Z. Naturforsch. 2020; 75(2)a: 103ś111 Nimardeep Kaur, Rupinder Kaur and N. S. Saini* Ion-Acoustic Cnoidal Waves with the Density Efect of Spin-up and Spin-down Degenerate Electrons in a Dense Astrophysical Plasma https://doi.org/10.1515/zna-2019-0140 Received April 26, 2019; accepted November 4, 2019; previously published online December 7, 2019 Abstract: An investigation of nonlinear ion acoustic (IA) cnoidal waves in a magnetised quantum plasma is presented by using spin evolution quantum hydrodynam- ics model, in which inertial classical ions and degenerate inertialess electrons with both spin-up and spin-down states taken as separate species are considered. The Korteweg–de Vries equation is derived using the reductive perturbation method. Further, using the Sagdeev pseu- dopotential approach, the solution for IA cnoidal waves is derived with suitable boundary conditions. There is the formation of only positive potential cnoidal, and in the limiting case, positive solitary waves are observed. The effects of density polarisation and other plasma parame- ters on the characteristic features of cnoidal and solitary waves have been analysed numerically. It is seen that the spin density polarisation significantly affects the charac- teristics of cnoidal structures as we move from strongly spin-polarised (µ = 1) to a zero spin-polarisation case (µ = 0). The results obtained in the present investigation may be useful in comprehending various nonlinear excita- tions in dense astrophysical regions, such as white dwarfs, neutron stars, and so on. Keywords: Cnoidal Waves; Ion Acoustic; Spin-up and Spin-down Degenerate Electrons. 1 Introduction In recent years, dense quantum plasmas have emerged as an active field of research due to their great relevance in different areas of practical importance, e.g. nanoscale *Corresponding author: N. S. Saini, Department of Physics, Guru Nanak Dev University, Amritsar 143005, India, E-mail: nssaini@yahoo.com Nimardeep Kaur and Rupinder Kaur: Department of Physics, Guru Nanak Dev University, Amritsar 143005, India, E-mail: nimarphy@gmail.com (N. Kaur); rupinderkaur.rk568@gmail.com (R. Kaur) electromechanical systems [1, 2], laser interactions with atomic systems [3], and in dense astrophysical systems [4], such as neutron stars, white dwarfs, and so on. Due to the high number density and low particle tempera- ture of particles, quantum plasmas are distinguished sig- nificantly from the classical plasmas, where the density of particles is relatively low and possesses high plasma temperature. To investigate the various astrophysical phe- nomena in interstellar compact objects, dense quantum plasmas would be helpful in establishing a suitable frame. The density of the interiors of the interstellar objects is sig- nificantly high such that the nonthermal pressure is pro- vided by the degenerate fermion/electron pressure, as well as interaction of particles. Mathematically, Chandrashekhar [5–7] deduced the equation of state in such compact interstellar objects for the degenerate electrons with P e ∼ n 5 3 e for the nonrela- tivistic case and P e ∼ n 4 3 e for the ultrarelativistic case, where P e and n e are the pressure and number density of degenerate electrons. In highly compressed plasma species, the uncertainty in momenta is infinitely large, which implies that the degenerate plasma species must move very fast (despite that they are extremely cold), giving rise to a very high pressure, called as “degener- ate pressure.” The degenerate pressure depends only on the number density of electrons and not on their temper- ature. In the quantum hydrodynamic (QHD) model, which is considered as the quantum counterpart of the classical fluid model [8], the inclusion of the Fermi pressure and the Bohm potential term modifies the momentum equa- tion of the charged particles [9]. The quantum ion acoustic (IA) waves and the role of quantum diffraction effects have been studied by Haas et al. [10] using the QHD model. It has also been found that the system supports the travel- ling waves with periodic patterns in the fully nonlinear regime. Haas [11] devised an ideal quantum magnetohy- drodynamic (QMHD) model with the incorporation of the quantum diffraction effects with relevance to the dense astrophysical objects such as interiors of white dwarfs. Using the QHD and QMHD models, various nonlinear elec- trostatic and electromagnetic waves have been studied in quantum plasmas.