Neutron stars and black holes
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0. Neutron Stars and Black Holes. Why do we expect neutron stars exist? How do we know neutron stars exist? What theoretical arguments predict the existence of black holes? What evidence is there that black holes indeed exist?. Neutron stars: how do they form?. Neutron Stars:.

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Neutron Stars and Black Holes

Why do we expect neutron stars exist?

How do we know neutron stars exist?

What theoretical arguments predict the existence of black holes?

What evidence is there that black holes indeed exist?

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Neutron Stars:

If we pack electrons close enough together

 white dwarf (electron degenerate)

If we pack neutrons close enough together

 neutron star (neutron degenerate)

Q: Recall the Chandrasekhar limit (1.4 solar masses), what happens if the collapsing core is greater than this?

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Properties of neutron stars:

~ 10 km in radius

Density ~1014g/cm3

Between 1.4 and 3 Msun

Q: What happens when a NS becomes more massive than 3 Msun?

Spin rapidly


Strong magnetic field

Q: Why would we expect neutron stars to spin rapidly, be hot, and have strong magnetic fields?

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

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Internal structure of a neutron star:

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1967 Jocelyn Bell noticed pulses which repeated regularly in the sight line of a distant galaxy  first pulsar that was detected.

Periods range from ~ 0.030 to 3.75 seconds

Gradually slow down

Suppose it was a white dwarf of 12,000 km diameter emitting the pulse…

Since the near side is 12,000 km closer than the far side, the light from the near side would arrive ~0.04 s sooner than the light from the far side…

 The pulse would be smeared out over a longer interval.

Pulses last ~ 0.001 s

This places an upper limit on the size of the object emitting the pulse…

An object cannot change its brightness in an interval shorter than the time it takes light to travel its diameter.

 For a 0.001 s pulse interval, the diameter must be smaller than 300 km.

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The link between neutron stars and pulsars:

In 1968, astronomers discovered a pulsar in the Crab nebula.

The Crab Pulsar is roughly 25 km (~16 mi.) in diameter and rotates ~ 30 times/second!

It’s slowing in its rotation by 38 nanoseconds/day due to energy loss by the pulsar wind.

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Theoretical model of a pulsar:

Pulsars do not pulse, but rather emit beams of radiation that sweep around the sky as the neutron star rotates

Strong magnetic and electric fields are likely the cause of the intense beams of radiation

Note that we only can see the pulsars whose beams sweep over Earth.

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The evolution of pulsars:

Q: the Crab pulsar is slowing down in its rotation by 38 nanoseconds/day… why?

Pulsars lose energy as they emit beams of radiation and the pulsar wind (high-speed atomic particles)

Q: Where, ultimately, does this energy come from?

 The energy of rotation! (That’s why they slow down)

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Roaming pulsars: Some pulsars appear to be moving at a high speed through space…

pulsar B1508+55 path 1000km/s

Q: What could explain these strange motions of pulsars that are observed?

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Compact Objects with Disks and Jets – x-rays:

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

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

Binary pulsars allow us to measure the mass and all the other good things we get from binaries…

 Looking for x-ray sources is one way to detect neutron stars (and black holes…).

Heats up to a few million K.

=> Strong X-ray source!

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Binary pulsars:

In 1974, Taylor and Hulse detected the first binary pulsar (PSR1913+16);

The pulses were changing, growing longer, and then shorter over a period of 7.75 hours

From Doppler shifts, the orbital velocities and masses were calculated…

and it turned out that this system was two neutron stars orbiting each other with a separation of roughly the radius of our sun!

PSR1913+16 held another surprise…

In 1916 Einstein predicted that a rapid change in a gravitational field should spread out like waves (gravitational radiation)

Taylor and Hulse were able to show that the orbital period was decreasing because the stars were spiraling toward each other.

They won the Nobel prize in 1993.

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Neutron Stars in Binary Systems: X-ray binaries – Her X-1:


Star eclipses the neutron star and accretion disk every 1.7 days hiding the x-ray pulses for a few hours

Her X-1

Pulses every 1.2 seconds

2 Msun (F-type) star

Orbital period = 1.7 days

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

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Masses of pulsars:

From Doppler shifts, astronomers have estimated the masses of dozens of binary pulsars.

Typical masses are ~ 1.35 solar masses.

Q: If the core must be at least 1.4 solar masses to form a NS, then how could the typical mass of a NS be 1.35?

A: A NS of slightly less than 1.4 solar masses can exist if the NS loses mass. Also, a 1.4 solar mass WD produces a 1.2 solar mass NS. Some of the mass is converted into binding energy.

The gravitational fields near neutron stars are so strong, that a marshmallow dropped onto a neutron star from a distance of 1AU would release the equivalent energy of a 3 Mt nuclear bomb! (~231 Hiroshima-sized bombs!)

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X-ray bursters:

  • Matter flows onto the NS where it accumulates until it becomes hot and dense enough to ignite

  • The result is a burst of x-rays

  • “x-ray burster”

    Notice the similarity between this and the mechanism which generates novae….

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This is possibly the result of a collision of a neutron star and a giant…

the NS then went into orbit inside the giant!


The X-Ray Burster 4U 1820-30

This is a neutron star orbiting a white dwarf

The period is only 11 minutes!

 The separation is only about a third of the Earth/moon distance!



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The fastest pulsars: and a giant…

The fastest pulsars go by the name “millisecond pulsars.”

Why are they so fast?

What happens to them when they rotate so fast?

Since the pulse period of the pulsar is the rotation period, these fast pulsars are probably flattened like pancakes!

Take PSR1937+21;

Assume it is 10 km in radius…

Spinning at 642 times a second, the period is 0.0016 seconds and the equatorial velocity is about 40,000 km/s!

Q: Would you expect a pulsar that pulses rapidly to be young or old?

Due to the gradual slowing of the rotation, one would expect young pulsars to blink rapidly and old pulsars to blink slowly, but…

A few that blink the fastest may be quite old….

One of the fastest (PSR1937+21) pulses 642 times a second!

The energy contained in the rotation of this pulsar is comparable to the total energy of a supernovae explosion!

Q: How could this be?

To explain this, it appears that this pulsar was sped up by accreting matter from a binary companion.

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0 and a giant…

Pulsar Planets:

Small Doppler shifts were observed in the spectra of PSR1257+12

Analysis revealed that this pulsar was orbited by at least two planets with masses roughly 4.3 and 3.9 Earth masses!

Further analysis revealed a third planet with a mass of about that of our moon!

And there is evidence that a fourth planet about 100 Earth masses orbits this pulsar with a much larger separation.

Q: How can a NS have planets?!? (Recall that NS are created by supernovae, and a giant star about to explode would envelop any planets within an AU or two…)

As a planet orbits around a pulsar, the planet causes it to wobble around, resulting in slight changes of the observed pulsar period.

These planets are probably the remains of a stellar companion that was devoured by the NS.

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0 and a giant…

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!

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Escape Velocity:

  • Escape velocity depends on two things;

  • Mass

  • Distance from CoM


Velocity needed to escape Earth’s gravity from the surface: ≈ 11.6 km/s (~25,000 mph).


  • Gravitational force decreases with distance (~ 1/r2)

  • Starting out high above the surface lower escape velocity.


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

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0 and a giant…

The Schwarzschild Radius:

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



Rs =


G = gravitational constant

Vesc = c

M = mass

Rs is called the Schwarzschild radius.

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0 and a giant…

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”

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0 and a giant…

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0 and a giant…

“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)

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0 and a giant…

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.

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General Relativity Effects Near Black Holes (II):

Time dilation

In SR:

In GR:

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

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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

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Observing Black Holes:

No light can escape a black hole

=> Black holes can not be observed directly.

But… 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!

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0 and a giant…

A compact object with > 3 Msun must be black hole!

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Jets of Energy from Compact Objects:

Your impression of a black hole might suggest that it’s impossible to get energy out of such an object.

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

These bipolar flows are formed the same way as they do for protostars.

(Bipolar flow - angular momentum  hot accretion disk  high-energy photons emitted  shot out via thermal & magnetic processes.

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Opposing jets of gas are streaming away from a supermassive black hole at Centaurus A´s galactic nucleus - remnants of a giant explosion.

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0 black hole at Centaurus A´s galactic nucleus - remnants of a giant explosion.

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 to near ¼ c (it’s receding and approaching!)

Lines shift back and forth across each other every 164 days due to jet precession

SS 433 is most likely a black hole!

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In 1963, a nuclear test ban treaty was signed – nuclear weapons tests were off limits…

In 1968, the U.S. had satellites designed to detect gamma rays – signs of a nuclear detonation…

Those satellites started detecting bursts of gamma rays at a rate of about one burst a day…

That data became declassified in 1973.

The bursts usually lasted only a matter of seconds…

They came from all directions of the sky and not from any particular region…

They occur without warning…

And they have more power than the most violent supernovae explosions….

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0 weapons tests were off limits…

Gamma-Ray Bursts (GRBs):

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

2 days after the GRB

Some of these GRBs repeat – known as “soft gamma-ray repeaters,” “soft” = low energy gamma rays.

We suspect that these originate from neutron stars with really strong magnetic fields (“magnetars”).

When shifts in the magnetic field breaks through the crust of a magnetar, bursts of gamma rays are emitted.

On August 27, 1998, one of these ionized Earth’s atmosphere and disrupted radio communications worldwide.

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0 weapons tests were off limits…

Gamma-Ray Bursts (GRBs) II:

Possible origins:

Could be the result of the merger of two neutron stars (recall the binary pulsar PSR1913+16 detected by Taylor and Hulse.)

and/or from the collapse of really massive stars (>25 solar masses) - “hypernovae”

  • March 29, 2003 GRB in Leo…

  • Left behind a spectrum which resembled that of a SN

  • Hypernovae are indeed responsible for some GRBs

    But the NS merger is not ruled out….

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GRBs III: weapons tests were off limits…

If a GRB occurred only 1,600 ly from Earth, we would be showered with the radiation equivalent to a 10,000 Mt nuclear blast!

Possibly every few hundred million years one could occur near enough to Earth for us to be affected.

Possibly one of these caused one of the mass extinctions that show up in the fossil record…

Q: How could something which seems so rare as a neutron star merger, be so common that we detect at least one of these GRBs every day?