PKS 0625-354 (z=0.055) was observed with the four H.E.S.S. telescopes in 2012 during 5.5 hours. The source was detected above an energy threshold of 200 GeV at a significance level of 6.1$sigma$. No significant variability is found in these observations. The source is well described with a power-law spectrum with photon index $Gamma =2.84 pm 0.50_{stat} pm 0.10_{syst}$ and normalization (at $E_0$=1.0 TeV) $N_0(E_0)=(0.58 pm 0.22_{stat} pm 0.12_{syst})times10^{-12}$ TeV$^{-1}$cm$^{-2}$s$^{-1}$. Multi-wavelength data collected with Fermi-LAT, Swift-XRT, Swift-UVOT, ATOM and WISE are also analysed. Significant variability is observed only in the Fermi-LAT $gamma$-ray and Swift-XRT X-ray energy bands. Having a good multi-wavelength coverage from radio to very high energy, we performed a broadband modelling from two types of emission scenarios. The results from a one zone lepto-hadronic, and a multi-zone leptonic models are compared and discussed. On the grounds of energetics, our analysis favours a leptonic multi-zone model. Models associated to the X-ray variability constraint supports previous results suggesting a BL Lac nature of PKS 0625-354, with, however, a large-scale jet structure typical of a radio galaxy.
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