Be X-ray binaries and the super-magnetic universe

8th December 2013

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

Artist's impression of a highly magnetic neutron star. Image credit: ESA/Christophe Carreau/CC-A.

For the last two years, I have been researching neutron stars at the University of Southampton, supervised by Professor Malcolm Coe and Dr Wynn Ho, and we have recently made a surprising discovery.

Neutron stars are the most magnetic objects in the universe, with some having magnetic fields so high that quantum behaviour comes into effect[1a][2a]. Only a few dozen objects in the universe were previously thought to have magnetic fields this high, but we have shown that perhaps over half of all neutron stars do[3][4]. This means that the universe may be much more magnetic than previously thought.

1. Neutron stars

Neutron stars form when main sequence stars 'die'[5][6][7][8]. Main sequence stars are fuelled by nuclear fusion, which pushes matter apart. The whole star would explode if it were not for the force of gravity keeping it together. When all of the fissionable material is used up, and fusion stops, there's no longer a strong outwards force to counteract gravity, and so the star will shrink.

Photograph of the Ring Nebula

The Ring Nebula, a planetary nebula. Image credit: NASA/ESA/Public domain.

Photograph of stellar nursery Gum 29

Gum 29, a stellar nursery. Image credit: ESO/CC-A.

A star like the Sun will shed its outer shell as a planetary nebula, leaving the core as a white dwarf, a dense ball of carbon and oxygen about the size of the Earth. Stars that are about ten times as massive as the Sun will undergo a supernova, where the core is squashed so tightly that protons and electrons combine to become neutrons, and the star shrinks to about the size of central London. It is then known as a neutron star. The cores of the most massive stars will be squashed even tighter still, becoming black holes.

Map of London, with the size of a neutron star circled. A neutron star is about 20 km wide, and covers central London.

Map of London, the black circle indicates the size of a neutron star. Image credit: modified by Helen Klus, original image by OpenStreetMap/CC-SA.

A magnetic field is created by a moving charge. Neutron stars have particularly high magnetic fields because they are very dense, spin extremely rapidly, and contain charged particles like electrons and protons[9].

2. Neutron stars in binaries

It's difficult to measure the magnetic field of isolated neutron stars, but fortunately, many neutron stars are part of binary star systems. Binary star systems are common because stars are formed together, in groups known as stellar nurseries[10]. Binary star systems are often split apart by the force of the supernova that creates the neutron star, but not always, and new binaries can form if neutron stars are 'captured' by the gravitational force of another nearby star[11].

When a neutron star is in a binary system with a main sequence star, matter from the main sequence star can fall onto the neutron star. When the matter hits the surface, its gravitational potential energy is mostly converted into heat, which interacts with matter, producing light that is so energetic it is in the X-ray spectrum[12a]. This is similar to how gravitational potential energy is converted to sound if your drop a heavy book.

X-rays can also be observed coming from binary star systems containing main sequence stars and white dwarfs or black holes, and from binary star systems that do not contain a main sequence star.

Binary systems containing stars that emit X-rays are known as X-ray binaries. Low mass X-ray binaries (LMXB) contain a white dwarf, neutron star, or black hole, and a companion that is around twice the mass of the Sun or less.

High mass X-ray binaries (HMXB) contain a white dwarf, neutron star or black hole, and a supergiant or massive main sequence star. The neutron stars that we have been studying are all in a type of HMXB known as Be X-ray binaries (BeXB).

2.1 Be X-ray binaries

BeXB are a type of high mass X-ray binary, where the companion is an OBe star. OBe stars are massive blue stars surrounded by a disc of gas with a radius of about 1 AU - the distance between the Earth and the Sun[12b].

In BeXB, matter from the disc surrounding the OBe star falls on to the neutron star whenever they are closest together. This matter can either fall directly onto the neutron star from all directions or, if it has too much angular momentum, it can first form a disc, known as an accretion disc.

The angular momentum of incoming matter can be determined from the radius of the OBe star's disc and the systems' orbital parameters - the eccentricity, orbital period, and total mass of the two stars. We used this information, taken from a variety of sources, to show that all the systems we studied have accretion discs.

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

Diagram of a typical BeXB (from the side), 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.

Diagram of a Be X-ray binary from the top.

Diagram of a typical BeXB (from the top), to scale with 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 spin particularly quickly because of the conservation of angular momentum. Angular momentum = Mass × Velocity × Radius, and the conservation of angular momentum means that this value must remain the same, both before and after the supernova that creates the neutron star. Since the radius is dramatically reduced when this happens, the velocity must increase. Neutron stars are 'born' spinning extremely quickly, but their spin periods can change.

Neutron stars in BeXB are affected by the influx of matter from their companion[12c]. If they are spinning too fast, then matter cannot settle, and is flung away. This is known as the 'propeller mechanism' because the same thing happens if you try to spill matter onto a fast moving propeller. If the propeller is gradually slowed down, then there will be a point when matter is able to settle, and this happens in BeXB as the neutron star is slowed by the drag of its magnetic field.

If matter is spilt onto a slow moving propeller in its direction of rotation, then it can push its blades around, causing it to speed up. This happens in BeXB if the accretion disc and neutron star orbit in the same direction. We expect this applies to most BeXB, and so matter from the accretion disc generally causes the neutron star to speed up.

The neutron star speeds up when it is close to the OBe star, and slows down - due to the drag of its magnetic field - when it is further away, with the neutron star's spin period oscillating around a period known as the equilibrium period[12d].

This means that the change in a neutron star's spin period relates to its magnetic field, and the amount of matter that falls onto it. The amount of matter that falls onto it is directly proportional to the amount of X-rays it emits - its X-ray luminosity, and so if you know the spin period of a neutron star in a BeXB on two different dates, and you know its X-ray luminosity at these times, then you can work out its magnetic field.

3. Neutron stars and the quantum critical field

We looked at data for 42 BeXB, all located in the Small Magellanic Cloud (SMC), one of the closest galaxies to the Milky Way. This data - which you can download here - came from NASA's Rossi X-ray Timing Explorer (RXTE) satellite, an X-ray telescope that has orbited the Earth since 1995, despite being decommissioned in 2012.

Image of the night sky, rollover revels labels for the Large and Small Magellanic Clouds and the plane of the Milky Way.

The Large and Small Magellanic Clouds (LMC and SMC) and the Milky Way, viewed from the site of the ESA's Very Large Telescope in Chile (rollover for labels). Image credit: ESO/Y. Beletsky/CC-A.

RXTE pointed at these systems every couple of months, and measured how many X-rays they were emitting. It did this for about 13 years. There is a peak in the number of X-rays every time the beam passes our line of sight, and so we could determine the neutron star's spin period and average X-ray luminosity every couple of months. We then used this information to determine the magnetic field of each system.

We found that over half of the systems we looked at have surface fields so high that classical mechanics is no longer applicable, and quantum electrodynamics (QED) is needed to describe them. This change occurs at 4.4x1013 Gauss (which is 4.4 billion Tesla), a value known as the quantum critical field. To put this in perspective, this is over 100,000 billion times the strength of the magnetic field at the Earth's surface.

When magnetic fields get this high, they have strange effects on light and matter[13]. Atoms become elongated so that they are hundreds of times thinner, and form new chemical bonds, photons can split in two, or merge together, and images are distorted and magnified. Only a few dozen objects in the universe were previously thought to have magnetic fields this high, most of which are isolated neutron stars known as magnetars[1b][2b].

The fact that over half of the neutron stars in our sample also have fields this high might mean that over half of all neutron stars do. It's just that isolated neutron stars with super-high magnetic fields are harder to detect. These results are unexpected and controversial because most neutron stars in BeXB have previously been found to have much lower magnetic fields, and it is currently unclear why this disparity exists.

We have published our results in Monthly Notices of the Royal Astronomical Society, and our papers can be read for free here and here. We are now going to look at the data in more detail, to see if there is further evidence that these neutron stars have magnetic fields this high.

UPDATE: Evidence that BeXB have magnetic fields above the quantum limit is given in my 2015 PhD thesis ‘Breaking the quantum limit: the magnetic field of neutron stars in extra-galactic Be X-ray binaries’, parts of this are summarised here. My thesis also outlines further proof that would be needed before this is accepted.

4. References

  1. (a, b) 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.

  2. (a, b) Kouveliotou, C., Duncan, R. C. and Thompson, C., 2003, 'Magnetars', Scientific American, 288, pp.34-41.

  3. Klus, H., Ho, W. C. G., 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.
    See also, Klus, H., 2015, 'Breaking the quantum limit: the magnetic field of neutron stars in extra-galactic Be X-ray binaries', PhD thesis.

  4. Ho, W. C. G., Klus, H., Coe, M. J. and Andersson, N., 2014, 'Equilibrium spin pulsars unite neutron star populations', Monthly Notices of the Royal Astronomical Society, 437, pp.3664-3669.

  5. 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.

  6. 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.

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

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

  9. Reisenegger, A., 2013, 'Magnetic fields of neutron stars', arXiv preprint arXiv:1305.2542.

  10. Duchêne, G. and Kraus, A., 2013, 'Stellar Multiplicity', Annual Review of Astronomy and Astrophysics, 51, pp.269-310.

  11. Lewin, W. H. G., van den Heuvel, E. P. J., and van Paradijs, J., 1997, 'X-ray Binaries' ,Cambridge University Press.

  12. (a, b, c, d) Reig, P., 2011, 'Be/X-ray binaries', Astrophysics and Space Science, 332, pp.1-29.

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

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