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We present H$\alpha$ spectroscopic observations and detailed modelling of theBalmer filaments in the supernova remnant Tycho. We used Galaxy H$\alpha$Fabry-P\'erot Spectrometer on the William Herschel Telescope with a3.4'$\times$3.4' field-of-view, 0.2" pixel scale and $\sigma_\rm{instr}=8.1$km/s resolution at 1" seeing for $\sim10$ hours, resulting in 82spatial-spectral bins that resolve the narrow H$\alpha$ line in the entireTycho's northeastern rim. For the first time, we can mitigate artificial linebroadening from unresolved differential motion, and probe H$\alpha$ emissionparameters in varying shock and ambient medium conditions. Broad H$\alpha$ lineremains unresolved within spectral coverage of 392 km/s. We employed Bayesianinference to obtain reliable parameter confidence intervals, and quantify theevidence for models with multiple line components. The median H$\alpha$narrow-line full-width at half-maximum of all bins and models is$W_\rm{NL}=(54.8\pm1.8)$ km/s at the $95\%$ confidence level, varying within[35, 72] km/s between bins and clearly broadened compared to the intrinsic(thermal) $\approx20$ km/s. Possible line splits are accounted for, significantin $\approx18\%$ of the filament, and presumably due to remaining projectioneffects. We also find wide-spread evidence for intermediate-line emission of abroad-neutral precursor, with median $W_\rm{IL}=(180\pm14)$ km/s ($95\%$confidence). Finally, we present a measurement of the remnant's systemicvelocity, $V_\rm{LSR}=-34$ km/s, and map differential line-of-sight motions.Our results confirm the existence and interplay of shock precursors in Tycho'sremnant. In particular, we show that suprathermal narrow-line emission isnear-universal in Tycho and that, in absence of an alternative explanation,collisionless supernova remnant shocks constitute a viable acceleration sourcefor Galactic TeV Cosmic-Ray protons.

Balmer filaments in Tycho's supernova remnant: an interplay between cosmic-ray and broad-neutral precursors