Work Function of Strongly Magnetized Neutron Star Crustal Matter and the Associated Magneto-Sphere
📝 Abstract
Following an extremely interesting idea \cite{R1}, published long ago, the work function at the outer crust region of a strongly magnetized neutron star is obtained using relativistic version of Thomas-Fermi type model. In the present scenario, the work function becomes anisotropic; the longitudinal part is an increasing function of magnetic field strength, whereas the transverse part diverges. An approximate estimate of the electron density in the magnetosphere due to field emission and photo emission current, from the polar cap region are obtained.
💡 Analysis
Following an extremely interesting idea \cite{R1}, published long ago, the work function at the outer crust region of a strongly magnetized neutron star is obtained using relativistic version of Thomas-Fermi type model. In the present scenario, the work function becomes anisotropic; the longitudinal part is an increasing function of magnetic field strength, whereas the transverse part diverges. An approximate estimate of the electron density in the magnetosphere due to field emission and photo emission current, from the polar cap region are obtained.
📄 Content
arXiv:0912.5446v1 [astro-ph.HE] 30 Dec 2009 Work Function of Strongly Magnetized Neutron Star Crustal Matter and the Associated Magneto-Sphere Arpita Ghosh and Somenath Chakrabarty† Department of Physics, Visva-Bharati, Santiniketan 731 235, West Bengal, India ‡E-mail:somenath.chakrabarty@visva-bharati.ac.in Following an extremely interesting idea [1], published long ago, the work function at the outer crust region of a strongly magnetized neutron star is obtained using relativistic version of Thomas- Fermi type model. In the present scenario, the work function becomes anisotropic; the longitudinal part is an increasing function of magnetic field strength, whereas the transverse part diverges. An approximate estimate of the electron density in the magnetosphere due to field emission and photo emission current, from the polar cap region are obtained. PACS numbers: 97.60.Jd, 97.60.-s, 75.25.+z The study of the formation of plasma in a pulsar magnetosphere is a quite old but still an unresolved astrophysical issue. In the formation of magnetosphere plasma, it is generally assumed that there must be an initial high energy electron flux from the magnetized neutron star. At the poles of a neutron star the emitted charged particles flow only along the magnetic field lines. Further a rotating magnetized neutron star generates extremely high electro- static potential difference near the poles. This potential difference is the driving force and plays the major role in the extraction of electrons as field emission or what is also called cold emission, from the crustal matter of strongly magnetized neutron stars near the poles. The flow of high energy electrons along the direction of magnetic field lines and their penetration through the light cylinder is pictured with the current carrying conductors. Naturally, if the conductor is broken near the pulsar surface the entire potential difference will be developed across a thin gap, called polar gap. This is based on the assumption that above a critical height, from the polar cap, because of high electrical conductivity of the plasma, the electric field E|| (= E0 in this article), parallel with the magnetic field near the poles is quenched. Further, a steady acceleration of electrons originating at the polar region of neutron stars, travelling along the field lines, will produce magnetically convertible curvature γ-rays. If these curvature γ-ray photons have energies > 2mec2, then pairs of e−−e+ will be produced in enormous amount with very high efficiency near the polar gap. These produced e−−e+ pairs form what is known as the magnetospheric plasma [2, 3, 4, 5, 6, 7, 8]. The process of extracting electrons from the outer crust region of strongly magnetized neutron stars, including the most exotic stellar objects, the magnetars, one requires a more or less exact description of the structure of matter in that region [9, 10, 11]. From the knowledge of structural deformation of atoms in strong magnetic field; the departure from spherical nature to a cigar shape, allows us to assume that the atoms in the outer crust region, which are fully ionized because of high density, may be replaced by Wigner-Seitz type cells of approximately cylindrical in structure. We further assume that the electron gas inside the cells are strongly degenerate and are at zero temperature. It is well known that the presence of extraordinarily large magnetic field not only distorts the crystalline structure of dense metallic iron, also significantly modifies the electrical properties of such matter. As for example, the electrical conductivity, which is otherwise isotropic, becomes highly anisotropic in presence of strong quantizing magnetic field. In presence of strong magnetic field iron crystal is highly conducting in the direction parallel to the magnetic field, whereas flow of current in the perpendicular direction is severely inhibited. The aim of this letter is to show that the work function, which is the most important parameter associated with the emission of electrons from the polar region of strongly magnetized neutron stars, will also show anisotropy in presence of strong magnetic field. In this article we have shown that the work function, associated with the emission of electrons along the field lines increases with magnetic field strength. Whereas its transverse component diverges, irrespective of the dimension of the cylindrically deformed atoms. The scenario is very much analogous to the charge transport mechanism in presence of strong magnetic field. To the best of our knowledge, the study of anisotropic nature of work function in presence of strong quantizing magnetic field, which has relevance, specially in the case of magnetized neutron star crustal region has not been studied before. It is also well known that the most important surface emission processes are thermal emission, may be enhanced by Schottky effect, field emission, caused by strong electric field at the poles and perhaps the other important process
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