the M subdwarfs observed with X-shooter in Table \[tab\_MplusTeff\_sdM:log\_obs\_Xshooter\] along with a summary of the logs of the observations.

X-Shooter is a multi wavelength cross–dispersed echelle spectrograph made of three arms covering simultaneously the ultraviolet (UVB; 0.3–0.55 $\mu$m), visible (VIS; 0.55–1.0 $\mu$m), and near–infrared (NIR; 1.0–2.48 $\mu$m) wavelength ranges thanks to the presence of two dichroics splitting the light. The spectrograph is equipped with three detectors: a 4096$\times$2048 E2V CCD44-82, a 4096$\times$2048 MIT/LL CCID20, and a 2096$\times$2096 Hawaii 2RG for the UVB, VIS, and NIR arms, respectively. We set the read-out mode to 400k and low gain without binning. We used the 1.6 arcsec slit in the UVB, 1.5 arcsec in the VIS, and 1.2 arcsec NIR, yielding resolving powers of 3300 (9.9 pixels per full-width-half-maximum), 5400 (9.7 pixels per full-width-half-maximum), and 3900 (5.8 pixels per full-width-half-maximum) in the UVB, VIS, and NIR arms, respectively.

We ran the latest version of the X-shooter pipeline (2.8.0)[^2] on the raw data downloaded from the ESO archive with their associated raw calibration files from our three programmes: 089.C-0140(A), 091.C-0264(A), and 093.C-0610(A). All spectra have their instrumental signature removed, including bias and flat-field. The spectra are wavelength-calibrated, sky-subtracted and finally flux-calibrated. The output products 