Lecture 19: Neutron Stars



End points of stellar evolution

Starting Mass Outcome Final Mass Final Size Density
> 20 MSun Black Hole any 2.95 (M/MSun) km N/A
8 < M < 20 MSun Neutron star < 3-4 MSun 10 &minus 20 km ( &darr M ) 1018 kg/m3
0.4 < M < 8 MSun White Dwarfs (Carbon) < 1.4 MSun 7000 km ( &darr M ) 109 kg/m3
0.08 < M < 0.4 MSun White Dwarfs (Helium) 0.08 < M < 0.4 MSun 14000 km ( &darr M )
M < 0.08 MSun Brown Dwarfs M < 0.08 MSun 105 km

Birth of a Neutron Star

  • The death of a high-mass star (such as Betelgeuse) will leave behind a neutron star.
  • Initially, the neutron star will be very hot, about 1011 K.
  • It will glow mainly in the X-ray part of the spectrum.
  • Over its first few hundred years of life, the neutron star's surface cools down to 106 K and continues to glow in the x-ray.
  • Young neutron stars are found in supernova remnants.

X-ray Image of the Puppis A Supernova Remnant

  • The small point-source is a neutron star.
  • The neutron star is not at the centre since it was violently kicked by the supernova explosion.
  • The neutron star moves with a velocity of 1000 km/s.
Puppis A SN remnant in X-rays




The Crab Nebula

  • In the year 1054 A.D. the Chinese Court astronomer/astrologer Yang Wei-Te noticed a bright new star which suddenly appeared in the constellation Taurus.
  • At its brightest (Supernovae explosion), it was almost as bright as Venus
  • It was visible during the daytime for 23 days and then continued to be visible to the naked eye at night for another 653 days.
  • In the year 1731 John Bevis observed a "fuzzy" white nebula at the same location as the new star.
  • Charles Messier observed the nebula in 1758. Messier was interested in finding comets and wanted to make a catalogue of "boring" non-comet fuzzy objects. This nebula became the first object in his catalogue, M1.
  • The fuzzy nebula is called the Crab Nebula or M1 today.

True Colour Photo of the Crab Nebula

  • Red = Hydrogen Balmer transition corresponding to ionized hydrogen recombining with electrons.
  • Blue = Synchrotron emission as electrons spiral around magnetic field lines.
  • photograph made by astrophotographer David Malin
  • The total power output by the Crab Nebula is 105 LSun
  • This is incredible, since it is almost 1000 years after the supernova explosion.
  • The neutron star inside this nebula rotates once every 33 ms (or about 30 times a second).
  • We see a bright spot on the neutron star, so the star appears to flash once every rotation period.
  • We now say this neutron star is a pulsar .
Crab SN remnant




The Nearest Neutron Star

  • Nearest to Earth neutron star is in Corona Australis - 200 light-years away.
  • This is a more detailed photo (in visible light) of RX J1856.5-3754 made with the ground-based telescope "Kueyen" in Chile.
  • Kueyen is an 8 m telescope which is part of 4 telescope array whose light will be combined to make an equivalent 16 m telescope.
  • This picture shows a faint red cloud around the neutron star.
  • The red light is Hydrogen Balmer Alpha emission.
  • Photons emitted by the hot neutron star (T = 700,000 K) are exciting the Hydrogen surrounding the neutron star.


Structure of a Neutron Star

  • A neutron star balances gravity with neutron degeneracy pressure.
  • The neutrons separated by a distance = d have a velocity given by the Heisenberg Uncertainty principle:
    v = h/(2 &pi m d)
    where m is the mass of the neutron and h is Planck's constant.
  • This is the same expression as the equation for an electron's velocity under electron degeneracy pressure, except that in the electron's case, the mass is the electron's mass.
  • The neutron is about 2000 times more massive than an electron, mn = 1800 me.
  • In order for the degenerate neutrons to have the same velocity as the degenerate electrons the neutrons must be 1800 times closer to each other than the electrons in a white dwarf star.
  • A neutron star with the same mass as a white dwarf has a radius about 1000 times smaller than a white dwarf.
  • Typical radius for a neutron star is 10 km.
  • Average density &rho of a 10 km star with a mass of 2 MSun is
    &rho = 4 x 1030 kg x 3/( 4 &pi x 1012 m3) = 1018 kg/m 3
  • This is one billion times more dense than a white dwarf.


Uncertainty about a neutron star's structure

  • It is not known what really lies at the core of a neutron star.
  • Exotic particles such as pions or unbound quarks might lie in the core.
  • Each theory about the dense core provides a correction to neutron degeneracy pressure.
  • Since the detailed nature of the core is unknown, the forces opposing gravity are not known exactly and the sizes of neutron stars are not known exactly.
  • For example, two different, but reasonable theories of neutron stars predict two different sizes for a neutron star with 1.4 MSun. One prediction is for a radius of 10 km, the other predicts a radius of 20 km.
  • If you could accurately measure the radius of a neutron star and measure its mass, you could rule out certain theories describing dense nuclear matter.
  • However, very difficult to measure the radius of a star this tiny.




Maximum Mass of a Neutron Star

  • White dwarfs can't have a mass larger than 1.4 MSun (the Chandrasekhar limit) since their electrons can't move faster than light.
  • Neutron stars have a similar type of limit.
  • Each theory of nuclear matter predicts a different maximum mass for neutron stars.
  • Maximum masses range from 1.5 to 4 MSun.
  • If you measure a neutron star's mass, you can rule out theories with predicted maxima below your measured mass.
  • The maximum mass is important for identifying black holes.
  • A black hole in a binary star system has properties very similar to a neutron star, so they are hard to identify.
  • Suppose that you observe a mysterious object which is probably either a neutron star or a black hole. If you measure the mass and find out that it is above the maximum mass limit for neutron stars, then it must be a black hole.


The Discovery of the First Neutron Star

  • Neutron stars were first theoretically predicted by Walter Baade and Fritz Zwicky in the 1930's.
  • The properties seemed so bizarre that nobody took the prediction very seriously.
  • In 1967 Jocelyn Bell was doing observations using a new radio telescope for her Ph.D. thesis.
  • She discovered a radio signal at one particular location which pulsed on and off with a period of 1.337 s.
  • She and her supervisor, Antony Hewish, first came to the conclusion that this was a signal from an alien civilisation and called the signal LGM = Little Green Men
  • After finding a 2nd similar object at another location they realised these must be real astronomical bodies.
  • They came to the conclusion that they must be pulsars.
  • In 1974 Hewish was awarded the Nobel prize in physics for the discovery of pulsars.
  • Now over 1000 neutron stars have been discovered. Among them 200 very fast millisecond pulsars
  • Pulses for some pulsars have been seen in gamma-rays, x-rays, visible light, infrared, and radio
Figure 23-2



Maximum Spin Rate of a Neutron Star

  • A rotating object can't spin too fast, or it will be torn apart by the "centrifugal force".
  • The spin period = P is the time for a star to make one rotation.
  • Equate gravitational force at the surface and centrifugal force

    GM/R2 = &omega2 R

    to find the maximum possible angular velocity &omega and, thus, the minimum possible period P=2 &pi/&omega
  • The minimum spin period for an object with mass M and radius R approximately:

    Pmin = 2 &pi (R3/(GM))1/2 = ( 3 &pi / (G &rho)) 1/2

  • The minimum spin period for some astronomical objects is:
    Object Pmin Actual spin period Actual period / Minimum period
    Earth 5100 s = 1.4 hours 1 day 17 x slower
    Jupiter 10,000 s = 2.8 hours 10 hours 4 x slower
    Sun 10,000 s = 2.8 hours 25 days 216 x slower
    White Dwarf about 9 s
    Neutron Star 0.5 ms Fastest is 1.4 ms 3 x slower

  • Neutron stars can spin very rapidly because they are tiny and very dense! One can immediately deduce that the density must be high. Even if P=1 s, &rho > 3 &pi/(G P2) = 1011 kg/m3. Could it be a white dwarf ? Perhaps, but Crab pulsar with 33 millisecond period can't be for sure !
  • In 1982 the most rapidly rotating neutron star had P = 1.6 ms (Spin frequency = 600 Hz).
  • In 2005 Jason Hessels (BSc. from U of A) discovered a neutron star with P = 1.4 ms (Spin frequency = 715 Hz).




Formation of a Rapidly Rotating, Magnetized Neutron Star

Same principles that we considered during collapse of protostars

  • A neutron star is formed from the collapse of a much larger star.
  • Angular momentum is conserved during a collapse, so the spin rate increases.
  • Spin period is proportional to (radius)2
  • For example: The Sun is about 5 orders of magnitude larger than a typical neutron star.
    • If we collapse the Sun down to the size of a neutron star, it will have a spin period 10-10 times smaller than the Sun.
    • ie. it would spin with a period of 0.2 ms
    • It is very easy to create a neutron star which spins with a period near a millisecond.
  • Similarly, magnetic flux is conserved during a collapse so that the magnetic field strength is proportional to 1/(radius)2
    • If the Sun collapses down to the size of a neutron star, its magnetic field will be 10 billion times stronger.
  • Typical magnetic fields on neutron stars are 1012 times stronger than the Sun's magnetic field.
  • A small number of neutron stars have magnetic fields 1014 times the Sun's magnetic field.
  • These ultra-strong magnetic field neutron stars are called magnetars.
  • See Feb. 2003 Scientific American for a great article on magnetars

Even small initial rotation and magnetic field of neutron stars is highly amplified during the collapse





The Pulsar Mechanism

  • The strong magnetic field of a neutron star creates a magnetosphere around the neutron star.
  • The magnetic poles are not usually aligned with the spin axis.
  • Inside the neutron star, the electromagnetic forces rip off the electrons on the surface and the electrons get trapped by the magnetic field.
  • The electrons get funnelled along lines of force pointing out of the north and south magnetic poles.
  • The electrons are highly accelerated and they radiate synchrotron radiation which is beamed outwards in the directions of the poles.
  • The spin of the star causes the beam of radiation to intersect our line of sight once a spin period.
  • We see a pulse of light which turns on and off with a regular period. (Light-house mechanism)
  • We call this type of neutron star a pulsar.
Figure 23-3
  • A magnet which spins about an axis different from its symmetry axis emits radiation which causes it to lose energy.
  • This loss of energy causes the magnet's spin to slow down.
  • The neutron star must slow down, which means that its spin period must increase slowly with time.



Pulsar Recycling

  • Neutron stars are born rapidly rotating but slow down due to the magnetic drain of their energy.
  • This would suggest that over time all old pulsars should spin slowly.
  • However, if a neutron star is in a binary system things change.
  • Matter can flow from the companion to the neutron star through an accretion disk.
  • As matter from the disk falls onto the neutron star, it adds mass and angular momentum (or spin) to the neutron star.
  • This slowly causes the neutron star to spin faster.
  • This process is called recycling.
  • The accretion disk is very hot and typically radiates x-rays.
  • When Hydrogen and Helium are dumped onto the surface, small nuclear explosions occur causing bursts of x-rays.
  • When the explosion takes place on only a small part of the star, we see the explosion only once every spin period, so the burst seems to flicker.
  • Flickering X-ray Bursting neutron stars have been observed which suggest that they spin with periods in the range of 3 ms to 1.6 ms.
Figure 24-11




Light Curve for an X-ray Burst

  • The large graph shows how brightness varies with time during an X-ray Burst.
  • If the time axis was expanded, you would be able to see a periodic wave with a frequency of 530Hz.
  • The inset shows a "Fourier Spectrum" which shows the dominant repetition frequency in the data.




The Crab Nebula in Radio, Optical and X-rays

  • This shows a recent composite picture of the innermost region of the Crab Nebula (made by combining images from the Chandra X-ray Telescope, Hubble Space telescope and NRAO radio telescopes).
  • Red = Radio emission
  • Green = Visible emission
  • Blue = X-ray emission
  • The Crab Pulsar is hidden in the centre of the rotating disk. The disk is caused by a wind originating from the pulsar.
  • The pulsar moves in the same direction as its spin axis! Suggests that the supernova gave a peculiar type of "kick" to the neutron star during its birth.
Crab Nebula in X-rays



Next lecture: Black Holes