We consider a relativistic, degenerate electron gas at zero-temperature under the influence of a strong, uniform, static magnetic field, neglecting any form of interactions. Since the density of states for the electrons changes due to the presence of the magnetic field (which gives rise to Landau quantization), the corresponding equation of state also gets modified. In order to investigate the effect of very strong magnetic field, we focus only on systems in which a maximum of either one, two or three Landau level(s) is/are occupied. This is important since, if a very large number of Landau levels are filled, it implies a very low magnetic field strength which yields back Chandrasekhar's celebrated non-magnetic results. The maximum number of occupied Landau levels is fixed by the correct choice of two parameters, namely the magnetic field strength and the maximum Fermi energy of the system. We study the equations of state of these one-level, two-level and three-level systems and compare them by taking three different maximum Fermi energies. We also find the effect of the strong magnetic field on the mass-radius relation of the underlying star composed of the gas stated above. We obtain an exciting result that, it is possible to have an electron degenerate static star, namely magnetized white dwarfs, with a mass significantly greater than the Chandrasekhar limit in the range 2.3 − 2.6M ⊙ , provided it has an appropriate magnetic field strength and central density.

Type Ia supernovae, sparked off by exploding white dwarfs of mass close to Chandrasekhar limit, play the key role to understand the expansion rate of universe. However, recent observations of several peculiar type Ia supernovae argue for its progenitor mass to be significantly super-Chandrasekhar. We show that strongly magnetized white dwarfs not only can violate the Chandrasekhar mass limit significantly, but exhibit a different mass limit. We establish from foundational level that the generic mass limit of white dwarfs is 2.58 solar mass. This explains the origin of over-luminous peculiar type Ia supernovae. Our finding further argues for a possible second standard candle, which has many far reaching implications, including a possible reconsideration of the expansion history of the universe.

Cold accretion disks with temperatures below ∼ 3000K are likely to be composed of highly neutral gas. The magnetorotational instability may cease to operate in such disks, so it is of interest to consider purely hydrodynamic mechanisms of generating turbulence and angular momentum transport. With this motivation, we investigate the growth of hydrodynamic perturbations in a linear shear flow sandwiched between two parallel walls. The unperturbed flow is similar to plane Couette flow but with a Coriolis force included. Although there are no exponentially growing eigenmodes in this system, nevertheless, because of the non-normal nature of the eigenmodes, it is possible to have a large transient growth in the energy of perturbations. For a constant angular momentum disk, we find that the perturbation with maximum growth is axisymmetric with vertical structure. The energy grows by more than a factor of 100 for a Reynolds number R = 300 and more than a factor of 1000 for R = 1000. Turbulence can be easily excited in such a disk, as found in previous numerical simulations. For a Keplerian disk, on the other hand, similar perturbations with vertical structure grow by no more than a factor of 4, explaining why the same simulations did not find turbulence in this system. However, certain other two-dimensional perturbations with no vertical structure do exhibit modest growth. For the optimum two-dimensional perturbation, the energy grows by a factor of ∼ 100 for R ∼ 10 4.5 and by a factor of 1000 for R ∼ 10 6 . Such large Reynolds numbers are hard to achieve in numerical simulations and so the nonlinear development of these kinds of perturbations are only beginning to be investigated. It is conceivable that these nearly two-dimensional disturbances might lead to self-sustained three-dimensional turbulence, though this remains 1 bmukhopa@cfa.harvard.edu 2 nafshord@cfa.harvard.edu 3 rnarayan@cfa.harvard.edu -2to be demonstrated. The Reynolds numbers of cold astrophysical disks are much larger even than 10 6 ; therefore, hydrodynamic turbulence may be possible in disks through transient growth.

We present a pseudo-Newtonian potential for accretion disk modeling around the rotating black holes. This potential can describe the general relativistic effects on accretion disk. As the inclusion of rotation in a proper way is very important at an inner edge of disk the potential is derived from the Kerr metric. This potential can reproduce all the essential properties of general relativity within 10% error even for rapidly rotating black holes.

Despite observational evidence for cold neutral astrophysical accretion disks, the viscous process which may drive the accretion in such systems is not yet understood. While molecular viscosity is too small to explain the observed accretion efficiencies by more than ten orders of magnitude, the absence of any linear instability in Keplerian accretion flows is often used to rule out the possibility of turbulent viscosity. Recently, the fact that some fine tuned disturbances of any inviscid shear flow can reach arbitrarily large transient growth has been proposed as an alternative route to turbulence in these systems. We present an analytic study of this process for 3D plane wave disturbances of a general rotating shear flow in Lagrangian coordinates, and demonstrate that large transient growth is the generic feature of non-axisymmetric disturbances with near radial leading wave vectors. The maximum energy growth is slower than quadratic, but faster than linear in time. The fastest growth occurs for two dimensional perturbations, and is only limited by viscosity, and ultimately by the disk vertical thickness.After including viscosity and vertical structure, we find that, as a function of the Reynolds number, R, the maximum energy growth is approximately 0.4(R/ log R) 2/3 , and put forth a heuristic argument for why R 10 4 is required to sustain turbulence in Keplerian disks. Therefore, assuming that there exists a non-linear feedback process to replenish the seeds for transient growth, astrophysical accretion disks must be well within the turbulent regime. However, large 3D numerical simulations running for many orbital times, and/or with fine tuned initial conditions, are required to confirm Keplerian hydrodynamic turbulence on the computer.