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Excitation of stellar oscillations by gravitational waves: hydrodynamic model and numerical results for the Sun  [PDF]
D. M. Siegel,M. Roth
Physics , 2011, DOI: 10.1088/0004-637X/729/2/137
Abstract: Starting from a general relativistic framework a hydrodynamic formalism is derived that yields the mean-square amplitudes and rms surface velocities of normal modes of non-relativistic stars excited by arbitrary gravitational wave (GW) radiation. In particular, stationary GW fields are considered and the resulting formulae are evaluated for two general types of GW radiation: radiation from a particular astrophysical source (e.g., a binary system) and a stochastic background of gravitational waves (SBGW). Expected sources and signal strengths for both types of GW radiation are reviewed and discussed. Numerical results for the Sun show that low-order quadrupolar g modes are excited more strongly than p modes by orders of magnitude. Maximal rms surface velocities in the case of excitation by astrophysical sources are found to be v {\le} 10^(-8) mm/s, assuming GW strain amplitudes of h {\le} 10^(-20). It is shown that current models for an SBGW produced by cosmic strings, with Omega_GW ~ 10^(-8)-10^(-5) in the frequency range of solar g modes, are able to produce maximal solar g-mode rms surface velocities of 10^(-5)-10^(-3) mm/s. This result lies close to or within the amplitude range of 10^(-3)-1 mm/s expected from excitation by turbulent convection, which is currently considered to be responsible for stellar g-mode excitation. It is concluded that studying g-mode observations of stars other than the Sun, in which excitation by GWs could be even more effective due to different stellar structures, might provide a new method to either detect GWs or to deduce a significant direct upper limit on an SBGW at intermediate frequencies between the pulsar bound and the bounds from interferometric detectors on Earth.
Stochastic excitation of stellar oscillations  [PDF]
Reza Samadi
Physics , 2001,
Abstract: Excitation of solar oscillations is attribued to turbulent motions in the solar convective zone. It is also currently believed that oscillations of low massive stars (M <2 Mo) - which possess an upper convective zone - are stochastically excited by turbulent convection in their outer layers. A recent theoretical work (Samadi & Goupil, 2001 ; Samadi et al, 2001) supplements and reinforces this theory. This allows the use of any available model of turbulence and emphasizes some recent unsolved problems which are brought up by these new theoretical developments.
Solar Oscillations and Convection: II. Excitation of Radial Oscillations  [PDF]
R. F. Stein,?. Nordlund
Physics , 2000, DOI: 10.1086/318218
Abstract: Solar p-mode oscillations are excited by the work of stochastic, non-adiabatic, pressure fluctuations on the compressive modes. We evaluate the expression for the radial mode excitation rate derived by Nordlund and Stein (Paper I) using numerical simulations of near surface solar convection. We first apply this expression to the three radial modes of the simulation and obtain good agreement between the predicted excitation rate and the actual mode damping rates as determined from their energies and the widths of their resolved spectral profiles. We then apply this expression for the mode excitation rate to the solar modes and obtain excellent agreement with the low l damping rates determined from GOLF data. Excitation occurs close to the surface, mainly in the intergranular lanes and near the boundaries of granules (where turbulence and radiative cooling are large). The non-adiabatic pressure fluctuations near the surface are produced by small instantaneous local imbalances between the divergence of the radiative and convective fluxes near the solar surface. Below the surface, the non-adiabatic pressure fluctuations are produced primarily by turbulent pressure fluctuations (Reynolds stresses). The frequency dependence of the mode excitation is due to effects of the mode structure and the pressure fluctuation spectrum. Excitation is small at low frequencies due to mode properties -- the mode compression decreases and the mode mass increases at low frequency. Excitation is small at high frequencies due to the pressure fluctuation spectrum -- pressure fluctuations become small at high frequencies because they are due to convection which is a long time scale phenomena compared to the dominant p-mode periods.
Resonant growth of stellar oscillations by incident gravitational waves  [PDF]
Yasufumi Kojima,Hajime Tanimoto
Physics , 2005, DOI: 10.1088/0264-9381/22/14/009
Abstract: Stellar oscillation under the combined influences of incident gravitational wave and radiation loss is studied in a simple toy model. The star is approximated as a uniform density ellipsoid in the Newtonian gravity including radiation damping through quadrupole formula. The time evolution of the oscillation is significantly controlled by the incident wave amplitude $h$, frequency $\nu$ and damping time $\tau$. If a combination $ h \nu \tau $ exceeds a threshold value, which depends on the resonance mode, the resonant growth is realized.
Non-radial oscillations of neutron stars and the detection of gravitational waves  [PDF]
Cecilia Chirenti,Patrick R. Silveira,Odylio D. Aguiar
Physics , 2012, DOI: 10.1142/S2010194512008185
Abstract: We study the non-radial oscillations of relativistic neutron stars, in particular the (fundamental) f-modes, which are believed to be the most relevant for the gravitational wave emission of perturbed isolated stars. The expected frequencies of the f-modes are compared to the sensitivity range of Mario Schenberg, the Brazilian gravitational wave spherical detector.
Coupling of Radial and Axial non-Radial Oscillations of Compact Stars: Gravitational Waves from first-order Differential Rotation  [PDF]
A. Passamonti,M. Bruni,L. Gualtieri,A. Nagar,C. F. Sopuerta
Physics , 2005, DOI: 10.1103/PhysRevD.73.084010
Abstract: We investigate the non-linear coupling between radial and non-radial oscillations of static spherically symmetric neutron stars as a possible mechanism for the generation of gravitational waves that may lead to observable signatures. In this paper we concentrate on the axial sector of the non-radial perturbations. By using a multi-parameter perturbative framework we introduce a complete description of the non-linear coupling between radial and axial non-radial oscillations; we study the gauge invariant character of the associated perturbative variables and develop a computational scheme to evolve the non-linear coupling perturbations in the time domain. We present results of simulations corresponding to different physical situations and discuss the dynamical behaviour of this non-linear coupling. Of particular interest is the occurrence of signal amplifications in the form of resonance phenomena when a frequency associated with the radial pulsations is close to a frequency associated with one of the axial w-modes of the star. Finally, we mention possible extensions of this work and improvements towards more astrophysically motivated scenarios.
Gravitational waves from perturbed stars  [PDF]
Valeria Ferrari
Physics , 2011,
Abstract: Non radial oscillations of neutron stars are associated with the emission of gravitational waves. The characteristic frequencies of these oscillations can be computed using the theory of stellar perturbations, and they are shown to carry detailed information on the internal structure of the emitting source. Moreover, they appear to be encoded in various radiative processes, as for instance in the tail of the giant flares of Soft Gamma Repeaters. Thus, their determination is central to the theory of stellar perturbation. A viable approach to the problem consists in formulating this theory as a problem of resonant scattering of gravitational waves incident on the potential barrier generated by the spacetime curvature. This approach discloses some unexpected correspondences between the theory of stellar perturbations and the theory of quantum mechanics, and allows us to predict new relativistic effects.
Instability of LBV-stars against radial oscillations  [PDF]
Yu. A. Fadeyev
Physics , 2009, DOI: 10.1134/S1063773710050075
Abstract: In this study we consider the nonlinear radial oscillations exciting in LBV--stars with effective temperatures 1.5e4 K <= Teff <= 3e4 K, bolometric luminosities 1.2e6 L_odot <= L <= 1.9e6 L_odot and masses 35.7 M_odot <= M <= 49.1 M_odot. Hydrodynamic computations were carried out with initial conditions obtained from evolutionary sequences of population I stars (X=0.7, Z=0.02) with initial masses from 70M_odot to 90 M_odot. All hydrodynamical models show instability against radial oscillations with amplitude growth time comparable with dynamical time scale of the star. Radial oscillations exist in the form of nonlinear running waves propagating from the boundary of the compact core to the upper boundary of the hydrodynamical model. The velocity amplitude of outer layers is of several hundreds of km/s while the bolometric light amplitude does not exceed 0.2 mag. Stellar oscillations are not driven by the kappa-mechanism and are due to the instability of the gas with adiabatic exponent close to the critical value Gamma_1 = 4/3 due to the large contribution of radiation in the total pressure. The range of the light variation periods (6 day <= P <= 31 day) of hydrodynamical models agrees with periods of microvariability observed in LBV--stars.
Gravitational Waves from Phase Transition of Accreting Neutron Stars  [PDF]
K. S. Cheng,Z. G. Dai
Physics , 1997, DOI: 10.1086/305040
Abstract: We propose that when neutron stars in low-mass X-ray binaries accrete sufficient mass and become millisecond pulsars, the interiors of these stars may undergo phase transitions, which excite stellar radial oscillations. We show that the radial oscillations will be mainly damped by gravitational-wave radiation instead of internal viscosity. The gravitational waves can be detected by the advanced Laser Interferometer Gravitational-Wave Observatory at a rate of about three events per year.
Gravitational Waves from Nonlinear Couplings of Radial and Polar Nonradial Modes in Relativistic Stars  [PDF]
Andrea Passamonti,Nikolaos Stergioulas,Alessandro Nagar
Physics , 2007, DOI: 10.1103/PhysRevD.75.084038
Abstract: The post-bounce oscillations of newly-born relativistic stars are expected to lead to gravitational-wave emission through the excitation of nonradial oscillation modes. At the same time, the star is oscillating in its radial modes, with a central density variation that can reach several percent. Nonlinear couplings between radial oscillations and polar nonradial modes lead to the appearance of combination frequencies (sums and differences of the linear mode frequencies). We study such combination frequencies using a gauge-invariant perturbative formalism, which includes bilinear coupling terms between different oscillation modes. For typical values of the energy stored in each mode we find that gravitational waves emitted at combination frequencies could become detectable in galactic core-collapse supernovae with advanced interferometric or wide-band resonant detectors.
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