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Relativistic Hydrodynamics
Gravitational Waveform Catalog

Section of Astrophysics, Astronomy and Mechanics

Aristotle University of Thessaloniki

Departamento de Astronomía y Astrofísica

Universidad de Valencia

Pulsations of rotating neutron stars could be excited in a number of astrophysical scenarios, such as rotating core collapse, accretion-induced collapse, core quakes due to a large phase-transition in the equation of state, or hypermassive neutron star formation in a binary neutron star merger. These pulsations are a potential source of detectable high-frequency gravitational waves. While for nonrotating stars the frequencies of normal modes can be computed with perturbative methods, there exist no accurate frequency determinations for rapidly rotating stars to date.

Most existing computations of oscillation modes in rapidly rotating relativistic stars use the Cowling approximation [Font, et al., 2001, Stergioulas, et al., 2004], where the evolution of the gravitational field is suppressed. As previous simulations have indicated, the pulsation frequency values computed in this approximation can overestimate the correct values by a factor of up to 2! In our new work [Dimmelmeier, et al., 2006] we were able to perform an accurate determination of several axisymmetric pulsation modes of rotating stars in general relativity.

Simulations:

Our study extends the results presented by [Stergioulas, et al., 2004] (which were obtained in the Cowling approximation) by incorporating the dynamics of the gravitational field in the evolutions. This is done by using the Isenberg--Wilson--Mathews approximation of general relativity, also known as the conformally flat condition (CFC) [Wilson, et al., 1996]. As we have shown in previous work [Dimmelmeier, et al., 2001, Dimmelmeier, et al., 2002a, Dimmelmeier, et al., 2002b, Dimmelmeier, et al., 2005], the approximation works well for rotating neutron star models (the scenario investigated here) as well as in highly dynamical situations like rotational stellar core collapse.

For small pulsation amplitudes we have identifies several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes as well as several axisymmetric inertial modes. The pulsations are studied along the same sequences of uniformly and differentially rotating neutron star models as in [Stergioulas, et al., 2004]. Differential rotation significantly shifts mode frequencies to smaller values, increasing the likelihood of detection by current gravitational wave interferometric detectors (like GEO 600, LIGO, or VIRGO). An important feature of the frequency spectrum, induced by rotation, is the observation of avoided crossings between different mode sequences This results is important for correctly identifying mode frequencies in case of detection.

In [Stergioulas, et al., 2004] a new non-linear damping mechanism for non-linear pulsations was found to operate in uniformly rotating models that are near the mass shedding limit. The damping of pulsations is due to mass shedding, when fluid elements near the equator become unbound due to the radial component of the velocity perturbation. This mass-shedding-induced damping could have severe consequences for, e.g., the f-mode gravitational-wave driven CFS instability, which grows on a secular time-scale. In our new work we have found that while the actual mass-shedding-induced damping does not occur on dynamical time-scales (as in the Cowling approximation) it is still present on secular time-scales, so that a detailed comparison to the f-mode growth rate is required in order to determine the outcome of the f-mode instability.

We have also investigated the gravitational wave signals emitted by the linear modes F, H₁, ²f, and ²p₁ for a slowly rotating neutron star model. In order to estimate the prospects for detectability of the signal by interferometric detectors, we have computed the signal frequency and amplitude for the sensitivity of several detectors. We infer that for a pulsation amplitude of the stellar central density of 5% a gravitational wave signal from the investigated modes is measurable by current detectors, if the signal is integrated over a time of at least 20 ms and the source is located in our Galaxy.

A summary of important quantities of the neutron star models and the frequencies of selected linear pulsation modes are given in several tables.

A more detailed overview about this project and the results can be found in a color slide presentation:

Presentation in PDF format (0.5 MB).

References:

• Dimmelmeier, H., Font, J.A., and Müller, E.,
  "Gravitational waves from relativistic rotational core collapse",
  Astrophys. J. Lett., 560, L163-L166, (2001),
  [Article in astro-ph].


• Dimmelmeier, H., Font, J.A., and Müller, E.,
  "Relativistic simulations of rotational core collapse. I. Methods, initial models, and code tests",
  Astron. Astrophys., 388, 917-935, (2002),
  [Article in astro-ph].


• Dimmelmeier, H., Font, J.A., and Müller, E.,
  "Relativistic simulations of rotational core collapse. II. Collapse dynamics and gravitational radiation",
  Astron. Astrophys., 393, 523-542, (2002),
  [Article in astro-ph].


• Dimmelmeier, H., Novak, J., Font, J.A., Ibáñez, J.M., and Müller, E.,
  "`Mariage des Maillages': A new numerical approach for 3D relativistic core collapse simulations",
  Phys. Rev. D, 71, 064023-1-30, (2005),
  [Article in astro-ph].


• Dimmelmeier, H., Stergioulas, N., and Font, J.A.,
  "Nonlinear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation",
  Mon. Not. R. Astron. Soc., 368, 1609-1630, (2006),
  [Article in astro-ph].


• Font, J.A., Dimmelmeier, H., Gupta, A., and Stergioulas, N.,
  "Axisymmetric modes of rotating relativistic stars in the Cowling approximation",
  Mon. Not. R. Astron. Soc., 325, 1463-1470, (2001),
  [Article in astro-ph].


• Stergioulas, N., Apostolatos, T.A., and Font, J.A.,
  "Non-linear pulsations in differentially rotating neutron stars: Mass-shedding-induced damping and splitting of the fundamental mode",
  Mon. Not. R. Astron. Soc., 352, 1089-1101, (2004),
  [Article in astro-ph].


• Wilson, J.R., Mathews, G.J., and Marronetti, P.,
  "Relativistic numerical model for close neutron-star binaries",
  Phys. Rev. D, 54, 1317-1331, (1996),
  [Article in gr-qc].