# Extracting Information on the Equation of State from Binary Neutron Stars

## Abstract

Recently Bauswein and Janka [6, 7] found that the typical frequency of a hypermassive neutron star, which is called \(f_2\) in this paper, is a simple function of the average rest-mass density, essentially independently of the equation of state considered. While expected, this result is very important to decide the system mass from observed gravitational waves. However in their simulations, the Einstein equations were solved by assuming conformal flatness and employing a gravitational radiation-reaction scheme within a post-Newtonian framework. Besides this mathematical approximation, there is also a numerical one in the use of smooth-particle hydrodynamics code, which is well-know to be particularly dissipative and that rapidly suppresses the amplitude of the bar-mode deformation and rapidly yields to an almost axisymmetric system. Therefore we have reinvestigated the calculations in their work improving on the two approximations discussed above (*i.e.*, conformal flatness and smooth-particle hydrodynamics) to obtain an accurate description both during the inspiral and after the merger. Then we have found another typical frequency with a clear peak, which is called \(f_\mathrm {LI}\) in this paper. Finally we show the relations between the initial masses and the \(f_\mathrm {LI}\) and \(f_2\) frequencies of the gravitational waves emission from a hypermassive neutron stars.

## Notes

### Acknowledgments

This work was supported in part by the DFG grant SFB/Transregio 7 and by “CompStar”, a Research Networking Programme of the ESF. The simulations were performed on SuperMUC at LRZ-Munich and on Datura at AEI-Potsdam.

## References

- 1.G.M. Harry et al., Class. Quantum Grav.
**27**, 084006 (2010)MathSciNetCrossRefADSGoogle Scholar - 2.T. Accadia et al., Class. Quantum Grav.
**28**, 114002 (2011)CrossRefADSGoogle Scholar - 3.Y. Aso, Y. Michimura, K. Somiya, M. Ando, O. Miyakawa, T. Sekiguchi, D. Tatsumi, H. Yamamoto, Phys. Rev. D
**88**, 043007 (2013)CrossRefADSGoogle Scholar - 4.J. Abadie et al., Class. Quantum Grav.
**27**, 173001 (2010)CrossRefADSGoogle Scholar - 5.N. Stergioulas, A. Bauswein, K. Zagkouris, H.T. Janka, Mon. Not. R. Astron. Soc.
**418**, 427 (2011)CrossRefADSGoogle Scholar - 6.A. Bauswein, H.T. Janka, Phys. Rev. Lett.
**108**, 011101 (2012)CrossRefADSGoogle Scholar - 7.A. Bauswein, H.T. Janka, K. Hebeler, A. Schwenk, Phys. Rev. D
**86**, 063001 (2012)CrossRefADSGoogle Scholar - 8.D. Alic, C. Bona-Casas, C. Bona, L. Rezzolla, C. Palenzuela, Phys. Rev. D
**85**, 064040 (2012)CrossRefADSGoogle Scholar - 9.L. Baiotti, I. Hawke, P.J. Montero, F. Löffler, L. Rezzolla, N. Stergioulas, J.A. Font, E. Seidel, Phys. Rev. D
**71**, 024035 (2005)CrossRefADSGoogle Scholar - 10.E. Schnetter, S.H. Hawley, I. Hawke, Class. Quantum Grav.
**21**, 146588 (2004)MathSciNetCrossRefGoogle Scholar - 11.J.S. Read, D.L. Benjamin, B.J. Owen, J.L. Friedman, Phys. Rev. D
**79**, 124032 (2009)CrossRefADSGoogle Scholar - 12.
- 13.J.S. Read, L. Baiotti, J.D.E. Creighton, J.L. Friedman, B. Giacomazzo, K. Kyutoku, C. Markakis, L. Rezzolla, M. Shibata, K. Taniguchi, Phys. Rev. D
**88**, 044042 (2013)CrossRefADSGoogle Scholar - 14.B.S. Sathyaprakash, B.F. Schutz, Living reviews in relativity (2009)Google Scholar