Determination of Orbital Parameters of Kepler Binary Stars Using Time-delay Method on 1646 Pulsatina δScuti Stars

Abstract

A binary system is a pair of stars that are held together in closed orbits around their common centre of gravity, under the influence of their mutual gravitation. The night sky presents a variety of double stars, ranging from wide, optical pairs to close binary systems. Close binary stars are magnificent laboratories in astrophysics. They affect each other's structure and evolution. Multiplicity is one fundamental property of stars. Binary systems are as common as single stars in the universe and about half of the stars in our galaxy are members of so-called binary star systems. Similar independent proportions of triple, quadruple and quintuple systems have been reported in the literature. The study of binary stars is fundamental to our understanding of stellar structure and evolution and also allows physical stellar parameters to be determined. Multiple systems are of particular interest. For example, in triple systems, masses and orbital parameters of the constituent stars can tell about the unclear process of the formation of systems of multiple stars. The orbital parameter of a triple star system can also inform about the final contraction of the interstellar cloud that formed the system, given that the dynamical evolution of the system leaves the initial configuration relatively unchanged. The main purpose of this thesis is to use the high quality data observed by the Kepler space telescope to identify binary stars from the samples that have 5 Set pulsation and to determine their orbital parameters (projected semi-major axis, a sin i, eccentricity, e, angle of periastron, w, time of periastron passage, T per, orbital period, P, and the two ancillary parameters:- semi-amplitude of radial velocity curve, K, and mass function, f(m)). The parameters of binary systems are generally obtained from astrometric, spectroscopic or photometric observations, and in favourable cases by a combination of two or even all three, of these methods. Time-delay is a periodic arrival time of light from a binary system caused by the

periodic distance variation while the star orbits around its binary companion. The time-delay method allows the determination of orbital parameters directly with high precision which avoids the need for spectroscopy. In this thesis we used the time-delay method and we attempted to achieve the following objectives. The first objective was to identify the most important pulsation frequencies. Possible binary stars and their orbital periods were then identified. To achieve this, we searched for peaks in the 'binarogram' , which is a plot of the time-delay as a function of orbital frequency. Once a star has been identified as a possible binary from the binarogram, we inspected a graph of time-delay as a function of time, as given by the 10 pulsation frequencies of highest amplitude. Since the presence of close pulsation frequencies distorts the time-delay, only a few of these will produce meaningful time-delay variations. The best time-delay curves were selected and fitted with a truncated Fourier series and distortions removed using a low-degree polynomial. These were averaged to produce the final time-delay variation. A code was developed to determine the best orbital parameters using non-linear least squares. The data for this analysis was downloaded from the Mikulski Archive for Space Telescopes (MAST) in FITS format. Data from the full 4-yr Kepler mission were used. These data were examined and 1646 candidate o Set stars were identified. These stars were observed in long-cadence mode which nominally allows only variations with frequencies less than about 24 cycles per day to be distinguished. Many o Set stars have pulsations of higher frequency. Fortunately, the slightly non-uniform time sampling allows pulsation frequencies higher than this nominal Nyquist limit to be determined with some confidence, provided their amplitudes are sufficiently high. Of the 1646 o Set stars examined, we detected 131 binary stars and 9 stars which appear to be triple or multiple systems.