Surface smoothness requirements for the mirrors of the IXO X-ray telescope

The International X-ray Observatory (IXO) is a very ambitious mission, aimed at the X-ray observation of the early Universe. This makes IXO extremely demanding in terms of effective area and angular resolution. In particular, the HEW requirement below 10 keV is 5 arcsec Half-Energy Width (HEW). At higher photon energies, the HEW is expected to increase, and the angular resolution to be correspondingly degraded, due to the increasing relevance of the X-ray scattering off the reflecting surfaces. Therefore, the HEW up to 40 keV is required to be better than 30 arcsec, even though the IXO goal is to achieve an angular resolution as close as possible to 5 arcsec also at this energy. To this end, the roughness of the reflecting surfaces has to not exceed a tolerance, expressed in terms of a surface roughness PSD (Power-Spectral-Density). In this work we provide such tolerances by simulating the HEW scattering term for IXO, assuming a specific configuration for the optical module and different hypotheses on the PSD of mirrors.