We study the temporal and energy spectral characteristics of the persistent black hole X-ray binary LMC X-1 using two XMM-Newton and a Suzaku observation. We report the discovery of low frequency (~ 26-29 mHz) quasi-periodic oscillations (QPOs). We a
lso report the variablity of the broad iron K-alpha line studied earlier with Suzaku. The QPOs are found to be weak with fractional rms amplitude in the ~ 1-2 % range and quality factor Q~2-10 . They are accompanied by weak red noise or zero-centered Lorentzian components with rms variability at the ~ 1-3 % level. The energy spectra consists of three varying components - multicolour disk blackbody (kT_{in} ~ 0.7-0.9 keV), high energy power-law tail (Gamma ~ 2.4 - 3.3) and a broad iron line at 6.4-6.9 keV. The broad iron line, the QPO and the strong power-law component are not always present. The QPOs and the broad iron line appear to be clearly detected in the presence of a strong power-law component. The broad iron line is found to be weaker when the disk is likely truncated and absent when the power-law component almost vanished. These results suggest that the QPO and the broad iron line together can be used to probe the dynamics of the accretion disk and the corona.
We study the validity of cosmic distance duality relation between angular diameter and luminosity distances. To test this duality relation we use the latest Union2 Supernovae Type Ia (SNe Ia) data for estimating the luminosity distance. The estimatio
n of angular diameter distance comes from the samples of galaxy clusters (real and mock) and FRIIb radio galaxies. We parameterize the distance duality relation as a function of redshift in four different ways and we find that the mock data set, which assumes a spherical isothermal $beta$ model for the galaxy clusters does not accommodate the distance duality relation while the real data set which assumes elliptical $beta$ model does.
