Neutron Stars and

Black Holes

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The Death of a Massive Star

Neutron Stars

A supernova explosion of a M > 8 Msun star blows away its outer layers. The central core will collapse

into a compact object of ~ a few Msun.

The Chandrasekhar LimitCan such a remnant of a few Msun be a white dwarf?

The more massive a white dwarf is, the smaller it is (radius decreases as mass increases)!

There is a limit of

1.4 Msun,

beyond which white dwarfs can

not exist:

Chandrasekhar Limit.

Formation of Neutron Stars

Compact objects more massive than the Chandrasekhar Limit (1.4 Msun) collapse beyond the

degenerate (white dwarf) state.

→ Pressure becomes so high that electrons and

protons combine to form stable neutrons throughout

the object:

p + e- → n + e

→ Neutron Star

Properties of Neutron Stars

Typical size: R ~ 10 km

Mass: M ~ 1.4 – 3 Msun

Density: ~ 1014 g/cm3

→ Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!

Pulsars / Neutron stars

Cassiopeia A

Neutron star surface has a temperature of ~ 1 million K.

Considering the typical surface temperature of a neutron star, they should be observable preferentially in which wavelength range?

1. radio

2. infrared

3. optical

4. ultraviolet

5. X-ray

Pulsars

=> Collapsing stellar core spins up to periods of ~ a few milliseconds.

Angular momentum conservation

=> Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars

Magnetic fields are amplified up to B ~ 109 – 1015 G.

(up to 1012 times the average magnetic field of the sun)

The Lighthouse Model of Pulsars

A Pulsar’s magnetic field has a dipole

structure, just like Earth.

Radiation is emitted

mostly along the magnetic

poles.

Images of Pulsars and other Neutron Stars

The vela Pulsar moving through interstellar space

The Crab nebula and

pulsar

The Crab Pulsar

Remnant of a supernova observed in A.D. 1054

Pulsar wind + jets

The Crab Pulsar

Visible lightX-rays

Which one of the following is a phenomenon through which white

dwarfs could be (indirectly) observed?

1. Supernova remnants

2. Globules

3. Pulsars.

4. X-ray binaries.

5. Solar eclipses.

Neutron Stars in Binary Systems: X-ray binaries

Accretion disk material heats to several million K => X-ray emission

Black Holes

Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass limit for neutron stars:

Neutron stars can not exist with masses > 3 Msun

We know of no mechanism to halt the collapse of a compact object with > 3 Msun.

It will collapse into a single point – a singularity:

=> A Black Hole!

The Concept of Black HolesEscape Velocity

Velocity needed to escape Earth’s gravity from the surface: vesc ≈ 11.6 km/s.

vesc

Ggravitational force decreases with distance (~ 1/d2) => lower escape velocity when starting at larger distance.

vesc

vesc

Compress Earth to a smaller radius => higher escape

velocity from the surface.

The Concept of Black HolesSchwarzschild Radius

=> limiting radius where the escape velocity reaches the speed of light:

Ves

c =

c

The Schwarzschild Radius, Rs

(Event Horizon)

Rs = 2GM ____ c2

G = Universal const. of gravity

M = Mass

Schwarzschild Radius and Event Horizon

Nothing (not even light) can escape from inside

the Schwarzschild radius

We have no way of finding out what’s

happening inside the Schwarzschild radius

“Event horizon”

Take a guess: How large is the Schwarzschild radius of the Earth?

(The actual radius of the Earth is 6380 km)

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1. 1.35 million km

2. 6380 km

3. 250 m

4. 0.9 cm

5. 12 nm

“Black Holes Have No Hair”Matter forming a black hole is losing

almost all of its properties.

Black Holes are completely determined by 3 quantities:

Mass

Angular Momentum

(Electric Charge)

General Relativity Effects Near Black Holes

Time dilation

Event Horizon

Clocks closer to the BH run more slowly.

Time dilation becomes infinite at the event horizon.

For how long would we – in principle – receive signals from a space probe that we are sending into a black hole (if there were no limit to how faint the signals are that it is sending back to us)? Assume

that the free-fall time to reach the event horizon (without GR effects) is 1 hr.

Event Horizon

c) 1 hr

b) More than 0, but less than 1 hr

d) Several hours

e) Forever

a) No time at all.

Falling into the Black Hole

Event Horizon

=> You will never actually see something “falling into the Black Hole”

(i.e., crossing the Event Horizon)!

The Distant Observer’s View

Falling into the Black Hole

Event Horizon

The Falling Observer’s View

“Spaghettification”

General Relativity Effects Near Black Holes

Spatial distortion of light → gravitational lensing

Deflection of Light by the Sun

Deflection of Light by the Sun

Einstein Cross

General Relativity Effects Near Black HolesGravitational Red Shift

Event Horizon

Wavelengths of light emitted from near the event horizon are stretched (red shifted).

What would happen to the Earth if the sun suddenly turned into a black hole (of the

same mass as the sun has now)

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1. It would be sucked into the black hole.

2. Its orbit around the black hole would be exactly the same as around the sun now.

3. It would be ejected from the solar system.

A Myth about Black Holes

Far away from the black hole, gravity is exactly the same as for the uncollapsed mass!

Getting Too Close to a Black Hole

Rs

3 Rs

There is no stable orbit within 3 Schwarzschild radii from the black hole.

Rs = Schwarzschild Radius

Observing Black HolesNo light can escape a black hole

=> Black holes can not be observed directly.

Black hole or Neutron Star in a binary system

Wobbling motion

Mass estimate

Mass > 3 Msun

=> Black hole!

Black Hole X-Ray Binaries

Strong X-ray sources

Rapidly, erratically variable (with flickering on time scales of less than a second)

Sometimes: Radio-emitting jets

Accretion disks around black holes