Neutron-star oscillation

Asteroseismology studies the internal structure of our Sun and other stars using oscillations. These can be studied by interpreting the temporal frequency spectrum acquired through observations.[1] In the same way, the more extreme neutron stars might be studied and hopefully give us a better understanding of neutron-star interiors, and help in determining the equation of state for matter at nuclear densities. Scientists also hope to prove, or discard, the existence of so-called quark stars, or strange stars, through these studies.[2]

Comparison between predicted frequencies in a totally fluid, and in a three-component neutron-star model.
(P. N. McDermott et al., The Astrophysical Journal, 325: 725-748, 1988; doi:10.1086/184553; Reproduced by permission of the American Astronomical Society)

Types of oscillations

The modes of oscillations are divided into subgroups, each with different characteristic behavior. First they are divided into toroidal and spherical modes, with the latter further divided into radial and non-radial modes. Spherical modes are oscillations in the radial direction while toroidal modes oscillate horizontally, perpendicular to the radial direction. The radial modes can be considered as a special case of non-radial ones, preserving the shape of the star in the oscillations, while the non-radial don’t. Generally, only the spherical modes are considered in studies of stars, as they are the easiest to observe, but the toroidal modes might also be studied.

In our Sun, only three types of modes have been found so far, namely p-, g- and f- modes. Helioseismology studies these modes with periods in the range of minutes, while for neutron stars the periods are much shorter, often seconds or even milliseconds.

An illustration of p-mode oscillations in a spherical body.
(R. Nilsson, MSc thesis (Lund Observatory), 2005; Reproduced by permission of author)

The extreme properties of neutron stars permit several others types of modes.

More details on stellar pulsation modes and a comparison with the pulsation modes of black holes can be found in the Living Review by Kokkotas and Schmidt.[11]

Oscillation excitation

Generally, oscillations are caused when a system is perturbed from its dynamical equilibrium, and the system, using a restoration force, tries to return to that equilibrium state. The oscillations in neutron stars are probably weak with small amplitudes, but exciting these oscillations might increase the amplitudes to observable levels. One of the general excitation mechanisms are eagerly awaited outbursts, comparable to how one creates a tone when hitting a bell. The hit adds energy to the system, which excites the amplitudes of the oscillations to greater magnitude, and so is more easily observed. Apart from such outbursts, flares as they are often called, other mechanisms have been proposed to contribute to these excitations:[12]

Mode damping

The oscillations are damped through different processes in the neutron star which are not yet fully understood. The damping time is the time for the amplitude of a mode to decay to e−1. A wide variety of different mechanisms have been found, but the strength of their impact differs among the modes.

Observations

So far, most data about neutron-star oscillations come from the blasts of four specific Soft Gamma Repeaters, SGR, especially the event of 27 December 2004 from SGR 1806-20. Because so few events have been observed, little is known for sure about neutron stars and the physics of their oscillations. The outbursts which are vital for analyses only happen sporadically and are relatively brief. Given the limited knowledge, many of the equations surrounding the physics around these objects are parameterized to fit observed data, and where data is not to be found solar values are used instead. However, with more projects capable of observing these kinds of blasts with higher accuracy, and the hopeful development of w-mode studies, the future looks promising for better understanding one of the Universe’s most exotic objects.

References

  1. M. Cunha; et al. (2007). "Asteroseismology and interferometry". Astronomy and Astrophysics Review 14 (3-4): 217–360. arXiv:0709.4613. Bibcode:2007A&ARv..14..217C. doi:10.1007/s00159-007-0007-0.
  2. "1122 Hz rotation of XTE J1739-285 as a probe of quark matter in the interior of the neutron star". arXiv:0712.4310. Bibcode:2007arXiv0712.4310Z.
  3. P. N. McDermott; et al. (1987). "Nonradial oscillations of neutron stars". The Astrophysical Journal 325: 726–748. Bibcode:1988ApJ...325..725M. doi:10.1086/166044.
  4. K. D. Kokkotas; B. F. Schutz (1986). "Normal modes of a model radiating system". General Relativity and Gravitation 18: 913–921. Bibcode:1986GReGr..18..913K. doi:10.1007/BF00773556.
  5. Y. Kojima (1988). "Two Families of Normal Modes in Relativistic Stars". Progress of Theoretical Physics 79 (3): 665–675. Bibcode:1988PThPh..79..665K. doi:10.1143/PTP.79.665.
  6. K. D. Kokkotas; B. F. Schutz (1992). "W-modes - A new family of normal modes of pulsating relativistic stars". Monthly Notices of the Royal Astronomical Society 255: 119–128. Bibcode:1992MNRAS.255..119K. doi:10.1093/mnras/255.1.119.
  7. S. Chandrasekhar; V. Ferrari (August 1991). "On the non-radial oscillations of a star. III - A reconsideration of the axial modes". Proceedings of the Royal Society of London A 434 (1891): 449–457. Bibcode:1991RSPSA.434..449C. doi:10.1098/rspa.1991.0104.
  8. N. Andersson; Y. Kojima; K. D. Kokkotas (1996). "On the Oscillation Spectra of Ultracompact Stars: an Extensive Survey of Gravitational-Wave Modes". The Astrophysical Journal 462: 855. arXiv:gr-qc/9512048. Bibcode:1996ApJ...462..855A. doi:10.1086/177199.
  9. M. Leins; H.-P. Nollert; M. H. Soffel (1993). "Nonradial oscillations of neutron stars: A new branch of strongly damped normal modes". Physical Review D 48 (8): 3467–3472. Bibcode:1993PhRvD..48.3467L. doi:10.1103/PhysRevD.48.3467.
  10. 1 2 R. Nilsson (2005), MSc Thesis (Lund Observatory), High-speed astrophysics: Chasing neutron-star oscillations.
  11. K. Kokkotas; B. Schmidt (1999). "Quasi-Normal Modes of Stars and Black Holes". Living Reviews in Relativity. arXiv:gr-qc/9909058. Bibcode:1999LRR.....2....2K. doi:10.12942/lrr-1999-2.
  12. R. Duncan (1998). "Global seismic oscillations in Soft Gamma Repeaters". Astrophysical Journal Letters 498 (1): L45. arXiv:astro-ph/9803060. Bibcode:1998ApJ...498L..45D. doi:10.1086/311303.

External links

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