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1.
An integral transform called the momentsA 2m of the light curves has been introduced by Kopal (1975) and utilized in the subsequent papers for an analysis of the light curves of eclipsing variables. The aim of the present paper is to generalize this integral transform by two distinct ways: (i) by introducing an exponential factor, and (ii) a Jacobi polynomial as multiplicative factor into the integrand of the transformA 2m. Observational values of these general transforms are likewise obtainable. They have been expressed in terms of eclipse elementsr 1,2,i andL 1. These expressions can be used to solve the eclipse elements in terms of observed quantities. Free parameters in the expressions increase the flexibility in applications and may be utilized to improve the determinacy of the elements.  相似文献   

2.
The main aim of this paper will be to develop explicit form of the moments of the light curvesA 2m(r 1,r 2,i) required for the solution for the geometrical elementsr 1,2 andi of eclipsing systems exhibiting annular eclipses (Sections 2 and 3), as well as partial eclipses (Section 4).In the concluding Section 5 we shall demonstrate that — regardless of the type of eclipse and distribution of brightness on the apparent disc of the eclipsed star, or indeed of the shape of the eclipsing as well as eclipsed components — the momentsA 2m satisfy certain simple functional equations — a fact which relates them to other classes of functions previously studied in applied mathematics.  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.
Photoelectric observations of FW Monocerotis inU,B, andV filters have been discussed. The depths of the primary minimum inU BV colours are 2 . m 63, 2 . m 17 and 1 . m 76, respectively. No variation in the period has been found and its revised value is 3 . d 8735868.  相似文献   

5.
The aim of the present paper will be to evaluate numerically Jacobian and other functions which have been discussed in more detail in a previous paper of this series (Edalati, 1978b, Paper XXII), and also choose the most convenient moments to obtain a good determination for the unknown eclipse parametersa andc 0. More than 12 different pairs ofg-functions for real values ofm have been investigated numerically and diagrammatically. The behaviour ofg-functions depends but very little on different combination of the moments, and related diagrams are approximately the same asg 2 andg 4 (Kopal and Demircan, 1978, Paper XIV).The behaviour of the vanishing Jacobian, arising from different pairs ofg-functions for real values ofm1 has been shown diagrammatically in terms ofa andc 0. Accordingly, we obtain the optimum combination of the moments (i.e.,A 6,A 7,A 8 andA 9) ing-functionsg 7 andg 8. It has been noted that the behaviour of theg-functions which depend on the combinations of the higher order moments (i.e.,m5) have been ruled out, because the proportional error of the momentsA 2m increases with increasing values of realm. The automated method has been tested successfully on the light curve of RT Per (Mancusoet al., 1977; Edalati, 1978a). Finally, a comparison is given of the elements of RT Per arising from two different pairs ofg-functions, i.e.,g 2,g 4 (Edalati, 1978a) andg 7,g 8 for the light curves analysis.  相似文献   

6.
Some properties of the quantitiesB 2m (Smith, 1977) inherent in the frequency-domain approach have been deduced, and a general expression for them in terms of the eclipse elementsr 1,2,i andL 1 of the basic model has been presented (Section 2).An expansion for the loss of light (1–l) into a Fourier sine series alone have been introduced, and its coefficientsb m presented (Section 3) in terms of the same eclipse elements. A method of increasing the rate of convergence of this series has been given in Section 4. The methods for obtaining the elements of eclipsing binaries by making use of all these quantities in the frequency-domain can likewise be generalized to cover the photometric effects of gravitational and radiative interaction between the components.  相似文献   

7.
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   

8.
The RS CVn-type eclipsing binary SZ Psc was observed in two coloursB andV, in 1981. The rate of change of the period was calculated using two different least-squares procedures. The amplitudes of the light variations at outside eclipses are 0 . m 181 and 0 . m 213 inB andV colours, respectively. The light curves of the system have been solved using a new approximation. The radius of the cooler component is only 82% of its Roche-radius and the system is detached one.  相似文献   

9.
In this paper, new trigonometric series representations of the orbital inclination functionF imp (i) in multiples of cosines or sines will be established for all possible values ofl, m, andp. For such representations, the literal analytical expressions and the recurrence formulae satisfied by their coefficients will be established. Moreover, an economic algorithm for the table formulation of these coefficients for the possible values ofl, m, andp is given. Finally, numerical examples of the representations forl=2(1)4;m=0(1)l;p=0(1)l are also included.  相似文献   

10.
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   

11.
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   

12.
Conditions are found which are satisfied by the coefficients of the expression being a second integral of the motion of an autonomous dynamical system with two degrees of freedom. The coefficientsA, B. , ,E are differentiable functions of the cartesian position coordinatesx, y. The velocity components are denoted by . It is shown that must be constant andB must be of the formB =f(x+y) +g(x-y) wheref, g are arbitrary.Given andB one can always find the remaining coefficientsA, E and also the corresponding potential and second integral. Depending on the specifica case at hand a certain number of arbitrary constants (or arbitrary functions) enter into the potential and the second integral. To each potential (which may be of the separable or nonseparable type in the coordinatesx andy)there corresponds one integral of the above form.  相似文献   

13.
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   

14.
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   

15.
UBV photoelectric observations of the W UMa-type binary V471 Cas were made from September to November 1984. Its colour indices were found to be(B-V)=0 . m 771±0 . m 02 and(U-B)=0 . m 196±0 . m 02. TheU, B, andV light curves of V471 Cas show some photometric fluctuations. We found that its orbital period is not 0.335998 days which was given by GCVS (1986), but 0.405356 days.Photometric orbital elements of V471 Cas were found using the Wilson-Devinney method. V471 Cas is a contact system, in which the overcontact factor is 0.19, its mass ratio of two components is 0.5947, and orbital minclination is in 83.29 degrees.  相似文献   

16.
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   

17.
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   

18.
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   

19.
It is proposed that the existence and nature of a planetary dynamo can be characterized by a dimensionless number Φ ≡ FeR/ϱλ2ω, called the energy flux number, where Fe is the energy flux available for dynamo generation, R is the core radius (or thickness of the dynamo generating region), ϱ is the fluid density, λ is the magnetic diffusivity and ω is the angular velocity. For Φ ≲ 1, there is no dynamo. For 1 ≲ Φ ≲ 102.5 there is an “energy-limited dynamo”, in which Fe is insufficient to enable the dynamo to reach the dynamically desirable state A ≡ B2/8πϱλω ∼ 1, where B is a typical field amplitude (in Gauss). For 102.5 ≲ Φ ≲ 105, there is a dynamically determined dynamo (Λ ∼ 1) in which the magnetic Reynolds number of turbulent eddies is small. For Φ ≳ 105, there is a turbulent dynamo. Probable planetary examples of these three dynamo states are Mercury (Φ ∼ 102-103), Earth (Φ ∼ 104) and Jupiter (Φ ∼ 1011), respectively.  相似文献   

20.
Peter Foukal 《Solar physics》1993,148(2):219-232
We analyze the record of facular areas compiled by the Royal Greenwich Observatory (RGO) from daily white-light observations between 1874 and 1976. Curiously, the relative amplitudes of the three largest sunspot cycles 17, 18, and 19 in this record are reversed when they are ranked by facular area. We show that this negative correlation arises from a general decrease of the ratioA F/A S, of facular to sunspot area, with increasingA S. Within a given cycle,A F/A Sdecreases in active regions of largeA S, butA F/A Sis also lower at allA S, in cycles of higher peak amplitude inA S. This decrease ofA F/A Sin large spot groups is consistent with its decrease in younger, more active solar-mass stars, and it may explain why stars only slightly more magnetically active than the Sun tend to exhibit much greater variability in broad-band photometry. We suggest that the physical explanation is an increased spatial filling factor of magnetic flux, favoring formation of sunspots over faculae. We also explain why the decrease inA F/ASis not seen in the disc-integrated Ca K plage areas, nor in theF10.7 microwave index, both of which exhibit remarkable linearity when plotted against smoothed sunspot area. This explanation suggests how complementary data on faculae and plages from RGO and Mt. Wilson could be used to improve empirical models of total irradiance variation, extending back to 1874.  相似文献   

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