Spectral Classes

Strange lettering scheme is a historical accident.

Spectral Class Surface Temperature Examples

OBAFGKM

30,000 K20,000 K10,000 K7000 K6000 K4000 K3000 K

RigelVega, Sirius

Sun

Betelgeuse

Further subdivision: BO - B9, GO - G9, etc. GO hotter than G9. Sun is a G2.

Main Sequence

White Dwarfs

Red Giants

Red Supergiants

Increasing Mass, Radius

on Main Sequence

The Hertzsprung-Russell (H-R) Diagram

Sun

A star’s position in the H-R diagram depends on its mass and evolutionary state.

H-R Diagram of Well-known StarsH-R Diagram of Nearby Stars

Note lines of constant radius!

Stellar Evolution:Evolution off the Main Sequence

Main Sequence Lifetimes

Most massive (O and B stars): millions of years

Stars like the Sun (G stars): billions of years

Low mass stars (K and M stars): a trillion years!

While on Main Sequence, stellar core has H -> He fusion, by p-p chain in stars like Sun or less massive. In more massive stars, “CNO cycle” becomes more important.

Evolution of a Low-Mass Star(< 8 M

sun , focus on 1 M

sun case)

- All H converted to He in core.

- Core too cool for He burning. Contracts. Heats up.

Red Giant

- Tremendous energy produced. Star must expand.

- Star now a "Red Giant". Diameter ~ 1 AU!

- Phase lasts ~ 109 years for 1 MSun

star.

- Example: Arcturus

- H burns in hot, dense shell around core: "H-shell burning phase".

Red Giant Star on H-R Diagram

Eventually: Core Helium Fusion

- Core shrinks and heats up to 108 K, helium can now burn into carbon.

"Triple-alpha process"

4He + 4He -> 8Be + energy8Be + 4He -> 12C + energy

- Core very dense. Fusion first occurs in a runaway process: "the helium flash". Energy from fusion goes into re-expanding and cooling the core. Takes only a few seconds! This slows fusion, so star gets dimmer again.

- Then stable He -> C burning. Still have H -> He shell burning surrounding it.

- Now star on "Horizontal Branch" of H-R diagram. Lasts ~108 years for 1 M

Sun star.

Core fusionHe -> C

Shell fusionH -> He

Horizontal branch star structure

More massive less massive

Helium Runs out in Core-- All He -> C. Not hot enough-for C fusion.

-- Core shrinks and heats up, as-does H-burning shell.

- Get new helium burning shell (inside H burning shell).

Red Supergiant

- High rate of burning, star expands, luminosity way up.

- Called ''Red Supergiant'' (or Asymptotic Giant Branch) phase.

- Only ~106 years for 1 MSun

star.

"Planetary Nebulae"

- Core continues to contract. Never hot enough for C fusion.

- He shell dense, fusion becomes unstable => “He shell flashes”.

- Eventually, shells thrown off star altogether! 0.1 - 0.2 MSun

ejected.

- Shells appear as a nebula around star, called “Planetary Nebula” (awful, historical name, nothing to do with planets).

- Whole star pulsates more and more violently.

White Dwarfs

- Dead core of low-mass star after Planetary Nebula thrown off.

- Mass: few tenths of a MSun

- Radius: about REarth

-- Density: 106 g/cm3! (a cubic cm of it would weigh a ton on Earth).

-- Composition: C, O.

- White dwarfs slowly cool to oblivion. No fusion.

Evolution of Stars > 12 MSun

Higher mass stars fuse heavier elements.

Result is "onion" structure with many shells of fusion-produced elements. Heaviest element made is iron. Strong winds.

Eventual state of > 12 MSun

starLow mass stars never gotpast this structure:

They evolve more rapidly. Example: 20 M

Sun star lives

"only" ~107 years.

Star Clusters

Comparing with theory, can easily determine cluster age from H-R diagram.

Open Cluster

Globular Cluster

Following the evolution of a cluster on the H-R diagram

100 LSun

Temperature

Lu

min

osit

y

LSun

LSun

LSun

LSun

LSun

Globular clusters formed 12-14 billion years ago. Useful info for studying the history of the Milky Way Galaxy.

Globular Cluster M80 and composite H-R diagram for similar-age clusters.

Schematic Picture of Cluster Evolution

Time 0. Cluster looks blue

Time: few million years.Cluster redder

Time: 10 billion years.Cluster looks red

Massive, hot, bright, blue, short-lived stars

Low-mass, cool, red, dim, long-lived stars

Fusion Reactions and Stellar Mass

In stars like the Sun or less massive, H -> Hemost efficient through proton-proton chain.

In higher mass stars, "CNO cycle" more efficient. Same net result: 4 protons -> He nucleusCarbon just a catalyst.

Need Tcenter

> 16 million K for CNO cycle to be

more efficient.

(mass) ->

Sun

Neutron Stars

If star has mass 12-25 MSun , remnant of supernova expected to be a tightly packed ball of neutrons.

Diameter: 10 km only!

Mass: 1.4 - 3(?) MSun

Density: 1014 g / cm3 !

A neutron star over the Sandias?

Please read about observable neutron stars: pulsars.

Rotation rate: few to many times per second!!!

Magnetic field: 1010 x typical bar magnet!

Black Holes and General Relativity

The Equivalence Principle

Here’s a series of thought experiments and arguments:

1) Imagine you are far from any source of gravity, in free space, weightless. If you shine a light or throw a ball, it will move in a straight line.

General Relativity: Einstein's (1915) description of gravity (extension of Newton's). It begins with:

2. If you are in freefall, you are also weightless. Einstein says these are equivalent. So in freefall, light and ball also travel in straight lines.

3. Now imagine two people in freefall on Earth, passing a ball back and forth. From their perspective, they pass it in a straight line. From a stationary perspective, it follows a curved path. So will a flashlight beam, but curvature of light path small because light is fast (but not infinitely so).

The different perspectives are called frames of reference.

4. Gravity and acceleration are equivalent. An apple falling in Earth's gravity is the same as one falling in an elevator accelerating upwards, in free space.

5. All effects you would observe by being in an accelerated frame of reference you would also observe when under the influence of gravity.

Examples:

1) Bending of light. If light travels in straight lines in free space, then gravity causes light to follow curved paths.

Observed! In 1919 eclipse.

Gravitational lensing. The gravity of a foreground cluster of galaxies distorts the images of background galaxies into arc shapes.

Saturn-massblack hole

2. Gravitational Redshift

Consider accelerating elevator in free space (no gravity).

time zero, speed=0

later, speed > 0light received when elevator receding at some speed.

light emitted when elevator at rest.

Received light has longer wavelength because of Doppler Shift ("redshift"). Gravity must have same effect! Verified in Pound-Rebka experiment.

3. Gravitational Time Dilation

Direct consequence of the redshift. Observers disagree on rate of time passage, depending on strength of gravity they’re in.

Escape Velocity

Velocity needed to escape an object’s gravitational pull.

vesc

= 2GM R

Earth's surface: vesc = 11 km/sec.

If Earth shrunk to R=1 cm, then vesc = c, the speed of light! Then nothing, including light, could escape Earth.

This special radius, for a particular object, is called the Schwarzschild Radius, R

S. R

S M.

Black Holes

If core with about 3 MSun

or more collapses, not even neutron

pressure can stop it (total mass of star about 25 MSun

?).

Core collapses to a point, a "singularity".

Gravity is so strong that not even light can escape.

RS for a 3 M

Sun object is 9 km.

Event horizon: imaginary sphere around object, with radius RS .

Event horizonR

S

Anything crossing the event horizon, including light, is trapped

Like a rubber sheet, but in three dimensions, curvature dictates how all objects, including light, move when close to a mass.

Black hole achieves this by severely curving space. According to General Relativity, all masses curve space. Gravity and space curvature are equivalent.

Curvature at event horizon is so great that space “folds in on itself”.

Effects around Black Holes

1) Enormous tidal forces.

2) Gravitational redshift. Example, blue light emitted just outside event horizon may appear red to distant observer.

3) Time dilation. Clock just outside event horizon appears to run slow to a distant observer. At event horizon, clock appears to stop.

Do Black Holes Really Exist? Good Candidate: Cygnus X-1

- Binary system: 30 MSun

star with unseen companion.

- Binary orbit => companion > 7 MSun

.

- X-rays => million degree gas falling into black hole.

1. White Dwarf If initial star mass < 8-12 M

sun .

2. Neutron Star If initial mass > 12 M

Sun and < 25 ? M

Sun .

3. Black Hole If initial mass > 25 ? M

Sun .

Final States of a Star