tokens: misalignment angles in 3C sources are known to extend up to values of about 12° or more ( Leahy Williams 1984 ). We thus consider the interpretation of the S5 0836+710 large-scale morphology as an FR II radio galaxy at a small viewing angle as realistic. 4.3. Derivation of the jet parameters The total jet power for a relativistic jet is parameterized as (see, e.g., Perucho et al. 2017 ): where is the jet specific enthalpy, Γ j is the jet Lorentz factor, ρ j is the jet rest mass density, v j is the jet velocity, c is the speed of light, B φ is the toroidal field in the observer’s frame, γ j is the ratio of specific heats of the jet gas, and A j is the jet cross-section. The first term in Eq. ( 2 ) includes the kinetic, internal, and rest-mass energy contributions, and the second term stands for the magnetic energy of the jet. We can assume (see Appendix B ) that the jet is kinetically dominated and in the cold regime (i.e., its magnetosonic Mach number is high). Furthermore, taking into account that the advance speed as measured by LOFAR is also so slow, the velocity of the bulk plasma flowing into the hotspot can be assumed to be only mildly relativistic at most (see also Appendix C for the relativistic derivation). Under these conditions, the magnetic and pressure terms can be neglected and Eq. ( 2 ) simplifies to Across a strong shock, the hotspot pressure is (e.g., Landau Lifshitz 1987 ) In this equation, we need to define the jet radius at the hotspot, R j, h , which can be approximated as the hotspot radius. Because we do not know whether the southern radio structure includes the hotspot and part of the lobe or if it is the hotspot, we considered half of the whole region as the jet radius (4.5 kpc) and half of the fitted component, which represents the brightest region within the hypothetical lobe (2.5 kpc). Although the polarization seems to favor the latter interpretation (see the previous section), we study both cases here. Furthermore, we need an estimate for v j at the hotspot, v j, h . As we show in the following paragraphs, any reasonable input value is sufficient because we define an iterative method to derive its convergence value. When the hotspot pressure is obtained, we can use equipartition between the nonthermal particles and the magnetic field, as reported for FR II hotspots (see e.g., Hardcastle Worrall 2000 ), to obtain a value of the magnetic field at the interaction site. The value of the magnetic field prior to the reverse shock can be constrained by assuming conservation of the magnetic flux from the 1.6 GHz jet to the interaction site 3 . Applying the magnetohydrodynamcis (MHD) jump conditions at the reverse shock that give rise to the hotspot, allows us to derive a new estimate for v j, h . Setting a convergence criterion for this parameter at a precision of 10 −3 , we can determine the relevant parameters of the problem. We applied this method to four different sets of hotspot velocity and radius: the possible
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