Relativistic model of radiating massive fluid sphere

In this paper we present a new class of nonsingular solutions representing time dependent balls of perfect fluid with matter-radiation in general relativity. The solution of the class is suitable for interior modeling of a quasar i.e. a massive radiating star. The interior solution is matched with a zero pressure Vaidya metric. From this solution we constructed a quasar model by assuming the life time of the quasar of ≈10⁷ year. We obtained a mass of the quasar of ≈10⁹ M _θ , linear dimension ≈10¹⁷ km and a rate of emission L _∞≈10⁴⁷ erg/s.     

Well-behaved relativistic charged super-dense star models

A new class of charged super-dense star models is obtained by using an electric intensity, which involves a parameter, K. The metric describing the model shares its metric potential g ₄₄ with that of Durgapal’s fourth solution (J. Phys. A, Math. Gen. 15:2637, 1982). The pressure-free surface is kept at the density ρ _b =2×10¹⁴ g/cm³ and joins smoothly with the Reissner-Nordstrom solution. The charge analogues are well-behaved for a wide range, 0≤K≤59, with the optimum value of X=0.264 i.e. the pressure, density, pressure–density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.22M _Θ and 20 km, respectively for X=0.264. For the charged solution, the maximum mass and radius are defined by the expressions M≈(0.0059K+4.22)M _Θ and r _b ≈−0.021464K+20 km respectively.     

Variety of well behaved exact solutions of Einstein–Maxwell field equations: an application to Strange Quark stars, Neutron stars and Pulsars

We present a variety of well behaved classes of Charge Analogues of Tolman’s iv (1939). These solutions describe charged fluid balls with positively finite central pressure, 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. These solutions give us wide range of parameter for every positive value of n for which the solution is well behaved hence, suitable for modeling of super dense stars. keeping in view of well behaved nature of these solutions, one new class of solutions is being studied extensively. Moreover, this class of solutions gives us wide range of constant K (0.3≤K≤0.91) for which the solution is well behaved hence, suitable for modeling of super dense stars like Strange Quark stars, Neutron stars and Pulsars. For this class of solutions the mass of a star is maximized with all degree of suitability, compatible with Quark stars, Neutron stars and Pulsars. By assuming the surface density ρ _b =2×10¹⁴ g/cm³ (like, Brecher and Caporaso in Nature 259:377, 1976), corresponding to K=0.30 with X=0.39, the resulting well behaved model has the mass M=2.12M _Θ, radius r _b ≈15.27 km and moment of inertia I=4.482×10⁴⁵ g cm²; for K=0.4 with X=0.31, the resulting well behaved model has the mass M=1.80M _Θ, radius r _b ≈14.65 km and moment of inertia I=3.454×10⁴⁵ g cm²; and corresponding to K=0.91 with X=0.135, the resulting well behaved model has the mass M=0.83M _Θ, radius r _b ≈11.84 km and moment of inertia I=0.991×10⁴⁵ g cm². For n=0 we rediscovered Pant et al. (in Astrophys. Space Sci. 333:161, 2011b) well behaved solution. These values of masses and moment of inertia are found to be consistent with other models of Neutron stars and Pulsars available in the literature and are applicable for the Crab and the Vela Pulsars.     

Artificial contradiction between cosmology and particle physics: the Λ problem

It is shown that the usual choice of units obtained by taking G=c=ℏ=1, giving the Planck’s units of mass, length and time, introduces an artificial contradiction between cosmology and particle physics: the lambda problem that we associate with ℏ. We note that the choice of ℏ=1 does not correspond to the scale of quantum physics. For this scale we prove that the correct value is ℏ≈1/10¹²², while the choice of ℏ=1 corresponds to the cosmological scale. This is due to the scale factor of 10⁶¹ that converts the Planck scale to the cosmological scale. By choosing the ratio G/c ³=constant=1, which includes the choice G=c=1, and the momentum conservation mc=constant, we preserve the derivation of the Einstein field equations from the action principle. Then the product Gm/c ²=r _g , the gravitational radius of m, is constant. For a quantum black hole we prove that ℏ≈r _g ²≈(mc)². We also prove that the product Λℏ is a general constant of order one, for any scale. The cosmological scale implies Λ≈ℏ≈1, while the Planck scale gives Λ≈1/ℏ≈10¹²². This explains the Λ problem. We get two scales: the cosmological quantum black hole (QBH), size ∼10²⁸ cm, and the quantum black hole (qbh) that includes the fundamental particles scale, size ∼10⁻¹³ cm, as well as the Planck’ scale, size ∼10⁻³³ cm.      

A new well behaved exact solution in general relativity for perfect fluid

We present a new spherically symmetric solution of the general relativistic field equations in isotropic coordinates. The solution is having positive finite central pressure and positive finite central density. The ratio of pressure and density is less than one and casualty condition is obeyed at the centre. Further, the outmarch of pressure, density and pressure-density ratio, and the ratio of sound speed to light is monotonically decreasing. The solution is well behaved for all the values of u lying in the range 0<u≤.186. The central red shift and surface red shift are positive and monotonically decreasing. Further, we have constructed a neutron star model with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. The maximum mass of the Neutron star comes out to be M=1.591 M _Θ with radius R _b ≈12.685 km. The most striking feature of the solution is that the solution not only well behaved but also having one of the simplest expressions so far known well behaved solutions. Moreover, the good matching of our results for Vela pulsars show the robustness of our model.     

Charged analogues of Schwarzschild interior solution in terms of pressure

Recently, Bijalwan (Astrophys. Space Sci., doi:, 2011a) discussed charged fluid spheres with pressure while Bijalwan and Gupta (Astrophys. Space Sci. 317, 251–260, 2008) suggested using a monotonically decreasing function f to generate all possible physically viable charged analogues of Schwarzschild interior solutions analytically. They discussed some previously known and new solutions for Schwarzschild parameter u( = \fracGMc²a ) ￡ 0.142u( =\frac{GM}{c^{2}a} ) \le 0.142, a being radius of star. In this paper we investigate wide range of u by generating a class of solutions that are well behaved and suitable for modeling Neutron star charge matter. We have exploited the range u≤0.142 by considering pressure p=p(ω) and f = ( f₀(1 - \fracR²(1 - w)a²) +f_a\fracR²(1 - w)a² )f = ( f_{0}(1 - \frac{R^{2}(1 - \omega )}{a^{2}}) +f_{a}\frac{R^{2}(1 - \omega )}{a^{2}} ), where w = 1 -\fracr²R²\omega = 1 -\frac{r^{2}}{R^{2}} to explore new class of solutions. Hence, class of charged analogues of Schwarzschild interior is found for barotropic equation of state relating the radial pressure to the energy density. The analytical models thus found are well behaved with surface red shift z _s ≤0.181, central red shift z _c ≤0.282, mass to radius ratio M/a≤0.149, total charge to total mass ratio e/M≤0.807 and satisfy Andreasson’s (Commun. Math. Phys. 288, 715–730, 2009) stability condition. Red-shift, velocity of sound and p/c ² ρ are monotonically decreasing towards the surface while adiabatic index is monotonically increasing. The maximum mass found to be 1.512 M _Θ with linear dimension 14.964 km. Class of charged analogues of Schwarzschild interior discussed in this paper doesn’t have neutral counter part. These solutions completely describe interior of a stable Neutron star charge matter since at centre the charge distribution is zero, e/M≤0.807 and a typical neutral Neutron star has mass between 1.35 and about 2.1 solar mass, with a corresponding radius of about 12 km (Kiziltan et al., [astro-ph.GA], 2010).     

Investigation of Quasi-periodic Variations in Hard X-Rays of Solar Flares. II. Further Investigation of Oscillating Magnetic Traps

In our recent paper (Jakimiec and Tomczak, Solar Physics 261, 233, 2010) we investigated quasi-periodic oscillations of hard X-rays during the impulsive phase of solar flares. We have come to the conclusion that they are caused by magnetosonic oscillations of magnetic traps within the volume of hard-X-ray (HXR) loop-top sources. In the present paper we investigate four flares that show clear quasi-periodic sequences of the HXR pulses. We also describe our phenomenological model of oscillating magnetic traps to show that it can explain the observed properties of the HXR oscillations. The main results are the following: i) Low-amplitude quasi-periodic oscillations occur before the impulsive phase of some flares. ii) The quasi-periodicity of the oscillations can change in some flares. We interpret this as being due to changes of the length of oscillating magnetic traps. iii) During the impulsive phase a significant part of the energy of accelerated (non-thermal) electrons is deposited within a HXR loop-top source. iv) The quick development of the impulsive phase is due to feedback between the pressure pulses by accelerated electrons and the amplitude of the magnetic-trap oscillation. v) The electron number density and magnetic field strength values obtained for the HXR loop-top sources in several flares fall within the limits of N≈(2 – 15)×10¹⁰ cm⁻³, B≈(45 – 130) gauss. These results show that the HXR quasi-periodic oscillations contain important information about the energy release in solar flares.     

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).     

Energy-Dependent Timing of Thermal Emission in Solar Flares

We report solar flare plasma to be multi-thermal in nature based on the theoretical model and study of the energy-dependent timing of thermal emission in ten M-class flares. We employ high-resolution X-ray spectra observed by the Si detector of the “Solar X-ray Spectrometer” (SOXS). The SOXS onboard the Indian GSAT-2 spacecraft was launched by the GSLV-D2 rocket on 8 May 2003. Firstly we model the spectral evolution of the X-ray line and continuum emission flux F(ε) from the flare by integrating a series of isothermal plasma flux. We find that the multi-temperature integrated flux F(ε) is a power-law function of ε with a spectral index (γ)≈−4.65. Next, based on spectral-temporal evolution of the flares we find that the emission in the energy range E=4 – 15 keV is dominated by temperatures of T=12 – 50 MK, while the multi-thermal power-law DEM index (δ) varies in the range of −4.4 and −5.7. The temporal evolution of the X-ray flux F(ε,t) assuming a multi-temperature plasma governed by thermal conduction cooling reveals that the temperature-dependent cooling time varies between 296 and 4640 s and the electron density (n _e) varies in the range of n _e=(1.77 – 29.3)×10¹⁰ cm⁻³. Employing temporal evolution technique in the current study as an alternative method for separating thermal from nonthermal components in the energy spectra, we measure the break-energy point, ranging between 14 and 21±1.0 keV.     

Flare Plasma Cooling from 30 MK down to 1 MK modeled from Yohkoh,GOES, and TRACE observations during the Bastille Day Event (14 July 2000)

We present an analysis of the evolution of the thermal flare plasma during the 14 July 2000, 10 UT, Bastille Day flare event, using spacecraft data from Yohkoh/HXT, Yohkoh/SXT, GOES, and TRACE. The spatial structure of this double-ribbon flare consists of a curved arcade with some 100 post-flare loops which brighten up in a sequential manner from highly-sheared low-lying to less-sheared higher-lying bipolar loops. We reconstruct an instrument-combined, average differential emission measure distribution dEM(T)/dT that ranges from T=1 MK to 40 MK and peaks at T ₀=10.9 MK. We find that the time profiles of the different instrument fluxes peak sequentially over 7 minutes with decreasing temperatures from T≈30 MK to 1 MK, indicating the systematic cooling of the flare plasma. From these temperature-dependent relative peak times t _peak(T) we reconstruct the average plasma cooling function T(t) for loops observed near the flare peak time, and find that their temperature decrease is initially controlled by conductive cooling during the first 188 s, T(t)∼[1+(t/τ_cond)]^−2/7, and then by radiative cooling during the next 592 s, T(t)∼[1−(t/τ_rad)]^3/5. From the radiative cooling phase we infer an average electron density of n _e=4.2×10¹¹ cm⁻³, which implies a filling factor near 100% for the brightest observed 23 loops with diameters of ∼1.8 Mm that appear simultaneously over the flare peak time and are fully resolved with TRACE. We reproduce the time delays and fluxes of the observed time profiles near the flare peak self-consistently with a forward-fitting method of a fully analytical model. The total integrated thermal energy of this flare amounts to E _thermal=2.6×10³¹ erg. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1014257826116     

Extremization of mass of charged superdense star models describe by Durgapal type space-time metric

In the present article, we have obtained a class of charged superdense star models, starting with a static spherically symmetric metric in curvature coordinates by considering Durgapal (J. Phys. A 15:2637, 1982) type metric i.e. g ₄₄=B(1+Cr ²) ⁿ , where n being any positive integer. It is observed that the maximum mass of the charged fluid models is monotonically increasing with the increasing values of n≤4. For n≥4, the maximum mass of the charged fluid models is throughout monotonically decreasing and over all maximum mass is attained at n=4. The present metric tends to another metric which describes the charged analogue of Kuchowicz neutral solution as n→∞. Consequently the lower limit of maximum mass of the charged fluid models could be determined and found to be 5.1165 solar mass with corresponding radius 18.0743 Km. While the upper limit of maximum mass of the model of this category is already known to be 5.7001 solar mass with corresponding radius 17.1003 Km for n=4. The solutions so obtained are well behaved.     

Accelerated expansion from?a?modified-quadratic gravity

We investigate the late-time dynamics of a four-dimensional universe based on modified scalar field gravity in which the standard Einstein-Hilbert action R is replaced by f(φ)R+f(R) where f(φ)=φ ² and f(R)=AR ²+BR _μν R ^μν,(A,B)∈ℝ. We discussed two independent cases: in the first model, the scalar field potential is quartic and for this special form it was shown that the universe is dominated by dark energy with equation of state parameter w≈−0.2 and is accelerated in time with a scale factor evolving like a(t)∝t ^5/3 and B+3A≈0.036. When, B+3A→∞ which corresponds for the purely quadratic theory, the scale factor evolves like a(t)∝t ^1/2 whereas when B+3A→0 which corresponds for the purely scalar tensor theory we found when a(t)∝t ^1.98. In the second model, we choose an exponential potential and we conjecture that the scalar curvature and the Hubble parameter vary respectively like R=hH[(f)\dot]/f,h ? \mathbbRR=\eta H\dot{\phi}/\phi,\eta\in\mathbb{R} and H=g[(f)\dot]^c,(g,c) ? \mathbbRH=\gamma\dot{\phi}^{\chi},(\gamma,\chi)\in\mathbb{R}. It was shown that for some special values of  χ, the universe is free from the initial singularity, accelerated in time, dominated by dark or phantom energy whereas the model is independent of the quadratic gravity corrections. Additional consequences are discussed.     

Magnetoacoustic Wave Trains in the 11 July 2005 Radio Event with Fiber Bursts

A dm-radio emission with fiber bursts observed on 11 July 2005 was analyzed using wavelet filtration and spectral methods. In filtered radio spectra we found structures with different characteristic period P and frequency drift FD: i) fiber substructures (composed of dot emissions) with P ₁≈ 0.5 s, FD₁=− 87 MHz s⁻¹ on average, ii) fiber structures with P ₂≈1.9 s, and iii) drifting structures with P ₃≈81.4 s, FD₂=− 8.7, + 98.5, and − 21.8 MHz s⁻¹. In the wavelet spectra we recognized patterns having the form of tadpoles. They were detected with the same characteristic periods P as found for the filtered structures. The frequency drift of the tadpole heads is found to be equal to the frequency drift of some groups of fibers for the long-period wavelet tadpoles (P ₃) and to the frequency drift of individual fibers for the short-period tadpoles (P ₂). Considering these wavelet tadpoles as signatures of propagating magnetoacoustic wave trains, the results indicate the presence of several wave trains in the fibers’ source. While the long-period wave trains trigger or modulate a whole group of fibers, the short-period ones look like being connected with individual fiber bursts. This result supports the model of fibers based on magnetoacoustic waves. Using a density model of the solar atmosphere we derived the velocities of the magnetoacoustic waves, 107 and 562 km s⁻¹, and setting them equal to the Alfvén ones we estimated the magnetic field in the source of fiber bursts as 10.7 and 47.8 G.     

Searching for curvature pion radiation from protons in strongly magnetized pulsars

By using rather conservative estimates based on the simplest polar cap model, we search the ATNF Pulsar Catalogue for strongly magnetized stars that could accelerate relativistic protons up to the curvature pion production threshold. The best candidate turns out to be the 16 ms pulsar J0537-6910, but the corresponding characteristic parameter χ=a/m _p is yet too small to give origin to observable signals. We show that, for pulsars with period P≈1 ms, a surface polar magnetic field B≈10¹² G is required in order to induce detectable curvature pion radiation from accelerated protons in the magnetosphere. Some other emission processes are also considered.     

Five dimensional LRS Bianchi type-I string cosmological model in Saez and Ballester theory

In this paper, it is shown that five dimensional LRS Bianchi type-I string cosmological models do not survive for Geometric and Takabayasi string whereas Barotropic string i.e. ρ=ρ(λ) survives and degenerates string with ρ+λ=0 in scalar tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986). Further we studied some physical and geometrical properties of the model.     

Evaluation of a Selected Case of the Minimum Dissipative Rate Method for Non-Force-Free Solar Magnetic Field Extrapolations

The minimum dissipative rate (MDR) method for deriving a coronal non-force-free magnetic field solution is partially evaluated. These magnetic field solutions employ a combination of three linear (constant-α) force-free-field solutions with one being a potential field (i.e., α=0). The particular case of the solutions where the other two α’s are of equal magnitude but of opposite sign is examined. This is motivated by studying the SOLIS (Synoptic Optical Long-term Investigation of the Sun (SOLIS), a National Solar Observatory facility) vector magnetograms of AR 10987, which show a global α value consistent with an α=0 value as evaluated by (∇×B) _z /B _z over the region. Typical of the current state of the observing technology, there is no definitive twist for input into the general MDR method. This suggests that the special α case, of two α’s with equal magnitudes and opposite signs, is appropriate given the data. Only for an extensively twisted active region does a dominant, nonzero α normally emerge from a distribution of local values. For a special set of conditions, is it found that (i) the resulting magnetic field is a vertically inflated magnetic field resulting from the electric currents being parallel to the photosphere, similar to the results of Gary and Alexander (Solar Phys. 186:123, 1999), and (ii) for α≈(α _max/2), the Lorentz force per unit volume normalized by the square of the magnetic field is on the order of 1.4×10⁻¹⁰ cm⁻¹. The Lorentz force (F _L) is a factor of ten higher than that of the magnetic force d(B ²/8π)/dz, a component of F _L. The calculated photospheric electric current densities are an order of magnitude smaller than the maximum observed in all active regions. Hence both the Lorentz force density and the generated electric current density seem to be physically consistent with possible solar dynamics. The results imply that the field could be inflated with an overpressure along the neutral line. However, the implementation of this or any other extrapolation method using the electric current density as a lower boundary condition must be done cautiously, with the current magnetography.     

Evidence for a disaggregation of the universe

Combining the kinematical definitions of the two dimensionless parameters, the deceleration q(x) and the Hubble t ₀ H(x), we get a differential equation (where x=t/t ₀ is the age of the universe relative to its present value t ₀). First integration gives the function H(x). The present values of the Hubble parameter H(1) [approximately t ₀ H(1)≈1], and the deceleration parameter [approximately q(1)≈−0.5], determine the function H(x). A second integration gives the cosmological scale factor a(x). Differentiation of a(x) gives the speed of expansion of the universe. The evolution of the universe that results from our approach is: an initial extremely fast exponential expansion (inflation), followed by an almost linear expansion (first decelerated, and later accelerated). For the future, at approximately t≈3t ₀ there is a final exponential expansion, a second inflation that produces a disaggregation of the universe to infinity. We find the necessary and sufficient conditions for this disaggregation to occur. The precise value of the final age is given only with one parameter: the present value of the deceleration parameter [q(1)≈−0.5]. This emerging picture of the history of the universe represents an important challenge, an opportunity for the immediate research on the Universe. These conclusions have been elaborated without the use of any particular cosmological model of the universe.     

Chromospheric Height and Density Measurements in a Solar Flare Observed with RHESSI – II. Data Analysis

We present an analysis of hard X-ray imaging observations from one of the first solar flares observed with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) spacecraft, launched on 5 February 2002. The data were obtained from the 22 February 2002, 11:06 UT flare, which occurred close to the northwest limb. Thanks to the high energy resolution of the germanium-cooled hard X-ray detectors on RHESSI we can measure the flare source positions with a high accuracy as a function of energy. Using a forward-fitting algorithm for image reconstruction, we find a systematic decrease in the altitudes of the source centroids z(ε) as a function of increasing hard X-ray energy ε, as expected in the thick-target bremsstrahlung model of Brown. The altitude of hard X-ray emission as a function of photon energy ε can be characterized by a power-law function in the ε=15–50 keV energy range, viz., z(ε)≈2.3(ε/20 keV)^−1.3 Mm. Based on a purely collisional 1-D thick-target model, this height dependence can be inverted into a chromospheric density model n(z), as derived in Paper I, which follows the power-law function n _e(z)=1.25×10¹³(z/1 Mm)^−2.5 cm⁻³. This density is comparable with models based on optical/UV spectrometry in the chromospheric height range of h≲1000 km, suggesting that the collisional thick-target model is a reasonable first approximation to hard X-ray footpoint sources. At h≈1000–2500 km, the hard X-ray based density model, however, is more consistent with the `spicular extended-chromosphere model' inferred from radio sub-mm observations, than with standard models based on hydrostatic equilibrium. At coronal heights, h≈2.5–12.4 Mm, the average flare loop density inferred from RHESSI is comparable with values from hydrodynamic simulations of flare chromospheric evaporation, soft X-ray, and radio-based measurements, but below the upper limits set by filling-factor insensitive iron line pairs.     

Equivalence principle (EP) and solar system constraints on $R(1\pm\epsilon\ln({R \over R_{c}}))$ model of gravity

Experiments on the violation of equivalence principle (EP) and solar system give a number of constraints in which any modified gravity model must satisfy them. We study these constraints on a kind of f(R) gravity as f(R) = R(1±eln([(R)/(R_c)]))f(R) = R(1\pm\epsilon\ln({R \over R_{c}})). For this investigation we use of chameleon mechanism and show that a spherically body has thin-shell in this model. So that we obtain an effective coupling of the fifth force which is suppressed through a chameleon mechanism. Also, we obtain γ _PPN =1±1.13×10⁻⁵ which is agreement with experiment results. At last, we show that for R _c ≈ρ _c this model is consistent with EP, thin shell condition and fifth force of chameleon mechanism for ε⋍10⁻¹⁴.     

New class of Well behaved exact solutions of relativistic charged <Emphasis Type="Italic">white-dwarf</Emphasis> star with perfect fluid

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 (0.3277≤K≤0.49), 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=0.3277 with X=−0.15, the maximum mass of the star comes out to be M=0.92M _Θ with radius r _b ≈17.15 km and the surface red shift Z _b ≈0.087187. It has been observed that under well behaved conditions this class of solutions gives us the mass of super dense object within the range of white-dwarf.