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 f2 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 smoothparticle 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.Thenwehave found another typical frequency with a clear peak, which is called fFI in this paper. Finally we show the relations between the initial masses and the fFI and f2 frequencies of the gravitational waves emission from a hypermassive neutron stars.