Scientific background : Variable stars, binary stars and their evolution, supernovae, pulsars and associated phenomena (even include testing theories of gravity using pulsars), accretion and associated phenomena (like x-ray bursts), gamma-ray bursts, rotating radio transients (RRATS), jets & outflows (micro-quasars etc), AGNs-blazars-QSOs.

Atomic structure: review of Schrodinger equation – overview of single and multiple electron systems – perturbations and level splittings – parity – spin orbit coupling – Zeeman effect – hyperfine structure – Boltzmann population of energy levels in thermal equilibrium – Saha equation. Radiative transitions: semi-classical theory – dipole approximation – Einstein coefficients and oscillator strengths – selection rules and transition rates.

Unpolarised light, Linear, Circular, Elliptical polarised light, Partially and fully polarised light, Stokes parameters, Dichroism, Birefringence, Poincare sphere – Mueller and Jones representations with applications – Complex plane of polarisation states. Generation of polarised light in astronomy – polarisation by reflection, scattering geometry, magnetic fields - dependence on refractive index – synchrotron emission – Faraday rotation – Dust in ISM. Instrumental polarisation errors and their calibration.

Basic cosmology – Expansion of the universe – scale factor – cosmological redshift – descriptive overview of inflation, unification of forces and fundamental particles. Primordial nucleosynthesis – elemental abundances: predictions and observations. Cosmic Microwave Background – detection, power spectrum, origin of CMB, anisotropies in the CMB and their origin – overview of COBE and WMAP probes – mission and instrumentation.

Introduction: Accretion as a source of energy – observational consequences. Accretion in binary system: Introduction – Interacting binary system – Roche lobe overflow – Disk formation – Viscous torque – The α disk viscosity – Low and high-mass X-ray binaries. Accretion disk (thin accretion disk) Theory: Basic concepts – Structure of thin disk – The emitted spectrum of steady α-disk – Time dependence and stability – the thermal disk instability model (dwarf novae) – wind accretion – Disk around young stars – confrontation with observations.

Introduction: How radiation affects the flow of matter – Cooling, Heating, Momentum transfer, Matter density variation due to annihilation/pair-production. Review of gas dynamics: Ideal fluids, Transport terms – Viscosity & heat conduction, Sound waves, Shocks – Rankine-Hugoniot relations. Review of radiation physics: Intensity, Flux, Energy density, Stress tensor, Transport equations, Diffusion approximation, Coupling terms in Euler's equations.

Imaging and detector basics – resolution, sensitivity, noise, dynamic range, efficiency, linearity – image formation at focal plane – Fourier transform – Deconvolution and Image reconstruction – Photography CCD -- Large optical/IR telescopes and their designs – thin lens – segmented mirrors – Active optics – Designs of few upcoming large telescopes (eg.

The interstellar medium and its phases – dust – molecular clouds – virial theorem analysis. Star clusters – OB associations – T and R associations – initial mass function. Heating and cooling of clouds – cloud thermal structure – build up of molecules – molecular transitions of H 2 , CO. Cloud equilibrium and stability – Jeans mass – isothermal spheres – basic magnetohydrodynamics – magnetic support – ambipolar diffusion – inside-out collapse – rotational effects.

Elements of probability theory – random variables – Gaussian distribution – stochastic processes – characterizations and properties – Gauss-Markov processes – Brownian motion process – Gauss-Markov models – Optimal estimation for discrete-time systems – fundamental theorem of estimation – optimal prediction. Optimal filtering – Weiner approach – continuous time Kalman Filter – properties and implementation – steady-state Kalman Filter – discrete-time Kalman Filter – implementation – sub-optimal steady-state Kalman Filter – Extended Kalman Filter – practical applications.

Radiation-matter interaction – Sources of high energy (UV-gamma rays) radiation in the universe – Detectors for high energy particles, X-rays, gamma rays and neutrinos – Space astronomy – Elements of General Relativity – compact stars – magnetospheric processes around neutron stars (pulsars and magnetars) – interacting binaries – Roche potential and accretion – Shkura-Sunyaev thin disk model – accretion phenomenology around compact objects – stellar mass black holes vs supermassive black holes – AGN phenomenology and unified scheme – Jet production and superluminal motion – Supernova remnan

Occurrence and state of cosmic diffuse matter – ionized, atomic, molecular gas and dust – heating and cooling, equilibrium phases – probes of diffuse matter (line and continuum radiations at various wavelengths) – Thermal and ionization equilibrium of HII regions – UV shielding in molecular gas – extinction/reddening/polarization due to dust – dust heating and IR emission – star forming regions - cosmic rays and non-thermal synchrotron emission – recombination and re-ionization of IGM – Lyman alpha forest, Mg absorption systems – Gunn Peterson effect – Heating of intracluster gas – Sunyaev-

Conservation laws – Euler’s Equations – Common Equations of State – Hydrostatic Equiibrium – Isothermal sphere – Virial Theorem – linear perturbation theory – acoustic waves – Jeans’ instability – Rayleigh Taylor instability – de Laval nozzle – Parker wind solution – Bondi accretion – Shock waves – Sedov solution – elements of plasma physics – Debye screening – orbit theory – elements of MHD – flux freezing – Alfven waves – Langmuir oscillations – dispersion relation of electromagnetic waves propagating in plasmas – plasma instabilities – transport phenomena.