Isochrone fitting of Galactic globular clusters -- III. NGC\,288, NGC\,362, and NGC\,6218 (M12)

We present new isochrone fits to colour-magnitude diagrams of the Galactic globular clusters NGC\,288, NGC\,362, and NGC\,6218 (M12). We utilize a lot of photometric bands from the ultraviolet to mid-infrared by use of data from the {\it HST}, {\it Gaia}, unWISE, Pan-STARRS, and other photometric sources. In our isochrone fitting we use theoretical models and isochrones from the Dartmouth Stellar Evolution Program and Bag of Stellar Tracks and Isochrones for $\alpha$-enhanced abundance [$\alpha$/Fe]$=+0.40$, different helium abundances, and a metallicity of about [Fe/H]$=-1.3$ adopted from the literature. We derive the most probable distances $8.96\pm0.05$, $8.98\pm0.06$, and $5.04\pm0.05$ kpc, ages $13.5\pm1.1$, $11.0\pm0.6$, and $13.8\pm1.1$ Gyr, extinctions $A_\mathrm{V}=0.08\pm0.03$, $0.11\pm0.04$, and $0.63\pm0.03$ mag, and reddenings $E(B-V)=0.014\pm0.010$, $0.028\pm0.011$, and $0.189\pm0.010$ mag for NGC\,288, NGC\,362, and NGC\,6218, respectively. The distance estimates from the different models are consistent, while those of age, extinction, and reddening are not. The uncertainties of age, extinction, and reddening are dominated by some intrinsic systematic differences between the models. However, the models agree in their relative age estimates: NGC\,362 is $2.6\pm0.5$ Gyr younger than NGC\,288 and $2.8\pm0.5$ Gyr younger than NGC\,6218, confirming age as the second parameter for these clusters. We provide reliable lists of the cluster members and precise cluster proper motions from the {\it Gaia} Early Data Release 3.