Fourier techniques for an analysis of eclipsing binary light curves: I

The Fourier techniques developed so far for an analysis of eclipsing binary light curves have been re-discussed. The Fourier coefficients for the analysis have been derived in a simple form of series expansions, in terms of eclipse elements, valid for any type of eclipse (regardless of whetherr ₁r ₂).These coefficients may be utilized to solve the eclipse elements in terms of the observed characteristics of the light curves. A general relation between the observed quantitiesl and , and the eclipse elementsr _1,2,i andL ₁ has also been given in the form of series expansions which can be used for the synthesis of the light curves.     

Fourier techniques for an analysis of eclipsing binary light curves,VII

A Laplace and a Hankel transform of the light curves of eclipsing binary star systems have been expressed in terms of the eclipse elements (L ₁,r _1,2 andi) of the spherical basic model. These general expressions can be used for the solution of the eclipse elements of the systems in terms of the observed quantities.     

Determinacy of the eclipse elements from a part of the light curves of eclipsing binaries

A part of the light curves of two detached (CD Tau and V909 Cyg) and one semi-detached (Algol) binaries have been analysed with the emphasis on the determinacy of the parameters of different systems from a part of their eclipse curves. A model light curve for whichr ₁=0.050,r ₂=0.150,i=90°, andL ₁=0.800 were chosen, has also been considered for a further clarification of the determinacy problem of the eclipse parameters. Some insight into the determinacy is gained by varying one parameter and adjusting the others for the best fit to the light curves in the considered eclipse phases. It was realised that the determinacy problem of the unknown parameters is stored in the determinacy of the type of the eclipse minima. The attempts of the solutions with a false choice of initial elements result in finding (i) no minimum of ² to give any acceptable solution, (ii) rapid departure from the false start and convergence on the correct solution, or (iii) a false solution mostly with a true inclinationi, but wrong sense of the ratio of the radii.     

Photometric investigation of the short period eclipsing binary star V719 Her

The Behlen observatory 0.76 m telescope CCD photometer is used to obtain 347 observations of the short period (P0^d.4) eclipsing binary star V719 Her. The observations done withV andR bandpass filters were made on 6 nights in 1993. Previously published light elements and the present five timings of minimum provide a new epoch and a more accurate orbital period of 0.4009828 days. Our analyses show that the period of the system appears to decrease. We recommend future monitoring of the eclipse minima for this system. No published spectral classification for V719 Her exists. From the color,V-R=0.391, we estimate it to be about F5.The 1993 version of the Wilson Devinney model gave the photometric solutions. The adopted solution indicates that V719 Her is a W UMa type contact binary. The mass ratio,q=(m ₂/m ₁, where star 1 eclipse at the primary minimum)=0.296 suggests that V719 Her is a WUMa system with type-A (transit during primary eclipse) configuration. The secondary minimum shows a total eclipse. V719 Her with period less than 0.5 and spectral class F5, is probably a zero-age contact system. Since our photometric solution shows that the luminosity difference between the components is very large, we suspect that V719 Her is most likely a single line spectroscopic binary. We recommend spectroscopic study of this system.     

Fourier analysis of the light curves of eclipsing variables,XV

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.     

Possible connection between period change and magnetic activity of the very short‐period binary VZ Piscium

New times of light minimum of the short‐period (P = 0^d.26) close binary system, VZ Psc, are presented. A period investigation of the binary star, by combining the three new eclipse times with the others collected from the literatures, shows that the variation of the period might be in an alternate way. Under the hypothesis that the variation of the orbital period is cyclic, a period of 25 years and an amplitude of 0.^d0030 for the cyclic change are determined. If this periodic variation is caused by the presence of a third body, the mass of the third body (m₃) should be no less than 0.081M_⊙. Since both components of VZ Psc are strong chromospherically active and the level of activity of the secondary component is higher than that of the primary one, the period may be more plausibly explained by cyclic magnetic activity of the less massive component. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fourier techniques for an analysis of eclipsing binary light curves. V

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.     

Fourier techniques for an analysis of eclipsing binary light curves: II

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.     

Multicolor Photometric Study of the NOVA V1494 Aql in 2002

R and I band CCD observations of the nova V1494 Aql during July-November 2002 are reported and the V, R, and I light curves are analyzed. The orbital light curve of this nova has an eclipse-like form with two unequal humps before and after the eclipse. The approach to the eclipse lasts twice as long as the emergence from it. The overall duration of the eclipse is about 0.45P _orb. The depth of eclipse increases with wavelength and averages 0^m.3 (V), 0^m.5 (R), and 0^m.7 (I). The secondary, shallow minimum has an average depth of 0^m.1 in R and I and about 0^m.03 in V. The hump at phase 0.65 is higher than the one at phase 0.17. The most probable explanation for the observed variations in the light with the phase of the orbital period may be self eclipsing of the accretion column in the magnetic exploding variable (white dwarf) together with partial eclipsing of the accretion region by the secondary component.     

Fourier analysis of the light curves of eclipsing variables,XVI

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.     

Time‐series high‐resolution spectroscopy and photometry of ε Aurigae from 2006–2013: Another brick in the wall

We present continuous and time‐resolved R = 55 000 optical échelle spectroscopy of ε Aurigae from 2006–2013. Data were taken with the STELLA Echelle Spectrograph of the robotic STELLA facility at the Observatorio del Teide in Tenerife. Contemporaneous photometry with the Automatic Photoelectric Telescopes at Fairborn Observatory in Arizona is presented for the years 1996–2013. Spectroscopic observations started three years prior to the photometric eclipse and are still ongoing. A total of 474 high‐resolution échelle spectra are analyzed and made available in this paper. We identify 368 absorption lines of which 161 lines show the characteristic sharp disk lines during eclipse. Another 207 spectral lines appeared nearly unaffected by the eclipse. From spectrum synthesis, we obtained the supergiant atmospheric parameters T_eff = 7395 ± 70 K, log g ≈ 1, and [Fe/H] = +0.02 ± 0.2 with ξ_t = 9 km s^–1, ζ_RT = 13 km s^–1, and v sin i = 28 ± 3 km s^–1. The residual average line broadening expressed in km s^–1 varies with a period of 62.6 ± 0.7 d, in particular at egress and after the eclipse. Two‐dimensional line‐profile periodograms show several periods, the strongest with ≈110 d evident in optically thin lines as well as in the Balmer lines. Center‐of‐intensity weighted radial velocities of individual spectral lines also show the 110‐d period but, again, additional shorter and longer periods are evident and are different in the Balmer lines. The two main spectroscopic Hα periods, ≈ 116 d from the line core and ≈ 150 d from the center‐of‐intensity radial velocities, appear at 102 d and 139 d in the photometry. The Hβ and Johnson V I photometry on the other hand shows two well‐defined and phase‐coherent periods of 77 d and 132 d. We conclude that Hα is contaminated by changes in the circumstellar environment while the Hβ and V I photometry stems predominantly from the non radial pulsations of the F0 supergiant. We isolate the disk‐rotation profile from 61 absorption lines and found that low disk eccentricity generally relates to low disk rotational velocity (but not always) while high disk eccentricity always relates to high velocity. There is also the general trend that the disk‐absorption in spectral lines with higher excitation potential comes from disk regions with higher eccentricity and thus also with higher rotational velocity. The dependency on transition probability is more complex and shows a bi‐modal trend. The outskirts of the disk is distributed asymmetrically around the disk and appears to have been built up mostly in a tail along the orbit behind the secondary. Our data show that this tail continues to eclipse the F0 Iab primary star even two years after the end of the photometric eclipse. High‐resolution spectra were also taken of the other, bona‐fide, visual‐binary components of ε Aur (ADS 3605BCDE). Only the C‐component, a K3‐4‐giant, appears at the same distance than ε Aur but its radial velocity is in disagreement with a bound orbit. The other components are a nearby (≈ 7 pc) cool DA white dwarf, a G8 dwarf, and a B9 supergiant, and not related to ε Aur. The cool white dwarf shows strong DIB lines that suggest the existence of a debris disk around this star. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multi‐epoch time‐resolved photometry of the eclipsing polar CSS081231:071126+440405

The eclipsing polar CSS081231:071126+440405 turned bright (V_max ∼ 14.5) in late 2008 and was subsequently observed intensively with small and medium‐sized telescopes. A homogeneous analysis of this comprehensive dataset comprising 109 eclipse epochs is presented and a linear ephemeris covering the five years of observations, about 24000 orbital cycles, is derived. Formally this sets rather tight constraints on the mass of a hypothetical circumbinary planet, M_pl ≤ 2 M_Jup. This preliminary result needs consolidation by long‐term monitoring of the source. The eclipse lasts 433.08 ± 0.65 s, and the orbital inclination is found to be i = 79.3°–83.7°. The centre of the bright phase displays accretion‐rate dependent azimuthal shifts. No accretion geometry is found that explains all observational constraints, suggesting a complex accretion geometry with possible pole switches and a likely non‐dipolar field geometry. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical calculation of Thomson scattering from inhomogeneous models of the corona,and application to streamers of the 1970 and 1972 eclipses

A general computer program has been developed to numerically integrate the Thomson scattered light from arbitrary inhomogeneous models of the solar corona. Conversion from the observer's to solar coordinates is totally general to eliminate restrictions on the lines-of-sight that may be investigated. The tangential and radial components (K _t and K _r ),or any combination thereof, are calculated. Four separate output modes are available, corresponding to the common formats used for coronal brightness and polarization data.This program was used to investigate the major NW streamer of the 1972 eclipse. The bifurcated profile of this feature is reproduced by the projection effect of a radially expanding blade, or fan, whose longitudinal axis is twisted to follow an underlying magnetic neutral line on the solar surface. Thus a purely geometrical effect accounts for the observed intensity profile. Published brightness data for the NE streamer of the 1970 eclipse are also reinterpreted using the radially-expanding fan model. The axial density gradients of 1970 and 1972 features are found to be virtually identical from 3 to 8 R .     

A model of the Algol type close binary TT hydrae

UBV photometric observations and elements of TT Hydrae obtained by Kulkarni and Abhyankar (1980) are combined with the radial velocity curve of Popper (1979, personal communication) to derive the absolute dimensions and. a model of this important Algol system. While the photometric ratios of radii inV andB are in agreement givingk = 0.3812 for a limb darkening coefficient ofx = 0.6, application of Irwin’s (1947) method givesx = 0.4 forU. The primary is found to be a main sequence Al V star of mass 2.61M _⊙ and radius 2.01 R_⊙, and the secondary is classified as a Kl III star of mass 0.70M _⊙ and radius 5.33R _⊙. The observed Fourier coefficients for the light outside the eclipse agree with those calculated from theory for the reflection and ellipticity effects. The system shows an ultraviolet excess of 0.5 to 0.6 magnitudes during primary eclipse, which is attributed to an asymmetric circumstellar distribution of matter around the primary. The evolutionary status of the secondary, which does not appear to fill its Roche lobe completely, is discussed.     

Orbital elements of the RS CVn eclipsing binary,SV Camelopardalis

The extensiveUBV observations of SV Camelopardalis by Patkos (1982) have been analysed to derive the orbital elements of the system. The data were corrected for the effect of third body (Sarma, Sarma & Abhyankar 1985) and for the ‘RS CVn’ distortion wave (Sarma, Vivekanandarao & Sarma 1988). The cleaned data were used to obtain a preliminary solution by a modified version of Wellmann method (Sarma & Abhyankar 1979) from which we concluded that the primary eclipse is a transit. The final orbital elements of SV Cam were obtained by the modified version (Sarma 1988; Sarmaet al. 1987) of WINK program by Wood (1972). The colour and median brightness variation are discussed. From the spectroscopic mass functionf(m) = 0.118 M_⊙ (Hiltner 1953), the absolute dimensions of the components are found to be 0.826 M_bd & 0.592 M_⊙ and 1.236 R_⊙ & 0.778 R_⊙ for the primary and secondary components, respectively. The age of the binary system is estimated to be 6.0 ± 1.0 × 10⁸ years     

Fourier techniques for an analysis of eclipsing binary light curves: IV

The aim of the present paper is to establish two further series expansions (alternative to those given in Demircan, 1979a, b, c), for the observed light changes of eclipsing binary system. The coefficients of these expansions have also been expressed in the form of general series expansions in terms of the eclipse elementsr _1.2,i andL ₁ of the spherical model on which all other distorted models may be based (Kopal, 1975, 1976) in an analysis in the frequency-domain.     

High energy phenomena in eta carinae

We have investigated with BeppoSAX the long term behaviour of the harder X-ray component of the supposed supermassive binary system η Car along its 5.52 year cycle. We have found that in March 1998 during egress from the last December 1997 eclipse, this component was the same as outside eclipse, but for a large (×3.5) increase of NH _h , that can be attributed to the presence or formation of opaque matter in front of the source near periastron. Unexpectedly, at that time the iron 6.7 keV emission line was 40% stronger. BeppoSAX has for the first time found ahard X-ray tail extending to at least 50 keV, that cannot be adequately fitted with an additional hotter thermal component. The 2–100 keV spectrum of η Car is instead well fitted with an absorbed powerlaw spectrum with photon index 2.53, suggesting non-thermal emission as an alternative model for the core source.     

Basic Functions of the Light Curve Analysis of Eclipsing Variables in the Frequency Domain

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.     

Fabry-Pérot line profiles in the λ5303 å and λ6374 å coronal lines obtained during the 1983 Indonesian eclipse

During the total solar eclipse of 11 June, 1983, an imaging dual-channel Fabry-Pérot interferometer was used to obtain line profiles simultaneously in the green 5303 Å [Fe xiv] and the red 6374 Å [Fe x] coronal lines at various positions in the corona. Extensive microdensitometry followed by multi-Gaussian curve-fitting analysis has resulted in the determination of coronal temperatures and velocity separations between different pockets of coronal gas in the line of sight over a large extent of the corona. Fewer high temperature zones are to be found in the corona of 1983 compared with our similar green-line measurements of the solar maximum corona of 1980. The data are consistent with a temperature maximum occurring at 1.2 R , as found at the 1980 eclipse, but our new data are insufficient to observe farther out than this radius and so determine the position of a maximum. The velocity field in the corona at the 1983 eclipse is less structured compared with that at the 1980 eclipse and is mainly confined to the zone 20–30km s^–1.     

Using a New Sky Brightness Monitor to Observe the Annular Solar Eclipse on 15 January 2010

For the future development of Chinese Giant Solar Telescope (CGST) in Western China, a new sky brightness monitor (SBM) has been produced for the site survey for CGST. To critically examine the performance and sensitivity of SBM, we used it in the observation of the annular solar eclipse in Dali City, Yunnan, on 15 January 2010. The observation met good weather conditions with an almost clear sky during the eclipse. The SBM measurement translates into the solar illuminance changes at a level of 2.4×10^?4 I?s^?1 during the eclipse. The time of the minimal sky brightness in the field of view (FOV) is found consistent with the time of maximum eclipse. Two local sky regions in the FOV are chosen to make a time series of the calibrated skylight profiles. The evolution of the sky brightness thus calibrated also shows good consistency with the eclipse, particularly between the second and the third contacts. The minimal sky brightness in each local sky region took place within half a minute from the corresponding predicted contact time. Such small time delays were mainly caused by occasional cirri. The minimal sky brightness measured during the eclipse is a few millionths of I _?? with standard deviation of 0.11 millionths of I _??. The observation supports that the single-scattering process (optically thin conditions) is the main contributor to the atmospheric scattering. We have demonstrated that many important aerosol optical parameters can be deduced from our data. We conclude that the new SBM is a sensitive sky photometer that can be used for our CGST and coronagraph site surveys.