[Paper Review] 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

Siyang Li, Stefano Casertano+1 more|arXiv (Cornell University)|Feb 22, 2022

Stellar, planetary, and galactic studies4 citations

TL;DR

This paper presents a maximum likelihood method to calibrate the tip of the red giant branch (TRGB) luminosity in the I-band using Gaia EDR3 parallaxes of high Galactic latitude field giants. It derives a TRGB magnitude of $M_I^{TRGB} = -3.91 \pm 0.05$ (stat) $\pm 0.09$ (sys) mag, offering a geometric, independent calibration that improves precision toward resolving the Hubble tension.

ABSTRACT

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. While APASS Data Release 9 all-sky photometry is insufficient to provide a reliable constraint on the shape of the Milky Way luminosity function, we estimate that the photometry from $Gaia$ Data Release 3 (mid-2022) will allow better constraints on the shape, and lower statistical uncertainties on the tip by a factor of 3. With expected releases of improved parallax measurements from $Gaia$, the method of calibrating the TRGB luminosity from field Giants is expected to reach $\sim$ 0.01 mag uncertainty, which is an important step toward a precise TRGB-based determination of the Hubble constant.

Motivation & Objective

• To develop a geometric, independent calibration of the TRGB luminosity using Gaia EDR3 parallaxes of Milky Way field giants.
• To address the uncertainty in TRGB zero-point calibration, a key source of tension in Hubble constant measurements.
• To improve statistical precision and reduce systematic errors in TRGB-based distance ladders.
• To leverage Gaia's astrometry to constrain the shape of the Milky Way luminosity function near the TRGB.
• To enable future high-precision TRGB calibrations with upcoming Gaia data releases.

Proposed method

• A maximum likelihood framework is used to jointly fit the observed parallax and magnitude distribution of high-latitude field giants.
• The method models the Milky Way stellar luminosity function and spatial density using simple parameterizations.
• Likelihood is optimized over parameters including the TRGB magnitude and the luminosity function shape parameter $\beta$, constrained by reference galaxies.
• Photometric uncertainties from APASS DR9 are used, with future improvements anticipated from Gaia DR3's wavelength-resolved photometry.
• Systematic uncertainties are estimated by comparing the Milky Way sample's luminosity function shape with those of similar external galaxies.
• The approach avoids the limitations of traditional Sobel-filter methods by accounting for distance and magnitude dispersion in a two-dimensional likelihood space.

Experimental results

Research questions

• RQ1 What is the most precise and independent geometric calibration of the I-band TRGB magnitude using Gaia EDR3 parallaxes of field giants?
• RQ2 How do uncertainties in the luminosity function shape near the TRGB affect the TRGB zero-point calibration?
• RQ3 To what extent can Gaia DR3 improve statistical constraints on the TRGB magnitude compared to current data?
• RQ4 How do systematic uncertainties from luminosity function shape variations compare to statistical errors in the TRGB calibration?
• RQ5 Can this likelihood-based method achieve sub-0.01 mag precision in TRGB calibration with future Gaia data releases?

Key findings

• The study derives a TRGB magnitude of $M_I^{TRGB} = -3.91 \pm 0.05$ (statistical) $\pm 0.09$ (systematic) mag using Gaia EDR3 parallaxes.
• The systematic uncertainty of 0.09 mag accounts for variations in the luminosity function shape across the Milky Way and reference galaxies.
• APASS DR9 photometry is insufficient to constrain the luminosity function shape, but Gaia DR3 is expected to reduce statistical uncertainty by a factor of three.
• Future Gaia DR4 and beyond are expected to improve parallax precision to ~0.01 mas, enabling TRGB calibration uncertainty below 0.01 mag.
• The method provides a geometric, independent calibration path that could resolve discrepancies in Hubble constant measurements.
• The TRGB calibration is consistent with recent local distance ladder results but implies a fainter tip than some prior calibrations, favoring a higher Hubble constant.