Derivation of the physical parameters of the jet in S5 0836+710 from stability analysis

A number of extragalactic jets show periodic structures at different scales that can be associated with growing instabilities. The wavelengths of the developing instability modes and their ratios depend on the flow parameters, so the study of those structures can shed light on jet physics at the scales involved. In this work, we use the fits to the jet ridgeline obtained from different observations of S5 B0836$+$710 and apply stability analysis of relativistic, sheared flows to derive an estimate of the physical parameters of the jet. Based on the assumption that the observed structures are generated by growing Kelvin-Helmholtz (KH) instability modes, we have run numerical calculations of stability of a relativistic, sheared jet over a range of different jet parameters. We have spanned several orders of magnitude in jet-to-ambient medium density ratio, and jet internal energy, and checked different values of the Lorentz factor and shear layer width. This represents an independent method to obtain estimates of the physical parameters of a jet. By comparing the fastest growing wavelengths of each relevant mode given by the calculations with the observed wavelengths reported in the literature, we have derived independent estimates of the jet Lorentz factor, specific internal energy, jet-to-ambient medium density ratio and Mach number. We obtain a jet Lorentz factor $\gamma \simeq 12$, specific internal energy of $\varepsilon \simeq 10^{-2}\,c^2$, jet-to-ambient medium density ratio of $\eta\approx 10^{-3}$, and an internal (classical) jet Mach number of $M_\mathrm{j}\approx 12$. We also find that the wavelength ratios are better recovered by a transversal structure with a width of $\simeq 10\,\%$ of the jet radius. This method represents a powerful tool to derive the jet parameters in all jets showing helical patterns with different wavelengths.