Accuracy of the ‘tip of the red giant branch’ distance determination method

Context. To solve the so-called Hubble tension problem, highly accurate methods of determining extragalactic distances are needed. Therefore, the accuracy and applicability of the tip of the red giant branch (TRGB) method is of the utmost importance. Aims. In this work, we aim to study variations in the TRGB versus radial distance and location in the M 33 galaxy disc. Methods. We used colour-magnitude diagrams of stars from the M 33 Subaru Suprime-Cam stellar photometry catalogue ( V and I -passbands of the Johnson-Cousins system) to test the accuracy and robustness of the TRGB method in determining extragalactic distances. Results. We derived radial (metallicity) and azimuthal (galaxy inclination) variations in the TRGB magnitude ( I TRGB ). We find the I TRGB = 20.638 ± 0.008 magnitude to be virtually constant over the radial distance from 7 to 11 kpc. Assuming the absolute TRGB magnitude, M I TRGB = −4.05, and foreground extinction, A I = 0.062, we derived the true distance modulus of the M 33 galaxy to be ( I TRGB − M I TRGB ) 0 = 24.626 ± 0.008 stat (∼842 kpc). Conclusions. We demonstrate the ability of the TRGB method to discern the distance difference between the proximal and distal parts of the galaxy disc, which is ∼1.3% of the distance to M 33 . We show that the TRGB method is highly accurate and can be reliably applied to the red giant branch star populations of a low metallicity ([Fe/H] ≲ −1.3). With a slightly lower accuracy, it can also be applied in cases of higher metallicity, which is more common for numerous low-mass spiral galaxies.