Astro 1050     Fri. Oct. 25, 2002

   Today: Astronomy Articles

      Homework #7 review

      Chapter 10: The Deaths of Stars

               Review for Exam

Homework #7

Q1. We see the Crab Nebula is about 1.35 parsecs in radius and is expanding at a rate of 1400 km/s. Extrapolate backwards in time and estimate about when would the supernova creating the Crab Nebula have exploded?

Distance/rate/time problem so…

1.35 pc = 1400 km/s x time

Convert pc to km: 1pc = 3.09 x 10¹³ km

Time = (4.2x10¹³km)/(1400 km/s) = 3 x 10¹⁰ s

Convert to years: 31.5 million seconds in a year

Time = 950 years (if you don’t round get 920)

Homework #7

Q2. If the stars turning off the main sequence in the H-R diagram of a star cluster have masses of about 15 times solar, how old is the cluster?

The cluster will be about as old as the main sequence lifetime. Can use lifetime (as fraction of solar lifetime) = 1/M^2.5and get 1/1000 of the solar lifetime or look up in the table in the slides. 15 solar masses is about a B star which have lifetimes of around 10 million years.

Homework #7

Q3. The Ring Nebula has an angular diameter of 72 arcsec, and we estimate it is 5000 light years away. What is its linear diameter?

Linear diameter = 5000 ly x 72/206265

Linear diameter = 1.7 light years

An aside. Exansion rate is 15 km/s, so the age is approximately 34,000 years old.

Homework #7

Q4. If a type G star like the sun expands to become a giant star with a radius 20 times larger, by what factor will its density decrease?

Density is mass/volume.

Volume of a sphere is 4/3πr³.

If r increase by a factor of 20, volume increases by a factor of 20 cubed, or 8000. Mass remains the same, so density decreases by 8000 times.

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

Temperature, density, etc., with radius

Sunspots/Magnetic Phenomena

What are they? Why do they exist?

Nuclear Fusion – proton-proton chain

What is it? How does it produce energy?

Solar Neutrino “Problem”

What is it? Is it still a problem?

Review Chapters 7-10

Chapter 7: The Sun – example questions

Q. The fusion process in the sun, the "proton-proton" chain, requires high temperatures because:

c of the ground-state energy of the Hydrogen atom.

c of the presence of Helium atoms.

c the colliding protons need high energy to overcome the Coulomb barrier.

c of the need for low density.

c the neutrinos carry more energy away than the reaction produces.

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

Chapter 8: Properties of Stars--examples

True/False: The main determinant of the lifetimes of stars is their mass.

Q. A star’s luminosity depends only on the star’s:

c distance and diameter.

c temperature and distance.

c distance.

c temperature and diameter.

c apparent magnitude

Another version of the question\ can be made for apparent magnitude .

Short answer: What are two methods for determining the distance to a star?

Another version of the question can be made for masses.

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. 9: The Formation & Structure of Stars

Example questions

True/false: The sun makes most of its energy via the CNO cycle.

Short answer question: Explain what keeps the nuclear reactions in a star under control.

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

Review Chapters 7-10

Ch. 10: The Deaths of Stars—examples

Short answer: Describe the ultimate fate of stars as a function of their initial mass.

Q. Massive stars cannot generate energy through iron fusion because:

c iron fusion requires very high densities.

c stars contain very little iron.

c no star can get high enough for iron fusion.

c iron is the most tightly bound of all nuclei.

c massive stars go supernova before they create an iron core.


	Today: Astronomy Articles
	Homework #7 review
	Chapter 10: The Deaths of Stars
	Review for Exam


Q1. We see the Crab Nebula is about 1.35 parsecs in radius and is expanding at a rate of 1400 km/s. Extrapolate backwards in time and estimate about when would the supernova creating the Crab Nebula have exploded?
	Distance/rate/time problem so…
		1.35 pc = 1400 km/s x time
		Convert pc to km: 1pc = 3.09 x 10¹³ km
		Time = (4.2x10¹³km)/(1400 km/s) = 3 x 10¹⁰ s
		Convert to years: 31.5 million seconds in a year
		Time = 950 years (if you don’t round get 920)


	Q2. If the stars turning off the main sequence in the H-R diagram of a star cluster have masses of about 15 times solar, how old is the cluster?
		The cluster will be about as old as the main sequence lifetime. Can use lifetime (as fraction of solar lifetime) = 1/M^2.5and get 1/1000 of the solar lifetime or look up in the table in the slides. 15 solar masses is about a B star which have lifetimes of around 10 million years.


Q3. The Ring Nebula has an angular diameter of 72 arcsec, and we estimate it is 5000 light years away. What is its linear diameter?
	Linear diameter = 5000 ly x 72/206265
	Linear diameter = 1.7 light years

		An aside. Exansion rate is 15 km/s, so the age is approximately 34,000 years old.


	Q4. If a type G star like the sun expands to become a giant star with a radius 20 times larger, by what factor will its density decrease?
		Density is mass/volume.
		Volume of a sphere is 4/3πr³.
		If r increase by a factor of 20, volume increases by a factor of 20 cubed, or 8000. Mass remains the same, so density decreases by 8000 times.


	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
		Temperature, density, etc., with radius
	Sunspots/Magnetic Phenomena
		What are they? Why do they exist?
	Nuclear Fusion – proton-proton chain
		What is it? How does it produce energy?
	Solar Neutrino “Problem”
		What is it? Is it still a problem?


	Chapter 7: The Sun – example questions
	Q. The fusion process in the sun, the "proton-proton" chain, requires high temperatures because:
	c of the ground-state energy of the Hydrogen atom.
	c of the presence of Helium atoms.
	c the colliding protons need high energy to overcome the Coulomb barrier.
	c of the need for low density.
	c the neutrinos carry more energy away than the reaction produces.


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


	Chapter 8: Properties of Stars--examples
		True/False: The main determinant of the lifetimes of stars is their mass.

	Q. A star’s luminosity depends only on the star’s:
	c distance and diameter.
	c temperature and distance.
	c distance.
	c temperature and diameter.
	c apparent magnitude
		Another version of the question\ can be made for apparent magnitude .

	Short answer: What are two methods for determining the distance to a star?
		Another version of the question can be made for masses.


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. 9: The Formation & Structure of Stars
		Example questions

		True/false: The sun makes most of its energy via the CNO cycle.

		Short answer question: Explain what keeps the nuclear reactions in a star under control.


	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


	Ch. 10: The Deaths of Stars—examples
		Short answer: Describe the ultimate fate of stars as a function of their initial mass.

	Q. Massive stars cannot generate energy through iron fusion because:
	c iron fusion requires very high densities.
	c stars contain very little iron.
	c no star can get high enough for iron fusion.
	c iron is the most tightly bound of all nuclei.
	c massive stars go supernova before they create an iron core.