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Understanding the sources of instrumental systematic noise is a must toimprove the design of future spectrographs. In this study, we alternatedobservations of the well-suited pair of M-stars GJ 725A+B to delve into thesub-night HARPS-N response. Besides the possible presence of a low-mass planetorbiting GJ 725B, our observations reveal changes in the spectral energydistribution (SED) correlated with measurements of the width of theinstrumental line profile and, to a lower degree, with the Dopplermeasurements. To study the origin of these effects, we searched forcorrelations among several quantities defined and measured on the spectra andon the acquisition images.  We find that the changes in apparent SED are very likely related to fluxlosses at the fibre input. Further tests indicate that such flux losses do notseriously affect the shape of the instrumental point spread function ofHARPS-N, but identify an inefficient fitting of the continuum as the mostlikely source of the systematic variability observed in the FWHM. This index,accounting for the HARPS-N cross-correlation profiles width, is often used todecorrelate Doppler time-series. We show that the Doppler measurement obtainedby a parametric least-squares fitting of the spectrum accounting for continuumvariability is insensitive to changes in the slope of the SED, suggesting thatforward modeling techniques to measure moments of the line profile are theoptimal way to achieve higher accuracy. Remaining residual variability at ~1m/s suggests that for M-stars Doppler surveys the current noise floor still hasan instrumental origin.

High-cadence spectroscopy of M-dwarfs. I. Analysis of systematic effects in HARPS-N line profile measurements on the bright binary GJ 725A+B