Neutron stars and extreme physics

1st July 2015

Parts of this article were previously published in my PhD thesis 'Breaking the quantum limit: the magnetic field of neutron stars in extra-galactic Be X-ray binaries'.

Artist’s impression of a neutron star with a magnetosphere that extends well beyond the neutron star’s radius.

Artist’s impression of a neutron star and its magnetosphere. Image credit: NASA's Goddard Space Flight Center/Public domain.

1. Neutron stars

Neutron stars are some of the most extreme objects in the universe, and so they can be used as ‘natural laboratories’ where we can observe matter behaving in ways we could never replicate on Earth.

Neutron stars form when massive stars (O-B-type stars, which are about 8-20 times as massive as the Sun) stop fusing matter. The energy released from fusion causes an outwards force that is counterbalanced by the inwards force of gravity; this prevents stars from blowing apart. When fusion ceases, so does the outwards force, and so the core of the star collapses in on itself in what’s known as a Type II supernova[1][2][3][4].

In a Type II supernova, the force of gravity is strong enough to overcome electron degeneracy pressure. Degeneracy pressure is a manifestation of the Pauli exclusion principle, which states that two fermions – like electrons, protons, and neutrons - cannot simultaneously occupy the same quantum state. When every electron energy level is filled, electron degeneracy pressure prevents the core from becoming any denser. It is then referred to as a white dwarf. White dwarfs have a mass that is comparable to the mass of the Sun, but they are compacted to a size comparable to the size of the Earth.

In a Type II supernova, however, electron degeneracy pressure can be overcome. This allows electrons to merge with protons to become neutrons, and an object about 1.4 times as massive as the Sun fits into a sphere with a radius of about 10 km. The core is prevented from collapsing further due to neutron degeneracy pressure. This makes neutron stars extremely dense; if the force of gravity were strong enough to overcome neutron degeneracy pressure, then they would become black holes.

As well as being some of the densest objects in the known universe, neutron stars are also some of the fastest spinning objects, rotating up to thousands of times a second[5], and have the highest magnetic fields ever observed[6].

Neutron stars can have magnetic fields so high that they cannot be described with classical physics[7], and have magnetospheres that can extend for thousands of times their radius, where the magnetosphere is the volume of space around an object that's controlled by that object's magnetic field[8a].

All of this means that physicists can use observations of neutron stars in order to test and expand fundamental laws of physics.

1.1 Observations with telescopes

Everything we know about neutron stars comes from observations with telescopes. A telescope collects light, and many telescopes can also measure the light’s energy and direction. We can learn a remarkable amount from this information.

Neutron stars do not produce light in nuclear reactions, like ‘normal’ (main sequence) stars do. Instead, isolated neutron stars are visible because charged particles, like electrons, produce radiation when they are accelerated by the neutron star’s magnetic field[9][10a]. This is known as synchrotron radiation and is often in the radio spectrum. This means that isolated neutron stars can be observed with radio telescopes.

This radiation is emitted from the neutron star's magnetic poles, and so can travel past our line-of-sight as the star rotates. This makes the neutron star appear to pulsate, and so neutron stars that emit beamed radiation are known as pulsars.

The spin period of a pulsar can be determined by observing how the amount of light it emits changes as it rotates[10b]. If a single magnetic pole is visible, then the amount of light increases as the pole appears on the neutron star's horizon and rotates towards our line-of-sight. It then decreases as the pole disappears over the horizon, and increases again when it reappears. The spin period of the pulsar can be determined by measuring the time between maximum outbursts of light.

Animation of a neutron star rotating.

Image credit: NASA's Goddard Space Flight Center/Public domain.

Isolated pulsars that have particularly strong magnetic fields can also emit bursts of X-ray and gamma ray radiation, and so can be observed with X-ray and gamma ray telescopes[11][12]. This occurs when the magnetic field lines twist, causing stress that can break the crust on the neutron star’s surface. These are known as magnetars[13][14].

Neutron stars may also emit X-ray radiation if they are in a binary system, and matter from another star falls towards its magnetosphere[15a]. If the neutron star is spinning too fast, then it will be expelled by the centrifugal force. This is known as the propeller mechanism, because the same effect happens if you pour sand onto a horizontal propeller. If the propeller is slow enough, then the sand can build up on its surface, if the propeller speeds up, then eventually it will blow all the sand away.

If the neutron star is slow enough, then this matter falls down the magnetic field lines at tremendous speeds, reaching free-fall velocities of up to 70% of the speed of light[16]. When the matter hits the magnetic poles, its velocity suddenly becomes zero and so its kinetic energy must be converted into other forms of energy.

When you drop a heavy object on Earth, for example, then its kinetic energy is mostly converted into sound, and that’s why heavier objects make more noise than lighter objects when you drop them. Some kinetic energy is also converted into heat. This is usually not noticeable if you drop a heavy object on Earth, but it makes a big difference on a neutron star, when something is dropped at close to the speed of light. All of this excess heat causes particles to scatter, emitting X-rays. This matter can build up, in a process known as accretion, forming ‘mountains’ on the neutron star’s magnetic poles.

2. Neutron stars in binaries

Binary star systems that emit X-ray radiation are known as X-ray binaries, and these can contain white dwarfs and black holes as well as neutron stars[15b].

There are generally two types of neutron star X-ray binaries: low mass X-ray binaries (LMXB), which are composed of a neutron star and another star less than twice the mass of the Sun (a white dwarf or a luminosity class III-V, K-M-type star), and high mass X-ray binaries (HMXB), which are composed of a neutron star and another star that is over 8 times as massive as the Sun[17].

There are two types of HMXB; these are known as supergiant X-ray binaries (SGXB) and Be X-ray binaries (BeXB). Neutron star SGXB are composed of a neutron star and a supergiant star (a luminosity class I-II, O-B-type star), and neutron star BeXB are composed of a neutron star and an OBe star (a luminosity class III-V, Oe-Be-type star).

There are very few intermediate mass X-ray binaries (IMXB), X-ray binaries composed of neutron stars and stars with masses between 2 and 8 times the mass of the Sun. This is because IMXB have relatively short lifetimes, quickly losing enough mass to become LMXB[18].

2.1 Low mass X-ray binaries (LMXB)

Some of the fastest spinning neutron stars are in LMXB. These form when a neutron star’s magnetic field has decayed, and it has slowed enough so that it rotates once every ten seconds or so. This is so slow that it no longer produces observable radio waves. It's then sped up again by the material that falls on it, so that it can rotate up to thousands of times a second[15c].

In LMXB, material is loosely bound to the low-mass star, which is close enough to the neutron star so that material can constantly fall onto it. This material brings with it angular momentum, which causes the neutron star to speed up. There is so much material that a disc forms around the neutron star. This is known as an accretion disc[15d].

Animation of a neutron star rotating while orbiting a low-mass star. Matter from the low-mass star forms a disc around the neutron star.

A neutron star in a LMXB. Image credit: NASA/Public domain.

Animation of a neutron star in a low-mass binary showing. The disc spins as the neutron star rotates.

A neutron star in a LMXB. Image credit: NASA/Public domain.

LMXB typically last for about 10 million to a billion years before there's no longer enough matter to produce X-rays.

Low mass stars are typically older than high mass stars. This is because massive stars undergo nuclear fusion faster, and so run out of fuel quicker. Stars over 8 times as massive as the Sun can fuse all of their material within a million years, whereas stars like the Sun will last for about 10 billion years. This means that LMXB are found in parts of the Galaxy that contain older stars, like in the Galactic bulge and in globular clusters[19a].

LMXB have also been observed in other galaxies, including the Large Magellanic Cloud (LMC)[20], an irregular galaxy that is gravitationally bound to our own, and in M31, also known as the Andromeda Galaxy[21]. This is the closest spiral galaxy to our own.

2.2 High mass X-ray binaries (HMXB)

There are two types of HMXB: supergiant X-ray binaries (SGXB) and Be X-ray binaries (BeXB). SGXB contain supergiant stars, which can either lose material in the same way that the stars in LMXB do, or through strong stellar winds (these can reach velocities of up to 2000 km/s, which is over 4 million miles/hour[22]). Either way, material tends to constantly fall onto the neutron stars in SGXB. The neutron stars in SGXB tend to rotate about once every 10 minutes, and complete one orbit every 7 days or so[15e].

Artist’s impression of a neutron star orbiting a supergiant star

A neutron star in a SGXB. Image credit: ESA/AOES Medialab/CC-A.

Artist’s impression of a neutron star orbiting an OBe star – a blue star surrounded by a large disc of material expelled from the star.

A neutron star in a BeXB. Image credit: Walt Feimer, NASA/Goddard Space Flight Center/Public domain.

BeXB contain OBe stars. These are massive blue stars that are orbited by a disc of material known as a circumstellar disc. The circumstellar disc contains material that's been expelled from the star, and can extend for a distance of over 1 AU (where 1 AU is the distance between the Earth and the Sun). The neutron star can sometimes pass within this disc, and this causes material to fall onto it[15f].

The orbital period of the neutron star can then be determined from the time between X-ray outbursts, and is typically tens to hundreds of days. The circumstellar disc can change in size, however, sometimes enlarging so that the neutron star is always within the disc, and so always accreting[15g].

Animation showing how the size of the disc of an OBe star can change over time. In 1995, the OBe star in SXP2.37 had a disc that was smaller than the orbit of the neutron star. In 2001, it was much larger, and in 2009, it was smaller again.

BeXB SXP2.37 over 14 years, to scale (NS = neutron star). Image credit: Helen Klus/CC-NC-SA.

Diagram of a Be X-ray binary system. The neutron star is generally about 1 AU from the OBe star.

Diagram of a typical BeXB, to scale with the neutron star radius ×100 and the radius of the neutron star’s magnetosphere ×20 (1 AU is the distance between the Earth and the Sun). Image credit: Helen Klus/CC-NC-SA.

Neutron stars in BeXB typically rotate faster if they have shorter orbital periods[23]. This is because accreted material makes them spin faster, and systems with short orbital periods accrete more often, and have less time to slow down between accretion events. The fastest neutron stars in BeXB tend to rotate once every second, and the slowest once every hour.

Massive stars have relatively short lifetimes, and rapidly lose material, and so HMXB tend to only last for about 100,000 years or so. This means that HMXB are mostly found in star-forming regions in the Galactic plane[19b].

There are about 70 known SGXB in the Milky Way, and at least two outside of the Galaxy, one in the LMC (LMC X-4), and one (SMC X-1) in the Small Magellanic Cloud (SMC), an irregular dwarf galaxy gravitationally bound to the LMC[15h].

There are a roughly even number of SGXB and BeXB in the Galaxy, but there are many more BeXB outside of the Milky Way, with about 70 BeXB in the SMC, and about 10 in the LMC[15i].

3. The magnetic field of neutron stars

Neutron stars contain charged particles, like electrons and protons, and are some of the fastest spinning objects in the universe. This means they should have extremely high magnetic fields. The magnetic fields of neutron stars can be determined directly using scattering physics[24], or indirectly using accretion physics[25].

Some neutron stars have been found to have magnetic fields so high that they cannot be described with classical physics and quantum field theories must be used. This is because when magnetic fields get this high they affect the space around them causing images to be distorted and magnified[26]. These magnetic fields are 10,000 billion times larger than the magnetic field of the Earth at the Earth’s surface, and cannot be found anywhere else in the universe.

3.1 Scattering physics and the quantum limit

In BeXB, once matter passes through the neutron star's magnetosphere it's channelled by the magnetic field lines to the neutron star's magnetic polar caps.

If a relatively low amount of material falls to the surface, then this material forms a mound covering an area of about 1 km2. When material hits the surface, its kinetic energy is converted into heat. This causes matter on the surface to become more energetic and emit X-ray photons via black body radiation. These photons travel in the opposite direction to the falling matter, in a ‘pencil’ beam[27].

If a relatively large amount of material falls onto the pole, then it blocks the ‘pencil’ beam radiation, creating a shock wave about 1 km from the surface. This means that radiation can only escape from the sides, in a ‘fan’ beam.

Diagram showing the magnetic pole of a neutron star. Matter falls towards the pole, and radiation moves away.

‘Pencil’ beam geometry. Image credit: Helen Klus/CC-NC-SA.

Diagram showing the magnetic pole of a neutron star. When a lot of matter falls towards the pole, the radiation cannot move past it and moves away from the sides.

‘Fan’ beam geometry. Image credit: Helen Klus/CC-NC-SA.

X-ray radiation in a fan beam consists of black body radiation, and radiation caused by bremsstrahlung and cyclotron emission[28][29][30][31].

Bremsstrahlung (German for ‘braking radiation') occurs when charged particles, like electrons, are slowed down, and deflected, by particles of the opposite charge, like protons. The electron loses energy, emitting it in the form of an X-ray photon.

Diagram of Bremsstrahlung, where an electron is slowed by another particle, and releases a photon.

Bremsstrahlung. Image credit: NASA's Imagine the Universe/Public domain.

Cyclotron emission is produced by charged particles, like electrons, which emit X-ray photons when they are accelerated by the magnetic field. This is the same mechanism as the synchrotron radiation that occurs in isolated pulsars. The difference between cyclotron and synchrotron radiation is how fast the electron is travelling, where during synchrotron radiation the electron is travelling close to the speed of light.

Diagram of synchrotron radiation, where an electron moves in a spiral while in a magnetic field. This makes the electron release photons.

Synchrotron radiation. Image credit: NASA's Imagine the Universe/Public domain.

These X-ray photons do not always make it straight out into space, and can bump into other electrons, losing energy. This is known as Compton scattering. When this happens, it leaves gaps in the X-ray spectrum, which are known as absorption lines[32].

Diagram of Compton scattering, where a photon changes energy after interacting with a particle.

Compton scattering. Image credit: NASA's Imagine the Universe/Public domain.

These gaps corresponds to the amount of energy the electron ‘takes’ from the photon, and because the electrons are involved in cyclotron emission, the amount of energy that the electron takes depends on the strength of the magnetic field. The magnetic field places electrons into quantised positions, at quantised energies, known as Landau orbits.

This energy (Ecyc) is found using Ecyc = n
ħeB/mec
, where B is the magnetic field, and n, ħ, e, and me are all constants. n is the quantum number corresponding to the Landau level, where the lowest energy level is at n = 1, ħ = h/2π, where h is Planck's constant, e is the elementary charge, and me is the electron rest mass.

This equation shows that electrons in a stronger magnetic field have higher energies than electrons in weaker magnetic fields. Neutron stars that exhibit these gaps tend to have magnetic fields of up to 1013 (10,000 billion) Gauss (this is 1,000 million Tesla). For comparison, the magnetic field on the surface of the Earth is about 0.4 Gauss (0.00004 Tesla). If neutron stars have magnetic fields much higher than 1013 Gauss, then Ecyc becomes too high for these lines to be visible with X-ray telescopes.

Electrons orbit closer to the magnetic field line the stronger the magnetic field. The field can no longer be described with classical physics when electrons orbit so close that the orbital radius is equal to their de Broglie radius, and Ecyc = mec2.

n
ħeB/mec
= mec2 gives B =
me2c3/ħe
≅ 4.4×1013 Gauss, and so the effects of quantum mechanics are important above 4.4×1013 Gauss. This is known as the quantum critical field.

3.2 Accretion physics: beyond the quantum limit

The magnetic field of neutron stars can also be determined indirectly, using accretion physics. This means determining how the neutron star’s rotational velocity is changing; accreted material makes the neutron star speed up, like in LMXB, but the drag of the magnetic field slows the neutron star down[8b].

By working out how much material is accreted – from the neutron star’s luminosity – physicists can predict how much this should speed the neutron star up, and then compare this to its actual acceleration. The difference is due to the drag of the magnetic field, and the higher the magnetic field the more it slows the neutron star down. Accretion physics allows physicists to measure magnetic fields above the quantum critical field.

Systems with magnetic fields this high were thought to be unusual, but may in fact be common. As part of my PhD, which was supervised by Professor Malcolm Coe and Dr Wynn Ho, I applied accretion physics to a sample of over 40 neutron stars in the SMC and found that ~2/3 have magnetic fields over the quantum critical field[33]. These are shown in blue on the plot below.

Plot showing magnetic field against spin period for neutron stars. Those in binaries show the same relationship.

The magnetic field of almost all known neutron stars as a function of spin period. The dashed line indicates the quantum critical field. Image credit: Helen Klus/CC-NC-SA.

If 2/3 of neutron stars in BeXB do have magnetic fields over the quantum critical field, then this might mean that there are many more isolated neutron stars that also have magnetic fields this high.

If isolated neutron stars have magnetic fields over the quantum critical field, then their magnetic fields can usually only be measured when they undergo a magnetar-like outburst. The BeXB sources have not been observed to undergo these outbursts, and this suggests that perhaps these outbursts are not common for neutron stars with magnetic fields this high, and there is a population of isolated neutron stars with extremely high magnetic fields that cannot be observed.

By studying these systems further, physicists can learn more about how matter behaves in such extreme environments.

4. References

  1. Nomoto, K., 1984, 'Evolution of 8-10 solar mass stars toward electron capture supernovae I - Formation of electron-degenerate O+ NE+ MG cores', The Astrophysical Journal, 277, pp.791-805.

  2. Nomoto, K., 1987, 'Evolution of 8-10 solar mass stars toward electron capture supernovae II - Collapse of an O+ NE+ MG core', The Astrophysical Journal, 322, pp.206-214.

  3. Heger, A., et al, 2003, 'How massive single stars end their life', The Astrophysical Journal, 591, pp.288.

  4. Woosley, S. and Janka, T., 2005, 'The physics of core-collapse supernovae', Nature Physics, 1, pp.147-154.

  5. Bhattacharya, D. and van den Heuvel, E. P. J., 1991, 'Formation and evolution of binary and millisecond radio pulsars', Physics Reports, 203, pp.1-124.

  6. NASA, 'Magnetars, the Most Magnetic Stars In the Universe', last accessed 15-02-16.

  7. Harding, A. K. and Lai, D., 2006, 'Physics of strongly magnetized neutron stars', Reports on Progress in Physics, 69, pp.2631.

  8. (a, b) Klus, H., Ho, W. C., Coe, M. J., Corbet, R. H. and Townsend, L. J., 2014, 'Spin period change and the magnetic fields of neutron stars in Be X-ray binaries in the Small Magellanic Cloud', Monthly Notices of the Royal Astronomical Society, 437, pp.3863-3882.

  9. Pacini, F., 1967, 'Energy emission from a neutron star', Nature, 216, pp.567-568.

  10. (a, b) Lyne, A. G. and Graham-Smith, F., 2006, 'Pulsar Astronomy', Cambridge University Press.

  11. Thompson, C., Lyutikov, M. and Kulkarni, S. R., 2002, 'Electrodynamics of magnetars: implications for the persistent X-ray emission and spin-down of the soft gamma repeaters and anomalous X-ray pulsars', The Astrophysical Journal, 574, pp.332.

  12. Takata, J., Cheng, K. S. and Taam, R. E., 2012, 'X-ray and gamma-ray emissions from rotation powered millisecond pulsars', The Astrophysical Journal, 745, pp.100.

  13. Duncan, R. C. and Thompson, C., 1992, 'Formation of very strongly magnetized neutron stars-Implications for gamma-ray bursts', The Astrophysical Journal, 392, pp.9-13.

  14. Kouveliotou, C., Duncan, R. C. and Thompson, C., 2003, 'Magnetars', Scientific American, 288, pp.34-41.

  15. (a, b, c, d, e, f, g, h, i) Reig, P., 2011, 'Be/X-ray binaries', Astrophysics and Space Science, 332, pp.1-29.

  16. Kretschmar, P., et al, 2010, 'Understanding Cyclotron Lines in the Spectra of Accreting Neutron Stars', The Energetic Cosmos: from Suzaku to ASTRO-H, 1, pp.268-269.

  17. Grimm, H. J., Gilfanov, M. and Sunyaev, R., 2003, 'High-mass X-ray binaries as a star formation rate indicator in distant galaxies', Monthly Notices of the Royal Astronomical Society, 339, pp.793-809.

  18. Van den Heuvel, E. P. J., 1975, 'Modes of mass transfer and classes of binary X-ray sources', The Astrophysical Journal, 198, pp.109-112.

  19. (a, b) Tauris, T. M. and van den Heuvel, E. P. J., 2006, 'Formation and evolution of compactstellar x-ray sources' in 'Compact stellar X-ray sources', Cambridge University Press.

  20. Nazé, Y., 2009, 'The X-ray stellar population of the LMC', Proceedings of the International Astronomical Union, IAU Symposium, 256, pp.20-29.

  21. Peacock, M. B., Maccarone, T. J., Kundu, A. and Zepf, S. E., 2010, 'A systematic study of low-mass X-ray binaries in the M31 globular cluster system', Monthly Notices of the Royal Astronomical Society, 407, pp.2611-2624.

  22. Negueruela, I., 2010, 'Stellar Wind Accretion in High-Mass X-Ray Binaries', High Energy Phenomena in Massive Stars, 422, pp.57-68.

  23. Corbet, R. H. D., 1984, 'Be/neutron star binaries-A relationship between orbital period and neutron star spin period', Astronomy and Astrophysics, 141, pp.91-93.

  24. Trümper, J., et al, 1977, 'Evidence for Strong Cyclotron Emission in the Hard X-Ray Spectrum of Her X-1', Annals of the New York Academy of Sciences, 302, pp.538-544.

  25. Ghosh, P. and Lamb, F. K., 1979, 'Accretion by rotating magnetic neutron stars. III - Accretion torques and period changes in pulsating X-ray sources', Astrophysical Journal, 234, pp.296-316.

  26. Duncan, R. C., 2000, 'Physics in ultra-strong magnetic fields', Gamma-ray Bursts, 5th Huntsville Symposium, 526, pp.830-841.

  27. Becker, P. A., 1998, 'Dynamical structure of radiation-dominated pulsar accretion shocks', The Astrophysical Journal, 498, pp.790.

  28. Basko, M. M. and Sunyaev, R. A., 1975, 'Radiative transfer in a strong magnetic field and accreting X-ray pulsars', Astronomy and Astrophysics, 42, pp.311-321.

  29. Wang, Y. M. and Frank, J., 1981, 'Plasma infall and X-ray production in the magnetic funnel of an accreting neutron star', Astronomy and Astrophysics, 93, pp.255-268.

  30. Wang, Y. M. and Welter, G. L., 1981, 'An analysis of the pulse profiles of the binary X-ray pulsars', Astronomy and Astrophysics, 102, pp.97-108.

  31. Parmar, A. N., White, N. E. and Stella, L., 1989, 'The transient 42 second X-ray pulsar EXO 2030+ 375 II - The luminosity dependence of the pulse profile', The Astrophysical Journal, 338, pp.373-380.

  32. Becker, P. A. and Wolff, M. T., 2007, 'Thermal and bulk comptonization in accretion-powered X-ray pulsars', The Astrophysical Journal, 654, pp.435.

  33. Klus, H., 2015, 'Breaking the quantum limit: the magnetic field of neutron stars in extra-galactic Be X-ray binaries', PhD thesis.

Blog | Space & Time | Light & Matter | Mind & Multiverse | Timeline

RSS Feed | Images | About | Copyright | Privacy | Comments