A diffraction limit on the gravitational lens effect

The focussing of gravitational radiation by the interior and exterior gravitational field of a Newtonian gravitational lens is considered. A graphical method for determining the caustic structure of a Newtonian gravitational lens is presented and the caustic structure of a solar type gravitational lens is discussed. Estimates of the amplitude magnification in the caustic region indicate that waves with frequencies less than a critical cutoff frequency ω _c are not amplified significantly. For a lens of massM this cutoff frequency is ω _c ≈(10^-1πM)^-1; for the Sun ω _c ≈10⁴s^-1. Work supported in part by National Science Foundation Grant PHY78-05368.     

Gravitational Radiation of Relativistic <Emphasis Type="Italic">n</Emphasis> = 1 Polytropes

The gravitational radiation of n = 1 polytropes undergoing quasiradial pulsations is examined. The intensity of the gravitational radiation and the gravitational wave amplitudes are calculated for polytropic models of white dwarfs and neutron stars when the energy of rotation of the object serves as the source of the radiated energy. Calculations of h₀ show that objects with a polytropic equation of state can describe the expected gravitational radiation from white dwarfs and neutron stars. The gravitational radiation of polytropic models of galactic nuclei and quasars is also examined. These objects can create a high enough background of gravitational radiation at frequencies of 10^-8–10^-11 Hz for gravitational wave detectors operating in this frequency range. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 603–612 (November 2005).     

Bursts of gravitational radiation from active galactic nuclei and globular clusters

The characteristics of gravitational bursts from active galactic nuclei, and globular clusters are obtained for three astrophysical situations:(i) scattering of stars by massive black holes residued at the centers of galaxies and globular clusters; (ii) the close encounters of stars in the nuclear regions of these objects; (iii) scattering of stars by black holes of stellar mass containing in the stellar population of galactic nuclei and clusters. The most effective source of gravitational bursts appears to be a scattering of stars by the massive central black holes which produces the bursts with dimensionless amplitudeh10^–19–10^–21 and frequencies from 10^–1 to 10^–5 Hz. The characteristics obtained correspond to the possiblities of a future gravitational-wave experiment with use of laser Doppler tracking of interplanetary spacecrafts.     

Radial oscillations of finite-temperature white dwarfs

Models of finite temperature completely degenerate stellar configurations are considered. The frequencies of fundamental radial modes of oscillations for these white dwarf models have been computed for different values of the central degeneracy parameter 1/y ₀ ² and for uniform temperatures of 20×10⁶ K and 10⁸ K. A variational formulation as well as a direct approach is employed to calculate the temperature induced modifications in the frequencies of oscillation of these white-dwarf models.     

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).     

Simulating H2O Maser Emission in the Mass Outflows from Evolved Stars

The combination of a time-dependent spherically symmetric hydrodynamic model of stellar atmosphere pulsation and a radiation transport code, which incorporates maser saturation theory, enabled us to synthesise maps and spectra of H₂O maser emission from the circumstellar envelopes of long period variable stars. The synthetic maps and spectra compare favourably with observed 22, 321 and 325 GHz H₂O maser emission. As is observed in H₂O maser regions the peak emission occurs between 3–8 stellar radii from the star. The calculated H₂O maser regions are in conditions of n_H2 = 10⁶ − 10⁸ cm⁻³, assuming a fractional abundance of 10⁻⁴; kinetic temperatures of 550–3000 K; dust ensemble temperatures of 500–1200 K and an accelerating velocity field. The IR radiation field is explicitly included in the radiation transport model, incorporating the latest absorption efficiency data for silicates from Draine. We reproduce the features seen in high angular resolution MERLIN spectral line datacubes. This shows that a mass outflow model which extends the photosphere using pulsations and incorporates radiation pressure on silicate based dust particles can produce the observed data on small (10-mas) angular scales. This revised version was published online in September 2006 with corrections to the Cover Date.     

GRAS-F seismogravimeter for measuring gravity-inertial fields on the surface of Phobos

The problems of measuring the variations in the gravitational and inertial fields on Phobos related to librational oscillations, tidal effects, and seismic impacts have been considered in the paper. It has been indicated that thermal equilibrium noise in a mechanical oscillator, which forms the basis for a sensor, is responsible for the oscillator’s maximal sensitivity at a level of 8 × 10⁻⁹ m/s². The actual sensitivity of the designed three-dimensional seismogravimeter, which was estimated based on the calibration results, is ∼2 × 10⁻⁸ m/s². This makes it possible to measure the anticipated variations in the gravitational field and to obtain information about the seismic noise level with a surface oscillation amplitude resolution at a level of 2.5 × 10⁻⁷ m at frequencies of 0.1 Hz to ∼10⁻¹⁰ m at frequencies higher than 5 Hz.     

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.     

Signals from SN 1987A in Amaldi-Weber antennas as the possible detection of scalar gravitational waves

An equation is obtained for the cross section of a metal Weber cylinder for scalar gravitational waves, which are possible within the framework of the field theory of gravitation. It is shown that the signals detected by the Amaldi and Weber antennas during the explosion of supernova SN 1987A can be interpreted as the result of the action of scalar gravitational waves on solid-state detectors. The required energy of the gravitational waves is about 1 M_⊙c². Together with the observed excess (about 1 %) of gravitational radiation from the binary system containing the pulsar PSR 1913+16, the signals from SN 1987A are the second piece of observational evidence for the actual existence of scalar gravitational waves. The present-day, third-generation, solid-state antennas are capable of detecting scalar waves from events like SN 1987A at a distance up to 5 Mpc. The expected level of the signal from SN 19931 is about 7 mK. An experimental test of the longitudinal nature of scalar waves is possible using interferometric antennas based on free masses. Translated from Astrofizika, Vol. 40, No. 3, pp. 377–389, August, 1997.     

Models of dense stars

The aim of this paper is to present the results of a construction of five models of composite stellar configurations, consisting of an energy-generating convective core surrounded by source-free envelope in radiative equilibrium, and of sufficient density for the coefficient of absorption to vary approximately as inverse square of the local temperature. The principal characteristic of such models proved to be their very high degree of central condensation; their central densities being 10³–10⁴ times as large as the mean density of the composite configuration. The relevance of such models to the internal structure of subdwarf components of close binary systems with periods less than a day is briefly pointed out.Investigation supported in part by Contract N5 ori-07843 with the Office of Naval Research of the U.S. Navy Department.     

Modeling the luminosity function of galactic low-mass X-ray binaries

The evolution of the family of binaries with a low-mass star and a compact neutron star companion (low-mass X-ray binaries (LMXBs) with neutron stars) ismodeled by the method of population synthesis. Continuous Roche-lobe filling by the optical star in LMXBs is assumed to be maintained by the removal of orbital angular momentum from the binary by a magnetic stellar wind from the optical star and the radiation of gravitational waves by the binary. The developed model of LMXB evolution has the following significant distinctions: (1) allowance for the effect of the rotational evolution of a magnetized compact remnant on themass transfer scenario in the binary, (2) amore accurate allowance for the response of the donor star to mass loss at the Roche-lobe filling stage. The results of theoretical calculations are shown to be in good agreement with the observed orbital period-X-ray luminosity diagrams for persistent Galactic LMXBs and their X-ray luminosity function. This suggests that the main elements of binary evolution, on the whole, are correctly reflected in the developed code. It is shown that most of the Galactic bulge LMXBs at luminosities L _x > 10³⁷ erg s^?1 should have a post-main-sequence Roche-lobe-filling secondary component (low-mass giants). Almost all of the models considered predict a deficit of LMXBs at X-ray luminosities near ～10^36.5 erg s^?1 due to the transition of the binary from the regime of angular momentum removal by a magnetic stellar wind to the regime of gravitational waves (analogous to the widely known period gap in cataclysmic variables, accreting white dwarfs). At low luminosities, the shape of the model luminosity function for LMXBs is affected significantly by their transient behavior-the accretion rate onto the compact companion is not always equal to the mass transfer rate due to instabilities in the accretion disk around the compact object. The best agreement with observed binaries is achieved in the models suggesting that heavy neutron stars with masses 1.4–1.9M _⊙ can be born.     

Slow modes in stellar systems with nearly harmonic potentials: I. Spoke approximation,radial orbit instability

Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous (on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing, centrally symmetric ellipses (2: 1 orbits). Depending on the density distribution in the system and the degree of halo inhomogeneity, the orbit precession can be both prograde and retrograde, in contrast to systems with 1: 1 elliptical orbits where the precession is unequivocally retrograde. In the first paper, we show that in the case where at least some of the orbits have a prograde precession and the stellar distribution function is a decreasing function of angular momentum, an instability that turns into the well-known radial orbit instability in the limit of low angular momenta can develop in the system. We also explore the question of whether the so-called spoke approximation, a simplified version of the slow mode approximation, is applicable for investigating the instability of stellar systems with highly elongated orbits. Highly elongated orbits in clusters with nonsingular gravitational potentials are known to be also slowly precessing 2: 1 ellipses. This explains the attempts to use the spoke approximation in finding the spectrum of slow modes with frequencies of the order of the orbit precession rate. We show that, in contrast to the previously accepted view, the dependence of the precession rate on angular momentum can differ significantly from a linear one even in a narrow range of variation of the distribution function in angular momentum. Nevertheless, using a proper precession curve in the spoke approximation allows us to partially “rehabilitate” the spoke approach, i.e., to correctly determine the instability growth rate, at least in the principal (O(α _T^−1/2) order of the perturbation theory in dimensionless small parameter α _T, which characterizes the width of the distribution function in angular momentum near radial orbits.     

Formation and Evolution of Intermediate Mass Black Hole X-Ray Binaries

The evolution of young (≲ 10 Myr) star clusters with a density exceeding about 10⁵ star pc⁻³ are strongly affected by physical stellar collisions during their early lifetime. In such environments the same star may participate in several tens to hundreds of collisions ultimately leading to the collapse of the star to a black hole of intermediate mass. At later time, the black hole may acquire a companion star by tidal capture or by dynamical – three-body – capture. When the captured star evolves it starts to fill its Roche-lobe and transfers mass to its accompanying black hole. This then leads to a bright phase of X-ray emission, which lasts for the remaining main-sequence lifetime of the donor. If the star captured by the intermediate mass black hole is relatively low mass ≲ 2 M⊙) the binary will also be visible as a bright source in gravitational waves. Based on empirical models we argue that, for as long as the donor remains on the main sequence, the source will be ultraluminous L_x >rsim 10⁴⁰ ergs^-1 for about a week every few month. When the donor star is more massive >15 M⊙, or evolved off the main sequence the bright time is longer, but the total accretion phase lasts much shorter.     

The formation and evolution of low-mass close binaries with compact components

We discuss the formation and evolution of interacting low-mass close binaries with a He-1CO- or ONe-dwarf neutron star or a black hole as a compact component. Mass exchange leads to cataclysmic events in such systems. The rate of semidetached low-mass close binary formation is 5×10^–3 yr^–1 if the accreting component is a He degenerate dwarf, 5×10^–3 yr^–1 if it is a CO-dwarf and 3×10^–8 yr^–1 if it is a neutron star. Systems with compact accretors arise as the result of the common envelope phase of close binary evolution or due to collisions of single neutron stars or dwarfs with low-mass single stars in dense stellar clusters. Evolution of LMCB to the contact phase in semi-detached stages is determined mainly by the angular momentum losses by a magnetic stellar wind and radiation of gravitational waves. Numerical computations of evolution with momentum loss explain observed mass exchange rates in such systems, the absence of cataclysmic variables with orbital periods 2^h–3^h, the low number and the evolutionary status of systems with orbital periods shorter than 80^m. In conclusion we list unsolved problems related to magnetic stellar wind, the distribution of young close binaries over main initial parameters, stability of mass exchange.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

Resonant Transition Radiation and Solar Radio Bursts

This paper presents general relations for the intensity of the resonant transition radiation (RTR) and their detailed analysis. This analysis shows that the spectrum amplitude of the x-mode at some frequencies for high-energy electrons can grow with the magnetic field increase in some interval from zero value; it can even dominate over that for the o-mode. With further magnetic field increase, the intensity of the RTR x-mode decreases in comparison with the intensity of the o-mode and this decrease is higher for higher velocities of energetic electrons. The polarization of the RTR depends on the velocity of energetic electrons, too. For velocities lower than some velocity limit v<v _i the RTR emission is unpolarized in a broad interval of magnetic field intensities in the radio source. For reasonable values of indices of the power-law distribution functions of energetic electrons, the RTR is broadband in frequencies (df/f≈0.2−0.4). Furthermore, we show various dependencies of the RTR and its spectral characteristics. Assuming the same radio flux of the transition radiation and the gyro-synchrotron one at the Razin frequency, we estimate the limit magnetic field in the radio source of the transition radiation. Then, we analyze possible sources of small-scale inhomogeneities (thermal density fluctuations, Langmuir and ion-sound waves), which are necessary for the transition radiation. Although the small-scale inhomogeneities connected with the Langmuir waves lead to the plasma radiation, which is essentially stronger than RTR, the inhomogeneities of the ion-sound waves are suitable for the RTR without any other radiation. We present the relations describing the RTR for anisotropic distribution functions of fast electrons. We consider the distribution functions of fast electrons in the form of the Legendre polynomials which depend on the pitch-angle. We analyze the influence of the degree of the anisotropy (an increase of the number of terms in the Legendre polynomial) on spectral characteristics of the RTR. A comparison with previous studies is made. As an example of the use of the derived formulas for the RTR, the 24 December 1991 event is studied. It is shown that the observed decimetric burst can be generated by the RTR in the plasma with the density inhomogeneities at the level 〈ΔN ²〉/N ²=2.5⋅10⁻⁵.     

Dissipation of modified entropic gravitational energy through gravitational waves

The phenomenological nature of a new gravitational type interaction between two different bodies derived from Verlinde’s entropic approach to gravitation in combination with Sorkin’s definition of Universe’s quantum information content, is investigated. Assuming that the energy stored in this entropic gravitational field is dissipated under the form of gravitational waves and that the Heisenberg principle holds for this system, one calculates a possible value for an absolute minimum time scale in nature t = \frac1516 \fracL^1/2(^h/_2p) Gc⁴ ~ 9.27×10^-105\tau=\frac{15}{16} \frac{\Lambda^{1/2}\hbar G}{c^{4}}\sim9.27\times10^{-105} seconds, which is much smaller than the Planck time t _P =(ħG/c ⁵)^1/2∼5.38×10⁻⁴⁴ seconds. This appears together with an absolute possible maximum value for Newtonian gravitational forces generated by matter F_g=\frac3230\fracc⁷L (^h/_2p) G² ~ 3.84×10¹⁶⁵F_{g}=\frac{32}{30}\frac{c^{7}}{\Lambda \hbar G^{2}}\sim 3.84\times 10^{165} Newtons, which is much higher than the gravitational field between two Planck masses separated by the Planck length F _gP =c ⁴/G∼1.21×10⁴⁴ Newtons.     

Equation of state under nuclear statistical equilibrium conditions

We investigate a three-parameter equation of state for stellar matter under nuclear statistical equilibrium conditions in the ranges of temperatures 3×10⁹–10¹¹ K and densities 10⁴–10¹³ g cm^?3 and for various ratios of the total number of neutrons to the total number of protons within the range 1–1.5. These conditions correspond to the initial stages of the gravitational collapse of iron stellar cores that are accompanied by nonequilibrium matter neutronization. We analyze the effect of the excited levels of atomic nuclei on the thermodynamic properties of the matter. We show that this effect is insignificant at low densities, ρ?10¹⁰ g cm^?3, but it leads to an expansion of the instability region, γ<4/3, at higher densities. The incorporated effects of the Fermi degeneracy of free nucleons prove to be insignificant, because their concentrations are low at low temperatures. In the future, we plan to investigate the effects of Coulomb interactions and neutron-rich nuclei on the thermodynamic properties of the matter.     

Expanding shells in low and high density environments

The gravitational instability of expanding shells evolving in a homogeneous and static medium is discussed. In the low density environment (n = 1 cm^-3), the fragmentation starts in shells with diameters of a few 100 pc and fragment masses are in the range of 5 × 10³ - 10⁶ M _⊙. In the high density environment (n = 10⁵ - 10⁷ cm^-3), shells fragment at diameters of pc producing clumps of stellar masses. The mass spectrum in both environments is approximated by a power law dN/dm ∼ m ^-2.3. This is close to the slope of the stellar IMF. To reproduce the observed mass spectrum of clouds (the spectral index close to ∼ -2.0) we have to assume, that the cloud formation time is independent of the cloud size, similarly to the Jeans unstable medium. This revised version was published online in August 2006 with corrections to the Cover Date.     

The radio and infrared spectrum of DR 21

The radio and infrared spectrum of DR 21 is established over a wide range of frequencies (from 10² to 10⁸ MHz). Two physical processes, free-free emission from the ionized hydrogen at radio wavelengths and reradiation at infrared wavelengths of the original stellar ultraviolet radiation by dust grains have to be considered in the explanation of the derived spectrum. Physical parameters of the object deduced from its radio emission are also presented.     

The relationship betweenG andh in a closed Universe

In a closed expanding-contracting Universe, matter will be subject to an inward acceleration large enough to prevent perpetual expansion. A closed Universe must also perform a simple harmonic motion, which might consist either of one single cycle or of an infinite series of oscillations about a central point. It is the purpose of this study to find the rate ofa ₀, the cosmic acceleration, from which the gravitational constantG can be determined. It will be shown from Ampère's equation and Planck's radiation law that it is possible to derivea ₀=7.623×10^–12 ms^–2, a value which also conforms with the uncertainty principle. The relationship betweena ₀ and electromagnetic radiation is based on the concept that charges (such as electrons) must emit radiation while accelerating. The rate ofa ₀ yields a universal gravitational constant ofG=6.645×10^–11 N m² kg^–2.