$f$-mode oscillations of protoneutron stars

Abstract

We investigate nonradial $f$-mode oscillations of protoneutron stars in full general relativity, employing equations of state described by the Brueckner-Hartree-Fock theory or the relativistic mean field model, while assuming isentropy and fixed lepton fractions for the internal structure. The validity of various universal relations for cold neutron stars involving $f$-mode characteristics and macroscopic properties of the star is confirmed for those isentropic protoneutron stars. Prospects of observations are also discussed. According to simulation results, we then model details of the thermal and trapping profiles in a PNS with the canonical mass. The corresponding $f$-mode frequencies and gravitational-wave strain amplitudes are presented. The validity of the universal relations during the evolution to the formation of a cold neutron star is confirmed.

Figures (12)

• Figure 1: The energy density (a), proton fraction (b), electron fraction (c), muon fraction (d), and electron neutrino fraction (e) of (P)NSs as functions of pressure with BHF (left panels) and RMF (right panels) EOS, for various values of $S/A$ and lepton fractions, see the text for a detailed description of the notation. The vertical lines indicate $M_\text{max}$ configurations.
• Figure 2: The gravitational mass--radius relations of (P)NSs obtained with BHF (upper panel) and RMF (lower panel) EOSs. The maximum-mass configurations are indicated by circle markers. The horizontal bars indicate the limits on $R_{2.08}$, $R_{2.0}$, and $R_{1.4}$ obtained in the combined NICER+GW170817 data analyses of Miller21Pang21Raaijmakers21 (brown bars) and the recent Rutherford24 (lilac bars). The mass range of the heaviest currently known NS J0952-0607 is also shown. The notation is as in Fig. \ref{['f:eos']}.
• Figure 3: The dimensionless tidal deformability (upper panels) and the MOI (lower panels) of (P)NSs vs gravitational mass $M$ obtained with BHF (left panels) and RMF (right panels) EOSs. Observational values for GW170817 and the pulsar J0737-3039A are shown, see text. The notation is as in Fig. \ref{['f:eos']}.
• Figure 4: The GW frequencies (upper panels) and damping times (lower panels) of $(l=2)\ f$-mode oscillations vs gravitational mass $M$ obtained with BHF (left panels) and RMF (right panels) EOSs. The vertical bars indicate the GW170817 constraint Wen19.
• Figure 5: The radial mass distribution for $2\,M_\odot$ (P)NSs obtained with BHF (upper panels) and RMF (lower panels) EOSs. The vertical lines indicate the radius $R$ and the horizontal bars the extension of the crust.