Chapter X: Stellar Evolution

a) Conditions for star formation

Cool --> temperature can't overwhelm gravity

Dense --> more self gravity

Cool and Dense --> Molecular clouds with dust are "stellar nurseries"

Dust serves as a "cooler" for the gas to make collapse possible
But: Need IR or radio to see through dust into star-forming regions

b) Start of the collapse

clouds need to be a little denser to collapse --> trigger

shock wave, for example from a supernova can push gas together

c) Role of dust in star formation:

As a cloud collapses it heats up (compression heats)

--> temperature resists gravity

--> it would stop collapsing

The dust can radiate the heat, keep cloud cool enough to continue collapsing

Trigger of Star Formation

2. Formation of the solar system

Conservation of angular momentum --> collapsing cloud rotates faster

--> it would stop collapsing

Þ most of angular momentum in planets

Still not enough Þ angular momentum problem

Loss of angular momentum -> solar wind

-> magnetic field

Both carry angular momentum away

Collapse of Rotating Cloud

3. Mature stars

A) Range of stars

Masses 0.1 to 60 solar masses

Luminosities 10^-3 to 10⁶ solar luminosities

Smaller --> not enough central pressure to ignite Fusion

Brown Dwarfs may contribute to dark matter in universe

Larger --> higher radiation pressure than gravity

Fly apart Eddington Limit of stars

B) Basic model of stars (like sun)

Interior: pressure, density, temperature increase inwards

but gravity balanced by pressure from hot (burning) core

maintains burn rate --> star's thermostat

More massive star --> higher central pressure --> hotter, denser -->

more fusion --> more luminosity --> fuel used faster --> shorter life

a) H core "burns" first = Main Sequence:

Star on main sequence for long time (lots of hydrogen)

Thermostat in Aging Stars

b) Core compression:

Pressure goes as (particles per volume) x temperature

Fusion removes particles with time

Þ Volume must decrease (compression)

--> temperature and density increase

--> more fusion Þ more luminosity

"Early Sun Paradox": the sun was much dimmer when life began

Possible answer(?): more carbon dioxide --> stronger greenhouse effect

--> helped keep early Earth warm

4. Aging of stars

a) He core (no fusion), H-"burning" shell

He core shrinks to maintain pressure and drags down overlying H

Overlying H starts "burning" on an overheated oven

Luminosity increases: --> red giant

Surface expands and cools --> red

H-R Diagram

b) Degenerate He core

Electrons can't be packed closer --> (huge) "Degeneracy Pressure"

rising temperature does not increase pressure

--> thermostat does not work --> He fuses in flash

then a lot of heat overcomes problem

c) He core fusion Þ C, O

Core expands and shell "burning" less important

Luminosity decreases --> Surface shrinks and warms up

d) C, O core

He core burnt out --> He shell burning (similar to 2a)

e) Heavy elements made up to Fe (Fowler: Nobel Prize)

But: Heavier than Fe requires energy

Fe nucleus + (something) --> more mass than sum of parts

Requires energy to be converted into mass; from gravity

f.) No more fuel

Radiation balanced by loss of gravitational energy

--> contraction --> hotter

But: only up to when the electrons cannot compressed any further

Degeneracy Pressure as under 2b

Tests of the star model

- Temp - luminosity relation (the HR diagram)

- Mass-luminosity relation

- Abundances of heavy elements

- Star Tracks (clusters = same age stars)

Star model in H-R Diagram

5. Star deaths

A) low mass stars

a) White Dwarf is their corpse

Electrons can't be packed too close together

--> "electron degeneracy" --> huge pressure

White Dwarf supported by electron degeneracy pressure

M < 1.4 M_sun (Chandrasekhar: Nobel Prize)

b) Mass loss

via stellar winds and/or

pulsed ejection --> planetary nebulae

--> recycling

Star reduces mass to 1.4 M_sun limit

B) Binary Stars

a) Novae:

an example of mass transfer in a binary star system

White Dwarf gains mass (Hydrogen) from other star

--> explosive (degeneracy) fusion on surface (high temp & pressure)

b) Type I Supernova

an example of mass transfer in a binary star system

White Dwarf + more mass --> shrinks --> hotter interior

Collapse when M >1.4 M_S

--> sudden flash of fusion (very rapid due to degeneracy)

--> White Dwarf explodes --> recycling

Type I Supernovae have all the same luminosity

--> excellent bright Standard Candle

C) High mass stars

a) Type II Supernova Process

Heavy star with degenerate iron core (no more fuel) (see 2f)

Fe core gains mass from overlying layers to > 1.4 M_sun

--> electron degeneracy pressure fails

--> collapse --> neutron star core or black hole core

'Rebound' of falling material on core and neutrinos from core

--> expulsion of outer 80% of star

Energy source = gravity

Type II Supernove Explosion

Lots of neutrinos from collapse (Neutrino flash observed from SN1987)

Theory --> Type II SN's come from massive supergiants

SN 1987: a massive supergiant disappeared

b) Consequences of SN

Remnants: - Expanding hot nebula

some only visible with X-ray telescopes, only now discovered

- High-energy electrons (cosmic rays)

- Neutron star or black hole

Importance of SN's:

i. Neutrino astronomy

1987 SN: neutrinos Þ proof of neutron star formation

neutrinos arrived before light --> action was in the star's core

all neutrinos arrived at same time --> upper limit on neutrino mass

ii. Make elements heavier than Fe:

Fe nucleus + (something) --> more mass than sum of parts

Requires energy to be converted into mass; from gravity

1987 SN: gamma rays from radioactive cobalt

--> proof of heavy element formation

iii. Recycling of material (we are made of 'star stuff')

iv. Produce shocks = denser, higher pressure gas

v. Shocks initiate star formation "Life Cycle of Stars"

Consequences of Supernova Explosion

Density increases --> more self-gravity

Solar system formation triggered??

vi. Shocks --> cosmic rays via repeated bounces off converging "mirrors"

like at shocks in the solar wind (see IX.1.)

c) End products

Neutron star when M > 1.4 M_sun

e + p + squeeze --> neutron + neutrino (most of SN energy)

stable by Neutron degeneracy pressure if M < 3(?) M_sun

1 sugarcube of Neutron star material = 1 billion tons (Mt. Washington)

Observation: Pulsars rapidly pulsating radio sources (Hewish: Nobel Prize)

--> Rotating neutron stars with strong magnetism

Analogy: a lighthouse

conservation of angular momentum --> rapid rotation after collapse

compression of magnetic lines --> strong magnetism

strong magnetism --> synchrotron radiation

Importance of pulsars:

i. Proves neutron stars exist

ii. Found in SN remnants: Proves Type II SN scenario

iii. Energize SN remnants (e.g. synchrotron from Crab Nebula)

Hypothesis: Rotational energy from the pulsar powers the Crab Nebula

Prediction: The pulsar should gradually rotate more slowly

Test: It slows down at just the right rate

iv. Tell us where SN's have occurred: Globular clusters have had

many SN's which may have ejected stars from the clusters

v. Precise clocks in space:

e.g. Doppler effect --> the "new planet" around a pulsar

e.g. used to study interstellar plasma

Detection of Pulsars

d) Binary X-ray sources:

Examples of mass transfer:

Mass from normal star onto compact object --> compression

--> enormous heating --> X-rays (and gamma rays)

Determine mass of neutron star (black hole) Kepler's 3rd Law

Compact object has 'right' mass to be a neutron star
- evidence for existence of neutron stars
Breakdown of "classical physics"

Very strong gravity on surface of Neutron star

escape velocity > 0.5 speed of light --> special considerations

D) Life of stars with different masses

Low mass (< 0.4 M_s) H burn White Dwarf

Medium mass (~ 0.4 - 3) H burn Red Giant Mass Loss White Dwarf

High mass (~ 3 - 8) H burn Red Giant Supernova Neutron Star

Very high mass (> 8) H burn Red Giant Supernova Black Hole?

Go to Chapter XI

Cool --> temperature can't overwhelm gravity
Dense --> more self gravity
Cool and Dense	--> Molecular clouds with dust are "stellar nurseries"

	clouds need to be a little denser to collapse	--> trigger
	shock wave, for example from a supernova can push gas together

Conservation of angular momentum	--> collapsing cloud rotates faster
	--> it would stop collapsing
	Þ most of angular momentum in planets
Still not enough	Þ angular momentum problem
Loss of angular momentum	-> solar wind
	-> magnetic field

	Masses			0.1		to	60	solar masses
	Luminosities			10^-3		to	10⁶	solar luminosities
Smaller					--> not enough central pressure to ignite Fusion
		Brown Dwarfs			may contribute to dark matter in universe
Larger					--> higher radiation pressure than gravity
			Fly apart		Eddington Limit of stars

Interior:	pressure, density, temperature increase inwards
	but gravity balanced by pressure from hot (burning) core
	maintains burn rate	--> star's thermostat

More massive star		--> higher central pressure		--> hotter, denser -->
	more fusion	--> more luminosity	--> fuel used faster --> shorter life

Pressure goes as		(particles per volume) x temperature
	Fusion removes particles with time
	Þ Volume must decrease (compression)
	--> temperature and density increase
	--> more fusion		Þ more luminosity

	Possible answer(?): more carbon dioxide	--> stronger greenhouse effect
		--> helped keep early Earth warm

	He core shrinks to maintain pressure and drags down overlying H
	Overlying H starts "burning" on an overheated oven
	Luminosity increases:	--> red giant
	Surface expands and cools	--> red

Electrons can't be packed closer		--> (huge) "Degeneracy Pressure"
	rising temperature does not increase pressure
--> thermostat does not work		--> He fuses in flash

e) Heavy elements made up to Fe				(Fowler: Nobel Prize)
	But:		Heavier than Fe requires energy
		Fe nucleus + (something)		--> more mass than sum of parts
		Requires energy to be converted into mass; from gravity

Radiation balanced by loss of gravitational energy
		--> contraction --> hotter
But:	only up to when the electrons cannot compressed any further
		Degeneracy Pressure as under 2b

	- Temp - luminosity relation (the HR diagram)
	- Mass-luminosity relation
	- Abundances of heavy elements
	- Star Tracks (clusters = same age stars)

	via stellar winds	and/or
	pulsed ejection	--> planetary nebulae
		--> recycling

		White Dwarf gains mass (Hydrogen) from other star
		--> explosive (degeneracy) fusion on surface (high temp & pressure)

an example of mass transfer in a binary star system
	White Dwarf + more mass --> shrinks --> hotter interior
Collapse when M >1.4 M_S
		--> sudden flash of fusion (very rapid due to degeneracy)
		--> White Dwarf explodes		--> recycling
Type I Supernovae have all the same luminosity
			--> excellent bright Standard Candle

Heavy star with degenerate iron core (no more fuel) (see 2f)
Fe core gains mass from overlying layers to > 1.4 M_sun
	--> electron degeneracy pressure fails
	--> collapse	--> neutron star core or black hole core
'Rebound' of falling material on core and neutrinos from core
	--> expulsion of outer 80% of star

	Theory	--> Type II SN's come from massive supergiants
		SN 1987:	a massive supergiant disappeared

Remnants:			- Expanding hot nebula
		some only visible with X-ray telescopes, only now discovered
		- High-energy electrons (cosmic rays)
		- Neutron star or black hole
Importance of SN's:

	i. Neutrino astronomy
		1987 SN: neutrinos		Þ proof of neutron star formation
		neutrinos arrived before light		--> action was in the star's core
all neutrinos arrived at same time				--> upper limit on neutrino mass

	ii. Make elements heavier than Fe:
		Fe nucleus + (something)		--> more mass than sum of parts
		Requires energy to be converted into mass; from gravity
		1987 SN: gamma rays from radioactive cobalt
				--> proof of heavy element formation

	iii. Recycling of material (we are made of 'star stuff')

	iv. Produce shocks = denser, higher pressure gas

	v. Shocks initiate star formation "Life Cycle of Stars"

Density increases		--> more self-gravity
	Solar system formation triggered??

vi. Shocks --> cosmic rays via repeated bounces off converging "mirrors"
	like at shocks in the solar wind (see IX.1.)

		e + p + squeeze	--> neutron + neutrino (most of SN energy)
		stable by Neutron degeneracy pressure if M < 3(?) M_sun
		1 sugarcube of Neutron star material = 1 billion tons (Mt. Washington)

Observation: Pulsars			rapidly pulsating radio sources (Hewish: Nobel Prize)
		--> Rotating neutron stars with strong magnetism
Analogy:		a lighthouse

	conservation of angular momentum			--> rapid rotation after collapse
	compression of magnetic lines			--> strong magnetism
	strong magnetism			--> synchrotron radiation

i. Proves neutron stars exist

ii. Found in SN remnants:				Proves Type II SN scenario

iii. Energize SN remnants (e.g. synchrotron from Crab Nebula)
	Hypothesis:	Rotational energy from the pulsar powers the Crab Nebula
	Prediction:	The pulsar should gradually rotate more slowly
	Test:	It slows down at just the right rate

iv. Tell us where SN's have occurred: Globular clusters have had
	many SN's which may have ejected stars from the clusters

v. Precise clocks in space:
	e.g. Doppler effect		--> the "new planet" around a pulsar
	e.g. used to study interstellar plasma

	Mass from normal star onto compact object		--> compression
		--> enormous heating	--> X-rays (and gamma rays)

Low mass (< 0.4 M_s)	H burn	White Dwarf
Medium mass (~ 0.4 - 3)	H burn	Red Giant	Mass Loss	White Dwarf
High mass (~ 3 - 8)	H burn	Red Giant	Supernova	Neutron Star
Very high mass (> 8)	H burn	Red Giant	Supernova	Black Hole?