A new well behaved class of charge analogue of Adler’s relativistic exact solution

The paper presents a new class of parametric interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of electric field intensity. This solution gives us wide range of parameter, K (0.69≤K≤7.1), for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a superdense object is maximized with all degree of suitability by assuming the surface density of the star equal to the normal nuclear density ρ _nm=2.5×10¹⁷kg?m^?3. By this model we obtain the mass of the Crab pulsar M _Crab=1.401M _⊙ and the radius, R _Crab=12.98 km constraining the moment of inertia I _NS,38>1.61 for the conservative estimate of Crab nebula mass 2M _⊙ and M _Crab=2.0156M _⊙ with radius, R _Crab=14.07 km constraining the moment of inertia I _NS,38>3.04 for the newest estimate of Crab nebula mass 4.6M _⊙ which are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields the moments of inertia for PSR J0737-3039A and PSR J0737-3039B are I _A,38=1.4624 and I _B,38=1.2689 respectively. It has been observed that under well behaved conditions this class of parametric solution gives us the maximum gravitational mass of causal superdense object 2.8020M _⊙ with radius 14.49 km, surface redshift z _R =0.4319, charge Q=4.67×10²⁰ C, and central density ρ _c =2.68ρ _nm.     

Well behaved class of charge analogue of Heintzmann’s relativistic exact solution

We present a well behaved class of Charge Analogue of Heintzmann (Z. Phys. 228:489, 1969) solution. This solution describes charge fluid balls with positively finite central pressure and positively finite central density ; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of constant K (1.25≤K≤15) for which the solution is well behaved and therefore, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degrees of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to K=1.25 and X=0.42, the maximum mass of the star comes out to be 3.64M _Θ with linear dimension 24.31 km and central redshift 1.5316.     

A class of well behaved charged analogues of Vaidya–Tikekar type super-dense star

In the present article a model of well behaved charged superdense star with surface density 2×10¹⁴ gm/cm³ is constructed by considering a static spherically symmetric metric with t=const hypersurfaces as hyperboloid. So far well behaved model described by such metric could not be obtained. Maximum mass of the star is found to be 0.343457M _⊙ and the corresponding radius is 9.57459 km. The red shift at the centre and on the surface are given as 0.068887 and 0.031726 respectively.     

A family of well behaved charge analogues of?a?well behaved neutral solution in?general relativity

A family of charge analogues of a neutral solution with g ₄₄=(1+Cr ²)⁶ has been obtained by using a specific electric intensity, which involves a parameter K. Both neutral and charged solutions are analysed physically subject to the surface density 2×10¹⁴ gm/cm³ (neutron star). The neutral solution is well behaved for 0.0<Ca ²≤0.10477 while its charge analogues are well behaved for a wide range of a parameter K (0≤K≤72) i.e. pressure, density, pressure-density ratio, velocity of sound is monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and radius occupied by the neutral solution are 3.4126M _Θ and 18.9227 km for Ca ²=0.10447 respectively. While the red shift at centre Z ₀=0.9686 and red shift at the surface Z _a =0.4612. For the charged solution, the maximum mass and radius are 5.6111M _Θ and 17.2992 km respectively for K=3.0130 and Ca ²=0.2500, with the red shift Z ₀=3.0113 and Z _a =1.0538.     

A class of new solutions of generalized charged analogues of Buchdahl’s type super-dense star

The present paper reports a class of new solutions of charged fluid spheres expressed by a space time with its hypersurfaces t=const. as spheroid for the case 0<K<1 with surface density 2×10¹⁴ gm/cm³. When the Buchdahl’s type fluid spheres are electrified with generalized charged intensity and it is utilized to construct a super-dense star and found that star satisfies all reality conditions except the casual condition for 0<K≤0.05. The maximum mass occupied and the corresponding radius have been obtained 8.130871 M _Θ and 24.60916 km respectively. Further, the redshift at the centre and on the surface are noted by z ₀=0.933729 and z _a =0.383808 respectively.     

A family of well behaved charge analogues of Durgapal’s perfect fluid exact solution in general relativity

This paper presents a new family of interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of charge distribution. This solution gives us wide range of parameter, K, for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a star is maximized with all degree of suitability by assuming the surface density equal to normal nuclear density, ρ _nm=2.5×10¹⁷ kg?m^?3. By this model we obtain the mass of the Crab pulsar, M _Crab, 1.36M _⊙ and radius 13.21 km, constraining the moment of inertia >?1.61×10³⁸ kg?m² for the conservative estimate of Crab nebula mass 2M _⊙. And M _Crab=1.96M _⊙ with radius R _Crab=14.38 km constraining the moment of inertia >?3.04×10³⁸ kg?m² for the newest estimate of Crab nebula mass, 4.6M _⊙. These results are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields moments of inertia for PSR J0737-3039A and PSR J0737-3039B, I _A =1.4285×10³⁸ kg?m² and I _B =1.3647×10³⁸ kg?m² respectively. It has been observed that under well behaved conditions this class of solutions gives us the overall maximum gravitational mass of super dense object, M _G(max)=4.7487M _⊙ with radius $R_{M_{\max}}=15.24~\mathrm{km}$ , surface redshift 0.9878, charge 7.47×10²⁰ C, and central density 4.31ρ _nm.     

A family of well behaved charge analogues of Durgapal’s perfect fluid exact solution in general relativity II

This paper presents a family of two-parametric interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with particular form of charge distribution. This class of solutions gives us wide range of parameters, n and K, for which the solutions are well behaved hence, suitable for modeling of compact star (e. g. bare strange quark star). The mass of star is maximized with all degree of suitability by assuming the stellar “surface” density equal to strange (quark) matter density at zero pressure. It is hoped that our investigation may be of some help in connection of some study of stellar structure.     

A new class of charged analogues of Vaidya–Tikekar type super-dense star

First ever closed form solution for charged fluid sphere expressed by a space time with its hypersurfaces t= constant as spheroid is obtained for the case 0<K<1. The same is utilized to construct a superdense star with surface density 2×10¹⁴ gm/cm³. The star is seen to satisfy the reality and causality conditions for 0<K≤0.045 and possesses maximum mass and radius to be 0.065216M _Θ and 1.137496 km respectively. Moreover the interior of the star satisfy strong energy condition. However in the absence of the causality condition, the reality conditions are valid for a wider range 0<K≤0.13. The maximum mass and radius for the later case are 1.296798M _Θ and 2.6107 km respectively for the strong energy condition, while the said parameters for the weak energy condition read as 1.546269M _Θ and 2.590062 km respectively.     

Well behaved parametric class of relativistic charged fluid ball in?general relativity

The paper presents a class of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0≤K≤42) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to K=2 and X=0.30, the maximum mass of the star comes out to be 4.96 M _Θ with linear dimension 34.16 km and central redshift and surface redshift 2.1033 and 0.683 respectively. In absence of the charge we are left behind with the well behaved fourth model of Durgapal (J. Phys., A, Math. Gen. 15:2637, 1982).     

A class of exact isotropic solutions of Einstein’s equations and relativistic stellar models in general relativity

In this paper we have studied a particular class of exact solutions of Einstein’s gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/c ² R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538–52, LMC X-4, SAX J1808.4?3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.     

Spectral variability of LBV star V 532 (Romano’s star)

We present the results of studying the spectral and photometric variability of the luminous blue variable star V532 in M33. The photometric variations are traced from 1960 to 2010, spectral variations—from 1992 to 2009. The star has revealed an absolute maximum of visual brightness (1992–1994, high/cold state) and an absolute minimum (2007–2008, low/hot state) with a brightness difference of ΔB ≈ 2.3 ^m . The temperature estimates in the absolute maximum and absolute minimum were found to be T ∼ 22000 K and T ∼ 42000 K, respectively. The variability of the spectrum of V532 is fully consistent with the temperature variations in its photosphere, while both permitted and forbidden lines are formed in an extended stellar atmosphere. Broad components of the brightest lines were found, the broadening of these components is due to electron scattering in the wind parts closest to the photosphere. We measured the wind velocity as a difference between the emission and absorption peaks in the PCyg type profiles. The wind velocity clearly depends on the size of the stellar photosphere or on the visual brightness, when brightness declines, the wind velocity increases. In the absolute minimum a kinematic profile of the V532 atmosphere was detected. The wind velocity increases and its temperature declines with distance from the star. In the low/hot state, the spectral type of the star corresponds to WN8.5h, in the high/cold state—to WN11. We studied the evolution of V532 along with the evolution of AGCar and the massive WR binary HD5980 in SMC. During their visual minima, all the three stars perfectly fit with the WNL star sequence by Crowther and Smith (1997). However, when visual brightness increases, all the three stars form a separate sequence. It is possible that this reflects a new property of LBV stars, namely, in the high/cold states they do not pertain to the bona fide WNL stars.     

Measurements of radial velocities of α and: A spotted HgMn star?

Measurements of radial velocities from the SiII 6347A and 6371Alines and the HeI 6678A line based on observations of 1989–1994 are examined. The variability of the line shapes over the 96.6-day orbital period is analyzed. Evidence for a second component is found from lines in the spectrum of And which correspond to the silicon lines 6347 and 6371A. The preliminary value for the rotational velocity of the secondary component is 100–120 km/sec. Analysis of the variability of the radial velocities of the HeI 6678A line during the night has given the rotational period of the star of P_rot=I^d.012344 and indicates an inhomogeneous distribution either of the helium abundance or of the physical conditions over the surface. Thus, we have the first evidence for the existence of spots on the surface of an HgMn star.Translated fromAstrofizika, Vol. 39, No. 3, pp. 375–384, July–September, 1996.     

A hypothesis for explaining the origin of Przybylski’s star (HD 101065)

Many unidentified lines in the spectrum of Przybylski’s star (HD 101065) match well the spectral lines of radioactive elements, including the lines of short-lived isotopes. The origin of such isotopes in the atmosphere of the star remains unknown. We discuss a scenario in which some heavy nuclei of radioactive elements are produced in Przybylski’s star atmosphere as a result of its permanent exposure to the gamma flux (photon-nuclear reactions) or of the direct interaction of the free neutrons which arise in the atmosphere with seed nuclei of lighter elements (r-process). In both cases the gamma quanta and the free neutrons originate due to the presence of the neutron star which forms a close binary system with Przybylski’s star. This neutron star is the source of the fast electrons and positrons which produce gamma quanta when they are decelerated in their interaction with the atomic nuclei of the atmospheric plasma, while free neutrons can originate in the reactions of the direct capture of fast electrons by atmospheric protons (nuclei of hydrogen atoms).     

An impact model of Newton’s law of gravitation

The far-reaching gravitational force—in the approximation of Newton’s law of gravitation—is described by a heuristic model with hypothetical massless particles propagating at the speed of light in vacuum and transferring momentum and energy between physical entities through interactions on a local basis. The model has some similarities with the impact theory presented by Nicolas Fatio de Duillier to the Royal Society in 1690. Objections raised against this idea are dispelled by invoking the Special Theory of Relativity, considering non-local interactions, and replacing the shielding concept by a secular mass increase of massive bodies. Some consequences and applications of the model are discussed.     

When is star formation episodic? A delay differential equation 'negative feedback' model

We introduce a differential equation for star formation in galaxies that incorporates negative feedback with a delay. When the feedback is instantaneous, solutions approach a self-limiting equilibrium state. When there is a delay, even though the feedback is negative, the solutions can exhibit cyclic and episodic solutions. We find that periodic or episodic star formation only occurs when two conditions are satisfied. First the delay time-scale must exceed a cloud consumption time-scale. Secondly, the feedback must be strong. This statement is quantitatively equivalent to requiring that the time-scale to approach equilibrium be greater than approximately twice the cloud consumption time-scale. The period of oscillations predicted is approximately four times the delay time-scale. The amplitude of the oscillations increases with both feedback strength and delay time.
We discuss applications of the delay differential equation (DDE) model to star formation in galaxies using the cloud density as a variable. The DDE model is most applicable to systems that recycle gas and only slowly remove gas from the system. We propose likely delay mechanisms based on the requirement that the delay time is related to the observationally estimated time between episodic events. The proposed delay time-scale accounting for episodic star formation in galaxy centres on periods similar to   P ∼ 10 Myr  , irregular galaxies with   P ∼ 100 Myr  , and the Milky Way disc with   P ∼ 2  Gyr, could be that for exciting turbulence following creation of massive stars, that for gas pushed into the halo to return and interact with the disc and that for spiral density wave evolution, respectively.     

A model of the late universe with viscous Zel’ldovich fluid and decaying vacuum

Many have speculated about the presence of a stiff fluid in very early stage of the universe. Such a stiff fluid was first introduced by Zel’dovich. Recently the late acceleration of the universe was studied by taking bulk viscous stiff fluid as the dominant cosmic component, but the age predicted by such a model is less than the observed value. We consider a flat universe with viscous stiff fluid and decaying vacuum energy as the cosmic components and found that the model predicts a reasonable background evolution of the universe with de Sitter epoch as end phase of expansion. More over, the model also predicts a reasonable value for the age of the present universe. We also performed a dynamical system analysis of the model and found that the end de Sitter phase predicted by the model is stable.     

Production and imaging of energetic neutral atoms from Titan’s exosphere: a 3-D model

Energetic Neutral Atoms (ENAs) are formed when singly charged magnetospheric ions undergo charge exchange collisions with exospheric neutral atoms. The energy of the incident ions is almost entirely transferred to the charge exchange produced ENAs, which then propagate along nearly rectilinear ballistic trajectories. Thus the ENAs can be used like photons in order to form an image of the energetic ion distribution. The Cassini spacecraft is equipped with the Ion and Neutral Camera (INCA), a magnetospheric imaging ENA camera which is part of MIMI (Magnetospheric Imaging Instrument) [Mitchell, D.G., Cheng, A.F., Krimigis, S.M., Keath, E.P., Jaskulek, S.E., Mauk, B.H., McEntire, R.W., Roelof, E.C., Williams, D.J., Hsieh, K.C., Drake, V.A., 1993. INCA: the ion neutral camera for energetic neutral imaging of the Saturnian magnetosphere. Opt. Eng. 32, 3096; Krimigis, S.M., Mitchell, D.G., Hamilton, D.C. et al., 1998. Magnetospheric Imaging Instrument (MIMI) on the Cassini Mission to Saturn/Titan, Space Sci. Rev., submitted]. In this paper we study the production of energetic neutral atoms resulting from the interaction of Titan’s inner exosphere with Saturn’s magnetosphere. We then simulate the ENA images of this interaction, that we anticipate to get from INCA, by using a 3-D model of the ENA production. This first necessitated the development of a model for the altitude density profile and composition of the Titan exosphere [Amsif, A., Dandouras, J., Roelof, E.C., 1997. Modeling the production and the imaging of energetic neutral atoms from Titan’s exosphere. J. Geophys. Res. 102, 22,169]. We thus used the Chamberlain model [Chamberlain, J.W., 1963. Planetary corona and atmospheric evaporation. Planet. Space Sci. 11, 901] and included the five major species: H, H₂, N, N₂ and CH₄. The density and composition profiles obtained were then used to calculate the ENA production, considering a proton spectrum measured by Voyager in the Saturnian magnetosphere as the parent ion population. In order to generate simulated ENA images of the interaction of Titan’s exosphere with Saturn’s magnetosphere, we developed a model based on 3-D trajectory tracing techniques for the parent ions. Since the parent ions (E>10 keV) have gyroradii comparable with the Titan diameter, the screening effect of Titan on the parent ion population was also taken into account. This effect results in highly anisotropic ion distributions, which produce ‘shadows’ in the ENA fluxes, in certain directions. These shadows depend on the ENA energy and on the relative geometry of Titan, the magnetic field and the Cassini spacecraft position. The INCA images will thus enable us to remotely sense the ion fluxes and spectra. They are also expected to give information about the magnetic field in the vicinity of Titan and thus to Titan’s interaction with the magnetosphere of Saturn.     

A predator–prey model for moon-triggered clumping in Saturn’s rings

UVIS occultation data show clumping in Saturn’s F ring and at the B ring outer edge, indicating aggregation and disaggregation at these locations that are perturbed by Prometheus and by Mimas. The inferred timescales range from hours to months. Occultation profiles of the edge show wide variability, indicating perturbations by local mass aggregations. Structure near the B ring edge is seen in power spectral analysis at scales 200–2000 m. Similar structure is also seen at the strongest density waves, with significance increasing with resonance strength. For the B ring outer edge, the strongest structure is seen at longitudes 90° and 270° relative to Mimas. This indicates a direct relation between the moon and the ring clumping. We propose that the collective behavior of the ring particles resembles a predator–prey system: the mean aggregate size is the prey, which feeds the velocity dispersion; conversely, increasing dispersion breaks up the aggregates. Moons may trigger clumping by streamline crowding, which reduces the relative velocity, leading to more aggregation and more clumping. Disaggregation may follow from disruptive collisions or tidal shedding as the clumps stir the relative velocity. For realistic values of the parameters this yields a limit cycle behavior, as for the ecology of foxes and hares or the “boom-bust” economic cycle. Solving for the long-term behavior of this forced system gives a periodic response at the perturbing frequency, with a phase lag roughly consistent with the UVIS occultation measurements. We conclude that the agitation by the moons in the F ring and at the B ring outer edge drives aggregation and disaggregation in the forcing frame. This agitation of the ring material may also allow fortuitous formation of solid objects from the temporary clumps, via stochastic processes like compaction, adhesion, sintering or reorganization that drives the denser parts of the aggregate to the center or ejects the lighter elements. Any of these more persistent objects would then orbit at the Kepler rate. We would also expect the formation of clumps and some more permanent objects at the other perturbed regions in the rings… including satellite resonances, shepherded ring edges, and near embedded objects like Pan and Daphnis (where the aggregation/disaggregation cycles are forced similar to Prometheus forcing of the F ring).