Skip to main content
SpringerLink
Log in

Instabilities of Rotating Neutron Stars

  • Chapter
Relativistic Astrophysics

Abstract

This paper reviews the analysis of instabilities of rapidly rotating stellar models. Particular emphasis is given here to those instabilities driven by dissipative processes (e.g. viscosity and gravitational radiation emission) that are expected to play a significant role in influencing the observable properties of rotating neutron stars.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Backer, D.C., Kulkarni, S.R., Heiles, C., Davis, M.M., and Goss, W.M. (1989): A Millisecond Pulsar. Nature, 300, 615–618

    Article  Google Scholar 

  • Bonazzola, S., Frieben, J., and Gourgoulhon, E. (1996): Spontaneous Symmetry Breaking of Rapidly Rotating Stars in General Relativity. Astrophys. J., 460, 379–389

    Article  Google Scholar 

  • Bryan, G.H. (1889): The Waves on a Rotating Liquid Spheroid of Finite Ellipticity. Phil. Trans. Roy. Soc. London, A180, 187–219

    Article  Google Scholar 

  • Chandrasekhar, S (1969): Ellipsoidal Figures of Equilibrium. Yale University Press, New Haven

    MATH  Google Scholar 

  • Chandrasekhar, S. (1970a): Solutions of Two Problems in the Theory of Gravitational Radiation. Phys. Rev. Letters, 24, 611–615

    Article  Google Scholar 

  • Chandrasekhar, S. (1970b): The Effect of Gravitational Radiation on the Secular Stability of the Maclaurin Spheroid. Astrophys. J., 161, 561–569

    Article  MathSciNet  Google Scholar 

  • Clement, M.J. (1981): Normal Modes of Oscillation for Rotating Stars. I. The Effect of Rigid Rotation on Four Low-Order Pulsations. Astrophys. J., 249, 746–760

    Article  Google Scholar 

  • Cook, G.B., Shapiro, S.L., and Teukolsky, S.A. (1994): Rapidly Rotating Neutron Stars in General Relativity— Realistic Equations of State. Astrophys. J., 424, 823–845

    Article  Google Scholar 

  • Cutler, C. (1991): Post-Newtonian Effects on the Modes of Rotating Stars. Astrophys. J., 374, 248–254

    Article  MathSciNet  Google Scholar 

  • Cutler, C. and Lindblom, L. (1987): The Effect of Viscosity on Neutron Star Oscillations. Astrophys. J., 314, 234–241

    Article  Google Scholar 

  • Cutler, C. and Lindblom, L. (1992): Post-Newtonian Frequencies for the Pulsations of Rapidly Rotating Neutron Stars. Astrophys. J., 385, 630–641

    Article  Google Scholar 

  • Cutler, C., Lindblom, L., and Splinter, R.J. (1990): Damping Times for Neutron Star Oscillations. Astrophys. J., 363, 603–611

    Article  Google Scholar 

  • Detweiler, S.L. and Ipser, J.R. (1973): A Variational Principle and a Stability Criterion for the Non-Radial Motions of Pulsation of Stellar Models in General Relativity. Astrophys. J., 185, 685–707

    Article  MathSciNet  Google Scholar 

  • Detweiler, S.L. and Lindblom, L. (1977): On the Evolution of the Homogeneous Ellipsoidal Figures. Astrophys. J., 213, 193–199

    Article  MathSciNet  Google Scholar 

  • Detweiler, S. and Lindblom, L. (1985): On the Nonradial Pulsations of General Relativistic Stellar Models. Astrophys. J., 292, 12–15

    Article  Google Scholar 

  • Friedman, J. (1978): Generic Instability of Rotating Relativistic Stars. Comm. Math. Phys., 62, 247–278

    Article  MATH  Google Scholar 

  • Friedman, J.L. and Schutz, B.F. (1975): On the Stability of Relativistic Systems. Astrophys. J., 200, 204–220

    Article  MathSciNet  Google Scholar 

  • Friedman, J.L. and Schutz, B.F. (1978): Secular Instability of Rotating Newtonian Stars. Astrophys. J., 222, 281–296

    Article  MathSciNet  Google Scholar 

  • Friedman, J.L., Ipser, J.R., and Parker, L. (1986): Rapidly Rotating Neutron Star Models. Astrophys. J., 304, 115–139

    Article  Google Scholar 

  • Ipser, J.R. (1996): Relativistic Accretion Disks: Low Frequency Modes and Frame Dragging. Astrophys. J., 458 508–513

    Article  Google Scholar 

  • Ipser, J.R. and Lindblom, L. (1989): Oscillations and Stability of Rapidly Rotating Neutron Stars. Phys. Rev. Letters, 62, 2777–2780; Errata, 63, 1327

    Google Scholar 

  • Ipser, J.R. and Lindblom, L. (1990): The Oscillations of Rapidly Rotating Newtonian Stellar Models. Astrophys. J., 355, 226–240

    Article  Google Scholar 

  • Ipser, J.R. and Lindblom, L. (1991a): On the Adiabatic Pulsations of Accretion Disks and Rotating Stars. Astrophys. J., 379, 285–289

    Article  Google Scholar 

  • Ipser, J.R. and Lindblom, L. (1991b): The Oscillations of Rapidly Rotating Newtonian Stellar Models II. Dissipative Effects. Astrophys. J., 373, 213–221

    Article  Google Scholar 

  • Ipser, J.R. and Lindblom, L. (1992): On the Pulsations of Relativistic Accretion Disks and Rotating Stars: The Cowling Approximation. Astrophys. J., 389, 392–399

    Article  Google Scholar 

  • Ipser, J.R. and Managan, R.A. (1985): An Eulerian Variational Principle and a Criterion for the Occurrence of Nonaxisymmetric Neutral Modes Along Rotating Axisymmetric Sequences. Astrophys. J., 292, 517–521

    Article  MathSciNet  Google Scholar 

  • James, R.A. (1964): The Structure and Stability of Rotating Gas Masses. Astrophys. J., 140, 552–582

    Article  MathSciNet  Google Scholar 

  • Lebovitz, N.L. (1965): On Schwarzschild’s Criterion for the Stability of Gaseous Masses. Astrophys. J., 142, 229–242

    Article  MathSciNet  Google Scholar 

  • Lindblom, L. (1979): On the Secular Instability from Thermal Conductivity in Rotating Stars. Astrophys. J., 233, 974–980

    Article  Google Scholar 

  • Lindblom, L. (1983): Necessary Conditions for the Stability of Rotating Newtonian Stellar Models. Astrophys. J., 267, 402–408

    Article  MathSciNet  Google Scholar 

  • Lindblom, L. (1992): Determining the Nuclear Equation of State from Neutron Star Masses and Radii. Astrophys. J., 398, 569–573

    Article  Google Scholar 

  • Lindblom, L. (1995): Critical Angular Velocities of Rotating Neutron Stars. Astrophys. J., 438, 265–268

    Article  Google Scholar 

  • Lindblom, L. (1996): Stellar Stability According to Newtonian Theory and General Relativity. In Proceedings of the 14th International Conference on General Relativity and Gravitation (eds. M. Francavagilia, G. Longhi, L. Lussana, and E. Sorace). World Scientific, Singapore, in press

    Google Scholar 

  • Lindblom, L. and Detweiler, S.L. (1977): On the Secular Instabilities of the Maclaurin Spheroids. Astrophys. J., 211, 565–567

    Article  MathSciNet  Google Scholar 

  • Lindblom, L. and Detweiler, S.L. (1983): The Quadrupole Oscillations of Neutron Stars. Astrophys. J. Supp., 53, 73–92

    Article  Google Scholar 

  • Lindblom, L. and Hiscock, W.A. (1983): On the Stability of Rotating Stellar Models in General Relativity Theory. Astrophys. J., 267, 384–401

    Article  MathSciNet  Google Scholar 

  • Lindblom, L. and Splinter, R.J. (1990): The Accuracy of the Relativistic Cowling Approximation. Astrophys. J., 348, 198–202

    Article  Google Scholar 

  • Lynden-Bell, D. and Ostriker, J. (1967): On the Stability of Differentially Rotating Bodies. Mon. Not. Roy. Astron. Soc., 136, 293–310

    MATH  Google Scholar 

  • Managan, R. (1986): Nonaxisymmetric Normal Modes and Secular Instabilities of Rotating Stars. Astrophys. J., 309, 598–608

    Article  Google Scholar 

  • Press, W.H. and Teukolsky, S.A. (1973): On the Evolution of the Secularly Unstable, Viscous Maclaurin Spheroids. Astrophys. J., 181, 513–517

    Article  MathSciNet  Google Scholar 

  • Roberts, P.H. and Stewartson, K. (1963): On the Stability of a Maclaurin Spheroid of Small Viscosity. Astrophys. J., 137, 777–790

    Article  MATH  Google Scholar 

  • Sawyer, R.F. (1989): Bulk Viscosity of Hot Neutron-Star Matter and the Maximum Rotation Rates of Neutron Stars. Phys. Rev. D, 39, 3804–3806

    Article  Google Scholar 

  • Schwarzschild, M. (1958): Structure and Evolution of the Stars. Dover Publications, New York

    Google Scholar 

  • Skinner, D. and Lindblom, L. (1996): On the Viscosity Driven Secular Instability in Rotating Neutron Stars. Astrophys. J., 461, 920–926

    Article  Google Scholar 

  • Thompson, W. and Tait, P.G. (1883): Principles of Natural Philosophy. Clarendon Press, Oxford

    Google Scholar 

  • Thorne, K.S. (1969): Nonradial Pulsation of General-Relativistic Stellar Models. III. Analytic and Numerical Results for Neutron Stars. Astrophys. J., 158, 1–16

    Article  Google Scholar 

  • Thorsett, S.E., Arzoumanian, Z., McKinnon, M.M., and Taylor, J.H. (1993): The Masses of Two Binary Neutron Star Systems. Astrophys. J. Letters, 405, L29 — L32

    Article  Google Scholar 

  • Yoshida, S. and Eriguchi, Y. (1995): Gravitational Radiation Driven Secular Instability of Rotating Polytropes. Astrophys. J., 438, 830–840

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretical Astrophysics 130-33, California Institute of Technology, Pasadena, CA, 91125, USA

    Lee Lindblom

Authors
  1. Lee Lindblom
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Harald Riffert Hanns Ruder Hans-Peter Nollert Friedrich W. Hehl

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Fachmedien Wiesbaden

About this chapter

Cite this chapter

Lindblom, L. (1998). Instabilities of Rotating Neutron Stars. In: Riffert, H., Ruder, H., Nollert, HP., Hehl, F.W. (eds) Relativistic Astrophysics. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-11294-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-663-11294-5_10

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-663-11296-9

  • Online ISBN: 978-3-663-11294-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation