Astro 1050 Fri. Mar. 5, 2004

Today: More Ch. 10: The Deaths of Stars

Homework #5

Extra Credit articles

Homework 5 solutions

Q1. 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 = mass/volume

Mass is the same, volume of sphere = 4/3 π R³

Radius increases by 20, R³ and the volume increases by 20³ = 8000, so density decreases by 8000

Q2. In an H-R Diagram, stars with the largest radius are found in the upper right of the diagram. (Fill in the blank.)

Q3. The lifetime of high temperature main sequence O and B stars is much shorter than the lifetime of low temperature K and M stars. (Fill in the blank.)

Homework 5 solutions

Q4. 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

Q5. If we discover a type 1a supernova in a distant galaxy that at its brightest has an apparent magnitude of 17, how far away is the galaxy? (Assume the supernova has an absolute magnitude of -19.)

d (pc) = 10 ^(m-M+5)/5 = 10^8.2 = 1.6x10⁸ pc x 1Mpc/10⁶pc = 160 Mpc

Q6. 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 5 solutions

Q7. Sunsets appear red for the same reason that some stars in space appear red -- they are both seen through dust particles. Why does this make them appear red? b. The dust scatters blue light more than red light, such that more of the red light passes directly though the dust.

Q8. What do we see in the Orion nebula that indicates it is a region of new star formation?
a. Hot O stars b. Herbig-Haro Objects c. Dust Disks around stars d. All of the Above e. None of the Above

Q9. The Pleadies is an open star cluster not too far from us. It also represents a textbook example of a type of nebula. Which type is it? C. A reflection nebula

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 (e.g. 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 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 runs out of fuel after converting core to Fe

Type I: White dwarf in binary, which receives mass from its companion (collapse ignites carbon burning).

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


	Today: More Ch. 10: The Deaths of Stars
	Homework #5
	Extra Credit articles


	Q1. 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 = mass/volume
		Mass is the same, volume of sphere = 4/3 π R³
		Radius increases by 20, R³ and the volume increases by 20³ = 8000, so density decreases by 8000

	Q2. In an H-R Diagram, stars with the largest radius are found in the upper right of the diagram. (Fill in the blank.)
	Q3. The lifetime of high temperature main sequence O and B stars is much shorter than the lifetime of low temperature K and M stars. (Fill in the blank.)


	Q4. 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

	Q5. If we discover a type 1a supernova in a distant galaxy that at its brightest has an apparent magnitude of 17, how far away is the galaxy? (Assume the supernova has an absolute magnitude of -19.)
			d (pc) = 10 ^(m-M+5)/5 = 10^8.2 = 1.6x10⁸ pc x 1Mpc/10⁶pc = 160 Mpc

	Q6. 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


	Q7. Sunsets appear red for the same reason that some stars in space appear red -- they are both seen through dust particles. Why does this make them appear red? b. The dust scatters blue light more than red light, such that more of the red light passes directly though the dust.
	Q8. What do we see in the Orion nebula that indicates it is a region of new star formation? a. Hot O stars b. Herbig-Haro Objects c. Dust Disks around stars d. All of the Above e. None of the Above
	Q9. The Pleadies is an open star cluster not too far from us. It also represents a textbook example of a type of nebula. Which type is it? C. A reflection nebula



	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 (e.g. 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 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 runs out of fuel after converting core to Fe
	Type I: White dwarf in binary, which receives mass from its companion (collapse ignites carbon burning).

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