the core, the star readjusts to account for this new energy source. In the pre-main sequence star, both gravitational contraction and nuclear fusion provide energy.

Stage 3: Zero- Age Main Sequence

Finally, the rate of fusion becomes high enough to establish gravitational equilibrium. At this point, fusion becomes self-sustaining and the star settles into its hydrogen burning, main sequence life. The main sequence phase is the longest phase of a star's life, about 10 billion years for a star with one solar mass.

The main sequence is not a line, but a band in the H-R Diagram. The position of a star on the main sequence is determined by its mass and composition.

Sun's Age: 27 million years old

More massive stars have shorter lifetimes!

Chihuahuas live 14-15 years.

Great Danes only live 6-10 years.

tank 13 miles per gallon so…416 miles per Camry: 18.5 Gallon Gas tank gallon 28.5 miles per so…527 miles per tank

A small change in a star’s mass gives a big change in luminosity: L = M 3.5

where L = luminosity in solar luminosities M = mass in solar masses So, for a star that’s twice as massive as the sun: L = 2 3.5

= 11.3

It’s ~11 times more luminous!!

A star’s lifetime (t, in solar lifetimes) can be given by: t = Amount of fuel Rate of fuel consumption = M L = M M 3.5

= 1 M 2.5

So a star that’s twice as massive as the sun lives 2 -2.5

0.17 times as long as the sun. That 0.17*10 10 = 1.7 = billion years

Stage 4: End of Main Sequence

A star ends its life on the main sequence when it has used up all the hydrogen in its core. Once the core hydrogen has been exhausted, a shell of hydrogen surrounding the core begins to burn, providing energy to the star. During its life on the main sequence, the size and luminosity of the star has changed very little. Sun's Age: 10 billion years old

Stage 5: Post Main Sequence

Now that hydrogen is exhausted in the core, there is no energy to support the Helium core. Thus, the core contracts and energy is released. The hydrogen burning shell continues to provide energy to the outer layers of the star.

Sun's Age: 11 billion years

Stage 6: Red Giant – Helium Flash

As the helium core contracts, the temperature and pressure increases. This increase in temperature causes the rate of hydrogen fusion in the shell surrounding the core to go up. As a result, the star expands (by as much as 200 times!). The star is now very cool, but luminous – a

Red Giant

!

The contraction of the core causes the temperature and density to increase such that, by the time the temperature is high enough for Helium to fuse to form Carbon, the core of the star has reached a state of

electron degeneracy

.

Stage 7: Helium Burning Main Sequence

The pressure due to electron degeneracy is significantly different from the pressure produced by the Ideal Gas Law – it is independent of temperature! In the core, the temperatures reach 200 million Kelvin and Helium can now fuse into Carbon, known as the

Triple Alpha Process

. This happens quite suddenly and is known as the

Helium Flash

.

This process produces only about 20% as much energy as hydrogen burning, so the lifetime on the Helium Burning Main Sequence is only about 2 billion years.

When the Helium is exhausted in the core of a star like the sun, no further reactions are possible.

Stage 8: Planetary Nebula

Helium and Hydrogen burning shells will continue outside the core for a while. During Helium Shell Burning, a final thermal pulse produces a giant "hiccough" causing the star to eject as much of 10% of its mass, the entire outer envelope, known as a

Planetary Nebula

.

The Planetary Nebula phase is relatively short lived, estimated to be about 25,000 years, and there are about 10,000 planetaries in the Milky Way.

Stage 9: White Dwarf

As the nebula disperses, the shell nuclear reactions die out leaving the stellar remnant, known as a

White Dwarf

, supported by electron degeneracy, to fade away as it cools down. The white dwarf is small, about the size of the Earth, with a density of order 1 million g/cm 3 , about equivalent to crushing a Volkswagen down to a cubic centimeter or a "ton per teaspoonful." A white dwarf star will take

billions

of years to radiate away its store of thermal energy because of its small surface area. The white dwarf will slowly move down and to the right in the H-R Diagram as it cools until it fades from view as a "black dwarf"

Hertzsprung-Russell Diagram

Branches

Red Giant Branch

stars have a

hydrogen

burning shell and their core is contracting.

Horizontal Branch

stars have helium core burning and hydrogen shell-burning.

Asymptotic Giant Branch

stars have a

helium

burning shell and their core is contracting.