a b s t r a c tThe effect of strong quantizing magnetic field on the equation of state of matter at the outer crust region of magnetars is studied. The density of such matter is low enough compared to the matter density at the inner crust or outer core region. Based on the relativistic version of semi-classical Thomas-Fermi-Dirac model in presence of strong quantizing magnetic field a formalism is developed to investigate this specific problem. The equation of state of such low density crustal matter is obtained by replacing the compressed atoms/ions by Wigner-Seitz cells with nonuniform electron density. The results are compared with other possible scenarios. The appearance of Thomas-Fermi induced electric charge within each Wigner-Seitz cell is also discussed.

We have investigated some of the properties of dense sub-nuclear matter at the crustal region (both the outer crust and the inner crust region) of a magnetar. The relativistic version of ThomasFermi (TF) model is used in presence of strong quantizing magnetic field for the outer crust matter.The compressed matter in the outer crust, which is a crystal of metallic iron, is replaced by a regular array of spherically symmetric Wigner-Seitz (WS) cells. In the inner crust region, a mixture of iron and heavier neutron rich nuclei along with electrons and free neutrons has been considered.

The effect of strong quantizing magnetic field on low density stellar matter is investigated using Thomas-Fermi-Dirac (TFD) model. The Wigner-Seitz cell structure is assumed for the low density matter. The significant changes in the properties of such low density matter in presence of strong magnetic fields are discussed. It is seen that the decay time scale for magnetic field decreases by at least two orders of magnitude in such a model calculation.PACS numbers: 12.38. Mh, 12.15.Ji, 95.30.Cq, 97.60.Jd

Following some of the recent articles on hole super-conductivity and related phenomena by Hirsch (Phys. Lett. A 134:451, 1989; Phys. Rev. B 68:184502, 2003a; Phys. Rev. B 71:184521, 2005a and Phys. Lett. A 345:453, 2005b) a simple model is proposed to explain the observed low surface magnetic field of the expected quark stars. It is argued that the diamagnetic moments of the electrons circulating in the electro-sphere induce a magnetic field, which forces the existing quark star magnetic flux density to become dilute. For the sake of completeness, we have also included the analyses of instability at the normal-superconducting interface due to excess accumulation of magnetic flux lines. The instability at the interface has also been studied numerically.

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