Pulsar radio emission mechanism II. On the origin of relativistic Langmuir solitons in pulsar plasma

Observations suggest that coherent radio emission from pulsars is excited in a dense pulsar plasma by curvature radiation from charge bunches. Numerous studies propose that these charge bunches are relativistic charge solitons which are solutions of the non-linear Schr\"{o}dinger equation (NLSE) with a group velocity dispersion ($G$), cubic-nonlinearity($q$) and non-linear Landau damping ($s$). The formation of stable solitons crucially depends on the parameters $G, q$ and $s$ and the particle distribution function. In this work, we use realistic pulsar plasma parameters obtained from observational constraints to explore the parameter space of NLSE for two representative distribution functions (DF) of particles' momenta: Lorentzian (long-tailed) and Gaussian (short-tailed). The choice of DF critically affects the value of $|s/q|$, which, in turn, determines whether solitons can form. Numerical simulations show that well-formed solitons are obtained only for small values of $|s/q| \lesssim 0.1$ while for moderate and higher values of $|s/q| \gtrsim 0.5$ soliton formation is suppressed. Small values for $|s/q| \sim 0.1$ are readily obtained for long-tailed DF for a wide range of plasma temperatures. On the other hand, short-tailed DF provides these values only for some narrow range of plasma parameters. Thus, the presence of a prominent high-energy tail in the particle DF favours soliton formation for a wide range of plasma parameters. Besides pair plasma, we also include an iron ion component and find that they make a negligible contribution in either modifying the NLSE coefficients or contributing to charge separation.