A Maximum Likelihood Calibration of the Tip of the Red Giant Branch Luminosity from High Latitude Field Giants using Gaia Early Data Release 3 Parallaxes

Understand

The calibration of the tip of the red giant branch (TRGB) in the $I$-band has a direct role in determinations of the Hubble constant, a subject of recent interest due to the discrepancy between direct and indirect estimates of its value.

• We present a maximum likelihood (ML) method designed to obtain an independent calibration of the brightness of TRGB using $Gaia$ parallaxes from the Early Data Release 3 (EDR3) of Milky Way field Giants at high Galactic latitude.
• We adopt simple parameterizations for the Milky Way stellar luminosity function and density law and and optimize the likelihood of the observed sample as a function of those parameters.
• Using parameters to partially constrain the luminosity function from other galaxies similar to the Milky Way for which high quality TRGB data are available, we find values of the TRGB magnitude of $ M_I^{TRGB} = -3.91 \pm 0.05 $ (stat) $ \pm 0.09 $ (sys) mag, where the systematic uncertainty covers the range of shape parameters found in our Milky Way sample and in reference galaxies.