Noncommutative dispersion relation and mass-radius relation of white dwarfs

The equation of state of the electron degenerate gas in a white dwarf is usually treated by employing the ideal dispersion relation.However, the effect of quantum gravity is expected to be inevitably present and when this effect is considered through a non-commutative formulation, the dispersion relation undergoes a substantial modification.In this paper, we take such a modified dispersion relation and find the corresponding equation of state for the degenerate electron gas in white dwarfs.Hence we solve the equation of hydrostatic equilibrium and find that this leads to the possibility of the existence of excessively high values of masses exceeding the Chandrasekhar limit, although the quantum gravity effect is taken to be very small.It is only when we impose the additional effect of neutronization that we obtain white dwarfs with masses close to the Chandrasekhar limit with nonzero radii at the neutronization threshold.We demonstrate these results by giving numerical estimates for the masses and radii of helium, carbon and oxygen white dwarfs.     

Gravitational collapse of a rotating iron stellar core and physical properties of the accompanying neutrino emission

We have ascertained an important role of rotation effects in a collapsing stellar core using a quasi-one-dimensional hydrodynamic model with a rigorous allowance for the neutrino energy losses including the neutrino opacity stage. However, the neutrino scattering processes are not considered in the neutrino emission kinetics as secondary compared to the absorption processes. The quasi-one-dimensional approximation (with averaging of the expression for the centrifugal force over the polar angle) allows numerical calculations to be performed relatively easily up to the formation of a hydrostatically equilibrium neutron star after a very long stage of collapsar cooling by neutrino emission (about 2 s). We present detailed results of our numerical solution, including the neutrino spectra, with electron neutrinos making a dominant contribution to them and the contribution from electron antineutrinos being smaller by an order of magnitude. In the model under consideration, we solve the equation of matter neutronization kinetics by taking into account the main process of nuclear reactions on free nucleons, although the contribution from iron and helium nuclei is included in the equation of state.     

Neutrino fluxes from a core-collapse supernova in a model with three sterile neutrinos

The characteristics of the gravitational collapse of a supernova and the fluxes of active and sterile neutrinos produced during the formation of its protoneutron core have been calculated numerically. The relative yields of active and sterile neutrinos in corematter with different degrees of neutronization have been calculated for various input parameters and various initial conditions. A significant increase in the fraction of sterile neutrinos produced in superdense core matter at the resonant degree of neutronization has been confirmed. The contributions of sterile neutrinos to the collapse dynamics and the total flux of neutrinos produced during collapse have been shown to be relatively small. The total luminosity of sterile neutrinos is considerably lower than the luminosity of electron neutrinos, but their spectrum is considerably harder at high energies.     

Coulomb corrections to the equation of state of nuclear statistical equilibrium matter: implications for SNIa nucleosynthesis and the accretion-induced collapse of white dwarfs

Coulomb corrections to the equation of state of degenerate matter are usually neglected in high-temperature regimes, owing to the inverse dependence of the plasma coupling constant, Γ, on temperature. However, nuclear statistical equilibrium matter is characterized by a large abundance by mass of large- Z (iron group) nuclei. It is found that Coulomb corrections to the ion ideal gas equation of state of matter in nuclear statistical equilibrium are important at temperatures T ≲5–10×10⁹ K and densities ρ ≳10⁸ g cm⁻³. At a temperature T =8.5×10⁹ K and a density ρ =8×10⁹ g cm⁻³, the neutronization rate is larger by ≳28 per cent when Coulomb corrections are included. However, the conductive velocity of a thermonuclear deflagration wave in C–O drops by ∼16 per cent when Coulomb corrections to the heat capacity are taken into account. The implications for SNIa models and nucleosynthesis, and also for the accretion-induced collapse of white dwarfs, are discussed. Particularly relevant is the result that the minimum density for collapse of a white dwarf to a neutron star is shifted down to 5.5–6×10⁹ g cm⁻³, a value substantially lower than previously thought.     

Theoretical model of a magnetic white dwarf

In this paper a theoretical model of a magnetic white dwarf is studied. All numerical calculations are performed under the assumption of a spherically symmetric star. The obtained equation of state is stiffer with the increase of value of the magnetic field (B). Numerical values of the maximum mass and radius are presented. The influence of the magnetic field on the results is evident. Finally the departure from the condition of isothermality of a degenerate electron gas in the gravitational field is discussed.     

Gravitational collapse of polytropic, magnetized, filamentary clouds

For the case in which the gas of a magnetized filamentary cloud obeys a polytropic equation of state, gravitational collapse of the cloud is studied using a simplified model. We concentrate on the radial distribution and restrict ourselves to a purely toroidal magnetic field. If the axial motions and poloidal magnetic fields are sufficiently weak, we could reasonably expect our solutions to be a good approximation. We show that while the filament experiences gravitational condensation and the density at the centre increases, the toroidal flux-to-mass ratio remains constant. A series of spatial profiles of density, velocity and magnetic field for several values of the toroidal flux-to-mass ratio and the polytropic index, is obtained numerically and discussed.     

Models of rapidly rotating neutron stars: remnants of accretion-induced collapse

Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion-induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high-density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis. The ratio of the rotational kinetic energy to the gravitational potential energy of these neutron stars ranges from 0.13 to 0.26, suggesting that some of these objects may have a non-axisymmetric dynamical instability that could emit a significant amount of gravitational radiation.     

Diffusion in helium white dwarf stars

This paper is aimed at exploring the effects of diffusion on the structure and evolution of low-mass helium white dwarfs. To this end, we solve the multicomponent flow equations describing gravitational settling and chemical and thermal diffusion. The diffusion calculations are coupled to an evolutionary code in order to follow the cooling of low-mass, helium core white dwarf models having envelopes made up of a mixture of hydrogen and helium, as recently suggested by detailed evolutionary calculations for white dwarf progenitors in binary systems. We find that diffusion causes hydrogen to float and the other elements to sink over time-scales shorter than evolutionary time-scales. This produces a noticeable change in the structure of the outer layers, making the star inflate. Thus, in order to compute accurately the mass–radius relation for low-mass helium white dwarfs we need to account for the diffusion processes during (at least) the white dwarf stages of the evolution of these objects. This should be particularly important when studying the general characteristics of binary systems containing a helium white dwarf and a pulsar.
In addition, we present an analytic, approximate model for the outer layers of the white dwarf aimed at interpreting the physical reasons for the change in the surface gravity for low-mass white dwarfs induced by diffusion.     

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.     

The mass and radius of the M dwarf companion to GD 448

We present spectroscopy and photometry of GD 448, a detached white dwarf – M dwarf binary with a period of 2.47 h. We find that the Na  I  8200-Å feature is composed of narrow emission lines, owing to irradiation of the M dwarf by the white dwarf, within broad absorption lines that are essentially unaffected by heating. Combined with an improved spectroscopic orbit and gravitational redshift measurement from spectra of the Hα line, we are able to derive masses for the white dwarf and M dwarf directly (0.41 ± 0.01 and 0.096 ± 0.004 M_⊙, respectively). We use a simple model of the Ca II emission lines to establish the radius of the M dwarf assuming the emission from its surface to be proportional to the incident flux per unit area from the white dwarf. The radius derived is 0.125 ± 0.020 R_⊙. The M dwarf appears to be a normal main-sequence star in terms of its mass and radius, and is less than half the size of its Roche lobe. The thermal time-scale of the M dwarf is much longer than the cooling age of the white dwarf, so we conclude that the M dwarf was unaffected by the common-envelope phase. The anomalous width of the Hα emission from the M dwarf remains to be explained, but the strength of the line may be due to X-ray heating of the M dwarf owing to accretion on to the white dwarf from the M dwarf wind.     

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 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).     

Self-similar expansion of white dwarfs

Properties of plasma expansion that propagates in an electron-positron-ion dense plasma are investigated. Suitable hydrodynamic equations for the ions and ultrarelativistic degenerate electrons and positrons are used. Using self-similar transformation, the basic set of nonlinear equations is solved numerically. Typical values of white dwarf stars are used to estimate the behavior of the ion number density and ion fluid velocity. The positive ions are found to initially slowly escape with high velocity when the ion-to-electron density ratio increases. For higher values of the electron number density, the self-similar solution validity domain decreases. The relevance of the results to white dwarf expansion and collapse is highlight.     

Plane symmetric gravitational collapse and linear equation of state

This paper examines the gravitational collapse in plane symmetry with a perfect fluid using a linear equation of state p=kρ. We find a class of collapse models satisfying the Einstein field equations and also the regularity as well as energy conditions. For a given initial data, the outcome of the collapse turns out to be a black membrane or a naked singularity depending upon the equation of state parameter. We conclude that this parameter plays a crucial role in determining the final fate of the collapse.     

Stability of equilibrium self-gravitating models and the possibility of black hole formation in the jordan-brans-dicke theory

We show that, starting from the qualitative analysis of the solutions of the vacuum equations, one can conclude that, in contrast to the general theory of relativity, in the Jordan-Brans-Dicke theory gravitational collapse does not lead to the formation of black holes, but that no reliable determination of the existence or nonexistence of black holes in the Jordan-Brans-Dicke theory will be possible until the time-dependent equations have been solved numerically. We propose a method of solving the problem of stability of equilibrium self-gravitating configurations with respect to radial pulsations and state a criterion for stability.Translated fromAstrofizika, Vol. 38, No. 3, 1995.     

Gravitational wave radiation from the coalescence of white dwarfs

We compute the emission of gravitational radiation from the merging of a close white dwarf binary system. This is done for a wide range of masses and compositions of the white dwarfs, ranging from mergers involving two He white dwarfs, through mergers in which two CO white dwarfs coalesce, to mergers in which a massive ONe white dwarf is involved. In doing so we follow the evolution of the binary system using a smoothed particle hydrodynamics code. Even though the coalescence process of the white dwarfs involves considerable masses, moving at relatively high velocities with a high degree of asymmetry we find that the signature of the merger is not very strong. In fact, the most prominent feature of the coalescence is that in a relatively small time-scale (of the order of the period of the last stable orbit, typically a few minutes) the sources stop emitting gravitational waves. We also discuss the possible implications of our calculations for the detection of the coalescence within the framework of future space-borne interferometers like LISA.     

Gravitational wave radiation from a double white dwarf system inside our galaxy: a potential method for seeking strange dwarfs

Like the investigation of double white dwarf (DWD) systems, strange dwarf (SD) - white dwarf (WD) system evolution in Laser Interferometer Space Antenna (LISA)'s absolute amplitude-frequency diagram is investigated. Since there is a strange quark core inside an SD, SDs' radii are significantly smaller than the value predicted by the standard WD model, which may strongly affect the gravitational wave (GW) signal in the mass-transferring phases of binary systems. We study how an SD-WD binary evolves across LISA's absolute amplitude-frequency diagram. In principle, we provide an executable way to detect SDs in the Galaxy's DWD systems by radically new windows offered by GW detectors.     

Some properties of white-dwarf collapse in low-mass binaries

Conditions for collapse of an accreting white dwarf in a low-mass close binary are analysed. It is shown that if the magnetic strength on the surface of a white dwarf is less than 10⁵–10⁶ G, a rotation barrier appears which prevents the direct formation of a neutron star. As a result, a time-scale for the collapse is defined by a specific time of momentum dissipation rather than by free-fall time-scale. It is noted that a tidal deformation of a white dwarf, intensified in a process of collapse, renders collapse in a low-mass close binary sharply anisotropic. Consequently fast moving radiopulsars can arise with velocities of some thousands km s^–1.     

The triple degenerate star WD 1704+481

WD 1704+481 is a visual binary in which both components are white dwarfs. We present spectra of the H α line of both stars which show that one component (WD 1704+481.2=Sanduleak B=GR 577) is a close binary with two white dwarf components. Thus, WD 1704+481 is the first known triple degenerate star. From radial velocity measurements of the close binary we find an orbital period of 0.1448 d, a mass ratio, q M _bright M _faint, of 0.70±0.03 and a difference in the gravitational redshifts of 11.5±2.3 km s⁻¹. The masses of the close pair of white dwarfs predicted by the mass ratio and gravitational redshift difference combined with theoretical cooling curves are 0.39±0.05 and 0.56±0.07 M_⊙. WD 1704+481 is therefore also likely to be the first example of a double degenerate in which the less massive white dwarf is composed of helium and the other white dwarf is composed of carbon and oxygen.