Energy release on the surface of a rapidly rotating neutron star during disk accretion: A thermodynamic approach

The total energy E of a star as a function of its angular momentum J and mass M in the Newtonian theory, E=E(J, M) [in general relativity, the gravitational mass of a star as a function of its angular momentum J and rest mass m, M=M(J, m)], is used to determine the remaining parameters (angular velocity, chemical potential, etc.) in the case of rigid rotation. Expressions are derived for the energy release during accretion onto a cool (with constant entropy), rapidly rotating neutron star (NS) in the Newtonian theory and in general relativity. A separate analysis is performed for the cases where the NS equatorial radius is larger and smaller than the radius of the marginally stable orbit in the disk plane. An approximate formula is proposed for the NS equatorial radius for an arbitrary equation of state, which matches the exact equation of state at J=0.     

Spin limits of Solar System bodies: From the small fast-rotators to 2003 EL61

Holsapple [Holsapple, K.A., 2001. Icarus 154, 432-448; Holsapple, K.A., 2004. Icarus 172, 272-303] determined the spin limits of bodies using a model for solid bodies without tensile or cohesive strength, but with the pressure-induced shear strengths characteristic of dry sands and gravels. That theory included the classical analyses for fluid bodies given by Maclaurin, Jacobi and others as a special case. For the general solid bodies, it was shown that there exists a very wide range of permissible shapes and spin limits; and explicit algebraic results for those limits were given. This paper gives an extension of those analyses to include geological-like materials that also have tensile and cohesive strength. Those strengths are necessary to explain the smaller, fast-rotating asteroids discovered in the last few years. I find that the spin limits for these more general solids have two limiting regimes: a strength regime for bodies with a diameter <3 km, and a gravity regime for the larger bodies with a diameter >10 km (which is the case covered by the earlier papers). I derive explicit algebraic forms for the dependence of the spin limits on shape, mass density and material strength properties. The comparison of the theory to the database for the spins of asteroids and trans-neptunian objects (TNO's) objects shows excellent agreement. For large bodies (diameter D>10 km), the presence of cohesive and/or tensile strength does not permit higher spin rates than would be allowed for rubble pile bodies. Thus, the fact that the spin rates of all large bodies is limited to periods greater than about 2 h does not imply that they are rubble piles. In contrast, for small bodies (D<10 km) the presence of even a very small amount of strength allows much more rapid spins. Small bodies might then be rubble piles but require a small amount of bonding. Finally, I make some remarks about the application of the theory to the TNO's and large asteroids, and question whether a common assumption by researchers that those bodies must take on relaxed fluid shapes is warranted. If not, then the densities and shapes required by that assumption are not valid. I use 2003 EL61 as a prime example.     

Revisiting Noether gauge symmetry for F(R) theory of gravity

Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R)∝R ⁿ (where n≠1 is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than $F(R) \propto R^{\frac{3}{2}}$ is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n=2, which again does not satisfy the field equations. Thus, as noticed earlier, the only form that Noether symmetry admits is $F(R) \propto R^{\frac{3}{2}}$ . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.     

Local Lorentz transformation and exact solution in f(T) gravity theories

A general tetrad fields, with an arbitrary function of radial coordinate, preserving spherical symmetry, is provided. Such tetrad is split into two matrices: The first matrix represents a Local Lorentz Transformation (LLT), which contains an arbitrary function. The second matrix represents a proper tetrad fields which satisfy the field equations of f(T) gravitational theory. This general tetrad is applied to the field equations of f(T). We derive a solution with one constant of integration to the resulting field equations of f(T). This solution gives a vanishing value of the scalar torsion. We calculate the energy associated with this solution to investigate what is the nature of the constant of integration.     

Neutron stars in the bimetric Scalar-Tensor theory of gravitation. I. new solutions of the field equations

New solutions of the equations of the bimetric scalar-tensor theory of gravitation for neutron stars are found. In these solutions the scalar field is constant, φ = φ_φ, while the metric space-time tensor is determined by the equations of the general theory of relativity. The problem was to find a background metric corresponding to φ_φ. Solutions with a variable φ were studied earlier [M. R. Avakian, L. Sh. Grigorian, and A. A. Saharian, Astrofizika, 35, 121 (1991)] and are determined by the dimensionless parameter ζ of the theory. Differences between solutions with constant and variable ? are considerable for ¦ζ¦ ≤ 1.     

An attempt at a revival of Nordström’s first theory of gravitation

This reading makes the attempt to revive Nordström (1912)’s relativistic theory of gravitation which was rejected on the basis of it contravening observational reality in that it [theory] failed to account for the periastron precession of the planet Mercury and as-well as the gravitational bending of starlight barely grazing the limb of a massive gravitational object such as the Sun. By way of referencing to earlier works (Nyambuya, 2015a; 2015c; Nyambuya and Simango, 2014; Nyambuya, 2010) and putting these works into perspective with the present endaevours, it is argued that Nordström (1912)’s forgotten theory is — in-principle — able to explain these dire shortcomings. With this having been done, the stage is then set for one to re-consider this long forgotten theory. As already demonstrated (in the readings Nyambuya, 2018a; 2018b; 2018c; 2018d; Nyambuya et al., 2018), there is not only merit in doing so — but great hope that, this reconsideration will be able to bear good fruit by way of explaining a number of inexplicable gravitational anomalies and puzzles.     

Revisiting the classical electron model in general relativity

Motivated by earlier studies (Tiwari et al. in Astrophys. Space Sci. 182:105, 1984; Herrera and Varela in Phys. Lett. 189:11, 1994), we model electron as a spherically symmetric charged perfect fluid distribution of matter. The existing model is extended assuming a matter source that is characterized by quadratic equation of state in the context of general theory of relativity. For the suitable choices of the parameters, our charged fluid models almost satisfy the physical properties of electron.     

The ideal resonance problem,a comparison of two formal solutions,II

This paper is a sequel to an earlier article of the same title. The two formal analytical solutions of the Ideal Resonance Problem developed respectively by Garfinkel and Jupp are here compared, atsecond-order in the appropriate small parameter, with numerical integrations; the second-order circulation solution for Jupp's theory being presented for the first time. It transpires that throughout most of the deep resonance regime the second-mentioned solution provides greater accuracy. In addition, it is demonstrated that the first solution is not appropriate when general initial values of the variables are prescribed.     

Periodic orbits for a class of galactic potentials

In this work, applying general results from averaging theory, we find periodic orbits for a class of Hamiltonian systems H whose potential models the motion of elliptic galaxies.     

On the apsidal motion of BP Vulpeculae

BP Vulpeculae is a bright eclipsing binary system showing apsidal motion. It was found in an earlier study that it shows retrograde apsidal motion which contradicts theory. In this paper we present the first BV light curve of the system and its light curve solution as well as seven new times of the minima from the years 1959–1963. This way we could expanded the baseline of the investigation to five decades. Based on this longer baseline we concluded that the apsidal motion is prograde agreeing with the theoretical expectations and its period is about 365 years and the determined internal structure constant is close to the theoretically expected one.     

Dawn-dusk (y) component of the interplanetary magnetic field and the local time of the harang discontinuity

We describe a simple method for determining the time at which the meridian of a sub-auroral magnetic observatory crosses that of the Harang discontinuity—the separation of the eastward and westward electrojets which flow in the evening and morning sectors of the auroral oval. We then consider how this time, determined from examination of magnetograms from sub-auroral observatories varies with the dawn-dusk (y) component of the Interplanetary Magnetic Field. We find that the time at which the Harang discontinuity is identified in the Northern Hemisphere is earlier for B_y > 0 than the occasions when B_y < 0, and that the converse is observed in the Southern Hemisphere. Also we suggest that there is no significant seasonal variation in the relationship between the time of the discontinuity and B_y. The sense of the azimuthal shift of the auroral electrojet currents with changes in B_y is consistent with the theory of Cowley (1981). However, the magnitude of the observed shifts is approximately an order of magnitude greater than the theoretical predictions. We suggest that this difference between observation and theory arises from the use of a dipole magnetic field model at auroral zone latitudes in the theoretical estimation of azimuthal displacement.     

The genealogy of periodic orbits in a plane rotating galaxy

We study the various families of periodic orbits in a dynamical system representing a plane rotating barred galaxy. One can have a general view of the main resonant types of orbits by considering the axisymmetric background. The introduction of a bar perturbation produces infinite gaps along the central familyx ₁ (the family of circular orbits in the axisymmetric case). It produces also higher order bifurcations, unstable regions along the familyx ₁, and long period orbits aroundL ₄ andL ₅. The evolution of the various types of orbits is described, as the Jacobi constanth, and the bar amplitude, increase. Of special importance are the infinities of period doubling pitchfork bifurcations. The genealogy of the long and short period orbits is described in detail. There are infinite gaps along the long period orbits producing an infinity of families. All of them bifurcate from the short period family. The rules followed by these families are described. Also an infinity of higher order bridges join the short and long period families. The analogies with the restricted three body problem are stressed.     

Infrared albedos and rotation curves of the Galilean satellites

Infrared (1.5–5 μm) albedos and rotation curves of the Galilean satellites have been obtained. The data suggest that the rotational variation in the infrared is less than ±10% for all four satellites. While no conclusion about rotational variation could be reached for Io, the 1.57 μm data for the outer three satellites marginally suggest phase correlation with the visual variation. The geometric albedos obtained are in general agreement with earlier results. For Io, the absorption feature near 1.5 μm found by Pilcher et al. (1972) is confirmed, thus contradicting the flat spectrum measured by Fink et al. (1973). Io and Ganymede were observed in the 1.57 μm bandpass as they reappeared from eclipse. The curve for Io shows a slight (<10%) overshoot similar to those sometimes reported for visual measurements. This result is based on a single reappearance, and is extremely tentative.     

New approach to studying electromagnetic mode coupling in inhomogeneous magnetized plasma

Considering mode coupling as a consequence of the matching of boundary conditions at an infinitesimal discontinuity, a concept introduced by the same authors earlier, we derive explicit expressions for the coupling coefficients for electromagnetic waves propagating in a rather general direction in an inhomogeneous magnetized plasma. Some special cases of the theory are discussed.     

Radio Recombination Lines of Hydrogen

The impact theory of spectral line broadening is used to obtain complete profiles for radio recombination lines perturbed by electron and proton impact. The collisions can be divided into two types: inelastic, where transitions take place between hydrogen levels with different principal quantum number n and elastic, where the transitions are only between degenerate levels for a particular value of n. The widths of the radio lines are essentially determined by inelastic electron collisions and elastic proton collisions with the emitting hydrogen atom occupying either the upper or lower levels of the line.Here, earlier work is extended to examine the contribution from proton collisions to the line width in more detail, and it is shown that the trends in the behaviour of the widths again confirm previous results.     

The application of a Bessel transform to the determination of stellar rotational velocities

A method for analysing line profiles by means of a transform using Bessel functions is described. This yields the stellar rotational velocityv sini, to an accuracy of about ±1 km s^–1 for rotational velocities greater than about 5 km s^–1, provided that rotation is the major source of line broadening. The theory of the method is a special case of a general theory of linear transforms in data analysis, which is outlined in an appendix.     

Tidal Evolution of the Kepler Candidate Two-planet Systems

The tidal evolution of ten Kepler candidate two-planet systems is investigated by using the general secular perturbation theory, and then a general picture of tidal evolution for these systems is described. Taking the KOI 1239 system as an example, the tidal effect of the system is studied in detail, the results indicate that the dissipative term of the tidal effect causes the attenuation of planets’ orbital eccentricities, and it plays a dominant role in the process of orbital evolution, however, the conservative term of the tidal effect and the relativistic effect may damp the excitation of the eccentricity of the inner planet under the secular perturbation of the outer planet. In addition, the process of tidal evolution is also affected by both the initial eccentricity of the outer planet and the planet's tidal dissipation coeffcient. At the same time, the numerical simulation on the tidal evolution of the KOI 1239 system is also made, and the numerical results are consistent with those of general secular perturbation theory.     

Long term modulation of cosmic rays and inferable electromagnetic state in solar modulating region

It is demonstrated that the long term variation in cosmic ray intensity I(t) can be described by an integral equation,

$\text{I(t)=I}{}_{\mathrm{\infty }}\text{?}\text{∫}\text{0}\text{∞}\text{f(τ)S(t?τ)}\text{d}\text{τ}$

, which is derived from a generalization of Simpson's coasting solar wind model. A source function S(t?τ) is given by some appropriate solar activity index at a time t?τ(τ ? 0) and the characteristic functionf(τ)(?0 forτ ? 0) expresses the time dependence of the efficiency of the intensity depression due to solar disturbances represented by S(t ?τ) when the disturbances generated at the solar surface propagate through the modulating region with the solar wind. It is demonstrated further that the equation can be derived from the general diffusion-convection theory on some assumptions, and as a result, the source and characteristic functions can be related to diffusion coefficient and its transition in space. Assuming the sunspot number R (or two activity indices including R) as the source function, the characteristic function f(τ) [or f(τ)'s] is obtained with data of the cosmic ray intensity extended over several decades. Based on the theory, one can obtain from f(τ) the following physical quantities in space, such as the transition and life time of solar disturbances, the boundary of the modulating region, and the radial and time dependences of the diffusion coefficient, radial density gradient and modulated intensity of cosmic rays. Results deduced from the present analysis are consistent with those obtained directly or indirectly by space observations.     

Families <Emphasis Type="Italic">c</Emphasis> and <Emphasis Type="Italic">i</Emphasis> of periodic solutions of the restricted problem for μ = 5 × 10<Superscript>−5</Superscript>

We consider the circular planar restricted three-body problem with the mass parameter μ = 5 × 10^?5. Two families of periodic solutions are calculated: family c, starting from the collinear fixed point L ₁, and the initial part of familyi, which begins by direct circular orbits of an infinitely small radius around the body of bigger mass. The calculated families are very close to the generating ones, which we described earlier. In particular, the existence of the predicted zigzag structure of characteristics of family iis verified. New properties of the planar and vertical traces are discovered.