Neutron Stars

There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.

One of the biggest challenges we face in "wrapping our heads" around ideas in astronomy is the problem of scale. In earlier chapters you began to appreciate the enormity of the universe and found that our "earth-sized" scale for measuring distance is completely inadequate. Similarly, masses are beyond anything we can really intuitively understand. Neutron Stars present us with yet another challenge and also introduce us to an object whose density is unlike anything we have direct experience with.


Star Collapse - the "Big Squeeze"

In the previous chapter you encountered two types of supernovae. Both are triggered by the collapse of a star. In the case of the Type I supernovae it is very likely that the entire star is destroyed. When a Type II progenitor star collapses a rather remarkable thing occurs. As the star collapses its core density ramps up by orders of magnitude. When the density of the gas reaches about 1010 g/cm3 the electrons and protons are literally squeezed together to produce neutrons. By the time the star reaches a density of 1014 g/cm3 the interior consists of 80% neutrons in a degenerate neutron gas. The core stiffens dramatically and rapidly imploding material from above now collides with the core and rebounds. This is the "core bounce" phase and is what produces the outward shock wave that disrupts the star and spews its outer envelope back into space. At the same time the bounce compress the core even more. If the star is light enough it will reach a new configuration. It has become a Neutron Star.

Summary of Neutron Star Characteristics

  • Mass 1 - 2 Mo
  • Diameter about 15 km: As figure 11.1 depicts, a neutron star is about the size of a large Canadian city.
  • So dense that a sugar cube of neutron star mass would have a mass greater than all of humanity!
  • Core degenerate neutron gas surrounded by a crystalline mantle
  • Atmosphere is only a few tens of centimeters thick. It is still clear what the composition is likely a very dense mixture of helium and heavier elements. The surface temperature would be millions of degrees Kelvin
  Figure 11.1 A "typical" neutron star would fit comfortably within a city like Edmonton

Example 11.1 Estimate the density of a neutron star. Does the claim that a sugar cube of "neutron star stuff" would weigh more than all of humanity make sense?

Solution: Recall that density is just the ratio of the mass divided by the volume. Apply this to a neutron star:

and use the following values:

  • mass = 1 Mo = 2 x 1030 kg = 2 x 1033 g
  • radius = 15 km/2 = 7.5 km = 7.5 x 105 cm

A typical sugar cube is 1cm on a side so it has a volume of 1 cm3. From the calculation just performed you would conclude that a "neutron star sugar cube" would have a mass of 1.1 x 1015 g = 1.1 x 1012 kg. Assume that the average mass of a human is 75 kg, then our "neutron cube" would contain the equivalent mass of

The claim makes sense!


Evidence for Neutron Stars

No direct observations of Neutron stars exist. Their existence is inferred. The two best candidate phenomena are:
  • Pulsars
  • X-ray bursters.

Pulsars and "LGM's"

In 1967 Jocelyn Bell (while a PhD student at Cambridge) was monitoring the "twinkling" of objects at radio wavelengths. During her survey she found an object that was pulsing with a burst of radio waves precisely once every 1.33730113 seconds! This was astonishing for at least two different reasons:
  • it was very fast
  • it was very regular
Maybe it was a distant civilization beaming out into the universe - announcing "We're Here!". Maybe it was Little Green Men (LGM's)! Such suggestions appeared in the press for several months after the discovery was announced. We now have a simpler explanation.

Beacons in the Night

By 1974 the pieces in the Pulsar puzzle had begun to fall into place. The now accepted model of a Pulsar arises from several key factors:
  1. The compact neutron star core left behind in a supernova explosion should be spinning very rapidly ("figure skater" effect) - this is an example of the conservation of angular momentum.
  2. Any residual magnetic field in the neutron star will be intensified enormously by the contraction to such as small size. A star like our sun has a weak magnetic field. This field would be magnified by roughly a factor of 1015 (1000-trillion times!).
  3. the interaction of the intense, rapidly rotating magnetic field will produce a particle beam of electrons accelerated outward, along the magnetic axis. These will emit electromagnetic waves (synchrotron process) and a beam of radiation will sweep across space. This is called the "searchlight" effect.

  Figure 11.2 Artist's depiction of the "search light" or beacon produced by a rapidly rotating neutron star. Image courtesy NASA

Listen in On a Pulsar!

.As the particle beam of the pulsar sweeps across your line of sight you will receive a burst of electromagnetic energy. If a radio telescope intercepts this it will record a strong radio signal or "blip". The following sound clips and text are used with the kind permission of the The Princeton Pulsar Group

PSR 0329+54 is among the strongest known pulsars, and was one of the first discovered. It has a pulse period of about 0.715 seconds. click to play
PSR 0833-45 is in the Vela supernova remnant. It is much faster, with a period of 89.3 milliseconds. click to play
PSR 1937+21 is one of the fastest known pulsars, and was the first millisecond pulsar discovered. It spins on its axis every 1.56 milliseconds, or over 640 times per second. ("Faster than a kitchen blender!") click to play

Listening to a pulsar tells us that whatever produces the pulsar must be very small. Figure 11.3 shows a small set of pulse profiles for the sound you hear if you click on the sound clip for PSR 1937+21. This is just a graph showing how the signal received from the pulsar changes in time. Each "bump" represents the pulsar particle beam sweeping past our line of sight. and only takes 0.0016 ("sixteen milliseconds") to occur. A very important and simple principle in astronomy is that the time it takes an object to vary in brightness sets an upper limit on its

Figure 11.3 Pulse profiles for PSR 1937+21


possible size. This is because even though light travels very fast it still takes a small amount of time to traverse the object that is emitting the light. In the case of the pulsar, as the beam sweeps by, the light (or radio wave) from the point farthest from us arrives a little bit later than the light emitted nearest us. This smears out the profile. We can summarize this in the following "rule of thumb":

Upper limit on diameter = (Speed of Light) X (Length of Time of Variation in Light)

Example 11.2 Explain why we know that the Pulsar PSR 1937+21 cannot be a white dwarf.

Solution: If you use the "Light travel time rule of thumb" then it is possible to place an upper limit on the possible size of the object PSR 1937+21. Figure 11.3 shows that a pulse from this object last 0.0016 s. If we multiply this by the speed of light we get:

Upper limit = (300 000 km/s)(0.0016 s) = 480 km

The object PSR 1937+21 cannot be more than 480 km across which is about an order of magnitude smaller than the smallest possible white dwarf.

Starquakes and Spinning-Down Pulsars

By the 1980's observations were revealing that - as regular as pulsars are - pulsars:
  • undergo sudden changes in period or
  • show a slow but steady lengthening of period.
Both of these ideas are consistent with our model of what a pulsar is.

The Crab Nebula Pulsars and the "Supernovae-Produce-Neutron- Stars" Link

For decades the crab nebula - the magnificent supernova remnant of the 1054 AD event posed a puzzle. Why, after 900 years was the nebula as bright as it was? Where was the energy source that could cause the nebula to glow as brightly as it does? The discovery of a pulsar in the centre of the nebula, and especially the discovery that the period of the pulsar was slowly lengthening provided the answer. Figure 11.4 shows the pulsar in the centre of the crab nebula. High speed imagery taken with the 4 m Mayall telescope at Kitt Peak National Observatory, Arizona shows the pulsar blinking on and off 30 times per second.

As the particle beam produced by the intense magnetic field of the pulsar sweeps through the nebula it is able to transfer some of the rotational energy of the rapidly spinning neutron star to the gases in the nebula. This in turn heats the gas and supplies it with the energy needed to make the nebula glow. Figures 11.5a, b show movie clips of this process. The pulsar particle beam is visible as a faint jet in Figure 11.4b.

Figure 11.4 SN1054 remnant - the "Crab Nebula" with images of the pulsar "blinking on and off" shown as insets. Image courtesy of NOAO  


Figure 11.5a Visible light movie clip taken by Hubble showing the creation of outwardly moving wavefronts created by the spinning pulsar. To re-run video just double-click on image.

Credit: NASA/HST/ASU/J.Hester et al.

Figure 11.5b X-ray movie of the same region produced by combining 7 separate images from the Chandra space telescope.

Credit: NASA/CXC/ASU/J.Hester et al.


X-ray Bursters, Binary Pulsars and Accretion onto a Compact Source

In the mid 1960's the first x-ray telescopes were launched, for brief moments, into the upper atmosphere. Already then curious x-ray emissions were detected. Today we have orbiting x-ray telescopes that routinely detect brilliant bursts of x-rays. One of the best candidates for x-ray bursters and indirect evidence for neutron stars comes in the following scenario:
If a binary star system consists of a large, distended giant and a compact neutron star then interesting things can happen! If the giant star swells enough (to overflow its Roche Lobe) then it can transfer mass onto the neutron star. As the gas funnels and swirls into the compact companion star it heats up by a remarkable amount and forms a very hot disk around the neutron star. This is illustrated in Figure 11.6. The accretion disk can emit a wide range of wavelengths including x-rays. Occasionally matter will leak from the accretion disk down onto the surface of the neutron star. When this happens an astounding amount of energy is released. To understand this you must consider that the neutron star has a mass comparable to an ordinary star but is "squeezed" into an sphere no larger across than a modern large city! The intensity of the gravitational field is enormous! As just a small amount of matter hits the neutron star the energy released comes as an intense burst of x-rays or gamma rays. Most are absorbed by the accretion disk which shuts off further mass transfer for a while. Some x-rays, however, escape and can be detected by orbiting x-ray and gamma ray telescopes as intense bursts of energy. During the span of just a few seconds an x-ray burster will emit in x-rays the energy equivalent of the Sun's entire energy production in all wavelengths for a week!
  Figure 11.6 A red giant -neutron star (pulsar) and accretion disk.

Millisecond pulsars

Nearly two thousand pulsars have been catalogued since Jocelyn Bell's original discovery. Many pulsars are members of x-ray binary systems and many have been found, as expected, in supernova remnants. One of the most intriguing discoveries came with the discovery of very old and rapidly rotating pulsars. The pulsar PSR 1937+21 spins 640 times each second and was the first example of a millisecond pulsar. We know that these objects are very old because some have been discovered in globular clusters, which are objects in which star formation has not occurred for billions of years.

Example 11.3 Explain why it is surprising to find a very old pulsar spinning very rapidly.

Solution: The youngest know pulsar is the pulsar in the Crab Nebula which rotates approximately 30 times each second. By contrast, the very old pulsar PSR 1937+21 rotates more than 20 faster than this at 640 times each second. This is peculiar since we believe that it is the gradual slow-down of the pulsar that is the energy source that causes supernovae remnants like the crab nebula to glow as brightly as they do. There must be some mechanism that can cause an ancient pulsar to spin-up.

The solution of the millisecond pulsar "riddle" is mass transfer! There is very good evidence that millisecond pulsars are members of binary systems and the currently accepted explanation is that as matter accretes on the pulsar it gains angular momentum and hence "spins up". The fact that millisecond pulsars have rotation rates more than 20 times those of very young pulsars suggests that it must be a process that occurs after the initial formation of the neutron star - pulsar.

Binary Pulsars and Gravitational Waves

Occasionally both stars in a binary system evolve to become neutron stars and pulsars. When this happens astronomers have the rare opportunity to investigate one of the more subtle predictions of Einstein's theory of gravity (his General Theory of Relativity). Einstein's theory predicts that as masses move they create tiny ripples in the actual structure of space and time. As you walk across the room or lift your arm you are, in principle, creating gravitational waves and the result is analogous to what happens when you wiggle your toe in a pond and watch ripples spreading outward. Normally these gravitational waves are far too weak to detect. However, if a pair of neutron stars orbit each other then the ripples creating in space-time are significant and represent a way in which the stars can lose orbital energy. If that's the case then the stars' orbits should decay - their periods should decrease and the stars should spiral toward each other. Has this been observed? Yes! The binary pulsar PSR 1913+16 was discovered in 1974 and is doing precisely this. The orbit shrinks by about 3 mm each time the stars orbit and at this rate it is believed that the stars will collapse onto each other in about 300 million years.


  1. Explain in your own words the connection between neutron stars and pulsars. Are all neutron stars pulsars?
  2. Why is it reasonable to try to detect pulsars in supernova remnants?
  3. Even though we think that the surface temperatures of neutron stars must be millions of degrees Kelvin they are extremely faint - why is this?
  4. Explain how pulsars can provide the energy needed to cause supernova remnants to glow. What observational evidence can you offer to support this idea?
  5. What is the "searchlight model" for pulsars?
  6. Why was the discovery of pulsars so important in our understanding of stellar evolution?




To understand the formation and behaviour of neutron stars

Chp 14.1



















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The fastest know pulsar is PSR J1748-2446ad which spins at a dizzying 716 times each second. This pulsar was discovered by Jason Hessels of McGill University