Calibrating the tip of the red giant branch and measuring Magellanic Cloud distances to ∼2% exclusively with <i>Gaia</i>

We have calibrated the tip of the red giant branch (TRGB) using our recent catalogue of homogeneous globular cluster (GC) distances. The GC distances were determined via a global joint fit to optical period–Wesenheit relations of their member RR Lyrae stars and type-II Cepheids, anchored by trigonometric parallaxes; all data were taken from the ESA Gaia mission’s (early) third data release (GDR3). Using I -band measurements of 48 GCs from P. Stetson’s database, we determined M I ,0 = −3.948 +0.037 −0.034 mag (1.6% in distance). Calibrating the TRGB using Gaia ’s homogeneous, space-based RP photometry of 53 GCs, we found M RP ,0 = −3.807 +0.041 −0.035 mag (1.8%). The stated uncertainties include statistical and systematic effects, including the correlated nature of the GC distances. The robustness of our calibrations was evaluated via tests against small-number statistics and analysis choices. Within the (small) uncertainties, no significant metallicity effect is detected in our sample of old, low-metallicity GCs. We measured ∼2% distances to the Large and Small Magellanic Clouds, 18.447 +0.036 −0.042 mag (48.9 ± 0.9 kpc) and 18.898 +0.049 −0.054 mag (60.2 ± 1.4 kpc), respectively, using a single photometric system: RP (spectro-)photometry from GDR3. Our new TRGB distances, whose absolute scale derives from Gaia parallaxes, are fully independent of the well-known detached eclipsing binary (DEB) distances and agree with them to within the uncertainties. Combining our new TRGB and existing DEB distances, we illustrate how additional constraints can be incorporated into the Local Distance Network and obtain H 0 = 73.52 ± 0.80 km s −1 Mpc −1 . Expected improvements thanks to the upcoming fourth Gaia data release are discussed.