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Neutron Stars and Black Holes

Jan 01, 2016

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Leo Wilson

Neutron Stars and Black Holes. Please press “1” to test your transmitter. The Death of a Massive Star. Neutron Stars. A supernova explosion of a M > 8 M sun star blows away its outer layers. The central core will collapse into a compact object of ~ a few M sun. The Chandrasekhar Limit. - PowerPoint PPT Presentation
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Page 1: Neutron Stars  and  Black Holes

Neutron Stars and

Black Holes

Please press “1” to test your transmitter.

Page 2: Neutron Stars  and  Black Holes

The Death of a Massive Star

Page 3: Neutron Stars  and  Black Holes

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.

Page 4: Neutron Stars  and  Black Holes

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.

Page 5: Neutron Stars  and  Black Holes

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

Page 6: Neutron Stars  and  Black Holes

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!!!

Page 7: Neutron Stars  and  Black Holes

Pulsars / Neutron stars

Cassiopeia A

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

Page 8: Neutron Stars  and  Black Holes

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

Page 9: Neutron Stars  and  Black Holes

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)

Page 10: Neutron Stars  and  Black Holes

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.

Page 11: Neutron Stars  and  Black Holes

Images of Pulsars and other Neutron Stars

The vela Pulsar moving through interstellar space

The Crab nebula and

pulsar

Page 12: Neutron Stars  and  Black Holes

The Crab Pulsar

Remnant of a supernova observed in A.D. 1054

Pulsar wind + jets

Page 13: Neutron Stars  and  Black Holes

The Crab Pulsar

Visible lightX-rays

Page 14: Neutron Stars  and  Black Holes

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.

Page 15: Neutron Stars  and  Black Holes

Neutron Stars in Binary Systems: X-ray binaries

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

Page 16: Neutron Stars  and  Black Holes

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!

Page 17: Neutron Stars  and  Black Holes

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.

Page 18: Neutron Stars  and  Black Holes

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

Page 19: Neutron Stars  and  Black Holes

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”

Page 20: Neutron Stars  and  Black Holes

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

(The actual radius of the Earth is 6380 km)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

1. 1.35 million km

2. 6380 km

3. 250 m

4. 0.9 cm

5. 12 nm

Page 21: Neutron Stars  and  Black Holes
Page 22: Neutron Stars  and  Black Holes

“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)

Page 23: Neutron Stars  and  Black Holes

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.

Page 24: Neutron Stars  and  Black Holes

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.

Page 25: Neutron Stars  and  Black Holes

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

Page 26: Neutron Stars  and  Black Holes

Falling into the Black Hole

Event Horizon

The Falling Observer’s View

“Spaghettification”

Page 27: Neutron Stars  and  Black Holes

General Relativity Effects Near Black Holes

Spatial distortion of light → gravitational lensing

Page 28: Neutron Stars  and  Black Holes

Deflection of Light by the Sun

Page 29: Neutron Stars  and  Black Holes

Deflection of Light by the Sun

Page 30: Neutron Stars  and  Black Holes

Einstein Cross

Page 31: Neutron Stars  and  Black Holes
Page 32: Neutron Stars  and  Black Holes

General Relativity Effects Near Black HolesGravitational Red Shift

Event Horizon

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

Page 33: Neutron Stars  and  Black Holes

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

same mass as the sun has now)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

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.

Page 34: Neutron Stars  and  Black Holes

A Myth about Black Holes

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

Page 35: Neutron Stars  and  Black Holes

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

Page 36: Neutron Stars  and  Black Holes

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!

Page 37: Neutron Stars  and  Black Holes

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