The evolution of the galactic disc involves several time-dependent mechanisms which combination produces the present-day space-luminosity-velocity distribution : the heating rate of the disc, the star formation rate, and the initial distribution of stellar masses at different epochs. The luminosity function as it is observed in the solar neighbourhood result from the combination of these three processes. Due to the sparse nature of the available data for investigation of the IMF at masses greater than 1 in the solar neighbourhood, most investigations should rely upon assumptions concerning one or two of these processes, for which there exists, however, a rather weak observational or theoretical basis.
One of these assumptions, which is very efficient to work with, postulates that the distribution of stellar masses at birth has remained constant with time. This strong assumption has sometimes been alleviated with the bimodal hypotheses (Scalo (1986), Larson (1986)). From the observational point of view, a basic support for the bimodal hypotheses was the flattening or dip found in the observed luminosity function (hereafter LF) at =6-9, which was interpreted by Scalo as being due to a corresponding feature in the IMF. This suggestion has been seriously questioned by D'Antona & Mazzitelli (1986), Kroupa, Tout & Gilmore (1990, 1991, 1993) (hereafter KTG (1990), etc), and Haywood (1994), all attributing this feature in the LF to the non-linear behavior of the mass- relation. If the IMF in the corresponding mass range can be described by a single power law slope, one question nevertheless remains: Scalo gives evidence for a rise in the IMF at M 1 , if a decreasing or constant star formation rate is assumed. As noted by Scalo, such a change in the IMF at exactly 1 is an embarrassing result, which can only be avoided by exploring the following alternatives: either this feature tells us that constant or decreasing SFR are an inadequate description of SFR history in the galactic disc, or we should consider that the derivation of the IMF contains various sources of error which have been underestimated.
The second most important assumption concerns the density decrease perpendicular to the galactic plane. This decrease is usually assumed exponential in determinations of the local IMF (Miller & Scalo (1979), Scalo (1986)) and in Galaxy models (Bahcall & Soneira (1981), Gilmore (1984) etc), with a scale height of 300-350 pc. Recent determinations of the scale height of the galactic disc stars in the solar neighbourhood (Soubiran (1994), KTG (1993), and Ojha (1994)) have a systematic discrepancy with these values. This problem is quite important since a 30% uncertainty in scale height confers an equivalent uncertainty in the local surface density of stellar material in the disc. More generally, one may question the accuracy of the exponential representation of the vertical density of disc stars. Given the fact that the disc heating is a time-dependent process, the number of stars found at a given height above the plane depends on how many stars were formed at a given epoch. In all studies the fundamental interplay between IMF, SFR and vertical structure has been neglected. The present paper focuses on the local constraints available for the discussion of these three aspects, while Paper II is dedicated to comparison with star counts at the galactic poles.
The paper is organized as follows. Sect. 2 summarizes the main
features of the galactic disc model utilized. A set of models designed
to represent the galactic disc stellar evolution is then
proposed given different prescriptions for the SFR. In Sect. 3, we
compute the density gradient in z for these models and compare them
with the exponential profiles that are usually assumed for the
galactic disc at solar radius. In Sect. 4, we discuss the accuracy of
the IMF derived from the observed LF by various authors, then we study
the LF by directly computing the LF with our model. We conclude in
Sect. 5 and summarize the main questions that are to be addressed in
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998