Red supergiants in the LMC. IV. Calibration of intrinsic colours and the HRD

A new calibration of the (B - V)(o), (V - R)(o) and (V - I)(o) colours in t he I(ron-Cousins system for F to M supergiants and of the (V - K)(o) colour s in the SAAO system of K to M supergiants in the LMC as measures of effect ive temperature and bolometric correction is given. For F to G supergiants the theoretical T-eff-intrinsic colour- relations given by Lejeune et al. ( 1997) on the basis of their own model atmospheres agree mostly well with ou r observations. For K to M supergiants, however, their intrinsic colours ar e too red in most cases. The relations given by Bessell et al. (1998) based on the model atmospheres of Plez (1997) fit the observations better, but t heir synthetic colours are often also too red. The calibration of the bolom etric correction is not reproduced well by any of the models. The HRD of th e stars shows two distinct groups: one with log T-eff above 3.80 and one wi th log T-eff between 3.53 and 3.62. The upper luminosity and therefore the mass limit depends significantly on effective temperature. The F to G stars have M-bol UP to -9.8 mag (corresponding to 45 M-.), while the K to M star s do not exceed -9.0 mag (corresponding to 31 M-.) Neither the Geneva nor t he Padova models can fit the positions of the most luminous and the coolest supergiants. The discrepancy between theory and observation increases both with increasing mass loss rate and overshooting. Best agreement with the o bservations is reached by assuming mass loss rates of 2/3 of the de Jager e t al. (1988) mass loss rates. As shown both by the luminosity and initial m ass function, very luminous (i.e. massive) stars are overproportionally rar e. With -3.73 +/- 0.20 the slope of the initial mass function is very steep in the considered range of 16-35 M-. but confirms the results obtained by Massey ct al. (1995) from an extensive study of the field OB stars both in the Magellanic Clouds and the Galaxy.