Magnetoacoustic solitons and shocks in dense astrophysical plasmas with relativistic degenerate electrons

Abstract

Two-fluid quantum magnetohydrodynamic (QMHD) equations are employed to investigate linear and nonlinear properties of the magnetosonic waves in a semi-relativistic dense plasma accounting for degenerate relativistic electrons. In the linear analysis, a plane wave solution is used to derive the dispersion relation of magnetosonic waves, which is significantly modified due to relativistic degenerate electrons. However, for a nonlinear investigation of solitary and shock waves, we employ the reductive perturbation technique for the derivation of Korteweg–de Vries (KdV) and Korteweg–de Vries Burger (KdVB) equations, admitting nonlinear wave solutions. Numerically, it is shown that the wave frequency decreases to attain a lowest possible value at a certain critical number density $N_{c}^{(0)}$, and then increases beyond $N_{c}^{(0)}$ as the plasma number density increases. Moreover, the relativistic electrons and associated pressure degeneracy lead to a reduction in the spatial extents of the magnetosonic waves and a strengthening of the shock amplitude. The results might be important for understanding the linear and nonlinear magnetosonic excitations in dense astrophysical plasmas, such as in white dwarfs, magnetars and neutron stars, etc., where relativistic degenerate electrons are present.

Characteristics of solitary waves in a relativistic degenerate ion beam driven magneto plasma

“…On the other hand, Irfan et al studied the nonlinear Magneto-acoustic solitary and shock waves with relativistic degenerate electrons and found that for a certain density of the relativistic electrons the wave frequency reaches the lowest possible value and then increases. Moreover a spatial reduction thereby strengthening the wave amplitude was also reported by them [44]. …”

“…On the other hand, Irfan et al studied the nonlinear Magneto-acoustic solitary and shock waves with relativistic degenerate electrons and found that for a certain density of the relativistic electrons the wave frequency reaches the lowest possible value and then increases. Moreover a spatial reduction thereby strengthening the wave amplitude was also reported by them [44]. Mc Kerr et al investigated the conditions for occurrence as well as structural features of large amplitude nonlinear structures considering relativistically degenerate electrons and relativistically non-degenerate ions in astrophysical plasma environment and found that the amplitude of solitary pulses increases both with increased Mach number and also by moving the system towards more relativistic by increasing the density [45].…”

Modelling of relativistic ion-acoustic waves in ultra-degenerate plasmas

“…Recently, there has been a lot of interest on relativistic waves in degenerate plasmas, described by hydrodynamic equations (Haas & Kourakis 2010; Esfandyari-Kalejahi, Akbari-Moghanjoughi & Saberian 2011; Masood & Eliasson 2011; Ali & Ur Rahman 2014; Hussain, Mahmood & Ur Rehman 2014; McKerr, Haas & Kourakis 2014, 2016; Rahman, Kourakis & Qamar 2015; Irfan, Ali & Mizra 2016). The examination of the literature shows sometimes the use of questionable options, namely: choosing to work with the proper number density (which is the number density in a local reference frame where the fluid is at rest) in the equation of state, while using the laboratory number density in the continuity equation, with the same symbol for both objects; the use of relativistic equations of state inside otherwise non-relativistic fluid equations; the use of non-relativistic equations of state inside otherwise relativistic fluid equations; covariant or non-covariant form of the pressure term, including or not the respective time derivative; taking into account or not, the relativistic mass increase due to thermal effects.…”

Negative energy dust acoustic waves evolution in a dense magnetized quantum Thomas–Fermi plasma

“…Also, the magnetic field increase leads to an increase in the force and in situ increase in the amplitude as depicted in the same figures. This results from the fact that the waves propagate across the magnetic field, where the compression of magnetic field lines provides the acoustic restoring force for the wave propagation 37 .

Figure 3 The evolution of the potential of the DA waves that represented by Eq.

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