The MIRI/MRS Library I. Empirically correcting detector charge migration in unresolved sources

Context. The James Webb Space Telescope (JWST) has been collecting scientific data for over two years now. The Medium Resolution Spectrometer (MRS) of the Mid-InfraRed Instrument (MIRI) has been one of the telescope's most popular modes, and has already produced ground-breaking results. Scientists are now looking deeper into the data for new exciting discoveries, which introduces the need to characterise and correct known systematic effects to reach the photon noise limit. Five important limiting factors for the MRS are the pointing accuracy, non-linearity, detector charge migration, detector scattering - resulting in both spatial broadening and spectral interferometric fringing - the accuracy of the point-spread function (PSF) model, and the complex interplay between these. Aims. The Cycle 2 calibration programme 3779, entitled 'The MIRI/MRS Library', proposed a 72-point intra-pixel dither raster of the calibration star 10-Lac, which provides a unique dataset tailored for the purpose of addressing the limiting factors on the MRS data accuracy. In this first work of the paper series, we aim to address the degeneracy between the non-linearity and charge migration (brighter-fatter effect) that affect the pixel voltage integration ramps of the MRS. Due to the low flux in the longer wavelengths, we only do this in the 4.9-11.7 micron region (spectral channels 1 and 2). Methods. We fitted the ramps individually per pixel and dither, in order to fold in the deviations from classical non-linearity that are caused by charge migration. The ramp shapes should be repeatable depending on the part of the PSF that is sampled. By doing so, we defined both a grid-based linearity correction, and an interpolated linearity correction. Results. Including the change in ramp shape due to charge migration yields significant improvements compared to the uniform illumination assumption that is currently used by the standard JWST calibration pipeline. The standard deviation on the pixel ramp residual non-linearity is between 70 and 90% smaller than the current standard pipeline when self-calibrating with the grid. We are able to interpolate these coefficients to apply to any unresolved source not on the grid points, resulting in an up to 70% smaller standard deviation on the residual deviation from linearity. After applying the correction, the full-width at half maximum is up to 20% narrower for sources that cover the full pixel dynamic range. Furthermore, the depth of the fringes is now consistent up the ramp, improving the standard deviation on the difference in fringe depth between the start and ends of integrations by similar to 60%. Conclusions. Pointing-specific linearity corrections allow us to accurately model the pixel ramps across the PSF, and for the first time, fix the systematic deviation in the slopes. In this work we demonstrated this for unresolved sources. The discovered trends with PSF sampling suggest that, in the future, we may be able to model ramps for spatially extended and resolved illumination as well.