Freak waves in white dwarfs and magnetars

We report properties of ion acoustic freak waves that propagate in a plasma composed of warm ions and ultrarelativistic electrons and positrons. The dynamics of the nonlinear freak waves is governed by the nonlinear Schrödinger equation. The possible region for the freak waves to exist is defined precisely for typical parameters of white dwarfs and magnetars corona. It is found that for low wave number, the nonlinear ion-acoustic wave packets are structurally stable in magnetars corona than in white dwarfs. However, for large wave numbers the situation is opposite. The critical wave number threshold (k_c), which indicates where the modulational instability sets in, is defined for both applications. It is seen that near to k_c the freak wave amplitude becomes high, but it decreases whenever we stepped away from k_c. For the wave numbers close to k_c, the increase of the unperturbed density ratio of positrons-to-electrons (β) would lead to increase the freak wave amplitude, but for larger wave numbers the amplitude decreases with the increase of β.