Effect of a magnetic field on the strange star.

We study the effect of a magnetic field on the strage quark matter and apply to strange star. We found that the strange star becomes more compact in presence of strong magnetic field. PACS NO.: 04.40.-b, 97.60.Jd, 97.60.Gb, 98.35Eg Typeset using REVTEX 1 There are several different scenarios for estimation of the magnetic field strength at the surface of neutron star. These are: theoretical models of pulsar emission [1] the accretion flow in the binary X-ray sources [2] and observation of features in the spectra of pulsating X-ray sources which have been interpreted as cyclotron lines [3]. In a sample of more than 300 pulsars the range of values of the surface magnetic field strength runs into the interval 10.36 ≤ log(B) (G) ≤ 13.33 [4]. Very recently, several authors [5] have proposed two different physical mechanism leading to an amplification of some initial magnetic field in a collapsing star. Fields as strong as B ∼ 10 ∼ 10G , or even more, might be generated in new born neutron stars. In the interior of neutron star, it probably reaches ∼ 10G. Therefore, it is advisable to study the effect of strong magnetic field on compact neutron stars. There are strong reason for believing that the hadrons are composed of quarks , and the idea of quark stars has already been existed for about twenty years. If the neutron matter density at the core of neutron stars exceeds a few times normal nuclear density ( 3n0, n0 = 0.15 fm ) a deconfining phase transition to quark matter may take place. As a consequence, a normal neutron star will be converted to a hybrid star with an infinite cluster of quark matter core and a crust of neutron matter. In 1984, Witten suggested that strange matter, e.g., quark matter with strangeness per baryon of order unity, may be the true ground state [6]. The properties of strange matter at zero pressure and zero temperature were subsequently examined, and it was found that strange matter can indeed be stable for a wide range of parameters in the strong interaction calculations [7]. Therefore, at the core, the strange quarks will be produced through the weak decays of light quarks (u and d quarks) and ultimately a chemical equilibrium will be established among the participants. Since, the strange matter is energitically favourable over neutron matter, there is a possibility that whole star may be converted to a strange star. For a constant magnetic field along the z-axis ( ~ A = 0, ~ H = H(z) = H = constant), the single energy eigenvalue is given by [8]