May 13, 2013, jeb

Outline

• Main Sequence Star
• Aging of Main Sequence Star
• Physics Lesson on Energy Generation in Stars
• Birth of a Red Giant
• The Sun will become a Red Giant
• Helium Burning and Helium Flash
• Evolution of a Low-Mass Star
• Planetary Nebula
• Chandrasekhar Limit
• White Dwarf
• Lower Mass Stars (less than a Solar Mass)
• Blue Stragglers
• Evolution of Stars More Massive than the Sun
• Old Stars
• Observing Stellar Evolution in Star Clusters
• Close Binaries
• Summary

Introduction

How do we explain the diversity of stars observed in the sky?
• Nearby Stars
• Bright Stars

They include
• Red Giants
• Blue Giants
• White Dwarfs
• Red Dwarfs
• Sun-like Stars
• and more

We have begun by recognizing that stars are born to exist initially on the main-sequence

Main Sequence Star

After the collapsing phase to a main-sequence star,
along the path on the H-R diagram,
the star "burns" its core hydrogen fuel for 10 ⁶ to 10 ¹³ years. (the Universe is only about 14 x 10 ⁹ years old)

Estimated Stellar Lifetimes(in units of 106 years)

MASS (solar masses) SPECTRAL TYPE ON THE MAIN SEQUENCE PERIOD OF CONTRACTION TO MAIN SEQUENCE (106 yrs) ESTIMATED LIFETIME ON THE MAIN SEQUENCE (106 yrs) PERIOD FOR MAIN SEQUENCE TO RED GIANT (106 yrs) RED GIANT DURATION (106 yrs) 30 O5 0.02 4.9 0.55 0.3 15 B0 0.06 10 1.7 2 9 B2 0.2 22 0.2 5 5 B5 0.6 68 2 20 3 A0 3 240 9 80 1.5 F2 20 2,000 280   1.0 G2 50 10,000 680   0.5 M0 200 30,000     0.1 M7 500 107     Source: Fundamental Astronomy, edited by H. Karttunen et al., 1994

While main-sequence equilibrium is maintained between the inward force of gravity and the outward force of heat-generated pressure, the star stays on the main-sequence.


Eventually, the "burning" of hydrogen is completed, and the inner pressure no longer overcomes the force of gravity; this is the beginning of the eventual death of the star's main-sequence life.

Aging of Main Sequence Star




Star begins on zero-age main sequence (ZAMS) band
As the star ages, "burning" its hydrogen, the star moves just off the main sequence.


Core Hydrogen Burning:
Thermal equilibrium (balance between energy production and surface emission) lasts while hydrogen is "burning" in the core.


End of Main Sequence Phase:
Core hydrogen is all fused into helium.

This occurs after about 10 billion years for a G2 type star
Core cools and cannot support mass,
therefore core shrinks and heats
---> hydrogen "burning" spreads
Shell Hydrogen Burning

Physics Lesson on Energy Generation in Stars

The dominant thermonuclear reaction in a star changes with temperature

Thermonulclear Reactions

MINIMUM TEMPERATURE REACTION 10 x 106 K proton-proton chain 20 x 106 K CNO cycle 100 x 106 K triple alpha 200 x 106 K carbon-helium fusion 600 x 106 K carbon fusion


Collisions of nuclei at higher temperatures can overcome the repulsive force of heavier nuclei (or nuclei with more positive charge)

Birth of a Red Giant

Core is shrinking
Converting gravitational energy into thermal energy
Star heats, causing expansion
• Red giant
Helium Burning
When the core reaches 100,000,000 K, a new fusion reaction begins

• triple-alpha process
  • ⁴He + ⁴He -> ⁸Be + energy
  • ⁸Be + ⁴He -> ¹²C + energy
  • (effectively, 3 ⁴He -> ¹²C + energy)
• at even higher temperatures (like 200,000,000 K) Carbon-helium fusion forms Oxygen
  • ¹²C + ⁴He -> ¹⁶O + energy
    less likely is ¹²C + ¹²C -> ²⁴Mg + energy

The Sun will become a Red Giant



In 5 x 10⁹ years (after burning for 10 x 10 ⁹ years) the Sun will finish its core burning and begin expanding.


The Sun will be hotter at its core than now, but cooler on its surface.


Despite cooler surface, due to its much larger surface area, it will be much brighter.


The planets will be destroyed
• inner planets engulfed and vaporized
• outer planets heated leading to boiling off of atmosphere


The Sun will then be a RED GIANT

Helium Burning and Helium Flash

Stars with Masses greater than 2 M_SUN
• as Helium burning begins, the heated core heats and expands, slowing the helium burn
Stars with masses less than 2 M_SUN
• as Helium burning begins, heated core will not expand initially.
• Why?
  • The cores of these stars are supported by electron degeneracy resulting from the Pauli Exclusion Principle, (instead of thermal pressure)

    Pauli Exclusion Principle

    You can't have two things (electrons) in the same place at the same time.
    Applied at the atomic scale

• No expansion -> no cooling -> runaway helium burning -> helium flash (hours)
• Finally core expands and cools
• Now stable helium burning begins and star resides on the "Horizontal branch"
  • a "helium main sequence" of sorts, where stars remain for a time
• Can we observe this evolution in real stars?
  • Look at the H-R diagram for globular cluster M80
  • We do see the stars in various stages of evolution, just as the theory predicts

Helium Flash (re-stated)

After H burning stops in core

• Core is all helium
• core collapses due to loss of internal pressure (no hydrostatic eq)
• Collapse stopped by electron degeneracy: (10 ⁸ kg/m³)
  note: water = 10 ³ kg/m³
  
• Electron degeneracy results from the Pauli Exclusion Principle:
  No two electrons can occupy the same space (very tightly packed, but there is a limit to the packing)
• core heats to 100 x 10 ⁶ K
• Triple-alpha begins 3 He -> 12 C
• core heats more
• temperature rises
• no expansion-no cooling
• triple alpha rate increases even more
  • -> Helium Flash

Evolution of a Low-mass Star

(about 1 x M_SUN)

Collapse to a star in few x 10⁷ yrs

main sequence life lasts 10¹⁰ yrs

Helium core collapses and star expands into Red Giant

Helium flash- core reaches 10⁸K


Helium core burns into carbon and oxygen and eventually helium shell burning

with a Carbon core formed at the center of the star

Planetary Nebula is ejected (25 - 60% of mass ejected)

expands for about 50,000 yrs before fading

core collapses into white dwarf at center of planetary nebula

Planetary Nebula

Dying low-mass star ejects its outer layers of gas.

• As the star expands, and helium shell burning proceeds, a series of helium-shell flashes cause the star's radius to pulsate
• These pulsations help push the outer envelope of the star to greater and greater distances

These gases are ionized by star and glow.

(They look a bit like planets through small telescopes, but have nothing to do with planets)

Expand for about 50,000 years before fading.

Very common (20,000 to 50,000 in the Milky Way)

Examples:

• Abell 39
• Ring Nebula
• Eskimo Nebula
• Cat's Eye Nebula
• M2-9

Evolution Following Planetary Nebula Phase (solar mass star)


core is all carbon
very dense - degenerate
carbon ignition never occurs

• temperature never reaches 600 x 10⁶K
after 75,000 years white dwarf cooling to black dwarf.

Chandrasekhar Limit

Chandrasekhar Limit is the Maximum mass for a white dwarf star
Chandrasekhar Limit is 1.4 x M _SUN
If the mass is less than 1.4 x M _SUN the electron degeneracy pressure holds up the star

If the mass is greater than 1.4 x M _SUN, the electron pressure degeneracy cannot support the weight.

Low-mass stars (<3 x M _SUN) eject about half their mass in planetary nebula, so star ends up with <1.4 x M _SUN

Density in white dwarf is about 10⁶ g/cm³ (1 teaspoon = wt. of truck)




Densities of Interest (given in two units, g/cm³ and kg/m³)



WATER	1 g/cm3	103 kg/m3
LEAD	11 g/cm3	104 kg/m3
CORE OF SUN	150 g/cm3	1.5 x 105 kg/m3
WHITE DWARF	106 g/cm3	109 kg/m3

A single teaspoon of the material from a white dwarf would weigh tons

NEUTRON STAR	1015 g/cm3	1018 kg/m3

Deaths of Stars

Low-mass (lightweight) Stars (< 3 x M_SUN)

Planetary Nebula
White Dwarfs
Type I Supernova


High-mass (heavyweight) Stars

Type II Supernova
Neutron star and Supernova remnant
black hole and accretion disk

White Dwarf

After a low-mass star burns its core into carbon and oxygen, heat generation stops and the core collapses again.

The core will heat further as gravitational energy is released, but the collapse stops before the core is hot enough to burn carbon and oxygen because of the Pauli Exclusion Principle and Electron Degeneracy.

The density in the core will not collapse further and supports gravitational weight of star.

White dwarfs show up on the H-R diagram
Stars within about 5 pc of the Sun

These white dwarfs are cooling,
and will eventually become black dwarfs
• cold, dense, burned-out embers

Example of a White Dwarf: Sirius B

Sirius A is the brightest star in the sky.
Sirius A is member of a binary system with a faint companion: Sirius B



	abs. magnitude	Luminosity
SIRIUS A	1.4	24 LSUN
SIRIUS B	11.6	0.002 LSUN *

* - when the luminosity in the entire EM spectrum is considered, L_Sirius-B = 0.025 L_SUN

Sirius B surface temp is 27,000 K

Very hot, but very faint -> small radius
Sirius B radius is smaller than Earth, about 0.007 x R_SUN
but Sirius B mass is about 1.1 x M_SUN







Observation of White Dwarfs by the Hubble Space Telescope

There should be many white dwarfs in globular clusters
• globular clusters are old: > 10 billion years
• this is enough time for the lighter stars to evolve into white dwarfs
  • remember the stellar lifetimes: table
Hubble Space Telescope
• Image of M4 as seen from ground-based telescope
• Hubble Space Telescope zoomed in to photograph nearly one hundred white dwarfs in the globular cluster M4
  

Solar Mass Stars

• H-core burning begins
• H-core burning ceases
• H-shell burning
• Helium flash - He-core burn begins
• He-core burn/ H-shell burns
• core burning stops / shell burning continues
• expulsion of outer layers
• planetary nebula with central star
• all fusion stops
• white dwarf - slowly cooling
• eventually cools to become a black dwarf

Lower Mass Stars (less than a Solar Mass)


Many have not had time to age off the main sequence :
(example from: 0.74 M_sun "lives" 20 billion years as main sequence star
- longer than age of universe)

If mass < 0.08 M_sun
Never gets hot enough in core (8 x 10 ⁶ K) to start nuclear reactions
"BROWN DWARF"

Evolution of Stars More Massive than the Sun

High mass stars age more rapidly
check the table above
no helium flash if M > 2.5 x M_SUN
if M > 8 x M_SUN
Core temperature rises to 600 million K (6 x10⁸ K)
Carbon fusion is ignited
Fusion of even heavier elements occurs, as star gets hotter and hotter
The heavier stars follow a different path on the H-R diagram

Blue Stragglers

Globular Cluster M80
• H-R diagram for M80
• H-R diagram shows age of M80 is about 12 billion years
• stars more massive than 0.8 solar mass have evolved beyond the red-giant phase, becoming mainly white dwarfs
• Features of the expected H-R diagram for one solar mass appear clearly in the M80 H-R diagram
  • the red-giant, horizontal-branch, and asymptotic-giant-branch stars in M80 are all roughly one solar mass

Blue stragglers
• A few blue stragglers appear in the M80 H-R diagram
  • Why didn't these more massive stars evolve to white dwarfs long ago?
  • Answer- they are not as old as the other stars in the cluster
  • They have formed more recently through mergers of lower mass stars
  • In some cases the mergers are the result of the evolution of binary systems (see below)
  
  
  

Old Stars

old stars are "metal poor"

young stars are "metal rich"

WHY?

Metals are not produced in the stars until their death

When they die in an explosion they create metals and spread them into the interstellar medium.

Old stars were created before many stars had died and the interstellar gases had few metals

Young stars were created more recently, after many stars had died and enriched the interstellar medium with metals

Observing Stellar Evolution in Star Clusters

Star clusters are excellent test of our theory of stellar evolution
• the stars in the cluster formed at about the same time
  
• so these stars are all of the same age
theoretical evolution of star clusters on the H-R diagram

Open Clusters

Open clusters are "recently" formed clusters of stars
"double cluster" h and chi Persei
H-R diagram reveals age about 10 million years
Hyades cluster
H-R diagram reveals age about 500 million years

Globular Clusters

(10⁴ to 10⁵ stars clustered tightly within a few hundred light-years

No high mass main sequence stars -> so old cluster

47 Tucanae cluster H-R diagram: upper half of main-sequence missing--

They have become Red Giants



Horizontal branch - post helium flash - low mass stars

H-R diagram reveals age


Turnoff Point reveals age > 10 billion years old

Close Binary Stars


Stars separated by a few stellar diameters

Critical Surface - figure eight-shaped boundary around star defining gravity domain.
• Two lobes called Roche lobes
  • Each lobe defines region of gravitational dominance of each star

As a Star grows old, it may expand to become a Red Giant .
• If matter escapes the Roche lobe of the red giant, it may fall onto the companion star, resulting in Mass Transfer
  • This can change the evolution of the stars (determined by mass)
  • resulting in a mysterious age-mass relationship where the heaviest star is least evolved
Example: Algol


• This binary mechanism can explain the blue stragglers seen in the globular cluster M80

Summary

• Stars evolve: Protostar -> main sequence star -> Red Giant
• Main sequence phase ends when all hydrogen in core is burnt
• Red giant will have a hydrogen burning shell
• Temperature of core of Red Giant will increase, until helium fusion begins to produce Carbon and Oxygen
• Lighter Red Giants (< 2 M_SUN) will experience helium flash due to the role of the Pauli Exclusion Principle
• Ages of clusters can be determined from a turnoff point