Astro 1050 Mon. Mar. 8, 2004

Today: End Ch. 10: The Deaths of Stars

Start Ch. 11: Neutron Stars, Black Holes

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

Chapter 11: Neutron Stars and Black Holes
What happens to the collapsing core?

Neutron star

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

Another pic of the Crab, Pulsar

Why a “pulsar?”

“Lighthouse” Model for Pulsars

Another Neutron Star in a SNR

Other cool stuff about Neutron Stars

Novel Dragon’s Egg by Robert L. Forward

Short Story “Neutron Star” by Larry Niven

Binary Pulsars

Gamma Ray Bursts?

Pulsar Planets

Black Holes -- basics

Nothing can stop collapse after neutron pressure fails

Escape velocity from a surface at radius R:

As R shrinks (but M is fixed), V_escape gets larger and larger

At some point V_Escape= c (speed of light)

Happens at Schwarzschild radius:

Not even light can escape from within this radius

Examples:

The Schwarzschild Radius:

Mass in solar masses R_s (km)

10

3

2

1

0.000003 (Earth)

Examples:

The Schwarzschild Radius:

Mass in solar masses R_s (km)

10 30

3 9

2 6

1 3

0.000003 (Earth) 0.9 cm

Black Holes -- details

Remember – gravity is same as before, away from mass

Black holes do NOT necessarily pull all nearby material in

A planet orbiting a new black hole would just keep on orbiting as before (assuming the ejected material or radiated energy didn’t have an effect)

Any mass can potentially be made into a black hole – if you can compress it to a size smaller than R_S = 2GM/c²

1 M_Sun: 3.0 km 10⁶ M_Sun 3´10⁶ km 1 M_Earth 8.9 mm

Black Holes -- details

If you do make material fall into a black hole, material will be falling at close to the speed of light when it reaches R_S

If that falling gas collides with and heats other gas before it reaches R_S, then light from that hot material (outside R_S) can escape (important in quasars!).

Black Holes – detection

By definition – can’t see light from black hole itself

Can see large amounts of energy released by falling material just before it crosses R_S

Can see motion of nearby objects caused by gravity of black hole

Black Holes – detection

Example: Like White Dwarf accretion disk but w/ black hole instead

Gas from red giant companion spills over towards black hole

Gas spirals in toward black hole, through accretion disk

Gas will be much hotter because it falls further, to very small R_S

Gas will be moving at very high velocity

Much faster than with white dwarf since much closer (P² µ a³)

Signature of black hole: Very high energy release, very high velocity

We find MASSIVE black holes in centers of most galaxies

Cygnus X-1

More Cool Stuff About Black Holes

Time Dilation – originally “Frozen Stars”

Gravitational Redshift

Wicked Tidal Forces

Hawking Radiation


	Today: End Ch. 10: The Deaths of Stars
	Start Ch. 11: Neutron Stars, Black Holes


	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
	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


	Novel Dragon’s Egg by Robert L. Forward
	Short Story “Neutron Star” by Larry Niven

	Binary Pulsars
		Gamma Ray Bursts?
	Pulsar Planets


	Nothing can stop collapse after neutron pressure fails

	Escape velocity from a surface at radius R:

	As R shrinks (but M is fixed), V_escape gets larger and larger

	At some point V_Escape= c (speed of light)

		Happens at Schwarzschild radius:

		Not even light can escape from within this radius


The Schwarzschild Radius:
	Mass in solar masses R_s (km)
		10
		3
		2
		1
		0.000003 (Earth)


The Schwarzschild Radius:
	Mass in solar masses R_s (km)
		10 30
		3 9
		2 6
		1 3
		0.000003 (Earth) 0.9 cm



	Remember – gravity is same as before, away from mass
		Black holes do NOT necessarily pull all nearby material in
		A planet orbiting a new black hole would just keep on orbiting as before (assuming the ejected material or radiated energy didn’t have an effect)

	Any mass can potentially be made into a black hole – if you can compress it to a size smaller than R_S = 2GM/c²
		1 M_Sun: 3.0 km 10⁶ M_Sun 3´10⁶ km 1 M_Earth 8.9 mm




	If you do make material fall into a black hole, material will be falling at close to the speed of light when it reaches R_S
		If that falling gas collides with and heats other gas before it reaches R_S, then light from that hot material (outside R_S) can escape (important in quasars!).



	By definition – can’t see light from black hole itself

	Can see large amounts of energy released by falling material just before it crosses R_S

	Can see motion of nearby objects caused by gravity of black hole




Example: Like White Dwarf accretion disk but w/ black hole instead
	Gas from red giant companion spills over towards black hole
	Gas spirals in toward black hole, through accretion disk
		Gas will be much hotter because it falls further, to very small R_S
	Gas will be moving at very high velocity
		Much faster than with white dwarf since much closer (P² µ a³)

Signature of black hole: Very high energy release, very high velocity

We find MASSIVE black holes in centers of most galaxies


	Time Dilation – originally “Frozen Stars”

	Gravitational Redshift

	Wicked Tidal Forces

	Hawking Radiation