Isochrone fitting of Galactic globular clusters -- V. NGC6397 and NGC6809 (M55)

We fit various colour-magnitude diagrams (CMDs) of the Galactic globular clusters NGC,6397 and NGC,6809 (M55) by isochrones from the Dartmouth Stellar Evolution Database (DSED) and Bag of Stellar Tracks and Isochrones (BaSTI) for $\alpha$-enhanced [$\alpha$/Fe]$=+0.4$. For the CMDs, we use data sets from {\it HST}, {\it Gaia}, VISTA, and other sources utilizing 32 and 23 photometric filters for NGC,6397 and NGC,6809, respectively, from the ultraviolet to mid-infrared. We obtain the following characteristics for NGC,6397 and NGC,6809, respectively: metallicities [Fe/H]$=-1.84\pm 0.02\pm 0.1$ and $-1.78\pm 0.02\pm 0.1$ (statistic and systematic uncertainties); distances $2.45\pm 0.02\pm 0.06$ and $5.24\pm 0.02\pm 0.18$ kpc; ages $12.9\pm 0.1\pm 0.8$ and $13.0\pm 0.1\pm 0.8$ Gyr; reddenings $E(B-V)=0.178\pm 0.006\pm 0.01$ and $0.118\pm 0.004\pm 0.01$ mag; extinctions $A_{\mathrm{V}}=0.59\pm 0.01\pm 0.02$ and $0.37\pm 0.01\pm 0.04$ mag; extinction-to-reddening ratio $R_{\mathrm{V}}=3.32_{-0.28}^{+0.32}$ and $3.16_{-0.56}^{+0.66}$. Our estimates agree with most estimates from the literature. BaSTI gives systematically higher [Fe/H] and lower reddenings than DSED. Despite nearly the same metallicity, age, and helium enrichment, these clusters show a considerable horizontal branch (HB) morphology difference, which must therefore be described by another parameter. This parameter must predominantly explain why the least massive HB stars (0.58-0.63 solar masses) are only found within NGC 6809. Probably they have been lost by the core-collapse cluster NGC,6397 during its dynamical evolution and mass segregation. In contrast, NGC,6809 has a very low central concentration and, hence, did not undergo this process.