We present a broad-band (~0.3-70 keV) spectral and temporal analysis of NuSTAR observations of the luminous infrared galaxy NGC 6240, combined with archival Chandra, XMM-Newton and BeppoSAX data. NGC 6240 is a galaxy in a relatively early merger state with two distinct nuclei separated by ~1.5. Previous Chandra observations have resolved the two nuclei, showing that they are both active and obscured by Compton-thick material. Although they cannot be resolved by NuSTAR, thanks to the unprecedented quality of the NuSTAR data at energies >10 keV, we clearly detect, for the first time, both the primary and the reflection continuum components. The NuSTAR hard X-ray spectrum is dominated by the primary continuum piercing through an absorbing column density which is mildly optically thick to Compton scattering (tau ~ 1.2, N_H ~ 1.5 x 10^(24) cm^-2). We detect moderate hard X-ray (> 10 keV) flux variability up to 20% on short (15-20 ksec) timescales. The amplitude of the variability is maximum at ~30 keV and is likely to originate from the primary continuum of the southern nucleus. Nevertheless, the mean hard X-ray flux on longer timescales (years) is relatively constant. Moreover, the two nuclei remain Compton-thick, although we find evidence of variability of the material along the line of sight with column densities N_H <~ 2 x 10^(23) cm-2 over long (~3-15 years) timescales. The observed X-ray emission in the NuSTAR energy range is fully consistent with the sum of the best-fit models of the spatially resolved Chandra spectra of the two nuclei.
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