Neutron Stars

Walter Baade and Fritz Zwicky first suggested in 1934 that a neutron star might exist, only one year after the neutron itself was proved to exist by Sir James Chadwick. Whilst studying the origins of supernovae, it was suggested that a clump of neutrons could be produced towards the end of a large star's lifetime [1]. Neutron stars are around ~?10?^5 m in diameter with a mass not dissimilar to that of the sun. However, they are far denser than the earth, resulting in gravitational fields 11 orders of magnitude greater. [16]

Massive stars can end their normal lives in a number of ways, one of which is called a type II supernova. [6] In a massive star's formation, hydrogen and helium fuse together to form heavier elements. [7] This energy, along with electron 'degeneracy pressure' resists the complete collapse of a star under gravitational attraction. Electron degeneracy pressure is a consequence of the Pauli Exclusion Principle, which forbids any two electrons (or any other half-spin fermions, such as protons) to occupy the same state. [4] This limits how close two electrons can get to one another, and so the core retains its size. Once the heavier elements such as nickel and iron have been formed in the core, it is no longer energetically favourable for the star to continue fusion. [7] The gravitational attraction causes electrons and protons to form neutrons via inverse-beta decay, , and electron degeneracy pressure is replaced with neutron degeneracy pressure (since they too obey the Pauli Exclusion Principle). [2] The sudden collapse of the core as it overcomes electron degeneracy pressure results in an implosion, which in turn 'bounces' off the newly formed neutron core to form an explosion. This occurs in such a way that it strips the star of its outer layers, leaving behind a neutron star. [9]-[11]

However, a neutron star can only come into existence under certain conditions. If the star in question has a mass below 1.44M (where 1 M is 1 solar mass), known as the Chandresekhar limit, electron degeneracy pressure resists the core's collapse and a stable white dwarf is formed. [18] Above 20M, a supernova explosion still occurs, but the neutron star is replaced with a black hole. Above 40-50M, no explosion occurs, and the star forms a black hole immediately. [17] The gravitational binding energy released from the parent star's core to the neutron star is about 3 x 1053 erg (or centimetre-gram-seconds), which is almost a tenth of its potential mass energy, mc2. The remnants of the star expand with kinetic energy of between 1x1051 and 2x1051 erg and the total energy released by photons is one hundred times that. It is believed that the neutrinos in the core have the ability, assisted by convection, rotation and magnetic fields to eventually revitalize the shock, which accelerates outwards from the star and expels the stellar mantle. [9]-[11] Newly born neutron stars or proto-neutron stars are rich in leptons (subatomic particles, such as electrons, muons or neutrinos). Although astrophysicists understand the basic concepts that govern neutron star formation, not all of the detail is understood, but neutrinos play a vital role. [3]

Since the neutron star has a radius far shorter than that of a massive star (its parent), and since its moment of inertia is radically reduced, it forms at a fast rotational speed. [6] A neutron star takes between 1.4 milliseconds to 30 seconds to complete a whole rotation, which in turn results over seven hundred revolutions per second. As neutron stars get older the rate at which they rotate decreases usually by a constant rate; a neutron star now rotating in 1 second will be rotating in 1.000003 seconds in a century. [6] Occasionally there is a 'glitch' in a neutron star and its rotational speed increases, and astrophysicists had believed that this was to do with starquakes, but recent studies show that starquakes do not produce enough energy to do this. [15] Different transitions between energy levels in the neutron star's fluid core could explain this deviation. [15] It is estimated that a neutron star is no bigger than 30 kilometres across, which is small for stars, yet it is so dense that it can have a greater mass than the sun. A neutron star's density can be up to 9 orders of magnitude greater than that of the sun. [19] Within the star the density can vary [20] for example on the crust it is around one billion kilograms per metre cubed, whereas deeper inside it can be up to eight hundred quadrillion kilograms per metre cubed. This is because it has such a high gravitational field due to its sheer size and density. The binding energy, the energy that holds the neutrons, together is demonstrated by the equation . The gravitational field strength is so great that neutron stars can bend light traveling past them. It turns out that a neutron star's gravitational field is so strong that it becomes a gravitational lens and bends the radiation emitted from the star around so that previously invisible parts of the star now become visible. [21] Most neutron stars are observed as pulsars and by doing so emit photons from radio x-ray wavelengths, which are dominated by non-thermal emissions. Most of these appear to be created in the star's magnetosphere. There are about a dozen neutron stars that have been identified as having high thermal emissions, they are aged up to one million years old and are estimated to have surface temperatures between 3x105 and 106 K [5]; this means that the majority of the emitted radiation is either extreme Ultraviolet or X-ray light. There are a few cases where neutron stars are actually close enough to the earth for optic thermal emission to be detected, these stars have optical fluxes several times less than what a blackbody [13] extrapolation from the observed X-rays into the Rayleigh-Jeans optical domain would imply. [14]

References

[1] Baade, Walter and Zwicky, Fritz (1934). "Remarks on Super-Novae and Cosmic Rays".

[3] A. Burrows, Nature 403, 727 (2000).

[4] http://en.wikipedia.org/wiki/Pauli_exclusion_principle#Atoms_and_the_Pauli_principle and http://en.wikipedia.org/wiki/Pauli_exclusion_principle#Astrophysics_and_the_Pauli_principle

[5] D. Page, J. M. Lattimer, M. Prakash, A. W. Steiner,http://arxiv.org/abs/astro-ph/ 0403657.

[6] http://en.wikipedia.org/wiki/Neutron_star

[7] Richmond, Michael. "Late stages of evolution for low-mass stars". Rochester Institute of Technology.

[8] M=one solar mass (I.E) mass of the sun = 1.989x1030

[9] A. Burrows, J. M. Lattimer, Astrophys. J. 307, 178 (1986).

[10] K. Hirata et al., Phys. Rev. Lett. 58, 1490 (1987).

[11] R. M. Bionta et al., Phys. Rev. Lett. 58, 1494 (1987).

[12] See, e.g. A. Burrows and J.M. Lattimer, Astrophys. J. 318, L63 (1987).

[13] A Hypothetical object capable of absorbing all the electromagnetic radiation falling upon it.

[14] V. Burwitz et al., Astron. Astrophys. 379, L35 (2001)

[15] Alpar, M Ali (January 1, 1998). "Pulsars, glitches and superfluids".

[16] National Geographic Website: http://science.nationalgeographic.co.uk/science/space/solar-system/neutron-stars/

[17] Fryer, C. L.; New, K. C. B. (2006-01-24). "Gravitational Waves from Gravitational Collapse". Max Planck Institute for Gravitational Physics.

[18] On the Evolution of the Main-Sequence Stars, M. Schönberg and S. Chandrasekhar, Astrophysical Journal 96, #2 (September 1942), pp. 161-172.

[19] 3.7×1017 kg/m3 derives from mass 2.68 × 1030 kg / volume of star of radius 12 km; 5.9×1017 kg m?3 derives from mass 4.2×1030 kg per volume of star radius 11.9 km

[20] http://www.astro.umd.edu/~miller/nstar.html

[21] Zahn, Corvin (1990-10-09). "Tempolimit Lichtgeschwindigkeit"