1RXS J170849-400910 is one of four anomalous X-ray pulsars which emit persistent luminous radiation in soft X-rays (<10 keV) as well as in hard X-rays (>10 keV). In this paper we present detailed spectral and temporal characteristics over the whole X-ray band. For this purpose data have been used from INTEGRAL, RXTE and XMM-Newton. The hard X-ray (>10 keV) time-averaged total spectrum, accumulated over four years with the imager IBIS-ISGRI onboard INTEGRAL adding up to 5.2 Ms net exposure, can be described by a power law with a photon index Γ = 1.13 ± 0.06 and extends to ~175 keV. The 20-175 keV flux is (7.76 ± 0.34) × 10-11 erg cm-2 s-1 which exceeds the 2-10 keV (unabsorbed) flux by a factor of ~2.3. No evidence for a spectral break is found below 300 keV. Also, no significant long-term time variability has been detected above 20 keV on time scales of 1 and 0.5 year. Pulsed emission is measured with INTEGRAL up to 270 keV, i.e. to much higher energies than the total emission, with a detection significance of 12.3σ (20-270 keV). The pulse profiles from 0.5 keV up to 270 keV show drastic morphology changes below ~20 keV. Three different pulse components can be recognized in these pulse profiles: 1) a hard pulse peaking around phase 0.8 which contributes to the pulse profiles above ~4 keV; 2) a softer pulse which peaks around phase 0.4 not contributing in the hard X-ray domain and 3) a very soft pulse component below 2 keV. A combined time-averaged pulsed spectrum (2.8-270 keV) from INTEGRAL, RXTE-PCA and HEXTE (collected over nine years) can be described with a soft and a hard power-law component: Γs = 2.79 ± 0.07 and Γh = 0.86 ± 0.16. In the pulsed spectrum extracted from a 25.5 ks net exposure XMM-Newton observation we find a discontinuity between 2 keV and 3 keV. Above these energies the spectrum is consistent with the spectrum taken with RXTE-PCA. The pulse profiles and the total-pulsed spectrum prove to be stable over the whole nine-years time span over which the data have been taken. Also detailed phase-resolved spectroscopy of the pulsed emission confirms the long-term stability as the spectra taken at different epochs connect smoothly. The phase-resolved spectra reveal complex spectral shapes which do not follow the shape of the total-pulsed spectrum. The spectral shape gradually changes with phase from a soft single power law to a complex multi-component shape and then to a hard single power law. The spectrum switches from a very hard (Γ = 0.99 ± 0.05) to a very soft (Γ = 3.58 ± 0.34) single power-law shape within a 0.1-wide phase interval. The discontinuity measured between 2 keV and 3 keV with XMM-Newton is a result of a curved component. This component which is most apparent within phase interval 0.7-0.9 significantly contributes in the energy range between 4 keV and 20 keV. It has a very steep spectrum below 5 keV with a photon index Γ ~ -1.5. From the phase-resolved spectra we identify three independent components with different spectral shapes which together can accurately describe all phase-resolved spectra (2.8-270 keV). The three shapes are a soft power law (Γ = 3.54), a hard power law (Γ = 0.99) and a curved shape (described with two logparabolic functions). The phase distributions of the normalizations of these spectral components form three decoupled pulse profiles. The soft component peaks around phase 0.4 while the other two components peak around phase 0.8. The width of the curved component (~0.25 in phase) is about half the width of the hard component. After 4U 0142+61, RXS J1708-40 is the second anomalous X-ray pulsar for which such detailed phase-resolved spectroscopy has been performed. These results give important constraints showing that three dimensional modeling covering both the geometry and different production processes is required to explain our findings.
