Determination of properties of protoneutron stars toward black hole formation via gravitational wave observations

Abstract

We examine the frequencies of the fundamental (f -) and the gravity (gi-) mode in gravitational waves from accreting protoneutron stars (PNSs) toward black hole formation. For this purpose, we analyze numerical results of gravitational collapse of massive stars for two different progenitors with three equations of state. We adopt profiles of central objects obtained from the numerical simulations by solving general relativistic neutrinoradiation hydrodynamics under the spherical symmetry. Using a series of snapshots as a static configuration at each time step, we solve the eigenvalue problem to determine the specific frequencies of gravitational waves from the evolving PNSs with accretion from core bounce to black hole formation by the relativistic Cowling approximation. We find that the frequency of the f -mode gravitational waves can be expressed as a function of the average density of the PNS at each time step almost independently of the progenitor models in accord with the previous studies on ordinary PNSs. We also find that the ratio of the g1-mode frequency to the f -mode frequency is insensitive to the progenitor, but strongly depends on the compactness of the PNSs. Having a simultaneous observation of the f -and g1-mode gravitational waves, it would provide the information of the average density and compactness of PNS, which can reconstruct the evolution of mass and radius of the PNSs as a constraint on the equation of state at high densities. Furthermore, we show that the highest average density of the PNS with the maximum mass can be estimated with the detection of the f -mode gravitational waves together with the help of the neutrino observations.

Universal relation for supernova gravitational waves

“…In the same figure, we also show the empirical relation for the f -mode frequency derived in Ref. [46], which is The thick-solid line is the fitting formula for the g1-mode (f -mode) frequency before (after) the avoided crossing between the f -and g1-modes, which is given by Eq. ( 3), while thick-dashed line denotes the empirical formula derived in Ref.…”

“…On the other hand, the studies about asteroseismology on PNSs are gradually increasing (e.g., [20][21][22][23][24][25][40][41][42][43][44][45][46][47][48][49][50][51]). This may be partially thanks to progress of the numerical simulation of core-collapse supernovae, which can provide the background PNS models for making a linear analysis.…”

“…With using such a background model, mainly two different approaches have been done in the PNS asteroseismology. The first approach is that the PNS surface is defined by a specific surface density, e.g., ρ s = 10 11 g/cm 3 , and one considers the characteristic oscillations inside the PNS model, where the boundary condition imposed at the PNS surface is assumed to be the vacuum boundary condition, i.e., the Lagrangian perturbation of pressure should be zero [20][21][22][40][41][42][43][44][45][46], even though the matter still exists outside the PNS surface selected here. With this approach, one can classify the oscillation modes with the number of radial nodes in the eigenfunctions according to the standard asteroseismology, while there is uncertainty in the selection of the surface density.…”

Gravitational wave physics and astronomy in the nascent era

“…We revealed the characteristic feature in the frequencies of 53/89 GWs from the dynamical evolution of proto-neutron star toward the black hole formation. We analyzed the time evolution of accreting proto-neutron stars to determine the fundamental and gravity modes of GWs [380] by utilizing the results of the numerical simulations of massive stars with a set of equation of state [377]. The density increase toward the black hole mass leads to the rise of frequencies of GWs as a function of average density of the proto-neutron star.…”

Gravitational wave asteroseismology on cooling neutron stars

“…In a similar way, if one would observe the gravitational waves and identify it with a specific oscillation mode, one could extract the neutron star mass, radius, and EOS (e.g., [19][20][21][22][23][24][25][26][27][28]). Moreover, in order to understand the physical background behind the gravitational wave signals appearing in the numerical simulation data for core-collapse supernovae, the asteroseismology is becoming one of the important studies (e.g., [29][30][31][32][33][34][35][36][37][38]).…”