Not yet reviewed by Pith; the record is open.

Young supernova remnants (SNRs) shocks are believed to be the main sites of galactic cosmic rays production, showing X-ray synchrotron dominated spectra in the vicinity of their shock. While a faint thermal signature left by the shocked interstellar medium (ISM) should also be found in the spectra, proofs for such an emission in Tycho's SNR have been lacking. We perform an extended statistical analysis of the X-ray spectra of five regions behind the blast wave of Tycho's SNR using \textit{Chandra} archival data. We use Bayesian inference to perform extended parameter space exploration and sample the posterior distributions of a variety of models of interest. According to Bayes factors, spectra of all five regions of analysis are best described by composite three-component models taking into account non-thermal emission, ejecta emission and shocked ISM emission. The shocked ISM stands out the most in the Northern limb of the SNR. We find for the shocked ISM a mean electron temperature $kT_{\rm{e}}=0.96^{+1.33}_{-0.51}$ keV for all regions and a mean ionization timescale $n_{\rm e}t=2.55^{+0.5}_{-1.22}\times10^9$ cm$^{-3}$s resulting in a mean ambient density $n_{\rm e}=0.32^{+0.23}_{-0.15}$ cm$^{-3}$ around the remnant. We performed an extended analysis of the Northern limb, and show that the measured synchrotron cutoff energy is not well constrained in the presence of a shocked ISM component. Such results cannot currently be further investigated by analysing emission lines in the 0.5-1 keV range, because of the low \textit{Chandra} spectral resolution in this band. We show with simulated spectra that X-IFU future performances will be crucial to address this point.