Astro 1050 Mon. Oct. 21, 2002

Today: Review HW#6

Finish Ch. 9: Formation & Structure

Start Chapter 10: The Deaths of Stars

Homework #6

Q1. The “Blade Runner Question.” A star that burns half the lifetime of the sun does not burn twice as bright. How bright (luminous) is it?

Lifetime in solar units = M^-2.5 (solar m)

0.5 = M^-2.5

M^2.5 = 2

M = (2)^1/2.5 = 2^0.4= 1.3 solar masses

L in solar units = M^3.5 (solar units)

Luminosity = (1.3)^3.5 = 2.6 solar

Homework #6

Q2. Spectroscopic parallax. (Apparent) magnitude = 5.4 for an O6 V star. How far away is it? First need to get an absolute magnitude. Can estimate it several ways (H-R diagrams, mass-luminosity relation). I used M = -5.6. So:

d (pc) = 10 ^(m-M+5)/5 = 10^3.2 = 1585 parsecs

Homework #6

Q3. Lava lamps display heat transport via CONVECTION.

Q4. EGGs in the Eagle Nebula are Evaporating Gaseous Globules.

Q5. Interstellar reddening occurs because dust preferentially scatters blue light, letting more of the red light through the cloud.

Lifetime on Main Sequence

L µ M^3.5T µ fuel / L = M/M^{3.5 =} M^-2.5

Example: M=2 M_Sun L = 11.3 L_SunT =1/5.7 T_Sun

Width of Main Sequence – and Stellar Aging

As star converts H to He you have more massive nuclei

Pressure related to number of nuclei

Gravity related to mass of nuclei

Pressure would tend to drop unless something else happens

Temperature must rise (slightly) to compensate

Luminosity must rise (slightly) as heat leaks out faster

Orion Nebula: A Star-Forming Region

Red light = Hydrogen emission

Blue light = reflection nebula

Dark lanes = dust

Astronomy Picture of the Day:
http://antwrp.gsfc.nasa.gov/apod

Protoplanetary Disks in the Orion Nebula

Dusty disk seen in silhouette

Central star visible at long wavelengths

Herbig-Haro objects: The angular momentum problem

As clouds try to collapse angular momentum makes them spin faster

A disk forms around the protostar

Material is ejected along the rotation axis

Herbig-Haro 34 in Orion

Jet along the axis visible as red

Lobes at each end where jets run into surrounding gas clouds

Motion of Herbig-Haro 34 in Orion

Can actually see the knots in the jet move with time

In time jets, UV photons, supernova, will disrupt the stellar nursery

Chapter 9 Summary

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

Chapter 10 – The Deaths of Stars

What happens when the hydrogen runs out?

Star once again tries to contract and heat up inside

What might stop this?

“Unusual” fusion energy sources Þ giant stars

Hydrogen shell fusion

Heavy element fusion

Degenerate electron pressure Þ white dwarfs

Loss of material from the star

Hydrogen Shell Burning

Fusion stops in core when hydrogen runs out

Star has core of He, but T too low for fusion there

Heat loss makes star contract, T goes up in interior

Before T in core reaches He ignition point --

Hydrogen above He core begins “shell burning”

Shell burning changes the rules for structure

Still need dense core to allow high T, P for fusion

But high T on outside of core puts too much energy into outer parts of star

Outer parts responds to input energy by
expanding and cooling

Star in effect separates into two parts

Hot dense core where energy generation takes place

Extended envelope which shields and insulates core

Expansion into a Red Giant

For 5 M_Sun “red giant”

Outer part swells to 75 R_Sun

Inner core still contains most of mass

Why is it red?
Two equivalent ways to answer:

Thick envelope insulates outside from hot core

L µ R² T⁴ and

L is not much greater (so far)

R² is »(75/3)²=25² = 625 times larger

T must decrease to compensate

HR Motion for other Mass Stars

For higher mass (already luminous) stars

Motion is more horizontal (to red)

Hard to increase luminosity above already very high levels

Motion in the HR Diagram

During H core burning (main sequence)

L increases slowly as He accumulates in the core (and T_Core increases)

During H shell burning

At first R increases, T decreases

L then increases slowly as more He accumulates in core (and T_Coreincreases)

Eventually He ignites in the core

During He core, H shell burning

Moving some of E generation back into core shrinks size (and so raises T_Surface)

Eventually He in core runs out
leaving a C, O core inside the He region

Core contracts and heats up till He ignites in shell outside C, O core

During He shell, H shell burning

At first R increases, T_Surface decreases

L increases as more C,O accumulate and T_Core continues to increase

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


	Today: Review HW#6
	Finish Ch. 9: Formation & Structure
	Start Chapter 10: The Deaths of Stars


	Q1. The “Blade Runner Question.” A star that burns half the lifetime of the sun does not burn twice as bright. How bright (luminous) is it?
	Lifetime in solar units = M^-2.5 (solar m)
	0.5 = M^-2.5
	M^2.5 = 2
	M = (2)^1/2.5 = 2^0.4= 1.3 solar masses
	L in solar units = M^3.5 (solar units)
	Luminosity = (1.3)^3.5 = 2.6 solar


	Q2. Spectroscopic parallax. (Apparent) magnitude = 5.4 for an O6 V star. How far away is it? First need to get an absolute magnitude. Can estimate it several ways (H-R diagrams, mass-luminosity relation). I used M = -5.6. So:
			d (pc) = 10 ^(m-M+5)/5 = 10^3.2 = 1585 parsecs


	Q3. Lava lamps display heat transport via CONVECTION.

	Q4. EGGs in the Eagle Nebula are Evaporating Gaseous Globules.

	Q5. Interstellar reddening occurs because dust preferentially scatters blue light, letting more of the red light through the cloud.


	L µ M^3.5T µ fuel / L = M/M^{3.5 =} M^-2.5
	Example: M=2 M_Sun L = 11.3 L_SunT =1/5.7 T_Sun


As star converts H to He you have more massive nuclei
	Pressure related to number of nuclei
	Gravity related to mass of nuclei
		Pressure would tend to drop unless something else happens
Temperature must rise (slightly) to compensate
Luminosity must rise (slightly) as heat leaks out faster


	Red light = Hydrogen emission
	Blue light = reflection nebula
	Dark lanes = dust

	Astronomy Picture of the Day: http://antwrp.gsfc.nasa.gov/apod



	Dusty disk seen in silhouette

	Central star visible at long wavelengths



	As clouds try to collapse angular momentum makes them spin faster
	A disk forms around the protostar
	Material is ejected along the rotation axis



	Jet along the axis visible as red

	Lobes at each end where jets run into surrounding gas clouds



	Can actually see the knots in the jet move with time

	In time jets, UV photons, supernova, will disrupt the stellar nursery



	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



What happens when the hydrogen runs out?
	Star once again tries to contract and heat up inside

What might stop this?
	“Unusual” fusion energy sources Þ giant stars
		Hydrogen shell fusion
		Heavy element fusion
	Degenerate electron pressure Þ white dwarfs
	Loss of material from the star



	Fusion stops in core when hydrogen runs out
		Star has core of He, but T too low for fusion there
	Heat loss makes star contract, T goes up in interior
	Before T in core reaches He ignition point --
	Hydrogen above He core begins “shell burning”

	Shell burning changes the rules for structure
		Still need dense core to allow high T, P for fusion
		But high T on outside of core puts too much energy into outer parts of star
		Outer parts responds to input energy by expanding and cooling

	Star in effect separates into two parts
		Hot dense core where energy generation takes place
		Extended envelope which shields and insulates core



For 5 M_Sun “red giant”
	Outer part swells to 75 R_Sun
	Inner core still contains most of mass

Why is it red? Two equivalent ways to answer:

	Thick envelope insulates outside from hot core

	L µ R² T⁴ and
		L is not much greater (so far)
		R² is »(75/3)²=25² = 625 times larger
		T must decrease to compensate



	For higher mass (already luminous) stars
		Motion is more horizontal (to red)

		Hard to increase luminosity above already very high levels



	During H core burning (main sequence)
		L increases slowly as He accumulates in the core (and T_Core increases)
	During H shell burning
		At first R increases, T decreases
		L then increases slowly as more He accumulates in core (and T_Coreincreases)
		Eventually He ignites in the core

	During He core, H shell burning
		Moving some of E generation back into core shrinks size (and so raises T_Surface)
		Eventually He in core runs out leaving a C, O core inside the He region
		Core contracts and heats up till He ignites in shell outside C, O core
	During He shell, H shell burning
		At first R increases, T_Surface decreases
		L increases as more C,O accumulate and T_Core continues to increase



	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)