The Parallax of Omega Centauri Measured from Gaia EDR3 and a Direct, Geometric Calibration of the Tip of the Red Giant Branch and the Hubble Constant

We use data from the ESA Gaia mission Early Data Release 3 (EDR3) to measure the trigonometric parallax of $\omega$ Cen, the first high precision parallax measurement for the most massive globular cluster in the Milky Way. We use a combination of positional and high quality proper motion data from EDR3 to identify over 100,000 cluster members, of which 67,000 are in the magnitude and color range where EDR3 parallaxes are best calibrated. We find the estimated parallax to be robust, demonstrating good control of systematics within the color-magnitude diagram of the cluster. We find a parallax for the cluster of $0.191\pm0.001$ (statistical) $\pm0.004$ (systematic) mas (2.2\% total uncertainty) corresponding to a distance of $5.24\pm0.11$ kpc. The parallax of $\omega$ Cen provides a unique opportunity to directly and geometrically calibrate the luminosity of the Tip of the Red Giant Branch (TRGB) because it is the only cluster with sufficient mass to provide enough red giant stars, more than 100 one magnitude below the tip, for a precise, model-free measurement of the tip. Combined with the pre-existing and most widely-used measurements of the tip and foreground Milky Way extinction, we find $M_{I,TRGB}=-3.97\pm0.06$ mag for the $I$-band luminosity of the blue edge. Using the TRGB luminosity calibrated from the Gaia EDR3 parallax of $\omega$ Cen to calibrate the luminosity of SNIa results in a value for the Hubble constant of $H_0=72.1\pm2.0$ km s$^{-1}$ Mpc$^{-1}$. We make the data for the stars in $\omega$ Cen available electronically and encourage independent analyses of the results presented here.