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1.
In 1982 and 1993, we carried out highly accurate photoelectric WBVR measurements for the close binary IT Cas. Based on these measurements and on the observations of other authors, we determined the apsidal motion $\left[ {\dot \omega _{obs} = {{(11\mathop .\limits^ \circ 0 \pm 2\mathop .\limits^ \circ 5)} \mathord{\left/ {\vphantom {{(11\mathop .\limits^ \circ 0 \pm 2\mathop .\limits^ \circ 5)} {100 years}}} \right. \kern-0em} {100 years}}} \right]$ . This value is in agreement with the theoretically calculated apsidal motion for these stars $\left[ {\dot \omega _{th} = {{(14^\circ \pm 3^\circ )} \mathord{\left/ {\vphantom {{(14^\circ \pm 3^\circ )} {100 years}}} \right. \kern-0em} {100 years}}} \right]$ .  相似文献   

2.
Published photoelectric measurements over a wide wavelength range (0.36–18 µm) are used to study the continuum spectrum of the star Θ1 Ori C. The model that assumes the following three radiation sources is consistent with observations: (1) a zero-age main-sequence O7 star (object 1) of mass M 1=20M ⊙, radius R 1=7.4R ⊙, effective temperature T 2=37 000 K, and absolute bolometric magnitude $M\mathop {bol}\limits^1 = - 7\mathop .\limits^m 7$ ; (2) object 2 with M 2=15M ⊙, R 2=16.2R ⊙, T 2=4000 K, and $M\mathop {bol}\limits^2 = - 5\mathop .\limits^m 1$ ; and (3) object 3 with R 310 700 R ⊙, T 3=190 K, and $M\mathop {bol}\limits^3 = - 0\mathop .\limits^m 6$ . The visual absorption toward the system is $A_V = 0\mathop .\limits^m 95$ and obeys a normal law. The nature of objects 2 and 3 has not been elucidated. It can only be assumed that object 2 is a companion of the primary star, its spectral type is K7, and it is in the stage of gravitational contraction. Object 3 can be a cocoon star and a member of the system, but can also be a dust envelope surrounding the system as a whole.  相似文献   

3.
In the now classical Lindblad-Lin density-wave theory, the linearization of the collisionless Boltzmann equation is made by assuming the potential functionU expressed in the formU=U 0 + \(\tilde U\) +... WhereU 0 is the background axisymmetric potential and \(\tilde U<< U_0 \) . Then the corresponding density distribution is \(\rho = \rho _0 + \tilde \rho (\tilde \rho<< \rho _0 )\) and the linearized equation connecting \(\tilde U\) and the component \(\tilde f\) of the distribution function is given by $$\frac{{\partial \tilde f}}{{\partial t}} + \upsilon \frac{{\partial \tilde f}}{{\partial x}} - \frac{{\partial U_0 }}{{\partial x}} \cdot \frac{{\partial \tilde f}}{{\partial \upsilon }} = \frac{{\partial \tilde U}}{{\partial x}}\frac{{\partial f_0 }}{{\partial \upsilon }}.$$ One looks for spiral self-consistent solutions which also satisfy Poisson's equation $$\nabla ^2 \tilde U = 4\pi G\tilde \rho = 4\pi G\int {\tilde f d\upsilon .} $$ Lin and Shu (1964) have shown that such solutions exist in special cases. In the present work, we adopt anopposite proceeding. Poisson's equation contains two unknown quantities \(\tilde U\) and \(\tilde \rho \) . It could be completelysolved if a second independent equation connecting \(\tilde U\) and \(\tilde \rho \) was known. Such an equation is hopelesslyobtained by direct observational means; the only way is to postulate it in a mathematical form. In a previouswork, Louise (1981) has shown that Poisson's equation accounted for distances of planets in the solar system(following to the Titius-Bode's law revised by Balsano and Hughes (1979)) if the following relation wasassumed $$\rho ^2 = k\frac{{\tilde U}}{{r^2 }} (k = cte).$$ We now postulate again this relation in order to solve Poisson's equation. Then, $$\nabla ^2 \tilde U - \frac{{\alpha ^2 }}{{r^2 }}\tilde U = 0, (\alpha ^2 = 4\pi Gk).$$ The solution is found in a classical way to be of the form $$\tilde U = cte J_v (pr)e^{ - pz} e^{jn\theta } $$ wheren = integer,p =cte andJ v (pr) = Bessel function with indexv (v 2 =n 2 + α2). By use of the Hankel function instead ofJ v (pr) for large values ofr, the spiral structure is found to be given by $$\tilde U = cte e^{ - pz} e^{j[\Phi _v (r) + n\theta ]} , \Phi _v (r) = pr - \pi /2(v + \tfrac{1}{2}).$$ For small values ofr, \(\tilde U\) = 0: the center of a galaxy is not affected by the density wave which is onlyresponsible of the spiral structure. For various values ofp,n andv, other forms of galaxies can be taken into account: Ring, barred and spiral-barred shapes etc. In order to generalize previous calculations, we further postulateρ 0 =kU 0/r 2, leading to Poisson'sequation which accounts for the disc population $$\nabla ^2 U_0 - \frac{{\alpha ^2 }}{{r^2 }}U_0 = 0.$$ AsU 0 is assumed axisymmetrical, the obvious solution is of the form $$U_0 = \frac{{cte}}{{r^v }}e^{ - pz} , \rho _0 = \frac{{cte}}{{r^{2 + v} }}e^{ - pz} .$$ Finally, Poisson's equation is completely solvable under the assumptionρ =k(U/r 2. The general solution,valid for both disc and spiral arm populations, becomes $$U = cte e^{ - pz} \left\{ {r^{ - v} + } \right.\left. {cte e^{j[\Phi _v (r) + n\theta ]} } \right\},$$ The density distribution along the O z axis is supported by Burstein's (1979) observations.  相似文献   

4.
We examine the possibility that the observed cosmic-ray protons are of primary extragalactic origin. The present \(\bar p\) data are consistent with a primary extragalactic component having \(\bar p\) /p?3.2±0.7 x 10-4 independent of energy. Following the suggestion that most extragalactic cosmic rays are from active galaxies, we propose that most of the observed \(\bar p\) 's are alos from the same sites. This would imply the possibility of destroying the corresponding \(\bar \alpha \) 'sat the source, thus leading to a flux ratio \(\bar \alpha \) /α< \(\bar p\) /p. We further predict an estimate for \(\bar \alpha \) α～10-5, within the range of future cosmic-ray detectors. the cosmological implications of this proposal are discussed.  相似文献   

5.
The planar problem of three bodies is described by means of Murnaghan's symmetric variables (the sidesa j of the triangle and an ignorable angle), which directly allow for the elimination of the nodes. Then Lemaitre's regularized variables \(\alpha _j = \sqrt {(\alpha ^2 - \alpha _j )}\) , where \(\alpha ^2 = \tfrac{1}{2}(a_1 + a_2 + a_3 )\) , as well as their canonically conjugated momenta are introduced. By finally applying McGehee's scaling transformation \(\alpha _j = r^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \tilde \alpha _j\) , wherer 2 is the moment of inertia a system of 7 differential equations (with 2 first integrals) for the 5-dimensional triple collision manifold \(T\) is obtained. Moreover, the zero angular momentum solutions form a 4-dimensional invariant submanifold \(N \subset T\) represented by 6 differential equations with polynomial right-hand sides. The manifold \(N\) is of the topological typeS 2×S 2 with 12 points removed, and it contains all 5 restpoint (each one in 8 copies). The flow on \(T\) is gradient-like with a Lyapounov function stationary in the 40 restpoints. These variables are well suited for numerical studies of planar triple collision.  相似文献   

6.
If a satellite orbit is described by means of osculating Jacobi α's and β's of a separable problem, the paper shows that a perturbing forceF makes them vary according to $$\dot \alpha _\kappa = {\text{F}} \cdot \partial {\text{r/}}\partial \beta _k {\text{ }}\dot \beta _k = {\text{ - F}} \cdot \partial {\text{r/}}\partial \alpha _k ,{\text{ (}}k = 1,2,3).{\text{ (A1)}}$$ Herer is the position vector of the satellite andF is any perturbing force, conservative or non-conservative. There are two special cases of (A1) that have been previously derived rigorously. If the reference orbit is Keplerian, equations equivalent to (A1), withF arbitrary, were derived by Brouwer and Clemence (1961), by Danby (1962), and by Battin (1964). IfF=?gradV 1(t), whereV 1 may or may not depend explicitly on the time, Equations (A1) reduce to the well known forms (e.g. Garfinkel, 1966) $$\dot \alpha _\kappa = {\text{ - }}\partial V_1 {\text{/}}\partial \beta _k {\text{ }}\dot \beta _k = \partial V_1 {\text{/}}\partial \alpha _k ,{\text{ (}}k = 1,2,3).{\text{ (A2)}}$$ holding for all separable reference orbits. Equations (A1) can of course be guessed from Equations (A2), if one assumes that \(\dot \alpha _k (t)\) and \(\dot \beta _k (t)\) depend only onF(t) and thatF(t) can always be modeled instantaneously as a potential gradient. The main point of the present paper is the rigorous derivation of (A1), without resort to any such modeling procedure. Applications to the Keplerian and spheroidal reference orbits are indicated.  相似文献   

7.
A linear analysis of the asymmetries in Stokes profiles of magnetic lines is performed. The asymmetries in the linear and circular polarization profiles are characterized by suitable quantities, \(\delta \tilde Q\) and \(\delta \tilde V\) , strictly related to observed profiles. The response functions of \(\delta \tilde Q\) and \(\delta \tilde V\) to velocity fields are introduced and computed for various configurations of the magnetic field vector in a Milne-Eddington atmosphere. Some conclusions are drawn as to the importance of the asymmetries in Stokes profiles for recovering the velocity gradients from observations.  相似文献   

8.
We determine equilibrium configuration of Emden-Chandrasekhar axisymmetric, solid-body rotating polytropes, defined as EC polytropes, for polytropic indices ranging from 0 (homogeneous bodies) to 5 (Roche-type bodies). To this aim, we improve Chandrasekhar's method to determine equilibrium configurations on two respects: namely, (a) no distinction exists between undistorted and distorted terms in the expression of the potential, and (b) the comparison between the expressions of gravitational potential and its first derivatives inside and outside the body has to be made on the boundary of a sphere of radius ΞE, which does not necessarily coincide with the undistorted Emden's sphere of radius \(\bar \xi _0 \geqslant \Xi _{\text{E}} \) . We also allow different values of \(\bar \xi _0 \) for different physical parameters, and choose a special set which best fits more refined results (involving more complicated and more expensive computer codes) by James (1964). We find an increasing agreement with increasing values of polytropic indexn and vice-versa, while a large discrepancy arises for 0≤n<1, which makes the approximations used here too much rough tobe accepted in this range. A real slight non-monotonic trend is exhibited by axial rations and masses related to rotational equilibrium configurations — i.e., when gravity at the equator is balanced by centrifugal force-with extremum points for 4.8<n<4.85 in both cases. The same holds for masses related to spherical configurations, as already pointed out by Seidov and Kuzakhmedov (1978). Finally, it is shown that isotrophic, one-component models of this paper might provide the required correlation between the ratio of a typical rotation velocity to a typical peculiar velocity and the ellipticity, for about \(\tfrac{3}{4}\) of elliptical systems for which observations are available.  相似文献   

9.
This short article supplements a recent paper by Dr R. Broucke on velocity-related series expansions in the two-body problem. The derivations of the Fourier and Legendre expansions of the functionsF(v), \(\sqrt {F(\upsilon )} \) and \(\sqrt {{1 \mathord{\left/ {\vphantom {1 {F(\upsilon )}}} \right. \kern-0em} {F(\upsilon )}}} \) are given, where $$F(\upsilon ) = (1 - e^2 )/(1 + 2e\cos \upsilon + e^2 ), e< 1$$ In the two-body problem,v is identified with the true anomaly,e the eccentricity andF(v) equals (an/V)2. Some interesting relations involving Legendre polynomials are also noted.  相似文献   

10.
New photoelectric UBVRI observations of the eclipsing variable V 1016 Ori have been obtained with the AZT-11 telescope at Crimean Astrophysical Observatory and with the Zeiss-600 telescope at Mount Maidanak Observatory. Light curves are constructed from the new observations and from published and archival data. We use a total of 340, 348, 386, 185, and 62 magnitude estimates in the bands from U to I, respectively. An analysis of these data has yielded the following results. The photometric elements were refined; their new values are $Min I = JDH 2441966.820 + 65\mathop .\limits^d 4331E$ . The UBVRI magnitudes outside eclipse were found to be $5\mathop .\limits^m 95$ , $6\mathop .\limits^m 77$ , $6\mathop .\limits^m 75$ , $6\mathop .\limits^m 68$ , and $6\mathop .\limits^m 16$ , respectively. No phase effect was detected. We obtained two light-curve solutions: (1) assuming that the giant star was in front of the small one during eclipse, we determined the stellar radii, r s=0.0141 and r g=0.0228 (in fractions of the semimajor axis of the orbit); and (2) assuming that the small star was in front of the giant one, we derived r g=0.0186 and r s=0.0180 for the V band. The brightness of the primary star in the bands from U to I is L 1=0.96, 0.92, 0.90, 0.89, and 0.88, the orbital inclination is $i = 87^\circ .1$ , and the maximum eclipse phase is α0= 0.66. In both cases, we accepted the U hypothesis, assumed the orbit to be elliptical, and took into account the flux from the star Θ1 Ori E that fell within the photometer aperture. The first solution leads to a discrepancy between the primary radius determined by solving the light curve and the radial-velocity curve and its value estimated from the luminosity and temperature. This discrepancy is eliminated in the second solution, and it turns out that, by all parameters, the primary corresponds to a normal zero-age main-sequence star.  相似文献   

11.
The periodic solutions for an Hamiltonian system with $$H = \frac{1}{2}\mathop \Sigma \limits_1^3 (\dot x_\alpha ^2 + \omega _\alpha ^2 x_\alpha ^2 ) - \varepsilon x_1 x_\alpha ^2 - \eta x_2 x_\alpha ^2 $$ are investigated analytically. The frequencies ωα, α=1, 2, 3 are assumed near the ratio 4—4—1. We find different families of periodic solutions whose periods are in the vicinity of the period T′=2π/ω3=2π/ω′. As in the case of the problem with two degrees of liberty, for particular values of ω1, ω2, ω3 and ε, η, we find that the families near the x3-axis are discontinuous. These families are periodic with periods near the period T′ in a region for ε, η, approximatively [0; 0.4] if we choose \(\omega ' = \sqrt {0.1} \) and h=0.00765.  相似文献   

12.
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13.
The McGehee's study of the triple collision of the 3-body problem is here applied for the stability of an equilibrium. Let us consider the homogeneous Lagrangian: $$L = \frac{{\dot x^2 + \dot y^2 }}{2} + U(x,y)$$ whereU is polynomial, with degreek. We establish a necessary and sufficient condition onU for the stability of \(\omega (x = y = \dot x = \dot y = 0)\) .  相似文献   

14.
We present our photometric observations of an early B supergiant with an infrared excess, the protoplanetary object LSIV-12°111, and the previously suspected variable star NSV 24971. We confirm its photometric variability. During two observing seasons (2000–2001), the star exhibited rapid irregular light variations with amplitudes $\Delta V \sim 0\mathop .\limits^m 3$ , $\Delta B \sim 0\mathop .\limits^m 3$ , and $\Delta U \sim 0\mathop .\limits^m 4$ and a time scale of ～1d. There is no correlation between the colors and magnitudes of the star. The variability patterns of LSIV-12°111 and two other hot post-AGB stars, V886 Her and V1853 Cyg, are shown to be similar.  相似文献   

15.
Tearing modes in a plane collisionless current sheet with shear bulk flow are studied. An analytic expression for the growth rate is obtained for the case \(M^2 = (1 - \varepsilon {\text{ sech}}^m \bar z)\) , whereM is the Mach number,m the shear flow index, ε a positive constant less than unity, and \(\bar z\) the (normalized) co-ordinate normal to the current sheet. The growth rates are large and the unstable wave number domain is increased as compared to the case without flow. The relevance of these results to time-dependent reconnection processes in the Earth's magnetosphere is discussed.  相似文献   

16.
Using a new approach, we have obtained a formula for calculating the rotation period and radius of planets. In the ordinary gravitomagnetism the gravitational spin (S) orbit (L) coupling, $\vec{L}\cdot\vec{S}\propto L^{2}$ , while our model predicts that $\vec{L}\cdot\vec{S}\propto\frac{m}{M}L^{2}$ , where M and m are the central and orbiting masses, respectively. Hence, planets during their evolution exchange L and S until they reach a final stability at which MS∝mL, or $S\propto\frac{m^{2}}{v}$ , where v is the orbital velocity of the planet. Rotational properties of our planetary system and exoplanets are in agreement with our predictions. The radius (R) and rotational period (D) of tidally locked planet at a distance a from its star, are related by, $D^{2}\propto\sqrt{\frac{M}{m^{3}}}R^{3}$ and that $R\propto\sqrt{\frac {m}{M}}a$ .  相似文献   

17.
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   

18.
We obtained U BV R photometric and spectroscopic observations during the outburst of V838 Mon. Before its outburst, the B brightness of the star had been stable ( $\tilde15.^m 85$ ) for 45 years. This was a blue star with the color index $(B - V)_0 = - 0\mathop .\limits^m 03 \pm 0\mathop .\limits^m 1$ and may have been a cataclysmic variable. In the middle of March 2002, the outburst amplitude reached $8\mathop .\limits^m 1$ in B. The star has the counterpart V 1006/7 in M 31 in luminosity at maximum and in spectrum. The unusual spectrum at the premaximum stage originated in the expanding photosphere of a cool K-type giant. The expansion velocity of the photosphere was 150 km s?1; the maximum velocity in the expanding stellar envelope reached 500 km s?1. The absorption components of neutral metal lines were enhanced by a factor of 3 or 4 compared to a normal K-type star. No overabundance of s-process elements was found. One day before the brightness peak, an intense Hα emission line with broad wings, FWZI=3100 km s?1, and numerous lines of ionized metals appeared in V838 Mon, which is characteristic of normal classical novae. We show light, color, and spectral variations of the object.  相似文献   

19.
We present photoelectric and photographic observations of the supergiant HD 179821 with a large infrared excess, a candidate for protoplanetary objects. Over, ten years of our UBV observations, the star exhibited semiregular light variations with amplitudes $\Delta V = 0\mathop .\limits^m 10$ , $\Delta B = 0\mathop .\limits^m 15$ , and $\Delta U = 0\mathop .\limits^m 25$ , as well as systematic color and light variations. From 1990 until 1996, the yearly mean U-B and B-V color indices decreased by 0.25 and 0.15, respectively. After 1996, the motion of the star in the two-color (B-V)-(U-B) diagram upward and to the left slowed down. The color excess that we derived from our observations, by assuming that the star’s spectral type was F3 I in the 1990s, is E(B-V)=1.0. The photographic observations of HD 179821 from 1899 until 1989 show that its brightness m pg generally increased while significantly fluctuating. An analysis of the observational data suggests that HD 179821 is most likely a post-AGB star of intermediate or low mass.  相似文献   

20.
The projection of an axially symmetric satellite's orbit on a plane perpendicular to the rotation axis (z=const.) is given by the second-order differential equation. $$\frac{{y''}}{{1 + y'^2 }} = \bar \Psi _y - y'\bar \Psi _{x,}$$ where the prime denotes the derivative with respect tox and \(\bar \Psi (x,y)\) is a known function. Two integrability cases have been investigated and it has been shown that for these two cases the integration can be carried out either by quadratures or reduced to a first-order differential equation. Analytical and physical properties are expressed, and it is shown that the equation can be derived from the calssical plane eikonal equation of geometric optics.  相似文献   

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