Abstract
The value of the Hubble constant as constrained by type Ia supernovae is directly tied to the zero point of the extragalactic distance scale, which is in turn set by the calibration of astrophysical distance indicators such as the tip of the red giant branch (TRGB). In this article, a calibration of the TRGB luminosity is determined in the Magellanic Clouds. Composite colour–magnitude diagrams are constructed for the Small and Large Magellanic Clouds using regions in which the TRGB could be unambiguously identified. As a result, a sub-per-cent measurement of the TRGB in the Clouds is determined. The I versus (V − I) relation of the TRGB is found to be consistent with a constant I magnitude over colours 1.45 < (V−I)0 < 1.95 mag, and a shallow, quadratic curvature is confirmed when including more metal-rich (up to (V−I)0 = 2.2 mag) tip stars into the fit, and is the preferred solution. This study’s TRGB measurements also constrain the three-dimensional tilt of the Large Magellanic Cloud as well as the distance between the Small and Large Clouds. Both findings are in agreement with the independent, geometric constraints derived from the detached eclipsing binaries and establish a better than 0.02 mag cross-consistency (1% in distance) between the latest detached eclipsing binary measurements, red clump reddening maps and the TRGB measurements of this study.
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Data availability
All data used in this work are publicly accessible, including OGLE-III photometry (http://ogle.astrouw.edu.pl/cont/4_main/map/map.html), OGLE-IV reddening maps (http://ogle.astrouw.edu.pl/cgi-ogle/get_ms_ext.py), Gaia EDR3 astrometry (https://gea.esac.esa.int/archive/) and the Harris and Zaritsky SFH maps (https://cdsarc.unistra.fr/viz-bin/cat/J/AJ/138/1243).
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Acknowledgements
I am indebted to W. L. Freedman for her invaluable support and tutelage throughout my graduate studies, as well as insightful comments on and discussions regarding this manuscript. A. Udalski and the OGLE Collaboration are acknowledged for making publicly available the photometry from their revelatory survey. I thank D. and J. Skowron for making publicly accessible their reddening maps of the MCs. I thank J. Harris and D. Zaritsky for making publicly available their SFH maps of the LMC. I am thankful for the frequent, fundamental insights of B. Madore. I am grateful to H.-W. Chen for heartening and encouraging discussions. I thank R. Beaton for stimulating discussions regarding the Clouds. I highlight the work of M. Seibert who introduced the use of Voronoi tessellation to study resolved stellar populations, an approach that has since become common in the literature. I thank I. S. Jang for helpful comments and clarifications. I acknowledge M. Karouzos for helpful comments and suggestions. I thank C. Esmerian for his helpful comments. This work has made use of data from the European Space Agency mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the Data Processing and Analysis Consortium has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. Support was provided in part by NASA through grant number HST-GO-16743 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. A version of this article was presented as a dissertation to the Department of Astronomy and Astrophysics at The University of Chicago.
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Extended data
Extended Data Fig. 1 Two-staged Sample Selection Procedure.
a, First, a cut is made based on the width of the distribution of TRGB magnitudes I0,TRGB determined via bootstrapping the RGB LF for each of the 25 fields. The modal TRGB magnitude for each field is plotted as a function of half the 90% confidence interval for each bootstrapped realization. The points are colored according to the \({{}^{{r}_{1}}}^{{{{\rm{HZ}}}}09}\) parameter which is defined to trace intermediate-age stellar mass. A vertical dashed line indicates the first of two cuts used to clean the sample. Only the remaining 15 fields are considered in the next panel. b, Second selection based on the asymmetry of the edge detector response (EDR) and the bootstrapped interval width. The difference between the upper (84%) and lower (16%) limits of the 68% intervals is plotted on the x-axis, the same bootstrap 90% CI is plotted on the y-axis, and the points are colored according to their field number to aid in identification. A circle of radius 0.025 mag is plotted to represent the cutoff adopted for the calibration sample. The next closest point (Field 5) is located 0.043 mag from the origin, while the furthest points are up to 0.115 mag from the origin. The SMC lies in The five fields adopted for the calibration sample cluster together and exhibit unambiguous, singularly peaked TRGB features. All plotted values are tabulated in Extended Data Table 2. More details on both sets of cuts are provided in Supplementary Fig. 2 and 3.
Extended Data Fig. 2 Maps of Intermediate-age and Young Stellar Populations in the LMC.
The Harris & Zaritsky (HZ09)67 star-formation history (SFH) maps are integrated into mass bins that represent intermediate-age (panel a) and young (panel b) stellar populations (integrals defined in Equation (3)). A black outline indicates the coverage of the OGLE-III photometric maps adopted for this study. Known star-forming structures such as the LMC’s Northern spiral arm and the 30 Dor star-forming region (R.A. ~ 85 deg, Dec. ~ -69 deg) are apparent.
Extended Data Fig. 3 Spatial distributions of young astrophysical objects and this study’s sample selection.
a, Active regions of star formation in the LMC schematically drawn over the distribution of upper RGB stars from the adopted OGLE-III catalog (its survey footprint plotted by a black outline). b, Three sets of fields plotted over the same RGB stars: the calibration sample (blue regions), the sample cut in the first set of cuts (red), and in the second set of cuts (yellow). c, Cepheids from the OGLE-IV survey30 plotted on the OGLE-IV reddening map (red dots). Intensity corresponds to E(V − I) reddening. The calibration sample is again hued and outlined (blue). d, Same as c but for HI supergiant shells (red open circles)31 e, Same as c but for the DEBs (red filled circles)18.
Extended Data Fig. 4 Determination of the on-sky orientation of the LMC using the TRGB.
a, TRGB measurements derived from all 116 OGLE-III fields. b, Same as (a) but for the 37 OGLE-III fields adopted for their singularly-peaked EDRs. c, Model predictions for the best-fit parameters Θ = 153 ± 12∘, i = 27 ± 3∘. d, Residuals. The position of the best-fit line of nodes is plotted for reference. e, Three-dimensional visualization of the best-fit plane geometry, with the negative z-axis extending in the direction of the observer. A subset (20000 sources) of the total OGLE-III sample of RGB stars is overplotted (gray points).
Supplementary information
Supplementary Information
Supplementary Figs. 1–14, Table 1 and supplementary discussion on proper motion cleaning, sample selection, tests of geometric models and reproducibility of literature results.
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Hoyt, T.J. Sub-per-cent determination of the brightness at the tip of the red giant branch in the Magellanic Clouds. Nat Astron 7, 590–601 (2023). https://doi.org/10.1038/s41550-023-01913-1
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DOI: https://doi.org/10.1038/s41550-023-01913-1