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A number of extragalactic jets show periodic structures at different scalesthat can be associated with growing instabilities. The wavelengths of thedeveloping instability modes and their ratios depend on the flow parameters, sothe study of those structures can shed light on jet physics at the scalesinvolved. In this work, we use the fits to the jet ridgeline obtained fromdifferent observations of S5 B0836$+$710 and apply stability analysis ofrelativistic, sheared flows to derive an estimate of the physical parameters ofthe jet. Based on the assumption that the observed structures are generated bygrowing Kelvin-Helmholtz (KH) instability modes, we have run numericalcalculations of stability of a relativistic, sheared jet over a range ofdifferent jet parameters. We have spanned several orders of magnitude injet-to-ambient medium density ratio, and jet internal energy, and checkeddifferent values of the Lorentz factor and shear layer width. This representsan independent method to obtain estimates of the physical parameters of a jet.By comparing the fastest growing wavelengths of each relevant mode given by thecalculations with the observed wavelengths reported in the literature, we havederived independent estimates of the jet Lorentz factor, specific internalenergy, jet-to-ambient medium density ratio and Mach number. We obtain a jetLorentz factor $\gamma \simeq 12$, specific internal energy of $\varepsilon\simeq 10^{-2}\,c^2$, jet-to-ambient medium density ratio of $\eta\approx10^{-3}$, and an internal (classical) jet Mach number of $M_\mathrm{j}\approx12$. We also find that the wavelength ratios are better recovered by atransversal structure with a width of $\simeq 10\,\%$ of the jet radius. Thismethod represents a powerful tool to derive the jet parameters in all jetsshowing helical patterns with different wavelengths.

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