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Astro 101 Fall 2013 Lecture 9 Stars (continued) – Stellar evolution T. Howard. Spectral Classes. Strange lettering scheme is a historical accident. Spectral Class Surface Temperature Examples . 30,000 K 20,000 K 10,000 K 7000 K 6000 K 4000 K 3000 K.

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Astro 101

Fall 2013

Lecture 9

Stars (continued) – Stellar evolution

T. Howard


Spectral Classes

Strange lettering scheme is a historical accident.

Spectral Class Surface Temperature Examples

30,000 K

20,000 K

10,000 K

7000 K

6000 K

4000 K

3000 K

Rigel

Vega, Sirius

Sun

Betelgeuse

O

B

A

F

G

K

M

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


Increasing Mass, Radius on Main Sequence

The Hertzsprung-Russell (H-R) Diagram

Red Supergiants

Red Giants

Sun

Main Sequence

White Dwarfs

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


H-R Diagram of Well-known Stars

H-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 Msun , focus on 1 Msun case)

- All H converted to He in core.

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

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

- Tremendous energy produced. Star must expand.

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

- Phase lasts ~ 109 years for 1 MSun star.

- Example: Arcturus

Red Giant



Eventually: Core Helium Fusion

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

"Triple-alpha process"

4He + 4He -> 8Be + energy

8Be + 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 MSun star.


More massive less massive

Horizontal branch star structure

Core fusion

He -> C

Shell fusion

H -> He


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).

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

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

- Only ~106 years for 1 MSun star.

Red Supergiant


"Planetary Nebulae"

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

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

- Whole star pulsates more and more violently.

- 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).


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.


Star Clusters

Open Cluster

Globular Cluster

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


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

Luminosity

LSun

LSun

Temperature

100 LSun

LSun

LSun

LSun


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

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


Schematic Picture of Cluster Evolution similar-age clusters.

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

Time 0. Cluster looks blue

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

Time: few million years.

Cluster redder

Time: 10 billion years.

Cluster looks red


Evolution of Stars > 12 M similar-age clusters.Sun

Low mass stars never got

past this structure:

Eventual state of > 12 MSun star

Higher mass stars fuse heavier elements.

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

They evolve more rapidly. Example: 20 MSun star lives "only" ~107 years.


Fusion Reactions and Stellar Mass similar-age clusters.

In stars like the Sun or less massive, H -> He

most efficient through proton-proton chain.

In higher mass stars, "CNO cycle" more efficient. Same net result:

4 protons -> He nucleus

Carbon just a catalyst.

Need Tcenter > 16 million K for CNO cycle to be more efficient.

Sun

(mass) ->


Endpoints of Massive Stars similar-age clusters.

  • Stars with mass >~ 8 Msun Supernovae

    • Massive stellar explosions

    • Remnant core collapses (usually much less than 50% mass)

    • In most cases, core  neutron star

    • Electrons and protons “crushed together” creating neutrons

    • Many neutrinos emitted  these escape the star completely

    • Neutron stars often end up forming pulsars

  • What about even more massive stars?

    • Mass >~ 25 Msun  collapse to a Black Hole


Supernovae – extremely similar-age clusters.violent stellar explosions

  • Several types& subtypes (called type “I”, “Ia”, “II”, etc.)

  • Different types arise from

  • pre-explosion stellar

  • conditions

  • We can use the change

  • in brightness

  • over time to

  • distinguish them

Example supernova remnant—

Crabnebula in Taurus



Supernova remnant in Vela 


Light Curves of Supernovae Types similar-age clusters.


Neutron Stars similar-age clusters.

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 !

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

Magnetic field: 1010 x typical bar magnet!

A neutron star over the Sandias?

Please read about observable neutron stars: pulsars.


Pulsars discovered 1967 by similar-age clusters.

Jocelyn Bell Burnell & Anthony

Hewish.


Pulsars – “Lighthouse” model similar-age clusters.


Crab nebula in X-rays (Chandra) similar-age clusters.

 “Blinking” of the Crab pulsar

Off


A brief digression -- Relativity similar-age clusters.


1905: Special Theory of Relativity similar-age clusters.

1915: General Theory of Relativity


Relativity stars with assigning “frames of reference” (coordinates) to

the Observer and the Event (or Thing) in question

z

z

y

y

x

x

Special Relativity  covers situations where velocities may be

very high, but frames of reference are not

accelerated

General Relativity  as it says, the more general case: acceleration

between frames of reference is included


A (coordinates) tofundamental postulate of relativity:

The speed of light, c, in free (empty) space is a universal constant.

It does not get added to or subtracted from the frame of reference.

c = (approx.) 3 x 108 meters/sec

Note: the speed of light can be slower in solid, gaseous, or liquid media

(glass, water, air), but never faster than c.

This effect actually accounts for the bending of light rays in lenses,

when entering or leaving a body of water, etc.


Black Holes and General Relativity (coordinates) to

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

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.


2. If you are in (coordinates) tofreefall, 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. (coordinates) toGravity 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.


Some Consequences of General Relativity: (coordinates) to

Mass “warps” space  i.e., the amount of mass introduces

a “curvature” to what would otherwise be perfectly linear

(Euclidean) space.

This curvature of space is a different way of thinking about

gravity. It works, and explains a lot of things.

The curvature of space causes things to move in curved lines.

 Even rays of light!

“Matter tells space how to curve. Space tells matter how to move.”

(Misner, Thorne, and Wheeler, 1973)



Curvature of light Observed! In (coordinates) to1919 eclipse.

Einstein

Sir Arthur Eddington


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


Other consequences of General Relativity: (coordinates) to

Gravitational Waves – caused by massive violent events

(e.g., coalescence of binary pulsars, formation of Bl. Holes)

– cause asymmetric warping of space

The “ripples” move at speed c thru the universe.

Might be detectable (but very weak).

We are searching for them now.

USA: LIGO Project

Elsewhere: Virgo, GEO, others

Proposed Space-based GW Observatory: LISA


LIGO Facility at Hanford, WA (2 (coordinates) tond facility is at Livingston, LA)


Proposed LISA mission (NASA-ESA) (coordinates) to

This is just a schematic diagram. The spacecraft will be

~ 5 million km apart.


Other consequences of General Relativity (coordinates) to

light received when elevator receding at some speed.

2. Gravitational Redshift

later, speed > 0

Consider accelerating elevator in free space (no gravity).

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

time zero, speed=0

light emitted when elevator at rest.

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 (coordinates) to

Velocity needed to escape an object’s gravitational pull.

2GM

R

vesc =

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, RS. RSM.


Black Holes (coordinates) to

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 MSun object is 9 km.

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

Event horizon

Anything crossing the event horizon, including light, is trapped

RS


Saturn-mass (coordinates) to

black hole


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

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



Effects around Black Holes in on itself”.

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 in on itself”.

- Binary system: 30 MSun star with unseen companion.

- Binary orbit => companion > 7 MSun.

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


Final States of a in on itself”.Star (simplified)

1. White Dwarf

If initial star mass < 8-12 Msun .

2. Neutron Star

If initial mass > 12 MSun and < 25 ? MSun .

3. Black Hole

If initial mass > 25 ? MSun .


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