The combined observations of a planet’s transits and the radial velocity variations of its host star allow the determination of the planet’s orbital parameters, and most inter- estingly of its radius and mass, and hence its mean density. Observed densities provide important constraints to planet structure and evolution models. The uncertainties on the parameters of large exoplanets mainly arise from those on stellar masses and radii. For small exoplanets, the treatment of stellar variability limits the accuracy on the de- rived parameters. The goal of this PhD thesis was to reduce these sources of uncertainty by developing new techniques for stellar variability filtering and for the determination of stellar temperatures, and by robustly fitting the transits taking into account external constraints on the planet’s host star. To this end, I developed the Iterative Reconstruction Filter (IRF), a new post-detection stellar variability filter. By exploiting the prior knowledge of the planet’s orbital period, it simultaneously estimates the transit signal and the stellar variability signal, using a com- bination of moving average and median filters. The IRF was tested on simulated CoRoT light curves, where it significantly improved the estimate of the transit signal, particu- lary in the case of light curves with strong stellar variability. It was then applied to the light curves of the first seven planets discovered by CoRoT, a space mission designed to search for planetary transits, to obtain refined estimates of their parameters. As the IRF preserves all signal at the planet’s orbital period, t can also be used to search for secondary eclipses and orbital phase variations for the most promising cases. This en- abled the detection of the secondary eclipses of CoRoT-1b and CoRoT-2b in the white (300–1000 nm) CoRoT bandpass, as well as a marginal detection of CoRoT-1b’s orbital phase variations. The wide optical bandpass of CoRoT limits the distinction between thermal emission and reflected light contributions to the secondary eclipse. I developed a method to derive precise stellar relative temperatures using equiv- alent width ratios and applied it to the host stars of the first eight CoRoT planets. For stars with temperature within the calibrated range, the derived temperatures are con- sistent with the literature, but have smaller formal uncertainties. I then used a Markov Chain Monte Carlo technique to explore the correlations between planet parameters derived from transits, and the impact of external constraints (e.g. the spectroscopically derived stellar temperature, which is linked to the stellar density). Globally, this PhD thesis highlights, and in part addresses, the complexity of perform- ing detailed characterisation of transit light curves. Many low amplitude effects must be taken into account: residual stellar activity and systematics, stellar limb darkening, and the interplay of all available constraints on transit fitting. Several promising areas for further improvements and applications were identified. Current and future high precision photometry missions will discover increasing numbers of small planets around relatively active stars, and the IRF is expected to be useful in characterising them.

More than half a decade of X-ray astronomy with various balloon borne and space orbiting X-ray instruments, have led to discoveries and detailed studies of X-ray binaries. An important property of X-ray binaries is intensity variations of different magnitudes in a wide range of timescales from milliseconds (quasi-periodic oscillations, millisecond pulsations), to a few weeks (orbital and super-orbital modulations) or longer (outbursts etc). In this thesis, different types of variabilities of X-ray binaries are considered in X-ray binary population studies and to investigate certain aspects of some individual systems. In Chapter 1, we provide an introduction to various types of variabilities seen in different classes of X-ray binaries. We mention in detail the various periodic and aperiodic variabilities seen in X-ray binaries. In Chapter 2, we describe, in some detail, the various X-ray all sky monitors and X-ray observatories, data from which has been utilized in the work carried out in this thesis. We also describe the various data analysis techniques that we have used. The rest of the thesis is divided into two major sections: Variability studies of indi-vidual systems and X-ray binary population studies Variability studies of individual systems In Chapter 3, we report results from an investigation of energy resolved orbital in-tensity pro les and from exhaustive orbital phase resolved spectroscopic measurements of GX 301{2 with MAXI{GSC . The orbital variation of the spectral parameters, es-pecially the relation between the equivalent width of Fe line and the column density of absorbing matter are then utilized to examine the models for the mode of accretion onto the neutron star in GX 301{2: circumstellar disk model by Pravdo & Ghosh (2001), and the accretion stream model by Leahy & Kostka (2008). A very large equivalent width of the iron line along with a small value of the column density in the orbital phase range 0.10-0.30 after the periastron passage indicates an asymmetry in the distribution of the matter around the neutron star, strongly favoring the accretion stream model by Leahy & Kostka (2008). Presence of an eclipse in an X-ray binary can be useful in determining orbital param-eters like inclination and in estimating the orbital evolution by eclipse timing method, which is reported in Chapter 4. For the HMXB system IGR J16393{4643, we found a short eclipse in the Swift{BAT light-curve and utilized it to constrain the orbital in-clination of the system. We have also studied, for the rst time, broad-band pulsation and spectral characteristic of the system with a Suzaku observation, showing sub-orbital intensity variations. For another eclipsing and non-pulsing HMXB 4U 1700{37, the orbital evolution is studied using mid-eclipse times from observations with narrow eld instruments as well as from long term light-curves of X-ray all sky monitors. The orbital period decay rate is estimated to be 5 10 7 /yr, an order slower than a previous measurement by Rubin et al.(1996). Since no pulsations are detected in this system, it is difficult to estimate its orbital parameters, especially its eccentricity. Using mid-eclipse times from 10 years of Swift{BAT data, we have independently constrained the eccentricity of the binary system. X-ray binary population studies In Chapter 5, we report results from an analysis of the 16 years light-curves of X-ray binaries in 2-10 keV energy band of RXTE{ASM , used to construct the differential and integral probability distributions of count-rates. These distributions are then employed to construct multiple snapshots of X-ray binary luminosity functions of the Milky Way instead of averaging the luminosities, an improvement over previous analysis by Grimm et al. (2002). We found that the averaged luminosities of highly variable X-ray binaries do not represent their true positions in XLFs and the variability of X-ray binaries do indeed signi cantly affect the luminosity functions. In Chapter 6, the measurements of the averaged spectra of X-ray binaries using MAXI{GSC data are reported and are used for constructing the composite X-ray spec-trum. These composite X-ray binary spectra are useful in estimating the contribution of X-ray binaries in extra-galactic SEDs constructed from the simultaneous Chandra / XMM{Newton and NuSTAR observations of these galaxies. These SEDs will also serve as a useful input in estimating the contribution of X-ray binary heating at high redshift IGM during the Epoch of Re-ionization. In Chapter 7, we summarize the main conclusions of the work carried out in this thesis and discuss some future prospects related to this thesis.