Calibration of the Tip of the Red Giant Branch (TRGB)

TL;DR

This work delivers a robust, multi-wavelength absolute calibration of the TRGB using LMC TRGB stars tied to the geometric DEB distance, with extinction and reddening solved directly from the data. The authors validate the zero point through independent calibrations with the SMC DEB distance and a DEB-calibrated sample of Galactic globular clusters (notably 47 Tuc), while also accounting for LMC geometry and published reddening maps. Their final $I$-band TRGB zero point is $M_I^{TRGB} = -4.047 \,\pm\ 0.022 \,( ext{stat}) \,\pm\ 0.039 \,( ext{sys})$ mag, accompanied by color-dependent in-band calibrations for $V$, $JHK$ that tie to metallicity through the chosen pivot colors. The derived Hubble constant from this calibration is $H_0 = 69.6 \,\pm\ 0.8 \,( ext{stat}) \,\pm\ 1.7 \,( ext{sys}) \,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, underscoring the TRGB as a precise rung on the distance ladder and its relevance to cosmological scale measurements.

Abstract

The Tip of the Red Giant (TRGB) method provides one of the most accurate and precise means of measuring the distances to nearby galaxies. Here we present a VIJHK absolute calibration of the TRGB based on observations of TRGB stars in the Large Magellanic Cloud (LMC),grounded on detached eclipsing binaries (DEBs). This paper presents a more detailed description of the method first presented in Freedman et al. (2019) for measuring corrections for the total line-of-sight extinction and reddening to the LMC. In this method, we use a differential comparison of the red giant population in the LMC, first with red giants in the Local Group galaxy, IC 1613, and then with those in the Small Magellanic Cloud. As a consistency check, we derive an independent calibration of the TRGB sequence using the SMC alone, invoking its geometric distance also calibrated by DEBs. An additional consistency check comes from near-infrared observations of Galactic globular clusters covering a wide range of metallicities. In all cases we find excellent agreement in the zero-point calibration. We then examine the recent claims by Yuan et al. (2019), demonstrating that, in the case of the SMC, they corrected for extinction alone while neglecting the essential correction for reddening as well. In the case of IC 1613, we show that their analysis contains an incorrect treatment of (over-correction for) metallicity. Using our revised (and direct) measurement of the LMC TRGB extinction, we find a value of Ho = 69.6 +/-0.8 (+/-1.1% stat) +/- 1.7 (+/-2.4% sys) km/s/Mpc.

Figures (12)

• Figure 1: PARSEC isochrones for red giant branch stars with a constant age and a metallicity spread (upper panel) and a constant metallicity, but with an age spread (lower panel), are shown for $V$ (blue), $I$ (black) and $K$ (red) bandpasses, to the same scale, for comparison. In the upper panel, the isochrones have a constant age of 10 Gyr and a metallicity range from -2.0 $<$ [M/H] $<$ -0.1 dex; in the lower panel, the isochrones have a fixed metallicity of [M/H] = -1.8, and an age spread of 4 $<$ t $<$ 10 Gyr. The x-axis for the $V$ and $I$ isochrones is the $(V-I)$ color, while for $K$ it is $(J-K)$; however, for clarity the $V$-band isochrones have been shifted by -3.5 mag in $(V-I)$, and the $K$-band isochrones have been shifted by +4.0 mag in $(J-K)$. As can be seen, for older stellar populations ($>$4 Gyr), the RGB colors are very insensitive to age, while the colors track differences in metallicity very clearly.
• Figure 2: PARSEC isochrones for a single 10 Gyr age at $VIJHK$ wavelengths. The isochrones span a range of metallicities of -2.0 $<$ [M/H] $< -$-0.4 dex. These bandpasses correspond to those in the observed color-magnitude diagrams for the LMC, SMC and IC 1613 shown in Figures \ref{['fig:LMC_CMDs']} and \ref{['fig:SMC_1613_CMDs']}. These isochrones show the well-known behavior of the TRGB stars as a function of wavelength: the tip stars increase in brightness in the infrared; they are nearly constant in the $I$-band, and they decrease in the $V$-band.
• Figure 3: A schematic illustration of multi-wavelength TRGB seen in three representative bands labeled V, I and K from left to right, illustrating the effects of distance, extinction and reddening. See text for details.
• Figure 4: A schematic illustration of the process of using TRGB data to simultaneously determine the true distance modulus and reddening from multi-wavelength data. Dots enclosed in squares are the result of the first iteration on the reddening simply differencing the apparent magnitude of the tip stars with the intrinsic relations. The scatter is non-negligible. Open circles show alternate reddening solutions on both sides of the input value. These solutions also show increasing (non-zero) scatter, most easily seen in the dashed-line solutions passing above and below the $I$-band data point. The input reddening is shown by the circled dots and fit by the steep solid line which was recovered by simply mimimizing the dispersion about the fit. See text for details.
• Figure 5: Color-Magnitude Diagrams for the red giant branch population of stars outside of the bar region of the Large Magellanic Cloud. The two plots across the top are for the optical ($VI$ band-passes and $(V-I)$ colors from OGLE-III), while the three across the bottom are for the near infrared ($JHK$ band-passes and $(J-K)$ color from 2MASS). All of the panels are zoomed into a two-magnitude vertical luminosity range and a lateral range in color of 2.0 mag in $(V-I)$ for the optical, and 1.0 mag in $(J-K)$ for the near infrared. The white lines mark the apparent magnitude level of the TRGB at each of the wavelengths, using predetermined slopes, fit to the data as described in the text. Arrows indicate the magnitude level in each bandpass at which the color calibration of the TRGB is normalized (i.e. at $(J-K)$ = 1.00 mag for $JH \& K$, and at $(V-I) =$ 1.80 mag in $V$ & $I$. The I-band selection function for the tracer stars is outlined by the white rectangle centrally-located in the upper right CMD.