  The Athena X-Ray Integral Field Unit (X-IFU) will provide spatially resolved
high-resolution spectroscopy (2.5 eV FWHM up to 7 keV) over the 0.2 to 12 keV
energy band. It will comprise an array of 3840 superconducting Transition Edge
Sensors (TESs) operated at 90 mK, with an absolute energy scale accuracy of 0.4
eV. Slight changes in the TES operating environment can cause significant
variations in its energy response function, which may result in degradation of
the detector's energy resolution, and eventually in systematic errors in the
absolute energy scale if not properly corrected. These changes will be
monitored via an onboard Modulated X-ray Source (MXS) and the energy scale will
be corrected accordingly using a multi-parameter interpolation of gain curves
obtained during ground calibration. Assuming realistic MXS configurations and
using the instrument end-to-end simulator SIXTE, we investigate here both
statistical and systematic effects on the X-IFU energy scale, occurring either
during ground measurements or in-flight. The corresponding impacts on the
energy resolution and means of accounting for these errors are also addressed.
We notably demonstrate that a multi-parameter gain correction, using both the
pulse-height estimate and the baseline of a pulse, can accurately recover
systematic effects on the gain due to realistic changes in TES operating
conditions within 0.4 eV. Optimisations of this technique with respect to the
MXS line configuration and correction time, as well as to the energy scale
parametrization are also show promising results to improve the accuracy of the
correction.
