Astro 1050 Wed. Oct. 23, 2002

Today: Chapter 10: The Deaths of Stars

Expected Evolution of the HR Diagram for a Cluster

A cluster consists of stars which all started to form at the same time (collapsing from the same fragmenting molecular cloud)

Higher mass stars contract to main sequence before low mass ones reach it

Higher mass stars are also the first to run out of H and leave the main sequence, becoming supergiants.

As time continues, lower and lower mass stars move off the main sequence (at the moving “turn off point”)

The original supergiants don’t live very long.
The lower mass stars produce giants

Tests of Stellar Evolution using the HR Diagram

Stellar evolution too slow to see changes in given cluster

Can observe clusters and look for predicted patterns

Complications in Stellar Evolution

Pressure forces other than thermal gas pressure

Reminder: We’ve been assuming that when star loses energy it contracts and actually heats up. Clearly not all objects do this (eg. Earth)

Convection bringing in fuel from outer regions

Mass loss from stellar wind, or mass gain from nearby star

Pauli Exclusion Principle

From quantum rules, electrons don’t like to be packed into a small space, either in atoms or in ionized gas

At normal ionized gas densities, electrons are so spread out quantum rules don’t matter.

As high enough ionized gas densities, quantum rules need to be considered, just has they have been in atoms

Think of each “atom sized” region of space having a set of energy levels associated with it (although it is really more complicated)

Effect of Degenerate Electron Pressure

Loss of energy does not reduce pressure

Star does not contract in response to loss of energy

Gravity not available as energy source to heat up star

Electrons are already in lowest energy states allowed
(equivalent to atoms in ground state) so no energy available there

If there is no other energy source, as energy is lost nuclei move slower and temperature drops.

Degenerate Pressure Can End Fusion

Degenerate Electron Pressure limits contraction and core temperature

“Stars” with M < 0.08 M_Sun never burn H    (brown dwarfs)

Stars    with M < 0.4   M_Sun never burn He   (red dwarfs)

Stars    with M < 4      M_Sun never burn C     (but do make red giants)

Stars    with M > 4      M_Sun do burn elements all the way to Fe

What happens to these objects?

Brown dwarfs never become bright – sort of like giant version of Jupiter

Red dwarfs have such long lives none have yet exhausted H

Red giants are related to white dwarfs

Massive stars explode as supernova

Effects of Convection

Energy can be moved by radiation or convection

Convection in core brings in new fuel

Cooler material more opaque
making radiation harder and convection more likely

Choice also depends on energy flux

Mass Loss from Giant Stars

Envelope of red giant very loosely held

Star is so big, gravity very weak at the surface

Degenerate core makes nuclear “thermostat” sluggish

Core doesn’t quickly expand and cool when fusion is to fast

Energy can be generated in “thermal pulses”

Low temperature opaque envelope can also “oscillate”

Energy is transmitted in “pulses” as envelope expands and contracts

Main cause of “Variable Stars”

White Dwarfs

Simple Planetary Nebula

IC 3568 from the Hubble Space Telescope

Complicated P-N in a Binary System

M2-9 (from the Hubble Space Telescope)

A Gallery of P-N from Hubble

Complications in Binary Systems

Can move mass between stars

1^st (massive) star becomes red giant

Its envelope transferred to other star

Hot (white dwarf) core exposed

2^nd star becomes red giant

Its envelope transferred to white dwarf

Accretion disk around white dwarf

Angular momentum doesn’t let material fall directly to white dwarf surface

Recurrent nova explosions

White dwarf hot enough for fusion, but no Hydrogen fuel

New fuel comes in from companion

Occasionally ignites explosively,
blowing away remaining fuel

Is a star stable against catastrophic collapse?

Imagine compressing a star slightly (without removing energy)

Pressure goes up (trying to make star expand)

Gravity also goes up (trying to make star collapse)

Does pressure go up faster than gravity?

If Yes: star is stable – it bounces back to original size

If No:   star is unstable – gravity makes it collapses

Ordinary gas: P does go up fast – stable

Non-relativistic degenerate gas:   P does go up fast – stable

Relativistic degenerate gas: P does not go up fast – unstable

Relativistic:   Mean are the electrons moving at close to the speed of light

Non-relativistic degenerate gas:   increasing r means not only more electrons, but faster electrons, which raises pressure a lot.

Relativistic degenerate gas:   increasing r can’t increase electron velocity (they are already going close to speed of light) so pressure doesn’t go up as much

Chandrasekhar Limit for White Dwarfs

Add mass to an existing white dwarf

Pressure (P) must increase to balance stronger gravity

For degenerate matter, P depends only on density (r), not temperature, so must have higher density

P vs. r rule such that higher mass star must actually have smaller radius to provide enough P

As M_star ® 1.4 M_Sun v_electron ® c

Requires much higher r to provide high enough P, so star must be much smaller.

Strong gravity which goes with higher r makes this a losing game.

For M ³ 1.4 M_Sun no increase in r can provide enough increase in P – star collapses

Implications for Stars

Stars less massive than 1.4 M_Sun can end as white dwarfs

Stars more massive than 1.4 M_Sun can end as white dwarfs, if they lose enough of their mass (during PN stage) that they end up with less than 1.4 M_Sun

Stars whose degenerate cores grow more massive than 1.4 M_Sun will undergo a catastrophic core collapse:

Neutron stars

Supernova

Supernova

When the degenerate core of a star exceeds 1.4 M_Sun it collapses

Type II: Massive star where it runs out of fuel after converting core to Fe

Type I: White dwarf in binary, which receives mass from its companion.

Events:

Star’s core begins to collapse

Huge amounts of gravitational energy liberated

Extreme densities allows weak force to convert matter to neutrons
p⁺ + e^-® n + n

Neutrinos (n) escape, carrying away much of energy, aiding collapse

Collapsing outer part is heated, “bounces” off core, is ejected into space

Light from very hot ejected matter makes supernova very bright

Ejected matter contains heavy elements from fusion and neutron capture

Core collapses into either:

Neutron stars or Black Holes (Chapter 11)

Supernova in Another Galaxy

Supernova 1994D in NGC 4526

Tycho’s Supernova of 1572

Now seen by the Chandra X-ray Observatory as an expanding cloud.

The Crab Nebula – Supernova from 1050 AD

Can see expansion between 1973 and 2001

Kitt Peak National Observatory Images

What happens to the collapsing core?

Neutron star (more in next chapter)

Quantum rules also resist neutron packing

Densities much higher than white dwarfs allowed

R ~ 5 km r ~ 10¹⁴ gm/cm³ (similar to nucleus)

M limit uncertain, ~2 or ~3 M_Sun before it collapses

Spins very fast (by conservation of angular momentum)

Trapped spinning magnetic field makes it:

Act like a “lighthouse” beaming out E-M radiation (radio, light)

pulsars

Accelerates nearby charged particles

Spinning pulsar powers the
Crab nebula

Red: Ha

Blue: “Synchrotron” emission from high speed electrons trapped in magnetic field

Review Chapters 7-10

Chapter 7: The Sun

Atmospheric Structure

Sunspots/Magnetic Phenomena

Nuclear Fusion – proton-proton chain

Solar Neutrino “Problem”

Review Chapters 7-10

Chapter 8: The Properties of Stars

Distances to Stars

Parallax and Parsecs

Spectroscopic Parallax

Intrinsic Brightness: Luminosity

Absolute Magnitude

Luminosity, Radius, and Temperature

Hertzsprung-Russell (H-R) Diagram

Luminosity Classes (e.g., Main Sequence, giant)

Masses of Stars

Binary Stars and Kepler’s Law

Mass-Luminosity Relationship

Review Chapters 7-10

Ch. 9: The Formation & Structure of Stars

Interstellar Medium

Types of Nebulae (emission, reflection, dark)

Interstellar Reddening from dust

Star formation

Protostar Evolution on H-R Diagram

Fusion (CNO cycle, etc.)

Pressure-Temperature “Thermostat”

Stellar Structure (hydrostatic equilibrium, etc.)

Convection, radiation, and opacity

Stellar Lifetimes

Review Chapters 7-10

Ch. 10: The Deaths of Stars

Evolution off the main sequence (=> giant)

Star Cluster Evolution on H-R Diagram

Degenerate Matter

Planetary Nebulae and White Dwarfs

Binary Star Evolution (Disks, Novae, etc.)

Massive Star Evolution and Supernovae



	A cluster consists of stars which all started to form at the same time (collapsing from the same fragmenting molecular cloud)

	Higher mass stars contract to main sequence before low mass ones reach it

	Higher mass stars are also the first to run out of H and leave the main sequence, becoming supergiants.

	As time continues, lower and lower mass stars move off the main sequence (at the moving “turn off point”) The original supergiants don’t live very long. The lower mass stars produce giants



	Stellar evolution too slow to see changes in given cluster
	Can observe clusters and look for predicted patterns



	Pressure forces other than thermal gas pressure
		Reminder: We’ve been assuming that when star loses energy it contracts and actually heats up. Clearly not all objects do this (eg. Earth)
	Convection bringing in fuel from outer regions
	Mass loss from stellar wind, or mass gain from nearby star



	From quantum rules, electrons don’t like to be packed into a small space, either in atoms or in ionized gas
	At normal ionized gas densities, electrons are so spread out quantum rules don’t matter.
	As high enough ionized gas densities, quantum rules need to be considered, just has they have been in atoms
	Think of each “atom sized” region of space having a set of energy levels associated with it (although it is really more complicated)


	Loss of energy does not reduce pressure
	Star does not contract in response to loss of energy
	Gravity not available as energy source to heat up star

	Electrons are already in lowest energy states allowed (equivalent to atoms in ground state) so no energy available there
	If there is no other energy source, as energy is lost nuclei move slower and temperature drops.



	Degenerate Electron Pressure limits contraction and core temperature
		“Stars” with M < 0.08 M_Sun never burn H (brown dwarfs)
		Stars with M < 0.4 M_Sun never burn He (red dwarfs)
		Stars with M < 4 M_Sun never burn C (but do make red giants)
		Stars with M > 4 M_Sun do burn elements all the way to Fe

	What happens to these objects?
		Brown dwarfs never become bright – sort of like giant version of Jupiter
		Red dwarfs have such long lives none have yet exhausted H
		Red giants are related to white dwarfs
		Massive stars explode as supernova


	Energy can be moved by radiation or convection
	Convection in core brings in new fuel
		Cooler material more opaque making radiation harder and convection more likely
		Choice also depends on energy flux


	Envelope of red giant very loosely held
		Star is so big, gravity very weak at the surface
	Degenerate core makes nuclear “thermostat” sluggish
		Core doesn’t quickly expand and cool when fusion is to fast
		Energy can be generated in “thermal pulses”
	Low temperature opaque envelope can also “oscillate”
		Energy is transmitted in “pulses” as envelope expands and contracts
		Main cause of “Variable Stars”


Can move mass between stars
1^st (massive) star becomes red giant
Its envelope transferred to other star
Hot (white dwarf) core exposed

2^nd star becomes red giant
Its envelope transferred to white dwarf
	Accretion disk around white dwarf
		Angular momentum doesn’t let material fall directly to white dwarf surface
	Recurrent nova explosions
		White dwarf hot enough for fusion, but no Hydrogen fuel
		New fuel comes in from companion
		Occasionally ignites explosively, blowing away remaining fuel


	Imagine compressing a star slightly (without removing energy)
		Pressure goes up (trying to make star expand)
		Gravity also goes up (trying to make star collapse)
	Does pressure go up faster than gravity?
		If Yes: star is stable – it bounces back to original size
		If No: star is unstable – gravity makes it collapses

	Ordinary gas: P does go up fast – stable
	Non-relativistic degenerate gas: P does go up fast – stable
	Relativistic degenerate gas: P does not go up fast – unstable

		Relativistic: Mean are the electrons moving at close to the speed of light

		Non-relativistic degenerate gas: increasing r means not only more electrons, but faster electrons, which raises pressure a lot.
		Relativistic degenerate gas: increasing r can’t increase electron velocity (they are already going close to speed of light) so pressure doesn’t go up as much


	Add mass to an existing white dwarf
	Pressure (P) must increase to balance stronger gravity

	For degenerate matter, P depends only on density (r), not temperature, so must have higher density

	P vs. r rule such that higher mass star must actually have smaller radius to provide enough P

	As M_star ® 1.4 M_Sun v_electron ® c
		Requires much higher r to provide high enough P, so star must be much smaller.
		Strong gravity which goes with higher r makes this a losing game.

		For M ³ 1.4 M_Sun no increase in r can provide enough increase in P – star collapses


	Stars less massive than 1.4 M_Sun can end as white dwarfs

	Stars more massive than 1.4 M_Sun can end as white dwarfs, if they lose enough of their mass (during PN stage) that they end up with less than 1.4 M_Sun

	Stars whose degenerate cores grow more massive than 1.4 M_Sun will undergo a catastrophic core collapse:

			Neutron stars
			Supernova


When the degenerate core of a star exceeds 1.4 M_Sun it collapses
	Type II: Massive star where it runs out of fuel after converting core to Fe
	Type I: White dwarf in binary, which receives mass from its companion.

Events:
	Star’s core begins to collapse
	Huge amounts of gravitational energy liberated
	Extreme densities allows weak force to convert matter to neutrons p⁺ + e^-® n + n
	Neutrinos (n) escape, carrying away much of energy, aiding collapse
	Collapsing outer part is heated, “bounces” off core, is ejected into space
		Light from very hot ejected matter makes supernova very bright
		Ejected matter contains heavy elements from fusion and neutron capture
	Core collapses into either:
		Neutron stars or Black Holes (Chapter 11)


	Now seen by the Chandra X-ray Observatory as an expanding cloud.


	Can see expansion between 1973 and 2001
		Kitt Peak National Observatory Images


Neutron star (more in next chapter)
	Quantum rules also resist neutron packing
		Densities much higher than white dwarfs allowed
			R ~ 5 km r ~ 10¹⁴ gm/cm³ (similar to nucleus)
		M limit uncertain, ~2 or ~3 M_Sun before it collapses

	Spins very fast (by conservation of angular momentum)

	Trapped spinning magnetic field makes it:
		Act like a “lighthouse” beaming out E-M radiation (radio, light)
			pulsars
		Accelerates nearby charged particles


	Red: Ha

	Blue: “Synchrotron” emission from high speed electrons trapped in magnetic field


	Chapter 7: The Sun
		Atmospheric Structure
		Sunspots/Magnetic Phenomena
		Nuclear Fusion – proton-proton chain
		Solar Neutrino “Problem”


Chapter 8: The Properties of Stars
	Distances to Stars
		Parallax and Parsecs
		Spectroscopic Parallax
	Intrinsic Brightness: Luminosity
		Absolute Magnitude
	Luminosity, Radius, and Temperature
	Hertzsprung-Russell (H-R) Diagram
	Luminosity Classes (e.g., Main Sequence, giant)
	Masses of Stars
		Binary Stars and Kepler’s Law
		Mass-Luminosity Relationship


Ch. 9: The Formation & Structure of Stars
	Interstellar Medium
		Types of Nebulae (emission, reflection, dark)
	Interstellar Reddening from dust
	Star formation
	Protostar Evolution on H-R Diagram
	Fusion (CNO cycle, etc.)
	Pressure-Temperature “Thermostat”
	Stellar Structure (hydrostatic equilibrium, etc.)
	Convection, radiation, and opacity
	Stellar Lifetimes


	Ch. 10: The Deaths of Stars
		Evolution off the main sequence (=> giant)
		Star Cluster Evolution on H-R Diagram
		Degenerate Matter
		Planetary Nebulae and White Dwarfs
		Binary Star Evolution (Disks, Novae, etc.)
		Massive Star Evolution and Supernovae