Pulsational mode and detection of gravitational wave source

Based on Chandrasekhar's and Lebovitz's treatment of the roto-vibrational modes of a homogeneous compressible neutron star, we calculate damping rates per unit eccentricity of toroidal mode and pulsational mode by gravitational radiation. It is found that the damping rate of the pulsational mode which becomes the quadrupole mode (emits gravitational wave) has a minimum at the eccentricity e = 0.72 for = 4/3, and 8/5 whereas both the pulsational mode with = 5/3 and the toroidal mode have no minima, i.e., the pseudo-radial mode can last many years longer than the toroidal mode. We suggest to measure the damping rate of pulsational mode only for the detection of a strong gravity wave source.Submitted for presentation in the 6th Asian Pacific Regional Meeting on Astronomy, I.A.U., to be held on 16–20 August 1993 at IUCAA, Pune, India.     

Gravitational radiation from white dwarfs with rough surfaces

A white dwarf rotating at a maximal angular velocity can take a form of a triaxial ellipsoid due to the rotation and to the presence of mountains on its surface. Such an object emits gravitational waves at a frequency of 2, where is the angular velocity of rotation, and the source of the radiated energy is the rotational kinetic energy. It is shown that the gravitational waves from rapidly rotating white dwarfs at an average distance of 50 pc from an terrestrial observer have an amplitude on the order of 10^–24, so they can be detected by the new generation of detectors. Gravitational radiation from a pulsating white dwarf with a rough surface is also examined. It is shown that quasiradial pulsations of a white dwarf are long-lived; that is, once perturbed, a white dwarf will emit gravitational waves during all lifetime.Translated from Astrofizika, Vol. 48, No. 1, pp. 69–78 (February 2005).     

Gravitational Radiation from Pulsating Magnetic White Dwarfs

Rotating white dwarfs undergoing quasi-radial oscillations can emit gravitational radiation in a frequency range from 0.1-0.3 Hz. Assuming that the energy source for the gravitational radiation comes from the oblateness of the white dwarf induced by the rotation, the strain amplitude is found to be 10^-25 for a white dwarf at 50 pc. We had calculated thermal energy losses through a magneto-hydrodynamic mechanism and found it smaller than estimated before. The galactic population of these sources is estimated to be 10⁷ and may produce a confusion-limited foreground for proposed advanced detectors in the frequency band between space-based and ground-based interferometers. Nearby oscillating white dwarfs may provide a clear enough signal to investigate white dwarf interiors through gravitational wave astroseismology.     

Gravitational tidal waves in Titan's upper atmosphere

Tidal waves driven by Titan's orbital eccentricity through the time-dependent component of Saturn's gravitational potential attain nonlinear, saturation amplitudes (|T^′|>10 K, , and ) in the upper atmosphere (?500 km) due to the approximate exponential growth as the inverse square root of pressure. The gravitational tides, with vertical wavelengths of ∼100-150 km above 500 km altitude, carry energy fluxes sufficient in magnitude to affect the energy balance of the upper atmosphere with heating rates in the altitude range of 500-900 km.     

Evolution of low-mass close binaries and the problem of orbital period gap in cataclysmic variables

Evolution of close binary composed of a white dwarf primary and a Main-Sequence secondary has been calculated. Angular-momentum loss via gravitational radiation and magnetic stellar wind have been taken into account. We have found that magnetic stellar wind with a rate greater than (10^–10–10^–9)M yr^–1 is able to drive the evolution with mass exchange. If the time-scale of switch-off of wind when the primary becomes fully convective is not longer than 10⁶ yr, mass exchange interrupts due to a contraction of the secondary and the system becomes unobservable. Mass exchange resumes when components approach one another due to loss of momentum via gravitational radiation. The location and width of the thus-arising gap in the orbital periods are comparable to those observed.     

Balanced earth satellite orbits

An analytic model for third-body perturbations and for the second zonal harmonic of the central body's gravitational field is presented. A simplified version of this model applied to the Earth-Moon-Sun system indicates the existence of high-altitude and highly-inclined orbits with their apsides in the equator plane, for which the apsidal as well as the nodal motion ceases. For special positions of the node, secular changes of eccentricity and inclination disappear too (balanced orbits). For an ascending node at vernal equinox, the inclination of balanced orbits is 94.56°, for a node at autumnal equinox 85.44°, independent of the eccentricity of the orbit. For a node perpendicular to the equinox, there exist circular balanced orbits at 90° inclination. By slightly adjusting the initial inclination as suggested by the simplified model, orbits can be found — calculated by the full model or by different methods — that show only minor variations in eccentricity, inclination, argument of perigee, and longitude of the ascending node for 10⁵ revolutions and more. Orbits near the unstable equilibria at 94.56° and 85.44° inclination show very long periodic librations and oscillations between retrogade and prograde motion.Retired from IBM Vienna Software Development Laboratory.     

Gravitational waves as a source for the polarization of the Cosmic Microwave Background

The polarization of the Cosmic Microwave Background (CMB) induced by gravitational waves (GWs) is studied by solving in a semi-analytical way the Chandrasekhar radiative transfer equation; following the Polnarev approach, the equation is written as a second-kind Volterra integral equation and its kernel is handled by performing a series expansion of the trigonometric functions it contains. In this way, a recursive calculation of the Volterra equation gets possible and the polarizing effect of the gravitational waves can be brought out.The polarization degree of the CMB coming from this analysis shows a peak for a wavenumber corresponding to GWs re-entering the horizon at the end of the recombination epoch: the position and the size of the maximum are in agreement with the results of other works, based on a totally numerical calculation. However, a difference quite relevant can be remarked when one looks at the shape of the polarization plot: a semi-analytical calculation of the solution of the Volterra integral equation gives a sharp peak due to the fact that the contribution of each packet of GWs of fixed wavenumberk is strongly singled out when one substitutes the integrals with series and sums.As a consequence, this solution method may have some usefulness when one wants to point out the contributions really dominating in producing a polarization for the CMB.From this analysis one can also infer that the best angular scales to test in order to detect a polarization for the CMB are 2°–3°, smaller than those investigated by COBE.     

Radio emission of fast cosmic ions

It is usually assumed that the ions of cosmic rays contribute nothing to the observable electromagnetic radiation. However, this is true only when these ions are moving in a vacuum or a quiet (nonturbulent) plasma. In the case of fast ions in a turbulent plasma, there is an effective nonlinear mechanism of radiation which is discussed in this paper. The fast ion (relativistic or nonrelativistic) moving in the plasma creates a polarization cloud around itself which also moves with the particles. The turbulent plasma waves may scatter on the moving electric field of this polarization cloud. In the process of this scattering an electromagnetic wave with frequency (2.7) is generated. Let ₁ and k₁ be the frequency and wave vector of turbulent plasma waves,V is the velocity of the ion, and is the angle between the wave vector of electromagnetic radiation and the direction of the ion velocity. The method of calculating the probability of the conversion of plasma waves (k₁) into electromagnetic waves (k) by scattering on an ion with velocityV is described in detal in Section 2 (Equation (2.14)).The spectral coefficients of spontaneous radiation in the case of scattering of plasma waves on polarization clouds created by fast nonrelativistic ions are given in (3.6) for an ion energy distribution function (3.4) and in (3.8) for more general evaluations. The Equations (3.9)–(3.13) describe the spectral coefficients of spontaneous emission for different modes of plasma turbulence (Langmuir (3.9), electron cyclotron in a weak (3.10) or strong (3.11) magnetic field and ion acoustic (3.12)–(3.13) waves). The coefficients of reabsorption or induced emission are given by Equations (3.14) and (3.16)–(3.19). There is a maser effect in the case of scattering of plasma waves on a stream of ions. The effective temperature of the spontaneous emission is given by Equation (3.15). The spectral coefficients of radiation due to scattering of plasma waves on relativistic ions are calculated in the same manner (Equations (4.14)–(4.15)). The total energy loss due to this radiation is given in Equations (4.23)–(4.25). The coefficients of induced emission are given in (4.26)–(4.28).The results are discussed in Section 5. It is shown that the loss of energy by nonlinear plasma radiation is much smaller than the ionization loss. However, the coefficients of synchrotron radiation of electrons and nonlinear radiation of ions under cosmic conditions may be comparable in the case of a weak magnetic field and fairly low frequencies (5.5)–(5.6). Usually the spectrum of nonlinear plasma radiation is steeper than in the case of synchroton radiation. Equation (5.10) gives the condition for nonlinear radiation to prevail over thermal radiation.Translated by D. F. Smith.     

Propagation and Damping of a Localized Impulsive Longitudinal Perturbation in Coronal Loops

We use linear analysis to simulate the evolution of a coronal loop in response to a localized impulsive event. The disturbance is modeled by injecting a narrow Gaussian velocity pulse near one footpoint of a loop in equilibrium. Three different damping mechanisms, namely viscosity, thermal conduction, and optically thin radiation, are included in the loop calculations. We consider homogeneous and gravitationally stratified, isothermal loops of varying length (50≤L≤400 Mm) and temperature (2≤T≤10 MK). We find that a localized pulse can effectively excite slow magnetoacoustic waves that propagate up along the loop. The amplitudes of the oscillations increase with decreasing loop temperature and increasing loop length and size of the pulse width. At T≥4 MK, the waves are dissipated by the combined effects of viscosity and thermal conduction, whereas at temperatures of 2 MK, or lower, wave dissipation is governed by radiative cooling. We predict periods in the range of 4.6?–?41.6 minutes. The wave periods remain unaltered by variations of the pulse size, decrease with the loop temperature, and increase almost linearly with the loop length. In addition, gravitational stratification results in a small reduction of the periods and amplification of the waves as they propagate up along the loop.     

Gravitational radiation from differentially rotating and oscillating white dwarfs

We examine the possible emission of gravitational waves from white dwarfs undergoing self-similar oscillations driven by the energy released during relaxation of their differential rotation. Two distributions of the initial angular momentum are considered. It is assumed that 1% of the energy dissipated by a rotating white dwarf is converted into the energy of self-similar oscillations and, therefore, into gravitational radiation. The relative amplitude of the gravitational radiation from an isolated white dwarf at a distance of 50 pc is found to be less than 10⁻²⁷. The emission from the galactic population of white dwarfs may create a background which overlaps the random cosmological background of gravitational radiation for the improved decihertz detectors currently being proposed. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 231–242 (May 2006).     

The gravitational influence of satellite Pan on the radial distribution of ring-particles in the region of the Encke-division in Saturn's a ring

Here we summarize the models and their similarities with respect to the gravitational influence of small satellites (moonlets) embedded in planetary rings, which have been developed by Petit and Hénon (1987a,b; 1988) and by Spahn (1987; Spahn et al. 1989; 1992). The results and their applicabilities are shown in the case of the Encke-gap Moon Pan located in the outer A-ring of Saturn's rings. To compare the model-profiles with the experimental ones (optical depth profile measured by Voyager-photopolarimeter), the structures embedded in the latter have been confirmed statistically using the wavelet analysis method. This analysis points to a size of Pan of about 13 km and an eccentricity of 10^–4 of its orbit.     

Collapsing supra-massive magnetars: FRBs,the repeating FRB121102 and GRBs

Fast Radio Bursts (FRBs) last for \(\sim \) few milli-seconds and, hence, are likely to arise from the gravitational collapse of supra-massive, spinning neutron stars after they lose the centrifugal support (Falcke & Rezzolla 2014). In this paper, we provide arguments to show that the repeating burst, FRB 121102, can also be modeled in the collapse framework provided the supra-massive object implodes either into a Kerr black hole surrounded by highly magnetized plasma or into a strange quark star. Since the estimated rates of FRBs and SN Ib/c are comparable, we put forward a common progenitor scenario for FRBs and long GRBs in which only those compact remnants entail prompt \(\gamma \)-emission whose kick velocities are almost aligned or anti-aligned with the stellar spin axes. In such a scenario, emission of detectable gravitational radiation and, possibly, of neutrinos are expected to occur during the SN Ib/c explosion as well as, later, at the time of magnetar implosion.     

Monopole gravitational waves from relativistic fireballs driving gamma-ray bursts

Einstein's general relativity predicts that pressure, in general stresses, plays a similar role to energy density,  ε=ρ c ²  (with ρ being the corresponding mass density), in generating gravity. The source of gravitational field, the active gravitational mass density, sometimes referred to as Whittaker's mass density, is  ρ_grav=ρ+ 3 p / c ²  , where p is pressure in the case of an ideal fluid. Whittaker's mass is not conserved, hence its changes can propagate as monopole gravitational waves. Such waves can be generated only by astrophysical sources with varying gravitational mass. Here we show that relativistic fireballs, considered in modelling gamma-ray burst phenomena, are likely to radiate monopole gravitational waves from high-pressure plasma with varying Whittaker's mass. Also, ejection of a significant amount of initial mass-energy of the progenitor contributes to the monopole gravitational radiation. We identify monopole waves with   h ¹¹+ h ²²  waves of Eddington's classification which propagate (in the z -direction) together with the energy carried by massless fields. We show that the monopole waves satisfy Einstein's equations, with a common stress-energy tensor for massless fields. The polarization mode of monopole waves is  Φ₂₂  , i.e. these are perpendicular waves which induce changes of the radius of a circle of test particles only (breathing mode). The astrophysical importance of monopole gravitational waves is discussed.     

MHD oscillations in radio spike radiation observed on May 16, 1981

We discovered quasi-periodic oscillation characteristics of 1.4–1.6 s in the spike radiation of the typical microwave outburst observed on May 16, 1981. We analysed the observations in terms of MHD waves (sausage mode) propagating inside and outside a loop. The waves can modulate the magnetic field and the pitch angle distribution of the electron beams in the source region. These affect the growth rates of the ECM instability and so quasi-periodic oscillations in the spike radiation are generated. In addition, we estimated quantitively some relevant physical parameters.     

Gravitational radiation from approaching neutron stars and the rotational explosion mechanism for collapsing supernovae

We consider the evolution of a neutron star binary system under the effect of two factors: gravitational radiation and mass transfer between the components. Gravitational radiation is specified under the justified assumption of a circular orbit and point masses and in the approximation of a weak gravitational field at nonrelativistic velocities of the binary components. During the first evolutionary phase determined only by gravitational radiation, the neutron stars approach each other according to a simple analytical solution. The second evolutionary phase begins at the time of Roche-lobe filling by the low-mass component, when the second factor, mass transfer as a result of mass loss by the latter, also begins to affect the evolution. Under the simplest assumptions of conservative mass transfer and exact equality between the Roche-lobe radius and the radius of the low-mass neutron star, it is still possible to extend the analytical solution of the problem of evolution to its second phase. We present this complete solution at both phases and, in particular, give theoretical light curves of gravitational radiation that depend only on two dimensionless parameters (m _t and δ ₀). Based on the solution found, we analyze the theoretical gravitational signals from SN 1987A; this analysis includes the hypothesis about the rotational explosion mechanism for collapsing supernovae.     

Kinetic Alfvén waves in extended radio sources

We study a model of extended radio sources (ERS), in particular, extragalactic jets and radio lobes, which are inhomogeneous and where noncompressive Alfvén and surface Alfvén waves (and not shocks and magnetosonic waves) are primarily excited. We assume that a negligible thermal population exists (i.e., the ion density at the low-energy cut-off of the power law distribution is greater than the ion density of the thermal population, if present). Due to internal instabilities and/or the interaction of the ERS with the ambient medium, surface Alfvén waves (SAW) are created. We show that even very small amplitude SAW are mode converted to kinetic Alfvén waves (KAW) which produce large moving accelerating potentials , parallel to the magnetic field. Neglecting nonlinear perturbations, and for typical physical parameters of ERS, we obtaine1 MeV. Wesuggest that these potentials are important in acceleration (e.g., injection energy) and reacceleration of electrons in ERS. We show that energy losses by synchrotron radiation can be compensated by reacceleration by KAW. The relation between KAW acceleration, and previously studied cyclotron-resonance acceleration by Alfvén waves, is discussed.     

Theory of gravitational radiation of the (Ω,A µν )-field

Further exploration of the -field theory as first proposed by Yu (1989) is here presented to cover the equation of motion of a test particle which induces gravitational radiation. The same theory is shown to contain an exact gravitational radiation equation derived as a logical consequence of field equations without extra postulates. In this general dynamic context the theory is renamed The (,A _µ )-field Theory.     

Gravitational and electromagnetic emission by magnetized coalescing binary systems

We discuss the possibility to obtain an electromagnetic emission accompanying the gravitational waves emitted in the coalescence of a compact binary system. Motivated by the existence of black hole configurations with open magnetic field lines along the rotation axis, we consider a magnetic dipole in the system, the evolution of which leads to (i) electromagnetic radiation, and (ii) a contribution to the gravitational radiation, the luminosity of both being evaluated. Starting from the observations on magnetars, we impose upper limits for both the electromagnetic emission and the contribution of the magnetic dipole to the gravitational wave emission. Adopting this model for the evolution of neutron star binaries leading to short gamma ray bursts, we compare the correction originated by the electromagnetic field to the gravitational waves emission, finding that they are comparable for particular values of the magnetic field and of the orbital radius of the binary system. Finally we calculate the electromagnetic and gravitational wave energy outputs which result comparable for some values of magnetic field and radius.     

Dark Matter Objects: Possible New Source of Gravitational Waves

Gravitational waves from mergers of black holes and neutron stars are now being detected by LIGO. Here we look at a new source of gravitational waves, i.e., a class of dark matter objects whose properties were earlier elaborated. We show that the frequency of gravitational waves and strains on the detectors from such objects (including their mergers) could be within the sensitivity range of LIGO. The gravitational waves from the possible mergers of these dark matter objects will be different from those produced by neutron star mergers in the sense that they will not be accompanied by electromagnetic radiation since dark matter does not couple with radiation.