5. Discussion and final remarks
In this paper, we have shown that the WD cooling sequence for a Simple Stellar Population can be divided into two portions with different characteristics, namely:
i) A portion at large luminosity ( L/L), where the distribution depends on cooling times only. This region has been used to place constraints upon the neutrino cooling efficiency (Blinnikow & Dunina-Barkoskaya 1994). At high luminosity the cooling times are affected by the residual nuclear burnings and, hence, by the thickness of the H and He-rich envelope. Thus, this region of the cooling sequence can be used to gather information on the mass-loss mechanisms which take place during the Asymptotic Giant Branch and Planetary Nebula phases.
ii) The bottom of the sequence that provides information about the cluster age and the IMF of WD progenitors. For ages higher than, about, 10 Gyr one expects also evidences to be connected with the debated problem of CO crystallization (see Wood 1995, Salaris et al. 1997).
The WD-cluster age connection has already been applied, in a pionieering paper, by von Hippel et al. (1995) to the cooling WD in NGC 2477, disclosing a discrepancy between WD and TO ages, the latter derived by assuming a relevant core overshooting during central H burning phases. We note that the WD termination in this cluster appears in good agreement with theoretical evolutionary computations by Castellani et al. (1992) where the efficiency of the core overshooting is negligible. Whereas this result would deserve further discussions in the light of the uncertainties recalled all througout this paper, it can be taken as an evidence that WD can give a relevant independent information about cluster ages, which can be of help in resolving open questions about theoretical stellar evolution.
It should be noted that, if the cluster metallicity is known, one can use the calibration of the luminosity of He burning stars in terms of metallicity to approach the problem of cluster distance modulus. In this context, the difference in magnitude between the He burning stars and the WD termination (WDT) can be easily calibrated, in analogy with the well known (HB-TO), as a distance-free age indicator. Furthermore, one finds that the luminosity of the WDT, for each given assumption on the chemical composition, decreases with the cluster age more rapidly than the TO luminosity. Thus, for each given chemical composition, the difference in magnitude between the WDT and the TO can be once again calibrated in terms of the cluster age. This quantity increases with the cluster age.
Let us finally notice that all along this paper we have neglected a mechanism that, at least in principle, can contribute to the WD luminosity: the accretion of interstellar matter. Accretion can (or must) at some time inhibit further cooling, maintaining WD surfaces at a temperature hotter than the one predicted by cooling laws alone (Castellani & Panagia 1971). However, according to the discussion in Iben & Tutukov (1984), this mechanism should be of little relevance here. Thus, we conclude that theoretical prescriptions concerning the cooling of WD can be safely assembled to provide relevant constraints on the cooling sequences of WD in stellar clusters. In spite of the current uncertainties on the theoretical scenario, cluster WD represent, in our opinion, a new relevant target for future observations.
© European Southern Observatory (ESO) 1999
Online publication: April 19, 1999