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1.
We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively. These solutions describe perfect 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 for these solutions. Keeping in view of well behaved nature of these solutions, one of the solution (I1) is studied extensively. The solution (I1) gives us wide range of Schwarzschild parameter u (0.138≤u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of Neutron star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming the surface density; ρ b =2×1014 g/cm3, the maximum mass of Neutron star comes out to be 1.34 M Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively.  相似文献   

2.
Based on the data on a spectral dependence of the geometric albedo of giant planet discs, we obtained depth variations in the optical thickness τ a of the aerosol component and relative concentration γ of methane (Uranium, Neptune) lnτ a = −0.720 + 1.507Δlnp (for −2.2085 ≤ lnp ≤ −1.0018), lnτ a = +1.224 + 1.160Δlnp (for −1.0018 ≤ lnp ≤ −0.0595), lnτ a = +2.318 + 0.192Δlnp (for −0.0595 ≤ lnp), γ = 0.0027 for Jupiter; lnτ a = −0.846 + 1.598Δlnp (for −3.3619 ≤ lnp ≤ −2.0575), lnτ a = +1.238 + 1.342Δlnp (for −2.0575 ≤ lnp ≤ −1.2074), lnτ a = +2.379 + 0.722 (for −1.2074 ≤ lnp ≤ −0.6501), lnτ a = +2.781 + 0.326Δlnp (for 0.6501 ≤ lnp), γ = 0.0027 for Saturn; lnτ a = −2.694 + 0.087Δlnp (for +0.3685 ≤ lnp ≤ +1.2314), lnτ a = −2.619 + 7.341Δlnp (for +1.2314 ≤ lnp ≤ +1.7556), lnτ a = +1.229 + 0.956Δlnp (for +1.7556 ≤ lnp) for Uranium; lnτ a = −1.861 + 1.248Δlnp (for +0.3204 ≤ lnp ≤ +0.9051), lnτ a = −1.131 + 0.347Δlnp (for +0.9051 ≤ lnp) for Neptune; depth-averaged relative methane concentration lnγ = −9.982 + 2.676Δlnp(0.3584 ≤ lnp ≤ 1.5445); ln γ = −9.738 + 2.561Δlnp(0.3237 ≤ lnp ≤ 1.6156) and γ = 0.00382(lnp ≥ 1.6156); 0.00554(lnp ≥ 1.6156) for Uranium and Neptune, respectively (p is in bar).  相似文献   

3.
The bifurcation of central configuration in the Newtonian N-body problem for any odd number N ≥ 7 is shown. We study a special case where 2n particles of mass m on the vertices of two different coplanar and concentric regular n-gons (rosette configuration) and an additional particle of mass m0 at the center are governed by the gravitational law he 2n+1 body problem. This system is of two degrees of freedom and permits only one mass parameter μ =m 0/m. This parameter μ controls the bifurcation. If n≥ 3, namely any odd N ≥ 7, then the number of central configurations is three when μ ≥ μ c , and one when μ ≥ μ c . By combining the results of the preceding studies and our main theorem, explicit examples of bifurcating central configuration are obtained for N ≤ 13, for any odd N ∈ [15,943], and for any N ≥ 945.  相似文献   

4.
The energy density of Vaidya-Tikekar isentropic superdense star is found to be decreasing away from the center, only if the parameter K is negative. The most general exact solution for the star is derived for all negative values of K in terms of circular and inverse circular functions. Which can further be expressed in terms of algebraic functions for K = 2-(n/δ)2 < 0 (n being integer andδ = 1,2,3 4). The energy conditions 0 ≤ p ≤ αρc 2, (α = 1 or 1/3) and adiabatic sound speed conditiondp dρ ≤ c 2, when applied at the center and at the boundary, restricted the parameters K and α such that .18 < −K −2287 and.004 ≤ α ≤ .86. The maximum mass of the star satisfying the strong energy condition (SEC), (α = 1/3) is found to be3.82 Mq· at K=−2/3, while the same for the weak energy condition (WEC), (α =1) is 4.57 M_ ⊙ atK=−>5/2. In each case the surface density is assumed to be 2 × 1014 gm cm-3. The solutions corresponding to K>0 (in fact K>1) are also made meaningful by considering the hypersurfaces t= constant as 3-hyperboloid by replacing the parameter R 2 by −R2 in Vaidya-Tikekar formalism. The solutions for the later case are also expressible in terms of algebraic functions for K=2-(n/δ2 > 1 (n being integer or zero and δ =1,2,3 4). The cases for which 0 < K < 1 do not possess negative energy density gradient and therefore are incapable of representing any physically plausible star model. In totality the article provides all the physically plausible exact solutions for the Buchdahl static perfect fluid spheres. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

5.
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.  相似文献   

6.
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) +fa\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).  相似文献   

7.
I. Sabbah 《Solar physics》2007,245(1):207-217
Neutron monitor data observed at Climax (CL) and Huancayo/Haleakala (HU/HAL) have been used to calculate the amplitude A of the 27-day variation of galactic cosmic rays (CRs). The median primary rigidity of response, R m, for these detectors encompasses the range 18 ≤R m≤46 GV and the threshold rigidity R 0 covers the range 2.97≤R 0≤12.9 GV. The daily average values of CR counts have been harmonically analyzed for each Bartels solar rotation (SR) during the period 1953 – 2001. The amplitude of the 27-day CR variation is cross-correlated to solar activity as measured by the sunspot number R, the interplanetary magnetic field (IMF) strength B, the z-component B z of the IMF vector, and the tilt angle ψ of the heliospheric current sheet (HCS). It is anticorrelated to the solar coronal hole area (CHA) index as well as to the solar wind speed V. The wind speed V leads the amplitude by 24 SRs. The amplitude of the 27-day CR variation is better correlated to each of the these parameters during positive solar polarity (A>0) than during negative solar polarity (A<0) periods. The CR modulation differs during A>0 from that during A<0 owing to the contribution of the z-component of the IMF. It differs during A 1>0 (1971 – 1980) from that during A 2>0 (1992 – 2001) owing to solar wind speed.  相似文献   

8.
We study the planar central configurations of the 1 +n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2≤n≤4. Numerically, first we provide evidence that when n9 the only central configuration is the regular n-gon with the large mass in its barycenter, and second we provide also evidence of the existence of an axis of symmetry for every central configuration. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

9.
In this paper, the problem of spatially homogeneous and an isotropic Bianchi type-1 space time with perfect fluid distribution is considered in Barber's second theory of gravitation. To obtain determinate solutions, we have assumed the equation of statep= γρ, 0 ≤ γ ≤ 1. It is observed that the general fluid distribution degenerates isotropic vacuum model whenγ = 1 and Λ < 0. Further it is observed that the vacuum model obtained in case of γ = 0, ρ = 0 andΛ = 0, reduces to well known Kasner model in Einstein's theory. Some physical and geometrical aspects of the models together with singularities in the models are also discussed This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

10.
For the case of Tycho’s supernova remnant (SNR) we present the relation between the blast wave and contact discontinuity radii calculated within the nonlinear kinetic theory of cosmic ray (CR) acceleration in SNRs. It is demonstrated that these radii are confirmed by recently published Chandra measurements which show that the observed contact discontinuity radius is so close to the shock radius that it can only be explained by efficient CR acceleration which in turn makes the medium more compressible. Together with the recently determined new value E sn=1.2×1051 erg of the SN explosion energy this also confirms our previous conclusion that a TeV γ-ray flux of (2–5)×10−13 erg/(cm2 s) is to be expected from Tycho’s SNR. Chandra measurements and the HEGRA upper limit of the TeV γ-ray flux together limit the source distance d to 3.3≤d≤4 kpc.  相似文献   

11.
The algorithm for determining effective optical thickness of absorption line formation in a plane-parallel homogeneous planetary atmosphere is presented. The case of anisotropic scattering is considered. The results of numerical calculations of τ e (μ0) at the scattering angle γ = π for some values of the single scattering albedo λ and the parameter of the Heyney-Greenstein scattering indicatrix g are given. The refined equation for the function T m (−μ, μ0) is presented.  相似文献   

12.
The variation of the fine-structure constant α = e 2 / ħc can be probed by comparing the wavelength of atomic transitions from the redshift of quasars in the Universe and laboratory over cosmological time scales t ~ 1010 yr. After a careful selection of pairs of lines, the Thong method with a derived analytical expression for the error analysis was applied to compute the α variation. We report a new constraint on the variation of the fine-structure constant based on the analysis of the CIV, NV, MgII, AlIII, and SiIV doublet absorption lines. The weighted mean value of the variation in α derived from our analysis over the redshift range 0.4939 ≤ z ≤ 3.7 is = ( 0.09 ± 0.07)×10−5. This result is three orders of magnitude better than the results obtained by earlier analysis of the same data on the constraint on Δα/α .  相似文献   

13.
The perihelion advance of the orbit of Mercury has long been one of the observational cornerstones for testing General Relativity (G.R.).The main goal of this paper is to discuss how, presently, observational and theoretical constraints may challenge Einstein's theory of gravitation characterized by β=γ=1. To achieve this purpose, we will first recall the experimental constraints upon the Eddington-Robertson parameters γ,β and the observational bounds for the perihelion advance of Mercury, Δωobs. A second point will address the values given, up to now, to the solar quadrupole moment by several authors. Then, we will briefly comment why we use a recent theoretical determination of the solar quadrupole moment, J 2=(2.0 ± 0.4) 10-7, which takes into account both surfacic and internal differential rotation, in order to compute the solar contribution to Mercury's perihelion advance. Further on, combining bounds on γ and J 2 contributions, and taking into account the observational data range for Δωobs,we will be able to give a range of values for β. Alternatively, taking into account the observed value of Δωobs, one can deduce a dynamical estimation of J 2 in the setting of G.R. This point is important as it provides a solar model independent estimation that can be confronted with other determinations of J 2 based upon solar theory and solar observations (oscillation data, oblateness...). Finally, a glimpse at future satellite experiments will help us to understand how stronger constraints upon the parameter space (γω J 2) as well as a separation of the two contributions (from the quadrupole moment, J 2, or purely relativistic, 2α2+2αγ–β) might be expected in the future. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

14.
Supernova Remnants (SNRs) are the most likely sources of the galactic cosmic rays up to energies of about 1015 eV/nuc. The large scale shock waves of SNRs are almost ideal sites to accelerate particles up to these highly non-thermal energies by a first order Fermi mechanism which operates through scattering of the particles at magnetic irregularities. In order to get an estimate on the total amount of the explosion energy E SNconverted into high energy particles the evolution of a SNR has to be followed up to the final merging with the interstellar medium. This can only be done by numerical simulations since the non-linear modifications of the shock wave due to particle acceleration as well as radiative cooling processes at later SNR stages have to be considered in such investigations. Based on a large sample of numerical evolution calculations performed for different ambient densities n ext, SN explosion energies, magnetic fields etc. we discuss the final ‘yields’ of cosmic rays at the final SNR stage where the Mach number of the shock waves drops below 2. At these times the cosmic rays start to diffuse out of the remnant. In the range of external densities of10-2 ≤ n ext/[cm-3] ≤ 30 we find a the total acceleration efficiency of about 0.15 E SN with an increase up to 0.24 E SN at maximum for an external density of n ext = 10 cm-3. Since for the larger ambient densities radiative cooling can reduce significantly the total thermal energy content of the remnant dissipation of Alfvén waves can provide an important heating mechanism for the gas at these later stages. From the collisions of the cosmic rays with the thermal plasma neutral pions are generated which decay subsequently into observable γ-rays above 100 MeV. Hence, we calculate these γ-ray luminosities of SNRs and compare them with current upper limits of ground based γ-raytelescopes. The development of dense shells due to cooling of the thermal plasma increases the γ-ray luminosities and e.g. an external density of n ext = 10 cm-3 with E SN = 1051 erg can lead to a γ-ray flux above 10-6 ph cm-2 s-1 for a remnant located at a distance of 1 kpc. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

15.
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.  相似文献   

16.
In this paper, we have investigated that tilted Bianchi Type I cosmological models for stiff perfect fluid under a supplementary condition A = B n between metric potentials, is not possible. The tilted solution is also not possible when we assume A = t ℓ, B = t m , C = t n ; ℓ, m and n are constants for ε = p. Thus to preserve tilted nature of model, we assume p = γε, 0 ≤ γ ≤ 1 (barotropic equation of state) for the case A = t ℓ B = t m and C = t n . The physical and geometrical aspects of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

17.
In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian n-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where n particles of mass m1 lie at the vertices of a regular n-gon, n particles of mass m2 lie at the vertices of another n-gon concentric with the first, but rotated of an angle π /n, and an additional particle of mass m0 lies at the center of mass of the system. This system admits two mass parameters μ = m0/m1 and ε = m2/m1. We show that, as μ varies, if n > 3, there is a degenerate central configuration and a bifurcation for every ε > 0, while if n = 3 there is a bifurcation only for some values of ε.  相似文献   

18.
The status of the Galactic thick disk is reviewed. Consideration of the recent literature suggests that its vertical scale height and normalisation with respect to the thin disk remain uncertain to within a factor two, with values reported in the ranges 750–1500 pc, and 0.02–0.13, respectively. The bulk of the thick disk has kinematics (σU, σV, σW) = (65, 54, 38 km s-1), and lags the thin disk by some 40 km s-1; differences of opinion exists as to whether kinematics change with distance from the Galactic plane. The bulk of the thick disk has [Fe/H] ∼ −0.6, with little or no evidence for a vertical gradient. The question of gradients is critical for an understanding of thick disk cosmogony and needs closer attention. The reality of the so-called metal-weak thick disk (material having disklike kinematics and [Fe/H] ≤ −1.0) is also considered. The case for such material seems to be steadily growing: in the range −1.6 ≤ [Fe/H] ≤ −1.0, recent estimates suggest ρMWTD/ρHalo ∼ 0.1-0.3. While many workers regard the thick disk as a discrete entity, the caveat is made that this is a sufficient condition, but not one necessarily required by the observations. Best practice requires that both the discrete model and the alternative extended configuration be compared with observational data to examine the relative likelihood of their relevance. Recent theoretical advances are also discussed, together with the need for in situ measurements of the thick disk away from the Galactic plane. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

19.
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.  相似文献   

20.
Cargill  Peter J. 《Solar physics》2004,221(1):135-149
It is well known that the interaction of an interplanetary coronal mass ejection (ICME) with the solar wind leads to an equalisation of the ICME and solar wind velocities at 1 AU. This can be understood in terms of an aerodynamic drag force per unit mass of the form F D/M=−(ρe AC D/M)(V i−V e)∣V i−V e∣, where A and M are the ICME cross-section and sum of the mass and virtual mass, V i and V e the speed of the ICME and solar wind, ρe the solar wind density, C D a dimensionless drag coefficient, and the inverse deceleration length γ=ρe A/M. The optimal radial parameterisation of γ and C D beyond approximately 15 solar radii is calculated. Magnetohydrodynamic simulations show that for dense ICMEs, C D varies slowly between the Sun and 1 AU, and is of order unity. When the ICME and solar wind densities are similar, C D is larger (between 3 and 10), but remains approximately constant with radial distance. For tenuous ICMEs, the ICME and solar wind velocities equalise rapidly due to the very effective drag force. For ICMEs denser that the ambient solar wind, both approaches show that γ is approximately independent of radius, while for tenuous ICMEs, γ falls off linearly with distance. When the ICME density is similar to or less than that in the solar wind, inclusion of virtual mass effects is essential.  相似文献   

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