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1.
The theoretical values of the momentsA 2m for any type of eclipses, expressed in terms of the elementsL 1,a andc 0, have been derived in the simple forms of rapidly convergent expansions to the series of Chebyshev polynomials, Jacobi polynomials and KopalJ-integrals (Kopal, 1977c) and hold good for any real (not necessarily integral) value ofm0.The aim of the present paper has been to establish explicit expressions for the Jacobian and its fast enough computation in the light changes of close eclipsing systems, arising from the partial derivative of different pairs ofg-functions (Kopal and Demircan, 1978, Paper XIV) with respect toa andc 0 2 , for any type of eclipses (be these occultations or transit, partial, total or annular) and for any arbitrary degreel of the adopted law of limb-darkening. The functional behaviour of this Jacobian would determine the reasonable light curve in connection with geometrical determinacy of the parametersa andc 0. In the expansion of Jacobian, the terms consist of two polynomials which satisfy certain three-term recursion relations having the eclipse parametersa andc 0, as their arguments.Closed form expressions forf-functions, as well as of the Jacobian (e.g.,m=1, 2, 3), obtaining in the case of total eclipses, are given for a comparative discussion with the theoretical values of Jacobian derived from partial derivative of different pairs ofg-functions.The numerical magnitude of Jacobian would determine the best combination of the momentsA 2m in the different pairs ofg-functions and definite results would follow in the subsequent paper of this series (Edalati, 1978c, Paper XXIV).  相似文献   

2.
The practical procedures for the solutions of the elements of any eclipsing system in the frequency-domain have been described in a previous paper of this series (Kopal and Demircan, 1978, Paper XIV). The fundamental quantities from which we depart in quest of our solution are twog-functions defining by the momentsA 2m (see Equations (2.13)–(2.16) in Paper XIV, or Equations (3.2)–(3.6) in Paper XV: Demircan, 1978b). If we establish the observational values for these functions, they constitute two independent relations between the unknown parametersa andc o, and can be numerically solved for them with the aid of the general expressions for the respective moments. However, the determinacy of these parameters depends on not only the accuracy of observations but also the employedg-functions. For better understanding of the geometrical determinacy of the eclipse parametersa andc o, different combinations of the momentsA 2m have been worked out asg-functions. For the index 2m, the values between 0 and 6 were applied. It has been noted that the behaviour of these functions vary but very little with applied different combinations of the moments. A choice of the most convenient moments to obtain a good determinacy for the eclipse elements were discussed. In this connection, (i) them-dependence of the moments, and the errors in their observational values have been considered, (ii) different practical procedures for the solution of eclipse elements were introduced, and (iii) different type of moments were tested.  相似文献   

3.
A new general expression for the theoretical momentsA 2m of the light curves of eclipsing systems has been presented in the form of infinite series expansion. In this expansion, the terms have been given as the product of two different polynomials which satisfy certain three-term recursion formulae, and the coefficients diminish rapidly with increasing number of terms. Thus, the numerical values of the theoretical momentsA 2m can be generated recursively up to four significant figures for any given set of eclipse elements. This can be utilized to solve the eclipse elements in two ways: (i) with an indirect method (for the procedures see Paper XIV, Kopal and Demircan, 1978), (ii) with a direct method as minimization to the observational momentsA 2m (area fitting). The procedures given in Paper XIV for obtaining the elements of any eclipsing system consisting of spherical stars have been automated by making use of the new expression for the momentsA 2m of the light curves. The theoretical functionsf 0,f 2,f 4,f 6,g 2 andg 4 which are the functions ofa andc 0, have been used to solve the eclipse elements from the observed photometric data. The closed-form expressions for the functionsf 2,f 4 andf 6 have also been derived (Section 3) in terms of Kopal'sI-integrals.The automated methods for obtaining the eclipse elements from one minimum alone have been tested on the light curves of YZ (21) Cassiopeiae under the spherical model assumptions. The results of these applications will be given in Section 5 which follows a brief introduction to the procedure we followed.  相似文献   

4.
The method of evaluating the photometric perturbationsB 2m of eclipsing variables in the frequency domain, developed by Kopal (1959, 1975e, 1978) for an interpretation of mutual eclipses in systems whose components are distorted by axial rotation and mutual tidal action. The aim of the present paper has been to establish explicit expressions for the photometric perturbationB 2m in such systems, regardless of the kind of eclipses and non-integral values ofm. Recently, Kopal (1978) introduced two different kinds of integrals with respect to associated α-functions andI-integrals which have been expressed in terms of certain general types of series that can be easily programmed for automatic computation within seconds of real time on highspeed computers. Following a brief introduction (Section 1) in which the need of this new approach will be expounded, in Section 3 we shall deduce the integral $$\int_0^{\theta \prime } {\tfrac{{\alpha _n^\prime }}{\delta }} d(sin^{2m} \theta )$$ in terms of a certain general type of series and also β-function, which should enable us to evaluate explicit expressions forf * (h) ,f 1 (h) ,f 2 (h) as well asB 2m .  相似文献   

5.
A comparison between model atmosphere grids with and without metal blanketing has been performed in the low-temperature range (T eff=6000 K to 10000 K) and for different metal contents (logA=0, –1, –2;A=scaled solar abundance). ForA10–1 andT eff7000 K, the Johnson colour indicesU-B andB-V, together with the Strömgrenu-b, b-y and the bolometric correction (BC) are little affected by metal blanketing ( mag<0 . m 04). On the other hand, the trend of the physical quantities and them 1 andc 1 colour indices reflect the inadequateness of the models even withA=10–2 andT eff=9500 K, where hydrogen line blanketing is expected to dominate. This fact discourages once and for all the use of metal unblanketed atmospheres other than for comparison of colour indices or the calculation of bolometric corrections for Population II A-F spectral types.  相似文献   

6.
A new kind of restricted 3-body problem is considered. One body,m 1, is a rigid spherical shell filled with an homogeneous incompressible fluid of density 1. The second one,m 2, is a mass point outside the shell andm 3 a small solid sphere of density 3 supposed movinginside the shell and subjected to the attraction ofm 2 and the buoyancy force due to the fluid 1. There exists a solution withm 3 at the center of the shell whilem 2 describes a Keplerian orbit around it. The linear stability of this configuration is studied assuming the mass ofm 3 to beinfinitesimal. Explicitly two cases are considered. In the first case, the orbit ofm 2 aroundm 1 is circular. In the second case, this orbit is elliptic but the shell is empty (i.e. no fluid inside it) or the densities 1 and 3 are equal. In each case, the domain of stability is investigated for the whole range of the parameters characterizing the problem.  相似文献   

7.
The photoelectricV observations of the Scuti star 59 Aur have been analysed using the techniques of periodogram analysis and least-squares solutions. The fundamental mode is found to be more prominent than the first overtone in the pulsation of 59 Aur. The period ratio of the first overtone to the fundamental (i.e.,P 1/P 0=0.748) indicates that the star pulsates in the radial mode. The absolute magnitude, effective temperature and mass of the star are derived to be 1 . m 22, 7300 K and 2.0M , respectively. No variations exceeding±0 . m 01 about the mean values ofB-V andU-B colours have been found during a pulsation cycle.  相似文献   

8.
The time-dependent equation of radiative transfer for isotropic scattering has been solved by integral equation technique in terms ofX- andY-functions appropriate for the problem. It is seen thatX- andY-functions are reducible to the corresponding function for steady-state problems by simply changing the Laplace transform parameters-i.e., byS0.  相似文献   

9.
R. W. Komm 《Solar physics》1995,156(1):17-28
I study the temporal variation of the solar rotation on time scales shorter than the 11-year cycle by analyzing the daily Mt. Wilson Doppler measurements from 1967 to 1992. The differential rotation is represented by the three coefficients,A, B, andC, of the following expansion: =A +B sin2() +C sin4(). TheA, B, andC time series show clearly the 11-year solar cycle and they also show high-frequency fluctuations. The Hurst analysis of these time series shows that a Gaussian random process such as observational noise can only account for fluctuations on time scales shorter than 20 days. For time scales from 20 days to 11 years, the variations of A give rise to a Hurst exponent ofH = 0.83, i.e., the variations ofA are persistent. The temporal variations ofB show the same behavior asC, which is different fromA. From one to 11 years, theB andC variations are dominated by the 11-year cycle, while for time lags shorter than about 250 days, theB andC fluctuations give rise to a Hurst exponent ofH = 0.66, which lies betweenH = 1/2, of a Gaussian random process, and the exponent of the persistent process shown byA. An analysis of the equivalent coefficients of the first three even Legendre polynomials, computed usingA, B, andC, provides additional information. For time scales between 100 and 1000 days, the ranges,R/S, of Legendre polynomial coefficients decrease with increasing order of the polynomials which suggests that the persistent process operates mainly on large spatial scales. The Hurst exponent ofH = 0.83 for variations inA is the same asH for monthly sunspot numbers with time scales between 6 months and 200 years and for14C radiocarbon data with time scales between 120 years and 3000 years, previously analyzed by other authors. The combined results imply that the underlying solar process shows the same persistent behavior for time scales as short as about 20 days up to time scales of a few thousand years.Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.  相似文献   

10.
The pulsed plasma probe technique has been expanded to include simultaneous determinations of absolute electron density, density fluctuations, electron temperature, and mean-ion-mass with resolution limited only by probe geometry, sheath size, and telemetry. The technique has been designed to test for coupling of electron density variations and ion composition irregularities in multi-component plasmas by the comparison of electron density fluctuation power spectraP N(k) and a newly-developed diagnostic parameter, the mean-ion-mass fluctuation spectraM i/M iP M(k). In addition, the experiment extends satellite-borne irregularity spectral analyses down to the 5–20 m range while attempting to identify F-region plasma instability processes on the basis of characteristics inN e,T e, N e,P N,M i, andP M. Initial results demonstrate the expanded diagnostic capability for high spatial resolution measurements of mean-ion-mass and provide experimental evidence for the role of ion composition in multi-stepped plasma instability processes. Specific results include a spectral indexX n inP N=A nf–X n of 1.6–2.9 over the wavelength range from 1 km to 6 m under conditions identified with an unstable equatorial nighttime ionosphere. Simultaneous measurements ofM i/M i(P M=A M f –X m) andN e/N e(P N=A n f –X n) have shown a general behavior tending to lower power (A m<A n) and softer spectra (X m<X n) in ion mass fluctuations when compared with fluctuations in total plasma density. Limited analyses of the two power spectral elements raise hopes for the differentiation between plasma mechanisms that can lead to similar indices inP N.Paper originally submitted to the journalSpace Science Instrumentation.  相似文献   

11.
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12.
We consider a large massM and two small massesm 1 andm 2 (m 1 m 2;m 1,m 2M). The orbit ofm 1 is initially circular and the motion ofm 2 hyperbolic with respect toM. The orbital elements of the small masses are strongly modified after a close, single encounter betweenm 1 andm 2.An approximative method, similar to the theory of stellar encounters, is used to determine the probabilities of collisions, hyperbolas, direct and retrograde ellipses, as well as the mean values of the semimajor axes and their root mean square deviation after the encounter.The results are close to those which are obtained if the massm 2 is negligibly small, (Mm 1m 2;m 2 0), as should be also expected on general grounds.  相似文献   

13.
Three-dimensional periodic motions of three bodies are shown to exist in the infinitesimal neighbourhood of their collinear equilibrium configurations. These configurations and some characteristic quantities of the emanating three-dimensional periodic orbits are given for many values of the two mass parameters, =m 2/(m 1+m 2) andm 3, of the general three-body problem, under the assumption that the straight line containing the bodies at equilibrium rotates with unit angular velocity. The analysis of the small periodic orbits near the equilibrium configurations is carried out to second-order terms in the small quantities describing the deviation from plane motion but the analytical solution obtained for the horizontal components of the state vector is valid to third-order terms in those quantities. The families of three-dimensional periodic orbits emanating from two of the collinear equilibrium configurations are continued numerically to large orbits. These families are found to terminate at large vertical-critical orbits of the familym of retrograde periodic orbits ofm 3 around the primariesm 1 andm 2. The series of these termination orbits, formed when the value ofm 3 varies, are also given. The three-dimensional orbits are computed form 3=0.1.  相似文献   

14.
An analytically tractable method of transforming the problem of light curve analysis of eclipsing binaries from the time domain into the frequency domain was introduced by Kopal (1975, 1979, 1990). This method uses a new general formulation of eclipse functions α, the so-called moments A 2m , and their combinations as g 2m = A 2m+2/(A 2m A 2m+4) functions for the basic spherical model. In this paper, I will review the use of these functions in the light curve analysis of eclipsing binaries.  相似文献   

15.
The thermal contrast , and the umbra-penumbraA u/A p, were calculated for 63 sunspots of various sizes and morphologies. Contrary to the assumptions of the PSI model, andA u/A p were found to be quite variable. The values of ranged from 0.1807 to 0.4266;A u/A p ranged from 0.0089 to 0.4899. The values of andA u/A p correlated well (r = 0.6018;p<0.005) and the regression for andA u/A p was obtained: = (0.220 ± 0.016) + (0.340 ± O.06)A u/A p. The values of andA u/A p were then compared with complexity ratings, magnetic field strength, time, and . The quantities andA u/A p were found to be independent of the complexity, magnetic field strength, and time factors. The correlation between andA u/A p lead to the proposed division of into an umbral thermal contrast u, and a penumbral thermal contrast p. These values were calculated from the photometric data: u = 0.57 ± 0.01 and p = 0.26 ± 0.006.  相似文献   

16.
The Ideal Resonance Problem, defined by the HamiltonianF=B(y)+2A (y) sin2 x, 1, has been solved in Garfinkelet al. (1971). There the solution has beenregularized by means of a special function j , introduced into the new HamiltonianF, under the tacit assumption thatA anB¨' are of order unity.This assumption, violated in some applications of the theory, is replaced here by the weaker assumption ofnormality, which admits zeros ofA andB inshallow resonance. It is shown here that these zeros generate singularities, which can be suppressed if j is suitably redefined.With the modified j , and with the assumption of normality, the solution is regularized for all values ofB, B¨', andA. As in the previous paper, the solution isglobal, including asymptotically the classical limit withB as a divisor of O(1).A regularized first-order aloorithm is constructed here as an illustration and a check.Presented at the XXII International Congress of I.A.F., Brussels, Belgium, Sept. 20, 1971.  相似文献   

17.
The RS CVn-type eclipsing binary AR Lac has been observed in two colours,B andV, in 1978 and 1979. Several times of minima have been obtained during the observations and the new light elements have been calculated. The orbital period of the system was found to be decreasing with an amount of 14.6 s century–1.The light curves of the system obtained inB andV show a significant wave-like distortion outside eclipses. The amplitudes of the wave-like distortion inB andV are about 0 . m 09 and 0 . m 10 in 1978, and, 0 . m 12 and 0 . m 13 in 1979, respectively. The minima of the wave-like distortion have shifted with an amount of 0 . p 40 in one year, thus indicating the migration period of the wave-like distortion is about 2.5 yr.A noticeable variation of light during the totality of primary minimum has also been observed. This variation can be attributed to the distortion wave which has been moving towards decreasing phases.  相似文献   

18.
The aim of the present paper is to deduce relations between the integral transformsA 2m, B2m,andF 1,2 of the light curves of eclipsing binary systems. The integral transformsA 2m, B2m,andF 1,2 have been related to one another by means of finite or rapidly converging infinite summations obtained by integrations of the series expansions of trigonometric functions.  相似文献   

19.
We show that the strong emission lines(Mg II, C III, C IV, and Ly and the absorption lineO VI (1035 A) of quasars, when passed through the maximum transmission ofU, B, V, andR light filters, leads to a continuous, and sometimes periodic variation in the dependence ofU-B onB-V. The correlation between the(U-B) and(B-V) colors in quasars with z<1.5 is expressed by the relation(U-B)=–0.92+1.15(B-V). We also give the dependence ofU-B onB-V for Seyfert galaxies of typeS1. We determine the mean variation of the(U-B, B-V) colors due to the strongest emission lines (Mg II, C IV, Ly). It amounts to magnitude0 . m 15.Translated fromAstrofizika, Vol. 38, No. 2, 1995.  相似文献   

20.
As previously shown (Rabe, 1970), two classes of small periodic librations exist, in the plane, elliptic restricted problem, for an infinite sequence of easily specified oscillation frequenciesZ j . The present paper considers the dependence ofZ on the eccentricitye of the primary motion, in addition to its dependence on the mass parameter , and determines the resulting relations between ande, for any given periodic frequencyZ j . These relationships are obtained from the conditionD (Z j ,, e)=0, where the basic determinantD has been expanded up to terms of orderZ 20, 5, ande 4.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972.  相似文献   

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