The Grouping of Stars in the H-R Diagram

The Major Categories of Stars 1. The Main Sequence, 2. The Supergiants, 3. The Giants, 4. The White Dwarfs.

• Main Sequence – healthy stars, fusing hydrogen in the core.

• Giants and supergiants – dying stars, fusing helium and heavier elements.

• White dwarfs – dead stars, core nuclear fusion have stopped.

Sizes scale 1 Rsun 10 Rsun 100 Rsun1000 Rsun

From Clouds to Protostar• Stars form in cold (10-30 K), dense (although still

very low density compared with the density we are used to) molecule clouds

– The molecule clouds are composed of mostly hydrogen and helium.

– The low temperature allows the formation of hydrogen molecule H2 – hence molecule clouds.

– Low temperature and high density allow gravity to compress the clouds with resistance from thermal pressure.

– Because of the low density, the gas can radiate away its thermal radiation quickly. Without thermal pressure to resist the gravitational contraction, the initial gravitational contraction proceeds quickly. The temperature of the gas remain low (below 100 K), and emits in the infrared wavelengths.

– As the cloud undergoes gravitational contraction, the gas heats up (to ~ 100 K) as the density increases, eventually forms a dense, hot protostar!

Molecule cloud glows in the infrared, but is dark in the visible light image!

Disks and Jets• The random motion of the molecule can contain

a net angular momentum, as the cloud contract, this angular momentum is conserved, and resulted in the fast rotation of the protostar, and the subsequent formation of a disk and jets

• Details of how the jets are formed is still unknown. Magnetic field probably plays an important role!

Star or Brown Dwarf? Whether a protostar eventually becomes a star depends on its mass.

• For protostar with mass larger than 0.08 M⊙, the temperature can eventually rise to more than 10 million K, hot enough to start nuclear fusion A Star Is Born!

• If the mass of the protostar is less than 0.08 M⊙, then nuclear fusion cannot start A Brown Dwarf!

Brown Dwarf slowly radiate away its thermal energy, contract into smaller and smaller size.

When subatomic particles are tightly compressed, electron degeneracy pressure arise to resist the contraction of gravitation!

Degeneracy Pressure – Chapter 13 Dead Stars

The Origin of Degenerate PressureDegenerate pressure arises from two fundamental laws of quantum physics: • Pauli’s Exclusion Principle (for the fermions, such as electrons, protons, and

neutrons). No two particles (fermions) can occupy the same quantum mechanical state simultaneously.

• Heisenberg’s Uncertainty Principle The product of the uncertainty in the position of a particle and its momentum is always greater than the Planck constant

x p ≥ h

where x is the uncertainty in the position of the particle, p is the uncertainty in the momentum of the particle, and h = 6.626 10-27 gm cm2/sec is the Planck’s constant.

To be continued…

The Grouping of Stars in the H-R Diagram

The Major Categories of Stars 1. The Main Sequence, 2. The Supergiants, 3. The Giants, 4. The White Dwarfs. 5. The Instability Strip (variable

stars).

• Main Sequence – healthy stars, fusing hydrogen in the core.

• Giants and supergiants – dying stars, fusing helium and heavier elements.

• White dwarfs – dead stars, core nuclear fusion have stopped.

Sizes scale 1 Rsun 10 Rsun 100 Rsun1000 Rsun

Relative Sizes of Stars—From Supergiants to White Dwarfs

Note that the sizes in this figure are not to scale!• Orbit of Mars• Orbit of

Mercury

Supergiant ~ 100 – 1000 Rsun

Giant ~ 10 – 100 Rsun

White Dwarf ~ 0.01 Rsun

About the size of Earth!Main-Sequence Star – Sun = 1Rsun

The Main Sequence Stars

Most of the stars we see in the sky are main sequence stars! Properties of Main Sequence Stars 1. Energy-generating mechanism: Hydrogen

burning (Fusion of hydrogen into helium).

2. The hot, blue stars are more massive, and larger in size.

3. The large, hot, blue stars has short lifetime.

4. Small, cool, red stars has long lifetime. 5. Upper limit of stellar mass: ~ 100 Msun

• The core temperature becomes so high that radiation pressure (pressure exerted by photons) upsets the equilibrium between the thermal pressure and the gravitational pull. The star becomes unstable.

• Lower limit of stellar mass: ~ 0.08 Msun

• The core temperature of objects with mass less than 0.08 Msun is not hot enough to trigger hydrogen burning.

• Jupiter is 0.001 Msu

Relative Sizes of Main Sequence Stars

The mass of the main-sequence star determine its luminosity, surface temperature, radius, and lifetime.• Massive stars – hotter,

brighter, larger, and shorter lifetime

• Light stars – cooler, dimmer, smaller, and longer lifetime.

Although the mass of Spica is 100 times that of Proxima Centauri, its lifetime is 100,000 times shorter.

Why?

~3 Rsun

1 Rsun

0.1 Rsun

~10 Rsun

The Lifetime of Stars

The lifetime of a star is determined by how fast it burns its supply of hydrogen…This hydrogen burning rate can be inferred from the luminosity of the star.

The Mass-Luminosity Relation Once we have observationally determined the luminosity and mass of many main sequence stars, we find that the higher the mass M of a star is, the higher is its luminosity (L).

L/L⊙ = (M/M⊙ )3.5

Note: The Mass-Luminosity relation applies to main-sequence stars only!

For exmaple, A 10 M⊙ star is roughly (103.5 ~ ) 3,000 brighter, or

burning its hydrogen times 3,000 faster. We know that the lifetime of the Sun is about 10 billion

years. The more massive star would have a lifetime of about

10 × 10 billion years ÷ 3,000 ~ 30 million years.

Star ClustersStars are formed from giant clouds of gas, with enough material to form many stars. Stars in the same cluster lie at about the

same distance from Earth Stars in the same cluster are formed

roughly at the same time. • Open Clusters

Found in the disk of the galaxy. Contains a few thousand stars. Span about 30 light-years.

• Globular Clusters Found both in the disk and in the halo

of the galaxy. Up to one million stars. Spans about 60 to 150 light-years.

The Pleiades

Dating the Age of Star Clusters

Temperature

Lum

inos

ity

• When a star cluster is born, it contains stars spanning the entire range of the H-R diagram.

• As the cluster ages, the high-luminosity, hot, blue stars move away from the main sequence curve first.

• The point where the curve of the H-R diagram deviates from the main sequence curve (the main-sequence turn-off point) indicates the age of the cluster.

Temperature

Lum

inos

ity

TemperatureL

umin

osit

yAge of the Cluster

Main sequence turn-off point

Main sequence curve

New-born 100 million years

10 billion years

Examples of H-R Diagram of Star Clusters

M4 main-sequence turn-off point • Age: 12 ~ 14 billion years. • Age of the universe must be at

least 12 ~ 14 billion years.

Low Mass Stars

Low Mass Stars: M < 8 – 10 M⊙

Evolutionary History 1. The helium produced by the proton-proton chain (hydrogen burning) accumulates at

the core. Because the temperature required to start helium burning is much higher (~ 100 million degrees), there isn’t enough thermal pressure at the core to resist the gravitational contraction (just yet).

2. As a main sequence star exhausts its core hydrogen supply, its energy output is reduced without the thermal pressure of the hydrogen fusion, gravitation contraction continue.

3. The core temperature rises, as well as the outer layer of the star where there are still substantial supply of hydrogen, triggering shell hydrogen burning, at a much higher temperature than that in the main sequence stars.

4. The high temperature shell hydrogen burning produces more energy than the same star in its main sequence core hydrogen burning stage Higher luminosity.

5. The high thermal pressure of the shell hydrogen burning push the envelop of the star outward, much larger than its size at the main sequence stage giant.

6. The large surface area of the giant cools off fast red giant.

Structure of Red Giants

1. Inert Helium core Most of the mass of the star is concentrated at the helium core.

2. Hydrogen-burning shell. 3. Hydrogen envelop.

Helium-Burning Star If a star is heavy enough, the temperature at its helium core can get high enough (>

100 million degrees) to start helium burning. Helium burning (triple alpha process): three helium nuclei (alpha particle) fuse to

form a carbon. The fusion of the core helium inflates the core of the star, pushing the hydrogen burning shell outward, causing its temperature to drop.

Lower total luminosity. The core helium eventually are exhausted, leaving a carbon core. Gravitational

contraction continue. Gravitational contraction eventually heat up the helium outside the core to start the shell helium burning at a higher temperature.

Shell helium burning, like shell hydrogen burning, generates much more energy than the star at core helium burning stage -- Red giant again

A steady stellar wind slowly push the outer envelop of the star away, forming planetary nebula.

The planetary nebula eventually disperse, leaving a cooling carbon core – White Dwarf

The Evolution of Low Mass Main-Sequence Star

Click image to start animation…

Planetary Nebulae