# High-frequency behavior of w-mode pulsations of compact stars

## Abstract

We study the asymptotic behavior of the quasinormal modes (QNMs) of w-mode pulsations of compact stars in the high-frequency regime. We observe that both the axial and polar w-mode QNMs attain similar asymptotic behaviors in spite of the fact that they are described by two totally different differential equation systems. We obtain robust asymptotic formulas relating w-mode QNMs of different polarities and different angular momenta. To explore the physical reason underlying such similarity, we first derive a high-frequency approximation for the polar w-mode oscillations to unify the descriptions for both cases. Then, we develop WKB-type analyses for them and quantitatively explain the observed asymptotic behaviors for polytropic stars and quark stars. We also point out that such asymptotic behaviors for realistic stars are strongly dependent on the equation of state near the stellar surface.

- Authors:

- Physics Department and Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin (Hong Kong)

- Publication Date:

- OSTI Identifier:
- 21537532

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 83; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.83.064012; (c) 2011 American Institute of Physics; Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR MOMENTUM; APPROXIMATIONS; ASYMPTOTIC SOLUTIONS; DIFFERENTIAL EQUATIONS; EQUATIONS OF STATE; OSCILLATION MODES; PULSATIONS; STARS; CALCULATION METHODS; EQUATIONS; MATHEMATICAL SOLUTIONS

### Citation Formats

```
Zhang, Y. J., Wu, J., and Leung, P. T.
```*High-frequency behavior of w-mode pulsations of compact stars*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVD.83.064012.

```
Zhang, Y. J., Wu, J., & Leung, P. T.
```*High-frequency behavior of w-mode pulsations of compact stars*. United States. doi:10.1103/PHYSREVD.83.064012.

```
Zhang, Y. J., Wu, J., and Leung, P. T. Tue .
"High-frequency behavior of w-mode pulsations of compact stars". United States. doi:10.1103/PHYSREVD.83.064012.
```

```
@article{osti_21537532,
```

title = {High-frequency behavior of w-mode pulsations of compact stars},

author = {Zhang, Y. J. and Wu, J. and Leung, P. T.},

abstractNote = {We study the asymptotic behavior of the quasinormal modes (QNMs) of w-mode pulsations of compact stars in the high-frequency regime. We observe that both the axial and polar w-mode QNMs attain similar asymptotic behaviors in spite of the fact that they are described by two totally different differential equation systems. We obtain robust asymptotic formulas relating w-mode QNMs of different polarities and different angular momenta. To explore the physical reason underlying such similarity, we first derive a high-frequency approximation for the polar w-mode oscillations to unify the descriptions for both cases. Then, we develop WKB-type analyses for them and quantitatively explain the observed asymptotic behaviors for polytropic stars and quark stars. We also point out that such asymptotic behaviors for realistic stars are strongly dependent on the equation of state near the stellar surface.},

doi = {10.1103/PHYSREVD.83.064012},

journal = {Physical Review. D, Particles Fields},

issn = {0556-2821},

number = 6,

volume = 83,

place = {United States},

year = {2011},

month = {3}

}