We present the results from Suzaku observations of the hottest Abell galaxy cluster A2163 at $z=0.2$. To study the physics of gas heating in cluster mergers, we investigated hard X-ray emission from the merging cluster A2163, which hosts the brightest synchrotron radio halo. We analyzed hard X-ray spectra accumulated from two-pointed Suzaku observations. Non-thermal hard X-ray emission should result from the inverse Compton (IC) scattering of relativistic electrons by the CMB photons. To measure this emission, the dominant thermal emission in the hard X-ray band must be modeled in detail. To this end, we analyzed the combined broad-band X-ray data of A2163 collected by Suzaku and XMM-Newton, assuming single- and multi-temperature models for thermal emission and the power-law model for non-thermal emission. From the Suzaku data, we detected significant hard X-ray emission from A2163 in the 12-60 keV band at the $28sigma$ level (or at the $5.5sigma$ level if a systematic error is considered). The Suzaku HXD spectrum alone is consistent with the single-T thermal model of gas temperature $kT=14$ keV. From the XMM data, we constructed a multi-T model including a very hot ($kT=18$ keV) component in the NE region. Incorporating the multi-T and the power-law models into a two-component model with a radio-band photon index, the 12-60 keV energy flux of non-thermal emission is constrained within $5.3 pm 0.9 (pm 3.8)times 10^{-12}~{rm erg, s^{-1} cm^{-2}}$. The 90% upper limit of detected IC emission is marginal ($< 1.2times 10^{-11}~{rm erg, s^{-1} cm^{-2}}$ in the 12-60 keV). The estimated magnetic field in A2163 is $B > 0.098~{rm mu G}$. While the present results represent a three-fold increase in the accuracy of the broad band spectral model of A2163, more sensitive hard X-ray observations are needed to decisively test for the presence of hard X-ray emission due to IC emission.
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