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1.
The outer convection zone of the low-temperature white dwarf Van Maanen 2 has been studied for two different atmospheric models given byWeidemann (1960). A slight modification of the standard mixing length theory and the abundances derived by Weidemann have been used.The thickness of the convection zone is about 8 km for the atmospheric model withT eff=5780 K,g=108 cm sec–2 and about 23 km forT eff=5040,g=3.16×107K. In both cases the temperature at the lower boundary of the convection zone is about 9.8×105K. It is shown that this temperature corresponds approximately to the transition temperatureT tr to the (almost) isothermal core of the white dwarf. This value is considerably lower than the values ofT tr discussed in the literature until now.The outer convection zone consists of an upper completely non-degenerate part and a lower part with moderate degeneracy. In this lower part the degree of degeneracy is practically independent of depth.  相似文献   

2.
It is shown that the equation of motion Du j/Ds = (e/mc 2)F ji u i , a natural generalization to the curved spacetime of the Heaviside-Lorentz law of ponderomotive force, is equivalent to the metric independent and covariant Van Dantzig's equations of motion dx j [jpi] = 0 or L v p i = 0, where p i is the conjugate momentum 4-vector and v a vector determined by the condition p i v i, only with respect to holonomic coordinates. With respect to an anholonomic system, the Heaviside-Lorentz equation is a particular case of the VD equations valid for a privileged class of anholonomic frames, those consisting of orthogonal unit vectors.  相似文献   

3.
In Sections 1–6, we determine an approximate analytical model for the density and temperature distribution in the protoplanetary could. The rotation of the planets is discussed in Section 7 and we conclude that it cannot be determined from simple energy conservation laws.The velocity of the gas of the protoplanetary cloud is found to be smaller by about 5×103 cm s–1 in comparison to the Keplerian circular velocity. If the radius of the planetesimals is smaller than a certain limitr 1, they move together with the gas. Their vertical and horizontal motion for this case is studied in Sections 8 and 9.As the planetesimals grow by accretion their radius becomes larger thanr 1 and they move in Keplerian orbits. As long as their radius is betweenr 1 and a certain limitr 2 their gravitational interaction is negligible. In Section 10, we study the accretion for this case.In Section 11, we determine the change of the relative velocities due to close gravitational encounters. The principal equations governing the late stages of accretion are deduced in Section 12, In Section 13 there are obtained approximate analytical solutions.The effect of gas drag and of collisions is studied in Sections 14 and 15, respectively. Numerical results and conclusions concerning the last and principal stage of accretion are drawn in Section 16.  相似文献   

4.
In the present article models of well behaved charged superdense stars with surface density 2×1014 gm/cm3 are constructed by considering a static spherically symmetric metric with t = const hypersurfaces as spheroids and hyperboloids. Maximum mass of the star is found to be 7.66300M Θ with radius 19.35409 km for spheroids case while 1.51360M Θ with radius 13.72109 km for hyperboloid case satisfying ultra-relativistic conditions. The solutions thus found satisfy all the reality and causality conditions. For brevity we don’t present a detailed analysis of the derived solutions in this paper.  相似文献   

5.
In the present article, a family of static spherical symmetric well behaved interior solutions is derived by considering the metric potential g 44=B(1−Cr 2)−n for the various values of n, such that (1+n)/(1−n) is positive integer. The solutions so obtained are utilised to construct the heavenly bodies’ like quasi-black holes such as white dwarfs, neutron stars, quarks etc., by taking the surface density 2×1014 gm/cm3. The red shifts at the centre and on the surface are also computed for the different star models. Moreover the adiabatic index is calculated in each case. In this process the authors come across the quarks star only. Least and maximum mass are fond to be 3.4348M Θ and 4.410454M Θ along with the radii 21.0932 km and 23.7245 km respectively.  相似文献   

6.
For single-lined spectroscopic binary stars (SBI), the mass ratioq=M sec/M prim is calculated from the mass functionf(m), which is determined from observations. For statistical investigations of the mass-ratio distribution, the term sin3 i, that remains in the cubic equation from whichq is solved, has to be dealt with.This paper compares the common practise of taking an average value for sin3 i to a deconvolution scheme that takes into account the precise (expected) behaviour ofP (sin3 i) d sin3 i. The behaviour ofP(sin3 i) d sin3 i depends on how orbital planes of binary stars are oriented in space. For a random orientation of orbital planes,P i(i) di=sini di. For the average value method, it is generally assumed thatP i(i) di=(4/) sin2 i di.For verification purposes, the deconvolution scheme is applied to an observed sample of double-lined spectroscopic binary stars (SBII), and to a synthetic sample of SBI systems, produced by a numerical model. In both cases, the scheme produces better results with the assumption thatP i(i) di=(4/gp) sin2 i di, rather than a purely random orientation of orbital planes. In the case of the synthetic sample of SBI systems, the deconvolution scheme does not produce better results than the method that assumes an average value for sin3 i.Application of the deconvolution method to the double-lined spectroscopic binary systems in theEighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars, provides results which are compatible with the assumption that the orbital planes of these systems are oriented randomly in space.  相似文献   

7.
The stability of the origin of an autonomous Hamiltonian system is investigated when the system possesses a third or fourth-order resonance.H 2, the quadratic part ofH isH 2=n i=1 i J i and the resonance condition is n i=1 k i i where thek 0,i = 1, 2, ...,n are the natural or fundamental frequencies. It is shown that the only case in which the origin can be unstable is ifk i0,i=1,2,...,n. The condition for instability is then given in terms of the coefficients of the higher order terms in the Hamiltonian. The transfer of energy between modes is also investigated when a near-resonant condition exists.  相似文献   

8.
As part of our study of the larger-scale remanent magnetic field of the Moon, we have examined the effects of cratering in an otherwise spherically symmetrical shell magnetized by a concentric dipolar magnetic fieldH o to an intensity of magnetizationc H o, wherec is a constant. In our initial model, we assume that the material excavated from the craters is distributed with random orientation and thus does not contribute to the remanent dipole momentM g . We further assume that the mare fill does not contribute significantly toM g . We choose the magnetizing dipole momentM o and the constantc such that the magnitude of the productcH o ≃ 3 × 10−4Г at the outer surface of the shell in the equatorial plane of the dipole. This value of the intensity of remanent magnetization was chosen to be within the range 10−7−10−3Г’; the intensities of thermo-remanent magnetization exhibited by Apollo samples. Finally, we use the locations and diameters of the 10 largest craters on the Moon and the depth-to-diameter ratios of Pike’s formulation to model approximately the excavation of the magnetized shell. The remanent dipole momentM g was calculated for each of three orthogonal orientations of the magnetizing dipoleM o. The three magnitudes ofM g fall in the range 4 × 1018−1 × 1019Г cm3 which is close to the upper limit of 1019Г cm3 estimated forM g from the field measurements obtained with the Apollo subsatellites. Further, the distribution of the craters is such as to produce a significant transverse component ofM g with acute angles between the spin axis andM g in the range 51°–77°.  相似文献   

9.
We present the condition of vanishing shear in a spatially homogeneous spacetime in terms of the Ricci rotation co-efficients corresponding to an orthonormal tetrad (ν α. A η α) (whereν α is the unit vector along the time axis and A η α are the three independent reciprocal group vectors). Assuming that the velocity vector can be expanded in the direction ofν α and any one of the A η α’s it is shown that shear-free motion is possible only in case of some special Bianchi types, and these cases are studied assuming the velocity vector to be geodetic and that there may be a nonvanishing heat flux term.  相似文献   

10.
An analysis of a spherically symmetric braneworld configuration is performed when the intrinsic curvature scalar is included in the bulk action. In the case when the electric part of the Weyl tensor is zero, all the exterior solutions are found; one of them is of the Schwarzschild-(A)dS 4 form, which is matched to a modified Oppenheimer-Volkoff interior solution. In the case when the electric part of the Weyl tensor is non zero, the exterior Schwarzschild-(A)dS 4 black hole solution is modified receiving corrections from the non-local bulk effects. A non-universal gravitational constant arises, depending on the density of the considered object and the Newton's law is modified for small and large distances; however, the conventional limits are easily obtained. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

11.
A closed form solution to the minimum DVtot2{\Delta V_{\rm tot}^2} Lambert problem between two assigned positions in two distinct orbits is presented. Motivation comes from the need of computing optimal orbit transfer matrices to solve re-configuration problems of satellite constellations and the complexity associated in facing these problems with the minimization of DVtot{\Delta V_{\rm tot}}. Extensive numerical tests show that the difference in fuel consumption between the solutions obtained by minimizing DVtot2{\Delta V_{\rm tot}^2} and DVtot{\Delta V_{\rm tot}} does not exceed 17%. The DVtot2{\Delta V_{\rm tot}^2} solution can be adopted as starting point to find the minimum DVtot{\Delta V_{\rm tot}}. The solving equation for minimum DVtot2{\Delta V_{\rm tot}^2} Lambert problem is a quartic polynomial in term of the angular momentum modulus of the optimal transfer orbit. The root selection is discussed and the singular case, occurring when the initial and final radii are parallel, is analytically solved. A numerical example for the general case (orbit transfer “pork-chop” between two non-coplanar elliptical orbits) and two examples for the singular case (Hohmann and GTO transfers) are provided.  相似文献   

12.
In the bounds of a theoretical scheme treating consistently gravitational interaction as dynamical (gauge) field in flat space-time, an expression was obtained for the density of energy-momentum-tension of gravitational field in vacuum around a collapsed object. A case was studied of an interacting static spherically-symmetric field of a collapsar in vacuum with taking into account of input of all the possible components (spin states of virtual gravitons) into the energy for the symmetric tensor of second rank ik . The radius of the sphere filled by matter for the collapsar of massM may achieve values up toGM/c 2.  相似文献   

13.
A two-dimensional potential energy surface of an H 2 + molecular ion is calculated for the case of the strong magnetic field of the neutron starB=1011–1013 G. It is shown that the dependence of the potential energy from the angle between the magnetic field direction and the internuclear axis becomes very sharp as the magnetic field increases. The obtained potential energy surfaces can be used for studying the vibrational-rotational structure of the H 2 + spectrum in a strong magnetic field and the development of the observational methods for the determination of the magnetic field of a neutron star.  相似文献   

14.
We have theoretically studied the influence of a far-infrared radiation (FIR) field from Hπ region on the cooling by C and O atoms, C+ ion and CO molecule in a photodissociation region, and a molecular cloud associated with Hπ region (hereinafter referred as HI region) at low temperatures (T k≤200 K). Comparisons have been made for cooling with and without FIR for two extreme abundances (10−4 and 10−7) of the mentioned species for temperatures ranging between 10 and 200K and an hydrogen particle density range 10 cm−3≤n o≤ 107 cm3. The cooling by the species with low line-splitting (CI, Cπ and CO) is significantly influenced by the radiation field for temperaturesT k < 100 K while the effect of radiation field on cooling by OI is significant even at higher temperatures (T k > 100 K). The effect of FIR field on the cooling of CO from low rotational transitions is negligibly small, whereas it is considerable for higher transitions. In general, the cooling terms related to the short-wavelength transitions are more affected by FIR than those related to longer wavelengths. It is also demonstrated here that in the determination of thermal structure of an HI region the dust grains play an important role in the heating of gas only through photoelectron emission following irradiation by far-ultraviolet (FUV) radiation, as the infrared radiation from the dust is too small to have substantial effect on the cooling. It is found that in the Hπ /HI interface the FIR field from grains in the Hπ region is not capable of modifying the temperature of the warmest regions but does so in the inner part where the temperature is low enough.  相似文献   

15.
We have detected new HD absorption systems at high redshifts, z abs = 2.626 and z abs = 1.777, identified in the spectra of the quasars J0812+3208 and Q1331+170, respectively. Each of these systems consists of two subsystems. The HD column densities have been determined: log N HDA = 15.70 ± 0.07 for z A = 2.626443(2) and log N HDB = 12.98 ± 0.22 for z B = 2.626276(2) in the spectrum of J0812+3208 and log N HDC = 14.83 ± 0.15 for z C = 1.77637(2) and log N HDD = 14.61 ± 0.20 for z D = 1.77670(3) in the spectrum of Q1331+170. The measured HD/H2 ratio for three of these subsystems has been found to be considerably higher than its values typical of clouds in our Galaxy.We discuss the problem of determining the primordial deuterium abundance, which is most sensitive to the baryon density of the Universe Ωb. Using a well-known model for the chemistry of a molecular cloud, we have estimated the isotopic ratio D/H=HD/2H2 = (2.97 ± 0.55) × 10−5 and the corresponding baryon density Ωb h 2 = 0.0205−0.0020+0.0025. This value is in good agreement with Ωb h 2 = 0.0226−0.00060.0006 obtained by analyzing the cosmic microwave background radiation anisotropy. However, in high-redshift clouds, under conditions of low metallicity and low dust content, hydrogen may be incompletely molecularized even in the case of self-shielding. In this situation, the HD/2H2 ratio may not correspond to the actual D/H isotopic ratio. We have estimated the cloud molecularization dynamics and the influence of cosmological evolutionary effects on it.  相似文献   

16.
T. Takakura 《Solar physics》1984,91(2):311-324
In some gradual hard X-ray bursts with high intensity, hard X-ray source (15–40 keV) is steadily located in the corona along with softer X-ray source (5–10 keV).Two stationary models, high density and high temperature models, are proposed to solve the difficult problem of confinement of hot (or nonthermal) plasma in the direction of the magnetic field along the loops in the corona. In both models, an essential point is that the effective X-ray source is composed of fine dense filamentary loops imbeded in a larger rarefied coronal loop, and the electron number density in the filaments is so high as 1011–1012 cm-3. If the density is so high heat conduction can be as reasonably small as of the order of 1027 erg s -1 for the given emission measures of observed X-rays, since the required cross-sectional area is small and also classical conduction is valid. Collisional confinement of thermal tail, and nonthermal electrons if any, up to 50–60 keV in the filaments is also possible, so that the hard X-ray images can be loop like structure instead of double source (foot points).High density model is applicable to the coronal filamentary loops with temperature T m < 5 × 107 K at the loop summit. The heat flow from the summit downwards is lost almost completely by the radiation from the loop during the conduction to the foot points. A continuous energy release is assumed near the summit to maintain the stationary temperature T m, and pressure balance is maintained along the loop. In this model, the number density at the summit is given by n m - 106 T m 2 /sm, where s m is the length of the loop from the summit to the foot point, and the distribution of temperature and density along the loop are given by T = T m(s/sm)1/3 and n = n m(s/sm)-1/3, respectively.High temperature model is applicable to the filamentary loops with higher temperature up to about 108.5 K and comparatively lower number density as 1011 cm-3 for the requirement of magnetic confinement of the hot plasma in radial direction. The radiation from the loop is negligibly small in this model so that the heat flux is nearly conserved down to the foot points. In this case, temperature gradient is smaller than that of the high density model, depending on the tapering of the magnetic bottle.In both models, the differential emission measure is maximum at the highest temperature T m and the brightness distribution along the loop shows a maximum around the summit of the loop if some magnetic tapering is taken into account.  相似文献   

17.
A new analytic approach to the solution of the Sitnikov Problem is introduced. It is valid for bounded small amplitude solutions (z max = 0.20) (in dimensionless variables) and eccentricities of the primary bodies in the interval (–0.4 < e < 0.4). First solutions are searched for the limiting case of very small amplitudes for which it is possible to linearize the problem. The solution for this linear equation with a time dependent periodic coefficient is written up to the third order in the primaries eccentricity. After that the lowest order nonlinear amplitude contribution (being of order z 3) is dealt with as perturbation to the linear solution. We first introduce a transformation which reduces the linear part to a harmonic oscillator type equation. Then two near integrals for the nonlinear problem are derived in action angle notation and an analytic expression for the solution z(t) is derived from them. The so found analytic solution is compared to results obtained from numeric integration of the exact equation of motion and is found to be in very good agreement. CERN SL/AP  相似文献   

18.
We study the anomalous flux ratio which is observed in some four-image lens systems, where the source lies close to a fold caustic. In this case two of the images are close to the critical curve and their flux ratio should be equal to unity, instead in several cases the observed value differs significantly. The most plausible solution is to invoke the presence of substructures, as for instance predicted by the Cold Dark Matter scenario, located near the two images. In particular, we analyze the two fold lens systems PG1115+080 and B1555+375, for which there are not yet satisfactory models which explain the observed anomalous flux ratios. We add to a smooth lens model, which reproduces well the positions of the images but not the anomalous fluxes, one or two substructures described as singular isothermal spheres. For PG1115+080 we consider a smooth model with the influence of the group of galaxies described by a SIS and a substructure with mass ∼105 M ⊙ as well as a smooth model with an external shear and one substructure with mass ∼108 M ⊙. For B1555+375 either a strong external shear or two substructures with mass ∼107 M ⊙ reproduce the data quite well.  相似文献   

19.
General forms of theB-p relation are investigated in both the isothermal and the non-isothermal regions. The magnetic flux dissipation either by ambipolar diffusion or by Ohmic dissipation has been studied. The rates of heating due to the magnetic dissipation processes have been calculated in comparison with the rate of compressional heating.The magnetic field strength is derived as a function of flux/mass ratio, mass, density, and geometry of the isothermal cloud. In the non-isothermal region, the temperature is added to the above-mentioned variables.It has been found that the magnetic flux starts to dissipate via ambipolar diffusion at neutral density ofn>3×109 cm–3. Ambipolar diffusion continues effective until reaching densities ofn>1011 cm–3, where Ohmic dissipation dominates. Under some conditions, the electrons evaporate from the grain surface atn>1013 cm–3, while the ions are still adsorbed on the grain surfce. In this case, the magnetic flux loss returns to be influenced by ambipolar diffusion.The rates of heating by both Ohmic dissipation OD and ambipolar diffusion AD are found to be smaller than the rate of compressional heating C in case of magnetic dissipation. Assuming that the magnetic field is frozen in the medium, then C is smaller than both OD and AD . The above results of heating were found in the non-isothermal region.  相似文献   

20.
This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH a (p, q)=1/2(p 1 2 +p 2 2 +a 1 q 1 2 +a 2 q 2 2 )+1/4q 1 4 +1/4a 3 q 2 4 + 1/2a 4 q 1 2 q 2 2 . We prove that the system is integrable for the cases: (A)a 1=a 2,a 3=a 4=1; (b)a 1=a 2,a 3=1,a 4=3; (C)a 1=a 2/4,a 3=16,a 4=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C.  相似文献   

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