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1.
From new observational material we made a curve of growth analysis of the penumbra of a large, stable sunspot. The analysis was done relative to the undisturbed photosphere and gave the following results (⊙ denotes photosphere, * denotes penumbra): $$\begin{gathered} (\theta ^ * - \theta ^ \odot )_{exe} = 0.051 \pm 0.007 \hfill \\ {{\xi _t ^ * } \mathord{\left/ {\vphantom {{\xi _t ^ * } {\xi _t }}} \right. \kern-\nulldelimiterspace} {\xi _t }}^ \odot = 1.3 \pm 0.1 \hfill \\ {{P_e ^ * } \mathord{\left/ {\vphantom {{P_e ^ * } {P_e ^ \odot = 0.6 \pm 0.1}}} \right. \kern-\nulldelimiterspace} {P_e ^ \odot = 0.6 \pm 0.1}} \hfill \\ {{P_g ^ * } \mathord{\left/ {\vphantom {{P_g ^ * } {P_g }}} \right. \kern-\nulldelimiterspace} {P_g }}^ \odot = 1.0 \pm 0.2 \hfill \\ \end{gathered} $$ The results of the analysis are in satisfactory agreement with the penumbral model as published by Kjeldseth Moe and Maltby (1969). Additionally we tested this model by computing the equivalent widths of 28 well selected lines and comparing them with our observations.  相似文献   

2.
The development of the post-nova light curve of V1500 Cyg inUBV andHβ, for 15 nights in September and October 1975 are presented. We confirm previous reports that superimposed on the steady decline of the light curve are small amplitude cyclic variations. The times of maxima and minima are determined. These together with other published values yield the following ephemerides from JD 2 442 661 to JD 2 442 674: $$\begin{gathered} {\text{From}} 17 {\text{points:}} {\text{JD}}_{ \odot \min } = 2 442 661.4881 + 0_{^. }^{\text{d}} 140 91{\text{n}} \hfill \\ \pm 0.0027 \pm 0.000 05 \hfill \\ {\text{From}} 15 {\text{points:}} {\text{JD}}_{ \odot \max } = 2 442 661.5480 + 0_{^. }^{\text{d}} 140 89{\text{n}} \hfill \\ \pm 0.0046 \pm 0.0001 \hfill \\ \end{gathered} $$ with standard errors of the fits of ±0 . d 0052 for the minima and ±0 . d 0091 for the maxima. Assuming V1500 Cyg is similar to novae in M31, we foundr=750 pc and a pre-nova absolute photographic magnitude greater than 9.68.  相似文献   

3.
The ratio between the Earth's perihelion advance (Δθ) E and the solar gravitational red shift (GRS) (Δø s e)a 0/c 2 has been rewritten using the assumption that the Newtonian constant of gravitationG varies seasonally and is given by the relationship, first found by Gasanalizade (1992b) for an aphelion-perihelion difference of (ΔG)a?p . It is concluded that $$\begin{gathered} (\Delta \theta )_E = \frac{{3\pi }}{e}\frac{{(\Delta \phi _{sE} )_{A_0 } }}{{c^2 }}\frac{{(\Delta G)_{a - p} }}{{G_0 }} = 0.038388 \sec {\text{onds}} {\text{of}} {\text{arc}} {\text{per}} {\text{revolution,}} \hfill \\ \frac{{(\Delta G)_{a - p} }}{{G_0 }} = \frac{e}{{3\pi }}\frac{{(\Delta \theta )_E }}{{(\Delta \phi _{sE} )_{A_0 } /c^2 }} = 1.56116 \times 10^{ - 4} . \hfill \\ \end{gathered} $$ The results obtained here can be readily understood by using the Parametrized Post-Newtonian (PPN) formalism, which predicts an anisotropy in the “locally measured” value ofG, and without conflicting with the general relativity.  相似文献   

4.
The non-linear stability of L 4 in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial plane coincident with the plane of motion. It is found that L 4 is stable in the range of linear stability except for three mass ratios:
where A1, A2 depend upon the lengths of the semi axes of the triaxial rigid body. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

5.
We investigate the ‘equilibrium’ and stability of spherically-symmetric self-similar isothermal blast waves with a continuous post-shock flow velocity expanding into medium whose density varies asr ?ω ahead of the blast wave, and which are powered by a central source (a pulsar) whose power output varies with time ast ω?3. We show that:
  1. for ω<0, no physically acceptable self-similar solution exists;
  2. for ω>3, no solution exists since the mass swept up by the blast wave is infinite;
  3. ? must exceed zero in order that the blast wave expand with time, but ?<2 in order that the central source injects a finite total energy into the blast wave;
  4. for 3>ωmin(?)>ω>ωmax(?)>0, where $$\begin{gathered} \omega _{\min } (\varphi ){\text{ }} = {\text{ }}2[5{\text{ }} - {\text{ }}\varphi {\text{ }} + {\text{ }}(10{\text{ }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 )^{1/2} ]^2 [2{\text{ }} + {\text{ (10 }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 {\text{)}}^{{\text{1/2}}} ]^{ - 2} , \hfill \\ \omega _{\max } (\varphi ){\text{ }} = {\text{ }}2[5{\text{ }} - {\text{ }}\varphi {\text{ }} - {\text{ }}(10{\text{ }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 )^{1/2} ]^2 [2{\text{ }} - {\text{ (10 }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 {\text{)}}^{{\text{1/2}}} ]^{ - 2} , \hfill \\ \end{gathered} $$ two critical points exist in the flow velocity versus position plane. The physically acceptable solution must pass through the origin with zero flow speed and through the blast wave. It must also pass throughboth critical points if \(\varphi > \tfrac{5}{3}\) , while if \(\varphi< \tfrac{5}{3}\) it must by-pass both critical points. It is shown that such a solution exists but a proper connection at the lower critical point (for ?>5/3) (through whichall solutions pass with thesame slope) has not been established;
  5. for 3>ω>ωmin(?) it is shown that the two critical points of (iv) disappear. However a new pair of critical points form. The physically acceptable solution passing with zero flow velocity through the origin and also passing through the blast wave mustby-pass both of the new critical points. It is shown that the solution does indeed do so;
  6. for 3>ωmin(?)>ωmax(?)>ω it is shown that the dependence of the self-similar solution on either ω or ? is non-analytic and therefore, inferences drawn from any solutions obtained in ω>ωmax(?) (where the dependence of the solutionis analytic on ω and ?) are not valid when carried over into the domain 3>ωmin(?)>ωmax(?)>ω;
  7. all of the physically acceptable self-similar solutions obtained in 3>ω>0 are unstable to short wavelength, small amplitude but nonself-similar radial velocity perturbations near the origin, with a growth which is a power law in time;
  8. the physical self-similar solutions are globally unstable in a fully nonlinear sense to radial time-dependent flow patterns. In the limit of long times, the nonlinear growth is a power law in time for 5<ω+2?, logarithmic in time for 5>ω+2?, and the square of the logarithm in time for 5=ω+2?.
The results of (vii) and (viii) imply that the memory of the system to initial and boundary values does not decay as time progresses and so the system does not tend to a self-similar form. These results strongly suggest that the evolution of supernova remnants is not according to the self-similar form.  相似文献   

6.
A spherically-symmetric static scalar field in general relativity is considered. The field equations are defined by $$\begin{gathered} R_{ik} = - \mu \varphi _i \varphi _k ,\varphi _i = \frac{{\partial \varphi }}{{\partial x^i }}, \varphi ^i = g^{ik} \varphi _k , \hfill \\ \hfill \\ \end{gathered} $$ where ?=?(r,t) is a scalar field. In the past, the same problem was considered by Bergmann and Leipnik (1957) and Buchdahl (1959) with the assumption that ?=?(r) be independent oft and recently by Wyman (1981) with the assumption ?=?(r, t). The object of this paper is to give explicit results with a different approach and under a more general condition $$\phi _{;i}^i = ( - g)^{ - 1/2} \frac{\partial }{{\partial x^i }}\left[ {( - g)^{1/2} g^{ik} \frac{\partial }{{\partial x^k }}} \right] = - 4\pi ( -g )^{ - 1/2} \rho $$ where ?=?(r, t) is the mass or the charge density of the sources of the field.  相似文献   

7.
Dynamical systems with three degrees of freedom can be reduced to the study of a fourdimensional mapping. We consider here, as a model problem, the mapping given by the following equations: $$\left\{ \begin{gathered} x_1 = x_0 + a_1 {\text{ sin (}}x_0 {\text{ + }}y_0 {\text{)}} + b{\text{ sin (}}x_0 {\text{ + }}y_0 {\text{ + }}z_{\text{0}} {\text{ + }}t_{\text{0}} {\text{)}} \hfill \\ y_1 = x_0 {\text{ + }}y_0 \hfill \\ z_1 = z_0 + a_2 {\text{ sin (}}z_0 {\text{ + }}t_0 {\text{)}} + b{\text{ sin (}}x_0 {\text{ + }}y_0 {\text{ + }}z_{\text{0}} {\text{ + }}t_{\text{0}} {\text{) (mod 2}}\pi {\text{)}} \hfill \\ t_1 = z_0 {\text{ + }}t_0 \hfill \\ \end{gathered} \right.$$ We have found that as soon asb≠0, i.e. even for a very weak coupling, a dynamical system with three degrees of freedom has in general either two or zero isolating integrals (besides the usual energy integral).  相似文献   

8.
The Ideal Resonance Problem, defined by the Hamiltonian $$F = B(y) + 2\mu ^2 A(y)\sin ^2 x,\mu \ll 1,$$ has been solved in Garfinkelet al. (1971). As a perturbed simple pendulum, this solution furnishes a convenient and accurate reference orbit for the study of resonance. In order to preserve the penduloid character of the motion, the solution is subject to thenormality condition, which boundsAB" andB' away from zero indeep and inshallow resonance, respectively. For a first-order solution, the paper derives the normality condition in the form $$pi \leqslant max(|\alpha /\alpha _1 |,|\alpha /\alpha _1 |^{2i} ),i = 1,2.$$ Herep i are known functions of the constant ‘mean element’y', α is the resonance parameter defined by $$\alpha \equiv - {\rm B}'/|4AB\prime \prime |^{1/2} \mu ,$$ and $$\alpha _1 \equiv \mu ^{ - 1/2}$$ defines the conventionaldemarcation point separating the deep and the shallow resonance regions. The results are applied to the problem of the critical inclination of a satellite of an oblate planet. There the normality condition takes the form $$\Lambda _1 (\lambda ) \leqslant e \leqslant \Lambda _2 (\lambda )if|i - tan^{ - 1} 2| \leqslant \lambda e/2(1 + e)$$ withΛ 1, andΛ 2 known functions of λ, defined by $$\begin{gathered} \lambda \equiv |\tfrac{1}{5}(J_2 + J_4 /J_2 )|^{1/4} /q, \hfill \\ q \equiv a(1 - e). \hfill \\ \end{gathered}$$   相似文献   

9.
Available satellite, rocket and balloon observations on cosmic X- and gamma ray background are critically examined to understand the spectral characteristics of the radiation. Appropriate corrections have been applied to the balloon observations to account for the multiple Compton scattering of X-rays in the atmosphere. It is shown that within the experimental uncertainties, all the available observations of cosmic X- and gamma ray background in the energy range 1 keV-1 MeV are consistent with a single spectrum of type $${\text{d}}N/{\text{d}}E = 30 E^{ - 2.0 \pm 0.2} {\text{photons cm}}^{{\text{ - 2}}} {\text{s}}^{{\text{ - 1}}} {\text{sr}}^{{\text{ - 1}}} {\text{keV}}^{{\text{ - 1}}} $$ .  相似文献   

10.
We have studied the effect of the flow in the accretion disk. The specific angular momentum of the disk is assumed to be constant and the polytropic relation is used. We have solved the structure of the disk and the flow patterns of the irrotational perfect fluid.As far as the obtained results are concerned, the flow does not affect the shape of the configuration in the bulk of the disk, although the flow velocity reaches even a half of the sound velocity at the inner edge of the disk. Therefore, in order to study accretion disk models with the moderate mass accretion rate—i.e.,
  相似文献   

11.
An attempt has been made to obtain an expression for the rate of stellar mass loss using dimensional analysis. The best expression for O and B stars is of the form: $$\dot M = A'{\text{ }}\left( {\frac{1}{{G^{1/2} c^4 }}} \right){\text{ }}L^{\text{2}} {\text{ (}}R/M)^{{\text{3/2}}} .$$ It is also found thatA′ increases as one goes from B→O stars and from O→O(f)→O(f)), but is not sensitive to luminosity.  相似文献   

12.
The possibility of chemical ‘trapping’ of the Ar+ ion in the reaction $$v{\text{ }} + {\text{ }}^{{\text{37}}} {\text{Cl}} \to {\text{ }}^{{\text{37}}} {\text{Ar}}^{\text{ + }} + {\text{ e}}^ - ,$$ when it takes place in tetrachloroethylene (C2Cl4) liquid, is examined in detail. It is concluded that if trapping does take place, the rate is much smaller than the charge neutralization rate. Therefore, this niechanism cannot explain the observed small rate of Ar production in the Brookhaven solar neutrino experiment. A detailed examination of a number of experiments which are sensitive to possible trapping lends strong support to this conclusion.  相似文献   

13.
EinsteinA-coefficients for transitions inSii, calculated with the atomic structure package CIV3, are used to derive the electron density sensitive emission line ratio
  相似文献   

14.
The discovery of ‘twin quasistellar objects’ arose interests among astronomers and astrophysicists to study gravitational lensing problems. The deviation of light from its straight line path is caused by two sources according to the general theory of relativity: (i) the presence of massive objects, i.e. the presence of gravitational field and (ii) the presence of a ‘vacuum field’ which arises because there is a non-zero cosmological vacuum energy. Recently, the research on the relationship between cosmological constant and gravitational lensing process is rather active (see reference [1, 2, 3]. According to the Kottler space time metric, we have deduced an explicit representation of the angular deviation of light path. The deviation term is found to be simply , where M is the mass of the ‘astronomical lens’, rmin is the distance between the point of nearest approach and the centre of M, other symbols have their usual meaning. The presence of this term may be meaningful to the study of cosmological constant using the concept of gravitational lensing; however more sophisticated analysis awaits. Consider a signal radar to be sent from one planet to another. We have found that the radar echo delay contributed by the existence of the cosmological constant Λ is expressible as This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

15.
If a dynamical problem ofN degress of freedom is reduced to the Ideal Resonance Problem, the Hamiltonian takes the form 1 $$\begin{array}{*{20}c} {F = B(y) + 2\mu ^2 A(y)\sin ^2 x_1 ,} & {\mu \ll 1.} \\ \end{array} $$ Herey is the momentum-vectory k withk=1,2?N, x 1 is thecritical argument, andx k fork>1 are theignorable co-ordinates, which have been eliminated from the Hamiltonian. The purpose of this Note is to summarize the first-order solution of the problem defined by (1) as described in a sequence of five recent papers by the author. A basic is the resonance parameter α, defined by 1 $$\alpha \equiv - B'/\left| {4AB''} \right|^{1/2} \mu .$$ The solution isglobal in the sense that it is valid for all values of α2 in the range 1 $$0 \leqslant \alpha ^2 \leqslant \infty ,$$ which embrances thelibration and thecirculation regimes of the co-ordinatex 1, associated with α2 < 1 and α2 > 1, respectively. The solution includes asymptotically the limit α2 → ∞, which corresponds to theclassical solution of the problem, expanded in powers of ε ≡ μ2, and carrying α as a divisor. The classical singularity at α=0, corresponding to an exact commensurability of two frequencies of the motion, has been removed from the global solution by means of the Bohlin expansion in powers of μ = ε1/2. The singularities that commonly arise within the libration region α2 < 1 and on the separatrix α2 = 1 of the phase-plane have been suppressed by means of aregularizing function 1 $$\begin{array}{*{20}c} {\phi \equiv \tfrac{1}{2}(1 + \operatorname{sgn} z)\exp ( - z^{ - 3} ),} & {z \equiv \alpha ^2 } \\ \end{array} - 1,$$ introduced into the new Hamiltonian. The global solution is subject to thenormality condition, which boundsAB″ away from zero indeep resonance, α2 < 1/μ, where the classical solution fails, and which boundsB′ away from zero inshallow resonance, α2 > 1/μ, where the classical solution is valid. Thedemarcation point 1 $$\alpha _ * ^2 \equiv {1 \mathord{\left/ {\vphantom {1 \mu }} \right. \kern-\nulldelimiterspace} \mu }$$ conventionally separates the deep and the shallow resonance regions. The solution appears in parametric form 1 $$\begin{array}{*{20}c} {x_\kappa = x_\kappa (u)} \\ {y_1 = y_1 (u)} \\ {\begin{array}{*{20}c} {y_\kappa = conts,} & {k > 1,} \\ \end{array} } \\ {u = u(t).} \\ \end{array} $$ It involves the standard elliptic integralsu andE((u) of the first and the second kinds, respectively, the Jacobian elliptic functionssn, cn, dn, am, and the Zeta functionZ (u).  相似文献   

16.
  相似文献   

17.
Stars are gravitationally stabilized fusion reactors changing their chemical composition while transforming light atomic nuclei into heavy ones. The atomic nuclei are supposed to be in thermal equilibrium with the ambient plasma. The majority of reactions among nuclei leading to a nuclear transformation are inhibited by the necessity for the charged participants to tunnel through their mutual Coulomb barrier. As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. Over the years various approaches have been made to derive closed-form representations of thermonuclear reaction rates (Critchfield, 1972; Haubold and John, 1978; Haubold, Mathai and Anderson, 1987). They show that the reaction rate contains the astrophysical cross section factor and its derivatives which has to be determined experimentally, and an integral part of the thermonuclear reaction rate independent from experimental results which can be treated by closed-form representation techniques in terms of generalized hypergeometric functions. In this paper mathematical/statistical techniques for deriving closed-form representations of thermonuclear functions, particularly the four integrals $$\begin{gathered} I_1 (z,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - zy^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ I_2 (z,d,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - zy^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ I_3 (z,t,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - z(y + 1)^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ I_4 (z,\delta ,b,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - by^\delta } e^{ - zy^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ \end{gathered} $$ will be summarized and numerical results for them will be given. The separation of thermonuclear functions from thermonuclear reaction rates is our preferred result. The purpose of the paper is also to compare numerical results for approximate and closed-form representations of thermonuclear functions. This paper completes the work of Haubold, Mathai, and Anderson (1987).  相似文献   

18.
Some useful results and remodelled representations ofH-functions corresponding to the dispersion function $$T\left( z \right) = 1 - 2z^2 \sum\limits_1^n {\int_0^{\lambda r} {Y_r } \left( x \right){\text{d}}x/\left( {z^2 - x^2 } \right)} $$ are derived, suitable to the case of a multiplying medium characterized by $$\gamma _0 = \sum\limits_1^n {\int_0^{\lambda r} {Y_r } \left( x \right){\text{d}}x > \tfrac{1}{2} \Rightarrow \xi = 1 - 2\gamma _0< 0} $$   相似文献   

19.
It is shown that the fractional increase in binding energy of a galaxy in a fast collision with another galaxy of the same size can be well represented by the formula $$\xi _2 = 3({G \mathord{\left/ {\vphantom {G {M_2 \bar R}}} \right. \kern-\nulldelimiterspace} {M_2 \bar R}}) ({{M_1 } \mathord{\left/ {\vphantom {{M_1 } {V_p }}} \right. \kern-\nulldelimiterspace} {V_p }})^2 e^{ - p/\bar R} = \xi _1 ({{M_1 } \mathord{\left/ {\vphantom {{M_1 } {M_2 }}} \right. \kern-\nulldelimiterspace} {M_2 }})^3 ,$$ whereM 1,M 2 are the masses of the perturber and the perturbed galaxy, respectively,V p is the relative velocity of the perturber at minimum separationp, and \(\bar R\) is the dynamical radius of either galaxy.  相似文献   

20.
Results of analysis of photoelectric observations of the RS CVn eclipsing binary WY Cancri in the standard passbands ofUBV during 1973-74, 1976-79 and inUBVRI during 1984-86 are reported. A preliminary analysis of the eclipses suggested the primary eclipse to be transit. A study of the percentage contribution of the distortion wave amplitudes in all the colours with respect to the luminosities of both components, showed the hotter component to be the source of the distortion wave. The clean (wave removed) light curves of different epochs have not merged, suggesting residual effects of spot activity. The reason for this is attributed to the presence of either (1) polar spots or (2) small spots uniformly distributed all over the surface of the hotter component. This additional variation is found to have a periodicity of about 50 years or more. The distortion waves in yellow colour are modelled according to Budding’s (1977) method. For getting the best fit of the observations and theory, it was found necessary to assume three or four spots on the surface of the hot component. Out of these four spot groups, three are found to have direct motion with migration periods of 1.01, 1.01 and 2.51 years while the fourth one has a retrograde motion with a migration period of 3.01 years. From these periods and the latitudes of the spots derived from the model a co-rotating latitude of 4ℴ is obtained. The temperatures of these spots are found to be lower than that of the photosphere by about 700ℴK to 800ℴK. Assuming the light curve of 1985-86, which is the brightest of all the observed seasons, to be least affected by the spots, the light curves of the other seasons are all brought up to the quadrature level of this season by applying suitable corrections. The merged curves in theUBVRI colours are analysed for the elements by the Wilson-Devinney method. This analysis yielded the following absolute elements:
  相似文献   

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