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0. Neutron Stars and Black Holes. Chapter 11:. 0. Neutron Stars. A supernova explosion of an M > 8 M sun star blows away its outer layers. P ressure becomes so high that electrons and protons combine to form stable neutrons throughout the object.

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Neutron Stars and Black Holes

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neutron stars


Neutron Stars

A supernova explosion of an M > 8 Msun star blows away its outer layers.

Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object.

The central core will collapse into a compact object of ~ a few Msun.

Typical size: R ~ 10 km

Mass: M ~ 1.4 – 3 Msun

Density: r ~ 1014 g/cm3

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

discovery of pulsars


Discovery of Pulsars

Angular momentum conservation

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

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

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

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

the crab pulsar


The Crab Pulsar

Pulsar wind + jets

Remnant of a supernova observed in A.D. 1054

the crab pulsar1


The Crab Pulsar

Visual image

X-ray image

the lighthouse model of pulsars


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


Images of Pulsars and other Neutron Stars

The Vela pulsar moving through interstellar space

The Crab Nebula and pulsar

the effects of pulsar winds


The Effects of Pulsar Winds

Pulsars blow off a constant stream (wind) of high-energy particles:

pulsar winds

proper motion of neutron stars


Proper Motion of Neutron Stars

Some neutron stars are moving rapidly through interstellar space.

This might be a result of anisotropies during the supernova explosion forming the neutron star.

binary pulsars


Binary Pulsars

Some pulsars form binaries with other neutron stars (or black holes)

Radial velocities resulting from the orbital motion lengthen the pulsar period when the pulsar is moving away from Earth

… and shorten the pulsar period when it is approaching Earth.


Neutron Stars in Binary Systems: X-ray binaries


Example: Her X-1

Star eclipses neutron star and accretion disk periodically

2 Msun (F-type) star

Neutron star

Orbital period = 1.7 days

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

compact objects with disks and jets


Compact Objects with Disks and Jets

Black holes and neutron stars can be part of a binary system.

Matter gets pulled off from the companion star, forming an accretion disk.

=> Strong X-ray source!

Heats up to a few million K.

the x ray burster 4u 1820 30


The X-Ray Burster 4U 1820-30

Several bursting X-ray sources have been observed:

Rapid outburst followed by gradual decay



pulsar planets


Pulsar Planets

Some pulsars have planets orbiting around them.

Just like in binary pulsars, this can be discovered through variations of the pulsar period.

As the planets orbit around the pulsar, they cause it to wobble around, resulting in slight changes of the observed pulsar period.

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!

escape velocity


Escape Velocity

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


Now, gravitational force decreases with distance (~ 1/d2) => Starting out high above the surface => lower escape velocity.


If you could compress Earth to a smaller radius => higher escape velocity from the surface.


the schwarzschild radius


The Schwarzschild Radius

=> There is a limiting radius where the escape velocity reaches the speed of light, c:



Vesc = c

Rs =


G = gravitational constant

M = mass

Rs is called the Schwarzschild radius.

schwarzschild radius and event horizon


Schwarzschild Radius and Event Horizon

No object can travel faster than the speed of light

=> 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”
black holes have no hair


“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:


angular momentum

(electric charge)

the gravitational field of a black hole


The Gravitational Field of a Black Hole

Gravitational Potential

Distance from central mass

The gravitational potential (and gravitational attraction force) at the Schwarzschild radius of a black hole becomes infinite.

general relativity effects near black holes


General Relativity Effects Near Black Holes

An astronaut descending down towards the event horizon of the black hole will be stretched vertically (tidal effects) and squeezed laterally.

general relativity effects near black holes ii


General Relativity Effects Near Black Holes (II)

Time dilation

Clocks starting at 12:00 at each point.

After 3 hours (for an observer far away from the black hole):

Clocks closer to the black hole run more slowly.

Time dilation becomes infinite at the event horizon.

Event horizon

general relativity effects near black holes iii


General Relativity Effects Near Black Holes (III)

gravitational redshift

All wavelengths of emissions from near the event horizon are stretched (redshifted).

 Frequencies are lowered.

Event horizon

observing black holes


Observing Black Holes

No light can escape a black hole

=> Black holes can not be observed directly.

If an invisible compact object is part of a binary, we can estimate its mass from the orbital period and radial velocity.

Mass > 3 Msun

=> Black hole!



Compact object with > 3 Msun must be a black hole!

jets of energy from compact objects


Jets of Energy from Compact Objects

Some X-ray binaries show jets perpendicular to the accretion disk

model of the x ray binary ss 433


Model of the X-Ray Binary SS 433

Optical spectrum shows spectral lines from material in the jet.

Two sets of lines: one blue-shifted, one red-shifted

Line systems shift back and forth across each other due to jet precession

gamma ray bursts grbs


Gamma-Ray Bursts (GRBs)

Short (~ a few s), bright bursts of gamma-rays

GRB of May 10, 1999: 1 day after the GRB

2 days after the GRB

Later discovered with X-ray and optical afterglows lasting several hours – a few days

Many have now been associated with host galaxies at large (cosmological) distances.

Probably related to the deaths of very massive (> 25 Msun) stars.