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Register a new userAmplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars
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Nonlinear growth of the bar-mode deformation is studied for a differentially rotating star with supercritical rotational energy. In particular, the growth mechanism of some azimuthal modes with odd wave numbers is examined by comparing a simplified mathematical model with a realistic simulation. Mode coupling to even modes, i.e., the bar mode and higher harmonics, significantly enhances the amplitudes of odd modes, unless they are exactly zero initially. Therefore, other modes which are not axially symmetric cannot be neglected at late times in the growth of the unstable bar-mode even when starting from an almost axially symmetric state.
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We investigate the nonlinear behaviour of the dynamically unstable rotating star for the bar mode by three-dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the unstable bar mode, and that its characteristic frequency is twice as that of the bar mode, which oscillates mainly along the equatorial plane. A possibility to observe Faraday resonance in gravitational waves is demonstrated and discussed.
Spinning bosonic stars (SBSs) can form from the gravitational collapse of a dilute cloud of scalar/Proca particles with non-zero angular momentum. In a recent work we found that the scalar stars are transient due to a non-axisymmetric instability which triggers the loss of angular momentum. We further study the dynamical formation of SBSs using 3-dimensional numerical-relativity simulations of the Einstein-(massive, complex)Klein-Gordon system and of the Einstein-(complex)Proca system. We incorporate a quartic self-interaction potential in the scalar case to gauge its effect on the instability; we investigate (m=2) Proca stars to assess their stability; we attempt to relate the instability of SBSs to the growth rate of azimuthal density modes and the existence of a corotation point. We show that: the self-interaction potential can only delay the instability in scalar SBSs; m=2 Proca stars always migrate to the stable m=1 spheroidal family; unstable m=2 Proca stars and m=1 scalar boson stars exhibit a corotation point. This establishes a parallelism with rotating neutron stars affected by dynamical bar-mode instabilities. We compute the gravitational waves (GWs) emitted and investigate the detectability of the waveforms comparing the characteristic strain of the signal with the sensitivity curves of a variety of detectors, computing the signal-to-noise ratio. By assuming that the characteristic damping timescale of the bar-like deformation in SBSs is only set by GWs emission and not by viscosity (unlike in neutron stars), we find that the post-collapse emission could be orders of magnitude more energetic than that of the bar-mode instability itself. Our results indicate that GW observations of SBSs might be within the reach of future experiments, offering a potential means to establish the existence of such stars and to place tight constraints on the mass of the bosonic particle.
Despite more and more observational data, stellar acoustic oscillation modes are not well understood as soon as rotation cannot be treated perturbatively. In a way similar to semiclassical theory in quantum physics, we use acoustic ray dynamics to build an asymptotic theory for the subset of regular modes which are the easiest to observe and identify. Comparisons with 2D numerical simulations of oscillations in polytropic stars show that both the frequency and amplitude distributions of these modes can accurately be described by an asymptotic theory for almost all rotation rates. The spectra are mainly characterized by two quantum numbers; their extraction from observed spectra should enable one to obtain information about stellar interiors.
We investigate the nature of low T/W dynamical instabilities in differentially rotating stars by means of linear perturbation. Here, T and W represent rotational kinetic energy and the gravitational binding energy of the star. This is the first attempt to investigate low T/W dynamical instabilities as a complete set of the eigenvalue problem. Our equilibrium configuration has constant specific angular momentum distribution, which potentially contains a singular solution in the perturbed enthalpy at corotation radius in linear perturbation. We find the unstable normal modes of differentially rotating stars by solving the eigenvalue problem along the equatorial plane of the star, imposing the regularity condition on the center and the vanished enthalpy at the oscillating equatorial surface. We find that the existing pulsation modes become unstable due to the existence of the corotation radius inside the star. The feature of the unstable mode eigenfrequency and its eigenfunction in the linear analysis roughly agrees with that in three-dimensional hydrodynamical simulations in Newtonian gravity. Therefore, our normal mode analysis in the equatorial motion proves valid to find the unstable equilibrium stars efficiently. Moreover, the nature of the eigenfunction that oscillates between corotation and the surface radius for unstable stars requires reinterpretation of the pulsation modes in differentially rotating stars.
Context: Mode identification has remained a major obstacle in the interpretation of pulsation spectra in rapidly rotating stars. Aims: We would like to test mode identification methods and seismic diagnostics in rapidly rotating stars, using oscillation spectra based on new theoretical predictions. Methods: We investigate the auto-correlation function and Fourier transform of theoretically calculated frequency spectra, in which modes are selected according to their visibilities. Given the difficulties in predicting intrinsic mode amplitudes, we experimented with various ad-hoc prescriptions for setting these, including using random values. Furthermore, we analyse the ratios between mode amplitudes observed in different photometric bands. Results: When non-random intrinsic mode amplitudes are used, our results show that it is possible to extract the large frequency separation or half its value, and sometimes twice the rotation rate, from the auto-correlation function. The Fourier transforms are mostly sensitive to the large frequency separation or half its value. When the intrinsic mode amplitudes include random factors, the results are far less favourable. We also find that amplitude ratios provide a good way of grouping together modes with similar characteristics. By analysing the frequencies of these groups, it is possible to constrain mode identification as well as determine the large frequency separation and the rotation rate.
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