2000A&A...359..601C

We present a precise determination of the apparent magnitude of the tip of the red giant branch (TRGB) in the I (0.8µm), J (1.25µm), and K_S (2.15µm) bands from the luminosity function of a sample of data extracted from the DENIS catalogue towards the Magellanic Clouds (Cioni et al., 2000A&AS..144..235C, Cat. II/228). From the J and K_S magnitudes we derive bolometric magnitudes m_bol. We present a new algorithm for the determination of the TRGB magnitude, which we describe in detail and test extensively using Monte-Carlo simulations. We note that any method that searches for a peak in the first derivative (used by most authors) or the second derivative (used by us) of the observed luminosity function does not yield an unbiased estimate for the actual magnitude of the TRGB discontinuity. We stress the importance of correcting for this bias, which is not generally done. We combine the results of our algorithm with theoretical predictions to derive the distance modulus of the Magellanic Clouds. We obtain m-M=18.55 ±0.04 (formal) ±0.08 (systematic) for the Large Magellanic Cloud (LMC), and m-M=18.99 ±0.03 (formal) ±0.08 (systematic) for the Small Magellanic Cloud (SMC). These are among the most accurate determinations of these quantities currently available, which is a direct consequence of the large size of our sample and the insensitivity of near infrared observations to dust extinction.