In this paper we make a phase dependent study of the effect of the distortion of local magnetic field due to confinement of accreted matter in X-ray pulsars on the cyclotron spectra emitted from the hotspot . We have numerically solved the Grad-Shafranov equation for axisymmetric static MHD equilibria of matter confined at the polar cap of neutron stars. From our solution we model the cyclotron spectra that will be emitted from the region, using a simple prescription and integrating over the entire mound. Radiative transfer through the accretion column overlying the mound may significantly modify the spectra in comparison to those presented here. However we ignore this in the present paper in order to expose the effects directly attributable to the mound itself. We perform a spin phase dependent analysis of the spectra to study the effect of the viewing geometry.
Neutron stars in high mass X-ray binaries have high magnetic fields (∼ 10 12 G) and accrete matter from their companion stars either via stellar winds or by disc accretion. Magnetospheric interaction with the accretion flow causes the matter to be channelled to the magnetic poles, forming accretion columns (see e.g. Ghosh et al. (1977), Ghosh & Lamb (1978), Koldoba et al. (2002) and Romanova et al. (2003)). The infalling plasma, with initial relativistic infall velocities, passes through an accretion shock at a height of a few kilometres from the neutron star surface and then settles down to a gradually slowing subsonic flow (Brown & Bildsten 1998;Cumming et al. 2001).
Such X-ray binary systems show characteristic cyclotron resonance scattering features (CRSF) in their spectra resulting from resonant scattering of radiation by electrons in the presence of strong magnetic field (for discussion on theory and observation of cyclotron scattering features see e.g. Harding & Preece (1987), Araya & Harding (1999), Araya-Góchez & Harding (2000), Schönherr et al. (2007) and Mihara et al. (2007)). In the immediate post shock region the flow velocities are still relativistic (∼ 0.16c for γ = 5/3 gas) and the plasma is optically thin to cyclotron scattering. As the accreted plasma descends and cools, it forms at the base a static mound confined by the magnetic field, and becomes optically thick to cyclotron scattering. Any distortion of the magnetic field in the mound due to pressure from the confined plasma will be reflected in the spectra emitted from the boundary of this region.
The nature and variation of the cyclotron spectra can give important clues regarding the properties of the emission region. Many systems show variations of line energies of the CRSF with the phase of rotation e.g. Vela X-1, Her X-1, 4U 0115+63,GX 301-2 etc. This can be due to the variation of the local magnetic field structure at one or both poles as a line of sight moves across the neutron star. Apart from the spin phase dependence, the cyclotron spectra are also seen to depend on the luminosity state of the system. Some systems like V0332+53 (Tsygankov et al. 2010) show a negative correlation between luminosity and cyclotron line energy while some like Her X-1 (Staubert et al. 2007) show a positive correlation. Such dependence of the line energy with change in accretion rate suggests change of local geometry or magnetic field structure. Some sources (e.g. 4U 1538-52, A 0535+26, V 0332+53 etc) show multiple absorption features with anharmonic separation which can be due to distortion of local field from dipolar magnetic field (Nishimura 2005(Nishimura , 2011)).
In this paper we examine the effect on the cyclotron spectra arising from the distortion of local magnetic field caused by the confined plasma. We consider an accreted mound in static equilibrium confined by the magnetic field at the magnetic pole of a neutron star. We construct the equilibrium solution by solving the Grad-Shafranov equation. We do not consider the effects of continued accretion in this paper. We model the X-ray emitting hotspot as a mound of accreted matter with finite height and no atmosphere. The Grad-Shafranov equation for the accreted matter on the neutron star poles has been previously solved by other authors e.g. Hameury et al. (1983), Brown & Bildsten (1998), Litwin et al. (2001), Melatos & Phinney (2001), Payne & Melatos (2004), Payne & Melatos (2007) and Vigelius & Melatos (2008) whose main aim was to study the extent of deformation and stability of the confined mound and also to deduce the effects of magnetic screening on the dipole moment of a neutron star. In this paper we extend this body of work to predict the cyclotron spectra emanating from such mounds.
We adopt a geometry similar to that used by Hameury et al. (1983), Brown & Bildsten (1998) and Litwin et al. (2001) and a numerical algorithm similar to the one developed by Mouschovias (1974) and Payne & Melatos (2004) (PM04) for solving the Grad-Shafranov equation. However our treatment differs from PM04 in several aspects. We work in an axisymmetric cylindrical coordinate system instead of the spherical coordinate system of PM04. We use a polytropic equation of state for the accreted gas instead of the isothermal equation of state of PM04. Finally, we consider the mound to be strictly confined to the polar cap region, while PM04 allowed a significant amount of mass loading outside the polar cap.
We simulate the cyclotron spectra emitted from the accreted mound and perform a phase resolved analysis of the emission. Our main objective in this paper is to perform a phase dependent study of the effects of accretion induced distortion of the local magnetic field on the emergent spectra. In this work we do not perform a detailed radiative transfer calculation of CRSF. Instead we use a Gaussian profile for the cyclotron feature originating from each point of the emission region, with the central line
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