Distance to the globular cluster M3 determined from individual RR Lyrae stars
The infrared surface brightness technique was used to determine distances to individual RR Lyrae stars in the M3 globular cluster. The average of their distances is 10.14 ± 0.19 kpc, precise to 1.8%. As an additional benefit, the radii of RR Lyrae stars were determined with precision of 0.5%.
Distance to the globular cluster M 3 from the infrared surface brightness technique applied to RR Lyrae stars
B. Zgirski, W. Gieren, G. Pietrzyński, G. Hajdu, P. Wielgórski, M. Górski, J. Storm, N. Nardetto, A. Gallenne, G. Bras, P. Kervella, P. Karczmarek, W. Narloch
Our Araucarians did it again! Again we measured a distance achieving a very competitive precision. This time the target was M3, the stars used were RR Lyrae, and the technique – the Infrared Surface Brightness (IRSB).
The IRSB technique is a specific application of the Baade-Wesselink method. Taking the full advantage of well-covered light curves in the visual and near-infrared domains, and radial velocity curves, the IRSB technique allows to determine distances to individual pulsating stars that is completely independent from the distance determinations using period-luminosity relations. It is also fully empirical, meaning that it bypasses the need for complex stellar atmosphere models that can introduce hidden biases. The only challange is observational – to collect all the required data. Luckily, the authors used the data already available in the literature.
The paper draws from the previous work of Zgirski et al. (2024), which used Gaia parallaxes to calibrate the IRSB technique, and now uses this very calibrated IRSB technique to deliver the distance to M3. The authors obtained a mean distance to M3 of 10.07 ± 0.19 ± 0.29 kpc, which corresponds to a distance modulus 15.015 ± 0.041 ± 0.063 mag, and a 7% scatter of individual stellar distances for 14 RR Lyrae stars in M3. They also obtained distances with other calibrations of the IRSB available in the literature, and reported a very good
agreement between the two fitting techniques. The first of them, the bisector fit, traditionally favored for its stability against noisy data, proved to be a biased estimator. The bias arose because the uncertainties in estimating a star’s angular diameter were significantly larger than the uncertainties in the radial velocity integral. The other one, the least-squares fit, yielded slightly larger uncertainties albeit being bias-free. The authors identified the bias of the bisector fit through extensive Monte Carlo simulations. It serves as a reminder that the most “stable” path in mathematics is not always the most truthful one.
As a byproduct the radii to all 14 individual RR Lyrae stars were determined with precision of 0.5%. To resolve the physical dimensions of a star 10 kiloparsecs away to within half a percent is a testament to modern methodological rigor. The radii show excellent agreement with a theoretical prediction of the period-radius relation for RRab stars available in the literature.
The study found that the IRSB method is virtually independent of metallicity and remarkably resilient against the obscuring effects of interstellar reddening – the factor that frequently plagues other distance indicators. By utilizing the recent Bailleul et al. (2025) surface brightness-color relation (SBCR), the authors demonstrated that tools calibrated for classical Cepheids can be applied to RR Lyrae stars with impressive efficacy.
The authors used the near-infrared K-band observations, because the near infrared data are far less sensitive to the star’s surface gravity and “line blanketing” (the effect where chemical elements in a star’s atmosphere block specific wavelengths of light). Even though, it was the raw data that was the largest contributor of uncertainty: a scatter of just 0.02 magnitudes in the K band contributed to a 7% scatter in individual stellar distances.
At the heart of the calculation lies the “p-factor” – the ratio of a star’s actual surface motion to the radial velocity determined from the RV curves. This factor is the most delicate “recipe” in the Baade-Wesselink method. The authors reported that different mathematical recipes for the p-factor yield results that can be shifted by 5%.
The final distance to M3 is just the beginning for other methods of distance determinations. Using the distance to M3, other methods can be better calibrated, such as the Tip of the Red Giant Branch (TRGB) method or Type II Cepheids. These additional distance determinators are useful tools in the toolbox of “cosmic distance scale” as they allow to determine distances independently from classical Cepheids, making them solid and welcomed aids in the quest to determine the Hubble constant.
