The galaxy M 87 harbors a kiloparsec-scale relativistic jet, whose origin coincides with a supermassive black hole. Observational mm-VLBI campaigns are capable of resolving the jet-launching region at the scale of the event horizon. In order to provide a context for interpreting these observations, realistic general-relativistic magnetohydrodynamical (GRMHD) models of the accretion flow are constructed. The characteristics of the observed spectral-energy distribution (SED) depend on the shape of the electrons energy-distribution function (eDF). The dependency on the eDF is omitted in the modeling of the first Event Horizon Telescope results. In this work, we aim to model the M 87 SED from radio up to NIR/optical frequencies using a thermal-relativistic Maxwell- Juttner distribution, as well as a relativistic $kappa$-distribution function. The electrons are injected based on sub-grid, particle-in-cell parametrizations for sub-relativistic reconnection. A GRMHD simulation in Cartesian-Kerr-Schild coordinates, using eight levels of adaptive mesh refinement (AMR), forms the basis of our model. To obtain spectra and images, the GRMHD data is post-processed with the ray-tracing code RAPTOR, which is capable of ray tracing through AMR GRMHD simulation data. We obtain radio spectra in both the thermal-jet and $kappa$-jet models consistent with radio observations. Additionally, the $kappa$-jet models also recover the NIR/optical emission. The models recover the observed source sizes and core shifts and obtain a jet power of $approx 10^{43}$ ergs/s. In the $kappa$-jet models, both the accretion rates and jet powers are approximately two times lower than the thermal-jet model. The frequency cut-off observed at $ u approx 10^{15}$ Hz is recovered when the accelerator size is $10^6$ - $10^8$ cm, this could potentially point to an upper limit for plasmoid sizes in the jet of M 87.
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