The oscillations of a merger remnant forming after the coalescence of two neutron stars are very characteristic for the high-density equation of state. The dominant oscillation frequency occurs as a pronounced peak in the kHz range of the gravitation
al-wave spectrum. We describe how the dominant oscillation frequency of the remnant can be employed to infer the radii of non-rotating neutron stars.
We present a novel method for revealing the equation of state of high-density neutron star matter through gravitational waves emitted during the postmerger phase of a binary neutron star system. The method relies on a small number of detections of th
e peak frequency in the postmerger phase for binaries of different (relatively low) masses, in the most likely range of expected detections. From such observations, one can construct the derivative of the peak frequency versus the binary mass, in this mass range. Through a detailed study of binary neutron star mergers for a large sample of equations of state, we show that one can extrapolate the above information to the highest possible mass (the threshold mass for black hole formation in a binary neutron star merger). In turn, this allows for an empirical determination of the maximum mass of cold, nonrotating neutron stars to within 0.1 M_sun, while the corresponding radius is determined to within a few percent. Combining this with the determination of the radius of cold, nonrotating neutron stars of 1.6 M_sun (to within a few percent, as was demonstrated in Bauswein et al., PRD, 86, 063001, 2012), allows for a clear distinction of a particular candidate equation of state among a large set of other candidates. Our method is particularly appealing because it reveals simultaneously the moderate and very high-density parts of the equation of state, enabling the distinction of mass-radius relations even if they are similar at typical neutron star masses. Furthermore, our method also allows to deduce the maximum central energy density and maximum central rest-mass density of cold, nonrotating neutron stars with an accuracy of a few per cent.
We investigate systematically the dynamical mass ejection, r-process nucleosynthesis, and properties of electromagnetic counterparts of neutron-star (NS) mergers in dependence on the uncertain properties of the nuclear equation of state (EoS) by empl
oying 40 representative, microphysical high-density EoSs in relativistic, hydrodynamical simulations. The crucial parameter determining the ejecta mass is the radius R_1.35 of a 1.35 M_sun NS. NSs with smaller R_1.35 (soft EoS) eject systematically higher masses. These range from ~10^-3 M_sun to ~10^-2 M_sun for 1.35-1.35 M_sun binaries and from ~5*10^-3 M_sun to ~2*10^-2 M_sun for 1.2-1.5 M_sun systems (with kinetic energies between ~5*10^49 erg and 10^51 erg). Correspondingly, the bolometric peak luminosities of the optical transients of symmetric (asymmetric) mergers vary between 3*10^41 erg/s and 14*10^41 erg/s (9*10^41 erg/s and 14.5*10^41 erg/s) on timescales between ~2 h and ~12 h. If these signals with absolute bolometric magnitudes from -15.0 to -16.7 are measured, the tight correlation of their properties with those of the merging NSs might provide valuable constraints on the high-density EoS. The r-process nucleosynthesis exhibits a remarkable robustness independent of the EoS, producing a nearly solar abundance pattern above mass number 130. By the r-process content of the Galaxy and the average production per event the Galactic merger rate is limited to 4*10^-5/yr (4*10^-4/yr) for a soft (stiff) NS EoS, if NS mergers are the main source of heavy r-nuclei. The production ratio of radioactive 232Th to 238U attains a stable value of 1.64-1.67, which does not exclude NS mergers as potential sources of heavy r-material in the most metal-poor stars.
Neutron-star (NS) merger simulations are conducted for 38 representative microphysical descriptions of high-density matter in order to explore the equation-of-state dependence of the postmerger ring-down phase. The formation of a deformed, oscillatin
g, differentially rotating very massive NS is the typical outcome of the coalescence of two stars with 1.35 $M_{odot}$ for most candidate EoSs. The oscillations of this object imprint a pronounced peak in the gravitational-wave (GW) spectra, which is used to characterize the emission for a given model. The peak frequency of this postmerger GW signal correlates very well with the radii of nonrotating NSs, and thus allows to constrain the high-density EoS by a GW detection. In the case of 1.35-1.35 $M_{odot}$ mergers the peak frequency scales particularly well with the radius of a NS with 1.6 $M_{odot}$, where the maximum deviation from this correlation is only 60 meters for fully microphysical EoSs which are compatible with NS observations. Combined with the uncertainty in the determination of the peak frequency it appears likely that a GW detection can measure the radius of a 1.6 $M_{odot}$ NS with an accuracy of about 100 to 200 meters. We also uncover relations of the peak frequency with the radii of nonrotating NSs with 1.35 $M_{odot}$ or 1.8 $M_{odot}$, with the radius or the central energy density of the maximum-mass Tolman-Oppenheimer-Volkoff configuration, and with the pressure or sound speed at a fiducial rest-mass density of about twice nuclear saturation density. Furthermore, it is found that a determination of the dominant postmerger GW frequency can provide an upper limit for the maximum mass of nonrotating NSs. The prospects for a detection of the postmerger GW signal and a determination of the dominant GW frequency are estimated to be in the range of 0.015 to 1.2 events per year with the upcoming Advanced LIGO detector.
The rapid neutron-capture process, or r-process, is known to be fundamental for explaining the origin of approximately half of the A>60 stable nuclei observed in nature. In recent years nuclear astrophysicists have developed more and more sophisticat
ed r-process models, by adding new astrophysical or nuclear physics ingredients to explain the solar system composition in a satisfactory way. Despite these efforts, the astrophysical site of the r-process remains unidentified. The composition of the neutron star outer crust material is investigated after the decompression that follows its possible ejection. The composition of the outer crust of a neutron star is estimated before and after decompression. Two different possible initial conditions are considered, namely an idealized crust composed of cold catalyzed matter and a crust initially in nuclear statistical equilibrium at temperatures around 10 GK. We show that in this second case before decompression and at temperatures typically corresponding to 8 GK, the Coulomb effect due to the high densities in the crust leads to an overall composition of the outer crust in neutron-rich nuclei with a mass distribution close to the solar system r-abundance distribution. Such distributions differ, however, from the solar one due to a systematic shift in the second peak to lower values. After decompression, the capture of the few neutrons per seed nucleus available in the hot outer crust leads to a final distribution of stable neutron-rich nuclei with a mass distribution of 80 < A < 140 nuclei in excellent agreement with the solar distribution, provided the outer crust is initially at temperatures around 8 GK and all layers of the outer crust are ejected. The decompression of the neutron star matter from the outer crust provides suitable conditions for a robust r-processing of the light species, i.e., r-nuclei with A < 140.
