Calibrating the Tip of the Red Giant Branch and measuring Magellanic Cloud distances to 2% exclusively with Gaia

Abstract

We have calibrated the Tip of the Red Giant Branch (TRGB) using our recent catalog of homogeneous, high-accuracy Globular Cluster (GC) distances. The GC distances were determined by 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 taken from the ESA Gaia mission's (early) third data release (GDR3). Using I-band measurements in 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 is demonstrated via tests against small-number statistics and analysis choices. Specifically, we found no significant metallicity effect for our sample of old, low-metallicity GCs. We measured $\sim 2\%$ distances to the Large (LMC) and Small Magellanic Clouds (SMC), $18.447^{+0.036}_{-0.042}$ mag ($48.9 \pm 0.9$ kpc) and $18.898^{+0.049}_{-0.054}$ mag ($60.2 \pm 1.4$ kpc), respectively, using a single well calibrated 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 may be incorporated in the Local Distance Network and obtain $H_0 = 73.52 \pm 0.80$ km/s/Mpc. Expected improvements due to the upcoming fourth Gaia data release are discussed.

Figures (7)

• Figure 1: Color-absolute magnitude diagram, LF, and Sobel filter response for the combined GC sample based on the Stetson photometry. The purple line marks the median TRGB magnitude derived from the bootstrap analysis, and the orange contour indicates the 16–84th interquartile range.
• Figure 2: Stability of the TRGB measurement under random star removal. The upper panel shows the median TRGB value as a function of sample size; the median decreases as the number of stars is reduced. The lower panel shows the corresponding evolution of the TRGB uncertainty.
• Figure 3: Mean reduced $\chi_{\mathrm{PSF}}$ as a function of absolute magnitude in the $I$ band, computed in bins of 0.1 mag.
• Figure 4: Comparison between Gaia synthetic photometry and Stetson photometry. No systematic bias is observed for stars brighter than the photometric standards, indicating that the Stetson photometry can be reliably used to measure the TRGB.
• Figure 5: Comparison between the Stetson photometry of stars brighter than the top 5% of the standards and the photometry obtained by applying transformations calibrated using fainter stars.