International audienceWe present a detailed spectral analysis of XMM-Newton and NuSTAR observations of the accreting transient black hole GRS 1739-278 during a very faint low hard state at ~0.02% of the Eddington luminosity (for a distance of 8.5 kpc and a mass of 10 M_sun ). The broad-band X-ray spectrum between 0.5-60 keV can be well-described by a power law continuum with an exponential cutoff. The continuum is unusually hard for such a low luminosity, with a photon index of Gamma = 1.39 +/- 0.04. We find evidence for an additional reflection component from an optically thick accretion disk at the 98% likelihood level. The reflection fraction is low with R_refl = 0.043(+0.033,-0.023). In combination with measurements of the spin and inclination parameters made with NuSTAR during a brighter hard state by Miller and co-workers, we seek to constrain the accretion disk geometry. Depending on the assumed emissivity profile of the accretion disk, we find a truncation radius of 15-35 Rg (5-12 R_ISCO ) at the 90% confidence limit. These values depend strongly on the assumptions and we discuss possible systematic uncertainties
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