The black hole transient GRS 1716-249 was monitored from the radio to the gamma-ray band during its 2016-2017 outburst. This paper focuses on the Spectral Energy Distribution (SED) obtained in 2017 February-March, when GRS 1716-249 was in a bright hard spectral state. The soft gamma-ray data collected with the INTEGRAL/SPI telescope show the presence of a spectral component which is in excess of the thermal Comptonisation emission. This component is usually interpreted as inverse Compton emission from a tiny fraction of non-thermal electrons in the X-ray corona. We find that hybrid thermal/non-thermal Comptonisation models provide a good fit to the X/gamma-ray spectrum of GRS 1716-249. The best-fit parameters are typical of the bright hard state spectra observed in other black hole X-ray binaries. Moreover, the magnetised hybrid Comptonisation model BELM provides an upper limit on the intensity of the coronal magnetic field of about 1E+06 G. Alternatively, this soft gamma-ray emission could originate from synchrotron emission in the radio jet. In order to test this hypothesis, we fit the SED with the irradiated disc plus Comptonisation model combined with the jet internal shock emission model ISHEM. We found that a jet with an electron distribution of p~2.1 can reproduce the soft gamma-ray emission of GRS 1716-249. However, if we introduce the expected cooling break around 10 keV, the jet model can no longer explain the observed soft gamma-ray emission, unless the index of the electron energy distribution is significantly harder (p<2).
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