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Table E.1.

Uncertainties included in TRGB calibration and LMC or SMC distances.

Uncertainties related to Considered elements σ [mag]
Milky Way GC TRGB calibration; see Table 1 0.035 + 0.041 Mathematical equation: $ ^{+0.041}_{-0.035} $
GC distances Covariant GC distance uncertainties from Lengen et al. (2026), which include: 0.022 + 0.023 Mathematical equation: $ ^{+0.023}_{-0.022}\ \dagger $
a) GC parallax uncertainties (Cruz Reyes et al. 2024) with
Individual parallax uncertainties (Lindegren et al. 2021b)
Parallax zero-point corrections (Lindegren et al. 2021a)
Angular covariance of GDR3 parallaxes (Maíz Apellániz et al. 2021)
Corrected GDR3 parallax uncertainties (Maíz Apellániz et al. 2021)
b) Photometric uncertainties (Clementini et al. 2023; Ripepi et al. 2023)
c) Intrinsic scatter of the period–luminosity relation
d) Metallicity dependence of PL relations
e) Model-fitting uncertainties
Photometry photometric quality cuts applied; see Sect. 2
bootstrap resampling in absolute magnitude space; see Appendix E 0.028 + 0.032 Mathematical equation: $ ^{+0.032}_{-0.028}\ \dagger $
Extinction Uncertainties of E(B − V) and consistency in the recent literature
RV differences for GCs not found to be significant in literature
Range of AI/E(B − V) yields only minor differences due to low average E(B − V)

mTRGB from Table 3 in KA24
smoothing bias, Sobel filter response, extinction, metallicity, among others
LMC uncertainty on GRP, 0 for SARGs 0.009
SMC uncertainty on GRP, 0 for SARGs 0.035

TRGB-based distance modulus MW GC TRGB calibration in RP band (joint stat. & syst.)
mTRGB (joint stat. & syst.)
homogeneous space-based GDR3 RP-band observations in GCs and LMC/SMC
identical TRGB measurement process (unweighted Sobel, smoothing insensitivity)
colour-based metallicity corrections: remains within 1σ

Notes. Statistical and systematic uncertainties are considered jointly in this analysis. The table provides an overview of the most significant elements with references for more information. † indicates items treated simultaneously to determine the uncertainties reported above (see Appendix E). Numbers reported in column σ must be considered for information only and were derived by running the analysis separately considering only the distance covariance matrix or bootstrap resampling. NB: the final calibration is based on a single joint inference that simultaneously incorporates both approaches. Its asymmetric uncertainties can thus not be exactly reproduced by a summing the values reported here in quadrature.

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