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The observed spectral energy distribution of an accreting supermassive blackhole typically forms a power-law spectrum in the Near Infrared (NIR) andoptical wavelengths, that may be interpreted as a signature of acceleratedelectrons along the jet. However, the details of acceleration remain uncertain.In this paper, we study the radiative properties of jets produced inaxisymmetric GRMHD simulations of hot accretion flows onto underluminoussupermassive black holes both numerically and semi-analytically, with the aimof investigating the differences between models with and without acceleratedelectrons inside the jet. We assume that electrons are accelerated in the jetregions of our GRMHD simulation. To model them, we modify the electrons'distribution function in the jet regions from a purely relativistic thermaldistribution to a combination of a relativistic thermal distribution and the$\kappa$-distribution function. Inside the disk, we assume a thermaldistribution for the electrons. We calculate jet spectra and synchrotron mapsby using the ray tracing code {\tt RAPTOR}, and compare the syntheticobservations to observations of Sgr~A*. Finally, we compare numerical models ofjets to semi-analytical ones. We find that in the $\kappa$-jet models, theradio-emitting region size, radio flux, and spectral index in NIR/optical bandsincrease for decreasing values of the $\kappa$ parameter, which corresponds toa larger amount of accelerated electrons. The model with $\kappa = 3.5$,$\eta_{\rm acc}=5-10\%$ (the percentage of electrons that are accelerated), andobserving angle $i = 30^{\rm o}$ fits the observed Sgr~A* emission in theflaring state from the radio to the NIR/optical regimes, while $\kappa = 3.5$,$\eta_{\rm acc}< 1\%$, and observing angle $i = 30^{\rm o}$ fit the upperlimits in quiescence.

General relativistic magnetohydrodynamical $\kappa$-jet models for Sgr A*