The Third Catalogue of Nearby Stars (CNS3) was analyzed. A study of the stellar luminosity function in the solar neighborhood with CNS3 was described. The luminosity function for main sequence stars derived from CNS3 was compared with that from CNS2 and that based on the method of photometric parallaxes. The results from CNS3 for stars with Mv <15.5 were well defined. Luminosity functions for the giants and A, F, G, K and M type main sequence stars are also given, based on CNS3.

Olson’s light curves of the Algol-type binary WW And, showing evidence of harbouring an accretion disk, were re-analysed. Two approaches were attempted to find a solution: the first one, the Roche geometry model assuming the system consisting of two stars, and the second one, including also the existence of an accretion disk around the hotter component. In both cases the Monte Carlo method was employed to search for the best solution. We found that adding an additional parameter, namely the third light, the data can be satisfactorily reproduced with only a marginal underfilling of the Roche lobe of the cool star, for the Roche geometry. A thorough search within the semidetached configuration, incuding an accretion disk around the hotter component, was performed. Although such a fit is slightly worse (as measured by the rms error) than that for the Roche geometry, it can explain the observed spectroscopic features. Absolute parameters of the components of this interacting binary are presented for both models.

There is no reason to believe that the prospects expressed in Part III are the ultimate ones for development of evidences about stellar evolutionary information. Instead, (and just as for all other domains of science) technology advances and the availability of funds and manpower will remain important discriminants for new knowledge. As it happened, a presentation of some significant and imminent and distant hardware programs was given at the JD8 and it has been chosen (out of sequence with its order in Kyoto)to end this report.

Directly measuring stellar evolution may be accomplished in at least two distinctly different ways. The first approach will be observing it in real time as the phenomenon is taking place; the examples will include explosive events in recurrent novae, stellar oscillations in Cepheid and RR Lyrae variables, and mass flow in and out of interacting binaries. The second approach will be to observe a number of stars that are believed to belong to the same class at different stages of their evolutionary paths.

In this talk, I will focus on the first method of direct observations. The most direct method will probably be to observe images of the events thatwe wish to investigate. The same astronomical phenomena can and should alsobe studied using high-time and spectroscopic resolution data; however, thisis already being done with increasingly better spectral-and-temporal resolutions and will probably be reported elsewhere in this Joint Discussion. It is also noted that over the past two decades multiwavelength observations, using various telescopes on the ground and in space, have come to play a crucial role in astronomy, although I am not addressing this subject in this paper. I will talk primarily about imaging using interferometry that will soon become possible due to the advances in technology.

Most of the mass near the Sun takes the form of stars less luminous than the Sun. A central problem of Galactic astronomy is the determination of how much mass these stars contain.

The only thoroughly reliable way of detecting mass is through its gravitational field. Classically this has been done by studying the Galaxy’s rotation curve and the Oort limit, both of which remain active areas of research. In the last few years an exciting new way of probing the Galaxy’s gravitational field has been opened up by large surveys for microlensing events. These surveys are yielding important information about the numbers of low-mass objects both in the disk and above it. Another truly dynamical probe for low-luminosity objects is provided by studies of clusters. JD 10 reviewed what we have learned about the density of low-luminosity stars from each of these approaches.

An important orthogonal approach to determining the density of low-luminosity stars involves seperately determining the luminosity function and the mass-luminosity relation for stars of a given spectral class (e.g. main-sequence stars) and then combining them to obtain the mass function. The development of infrared detectors and the refurbishment of the The Hubble Space Telescope have recently yielded important advances in each of these areas. A major difficulty with this line of research is the fact that, in the neighbourhood of M = 0.08 Mʘ, the main-sequence mass-luminosity relation is (i) steep and non-linear, and (ii) dependent not only on the masses of the faintest stars, but also on their ages, metallicities, rotation rates, binarity etc. Moreover, cool low-luminosity stars have extremely complex spectra, which are difficult to simulate with radiative transfer calculations. Similar difficulties are encountered in the determination of the mass-luminosity relation for white dwarfs. JD 10 reviewed the current status of these very difficult problems.

The radial distribution of mass in a disk galaxy is strongly constrained by its rotation curve. The separate contributions from the individual stellar populations and dark matter (DM) are not easily disentangled, however, especially since there is generally no feature to indicate where the component dominating the central attraction switches from luminous to dark matter. Here I summarize three recent thesis projects at Rutgers University which all suggest that DM has a low density in the inner parts of bright galaxies, and that most of the mass therefore resides in the disk. In addition, I present some preliminary work on the Milky Way. If we are able to determine the M/L of a typical disk stellar population, it should provide a useful constraint on the numbers of low mass stars.

During galaxy formation non-baryonic dark matter is not expected to pack down into a thin disk. Hence the mass-to-light ratio ϒd of the Galactic disk is a key number as the mass-to-light ratio of a purely baryonic system. If ϒd proves to be large, it suggests that the large values of ϒ that are detected elsewhere in the Universe are due to dark baryonic matter rather than some exotic form of matter. Conversely, a small value ϒd lends credence to the idea that most of the mass in the Universe is non-baryonic by suggesting that baryonic systems are well endowed with luminous stars.

The aim of this paper is to summarise the dynamical constraints on the contribution of low luminosity stars. Important restrictions come from disk stability and the Oort Limit. These are reviewed elsewhere in these Proceedings in the contributions from Sellwood and Binney. Here, our attention is concentrated on two further pieces of evidence - constraints from (1) the stochastic heating of wide binaries and from (2) microlensing.

What is known about the masses of main-sequence stars from the analysis of binary orbits? Double-lined eclipsing binaries are the main source of very precise stellar masses and radii (e.g. Andersen 1997), contributing more than 100 determinations with better than 2% precision over the range 0.6 to 20 Mʘ. For lower-mass stars we are forced to turn to nearby systems with astrometric orbits (e.g. Henry et al. 1993). Not only is the number of good mass determinations from such systems smaller, but also the precision is generally poorer. We are approaching an era when interferometers should have a major impact by supplying good astrometric orbits for dozens of double-lined systems. Already we are beginning to see the sorts of results to expect from this (e.g. Torres et al. 1997).

Figure 1. Mass vs. absolute V magnitude for eclipsing binaries (circles) and nearby astrometric binaries (squares)

Figure 1 is an updated version of a diagram presented by Henry et al. (1993, their Figure 2). It shows the general run of mass determinations from about 10 Mʘ down to the substellar limit near 0.075 Mʘ. Ninety of the points in Figure 1 are for eclipsing binary masses from Andersen’s review (1991) and are plotted as open circles. The results for eclipsing binaries published since 1991 are plotted as 30 filled circles, adopting the same limit of 2% for the mass precision. In most cases the uncertainties are similar to the size of the symbols. Especially noteworthy is the pair of new points for CM Draconis (Metcalfe et al. 1996) with masses near 0.25 Mʘ. Together with the points for YY Geminorum near 0.6 Mʘ, these are the only M dwarfs that have precise mass determinations. For the most part we are forced to rely on nearby stars with astrometric orbits, to fill in the M dwarf region of the diagram. We have used filled squares in Figure 1 for 29 such systems from Henry et al. (1993), updated using 14 new parallaxes from Hipparcos and 4 from the new Yale Parallax Catalog (1995). Gliese 508 is not included, because it is now known to be a triple, while Gliese 67AB, 570BC, and 623AB are not included because there are not yet any direct measurements of the V magnitude difference for these systems.

Most of what we know about the Luminosity and mass function of low-mass stars has been derived from analysis of ground-based photometric and astrometric Surveys. A major uncertainty in the Interpretation of such surveys lies in the appropriate correction for unresolved binaries and in the use of a reliable colour-magnitude relation. various new surveys are now uncovering large numbers of objects which should rapidly ameliorate these ambiguities.

The recent discovery of brown dwarfs and planets has highlighted the importance of low-luminosity stars. once we understand their spectra and colours and have statistically significant samples, it will be important to use them to reliably constrain theories of star formation and chemical evolution as well as to use them as a probe of galactic structure and to reliably ascertain their contribution to baryonic dark matter. In this brief review ishall focus on ground-based field searches. Hambly (1997) reviews the very successful searches that have recently been carried out in nearby clusters.

Until the 1970s, most work on the faint-star luminosity function was based on proper-motion searches primarily by dutch researchers, in particular Luyten (e.g. 1938, 1979). The Last 20 years have seen a switch from astrometric to photometric surveys employing plate-scanning machines or CCD cameras. Combined with substantial increases in computing power these technologies have led to the discovery of large numbers of very low-luminosity Stars.

In order to tackle the problems of low-mass end of the initial mass function (IMF) in star-forming regions and the formation mechanisms of brown dwarfs, we have conducted deep infrared surveys of nearby molecular clouds. We have found a significant population of very low-luminosity sources with IR excesses in the Taurus cloud and the Chamaeleon cloud core regions whose extinction corrected J magnitudes are 3 to 8 mag fainter than those of typical T Tauri stars in the same cloud. Some of them are associated with even fainter companions. Follow-up IR spectroscopy has confirmed for the selected sources that their photospheric temperature is around 2000 to 3000 K. Thus, these very low-luminosity young stellar sources are most likely very low-mass T Tauri stars, and some of them might even be young brown dwarfs.

The initial mass function of stars (IMF) at small masses depends on several factors. First, it depends on the mass function of cloud cores in which stars form. Second, there must be a lower limit to the core mass for contraction; very small mass cores may not contract even if they exist. This must affect greatly the IMF near its lower end. Third, not all core matter may become stars; we must determine the stellar mass M* , or the star formation efficiency M*/Mcc, as a function of the mass of the cloud core, Mcc. In this paper we discuss the second and third points.

White dwarf (WD) evolution is essentially a cooling problem in two parts. Degenerate electrons in the core provide the support while non-degenerate C and O ions provide the thermal reservoir (Koester & Chanmugam 1990, Kawaler 1996). The rate of energy loss through the non-degenerate envelope of H and He—segregated by gravitational settling—is meager enough that the vast majority of WDs have not had time to cool to undetectability in the ~10 Gyr age of the Galactic disk. Because WDs are a remarkably homogeneous class with a mass function sharply peaked about 0.6Mʘ, and because the cooling physics is relatively straightforward to calculate, the observed deficit of WDs below Mv = 16.5 [log(L/Lʘ) ≈ -4.5, Teff ʘ 4000 K; see Liebert et al. 1988 (LDM), Oswalt et al. 1996 (OSWH), and Leggett et al. 1997] provides constraints on the age and star-formation history of the Galactic disk (Winget et al. 1987 (WEA97), Wood 1992 (W92), Yuan 1992, Hernanz et al. 1994).

The maximum fractional surface layer masses that can remain following post-AGB evolution are log(qH) ~ —4 and log(qHe) ~ —2 (for a 0.6 Mʘ remnant—the values are inversely correlated with remnant mass), although we know from WD asteroseismology that surface H layer masses range from this value to smaller than logqH ~ —6 (e.g., Fontaine & Wesemael 1997). Some 75% ofWDs in the McCook & Sion (1987) catalog reveal pure-H photospheres (spectral type DA). The remainder are broadly classified as non-DAs, with most showing show pure-He spectra (DB) or continuous spectra (DC), and with ahandful that show mixed compositions (DAB), or C (DQ) or metal lines (DZ). See Bergeron et al. 1997 for a thorough discusion of the chemical evolutionof cool WDs.

The study of cluster white dwarfs (WDs) has been invigorated recently bythe Hubble Space Telescope (HST). Recent WD studies have been motivated by the new and independent cluster distance (Renzini et al. 1996), age (von Hippel et al. 1995; Richer et al. 1997), and stellar evolution (Koester & Reimers 1996) information that cluster WDs can provide. An important byproduct of these studies has been an estimate of the WD mass contribution in open and globular clusters. The cluster WD mass fraction is of importance for understanding the dynamical state and history of star clusters. It also bears an important connection to the WD mass fractions of the Galactic disk and halo. Current evidence indicates that the open clusters (e.g. von Hippel et al. 1996; Reid this volume) have essentially the same luminosity function (LF) as the solar neighborhood population. The case for the halo is less clear, despite the number of very good globular cluster LFs down to nearly 0.1 solar masses (e.g. Cool et al. 1996; Piotto, this volume), as the field halo LF is poorly known. For most clusters dynamical evolution should cause evaporation of the lowest mass members, biasing clusters to have flatter present-day mass functions (PDMFs) than the disk and halo field populations. Dynamical evolution should also allow cluster WDs to escape, though not in the same numbers as the much lower mass main sequence stars. The detailed connection between cluster PDMFs and the field IMF awaits elucidation from observations and the new combined N-body and stellar evolution models (Tout, this volume). Nevertheless, the WD mass fraction of clusters already provides an estimate for the WD mass fraction of the disk and halo field populations. A literature search to collect cluster WDs and a simple interpretive model follow. This is a work in progress and the full details of the literature search and the model will be published elsewhere.

The expression “low luminosity stars” is a descriptive category which spans a wide range of objects, from the oldest stellar remnants in the Galaxy (Wood) through failed stars (Jones, Gould) to the enigmatic MACHOs, discernible not in themselves but only through their effects on others (Bennet). All of these have attracted considerable attention in recent years, and significant progress has been achieved in each case, even if our understanding has failed to keep up with observations. However, it is in the area of brown dwarfs where the most dramatic results have been obtained. The existence of such objects has been predicted theoretically for well over thirty years, but predictions can fail. Thus the discovery of G1229B (Nakajima et al, 1995), an unambiguous substellar-mass object, followed by the detection of lithium in Teide 1 and Calar 3 in the Pleiades (Rebolo et al, 1996) mark a turning point in studies of brown dwarfs. The issue now is not whether they exist, but what are their properties as a class. With that in mind, a number of obvious questions arise.

First, what is the most effective method of finding brown dwarfs? Both brown dwarfs and VLM stars have effective temperatures below 2500K. Hence, many surveys concentrated on searching for objects which were very red at near-infrared wavelengths, and the blue JHK colours exhibited by Gl 229B cameas something of a surprise. This should not have been the case, of course, since Tsuji (1964) predicted the presence of methane in such cool atmospheres well before the term ’brown dwarf’ was invented. Current theory, as summarised in these sessions by Tsuji and Burrows, predicts that, as one moves to lower temperatures, grain formation initially drives (J-K) redward, before grains settle below τ ~ 1 and CH4 absorption sets in. Throughout, however, the optical-to-IR colours, straddling the peak in the emergent flux distribution, become progressively redder (Reid, 1994). Those colours therefore offer the most effective means of identifying both GD 165B-like and Gl 229B-like sources - an argument reinforced by the first results from the IJK DENIS survey (Delfosse et al, 1997).

In a recent survey for faint red stars from a digital stack of Schmidt plates a number of candidate objects were identified. Parallax’s for three of these objects have been reported showing them to have luminosities which interpreted within the available evolutionary models indicate them to be good brown dwarf candidates. Here we examine spectra of these objects and others from the plate stack. Using standard spectral indices we find that for a given spectral type their spectra are more consistent with the Pleiades brown dwarfs (PPL 15, Teide 1 and Calar 3) than with standard late-type M dwarfs. Our interpretation is that this is due to their selection by RF IN colours which at values > 3 preferentially selects objects with relatively low gravities. For late-type M dwarfs and brown dwarfs low gravities are expected to be a reliable indication of youth. We also notice that the stack objects generally have strong FeH absorption for their spectral type. Current model atmospheres suggest that FeH strongly increases in strength toward lower metallicities and lower temperatures. We believe that this is not consistent with the available observational evidence from late-type M dwarfs. It is possible that solid Fe is forming inthe low temperature atmospheres relatively depleting FeH strengths toward lower temperatures. We find some evidence that for dwarfs at low temperatures dust formation is less prevalent in lower gravity objects suggesting that dwarfs at low temperatures stronger FeH may be an indication of youth. In addition to the spectral evidence the three stack objects whose parallax’s have been measured show small tangential velocities which is a further indication of youth.

Photometric parallaxes derived from B, V, R, I photometry of wide binaries with white dwarf components were used to set a firm lower limit to the age of the Galactic disk (see Oswalt et al. 1996 and the article by Wood elsewhere in these proceedings). Here we show the distribution of projected semi-major axes derived from new B, V, R, I data for over 200 wide pairs.

Like clusters, wide binaries are gradually disrupted, primarily by the gentle but cumulative effects of encounters with the denser parts of giant molecular clouds (see Wasserman & Wienberg 1991 for a review). A sharp cut-off in semi-major axes > 0.1 pc was one of the predictions of competing models. Wood & Oswalt (1992) showed that additional orbital expansion occurs in wide pairs which have experienced isotropic post-MS mass loss. Can we see the signatures of these events in the wide binary sample?

Dwarf carbon (dC) stars are believed to be main-sequence stars which have received carbon-rich material from a former AGB carbon star companion. We have computed model atmospheres, synthetic spectra, and colours for dC stars and compared them with observations. Our models are computed with an updated version of the MARCS code (Jørgensen et al. 1992, A&A 261, 263) and include atomic and molecular line blanketing, grain formation, and collision-induced absorption (CIA) processes (Borysow et al. 1997, A&A 324, 185). The models assume hydrostatic equilibrium, which for giant stars (i.e., high luminosity and low gravity) would be inconsistent with the inclusion of dust. Typical gravities of dC stars are, however, considerably larger than the acceleration due to radiation pressure even on dust grains with a relatively high absorption coefficient.

For the cooler solar metallicity models, grain formation can be substantial, but it depends strongly on the assumed type of dust. In a test model of Teff = 2800 K, C/O = 1.17, and log(g) = 5, 1% of the free carbon (i.e., that not bound in CO molecules) condensed when the dust was assumed to be amorphous carbon, whereas as much as 30% condensed when nano-diamonds (of the extra-solar form which are abundant in carbonaceous chondrite meteorites and are believed to have formed in stellar outflows) were allowedfor. This difference in degree of condensation is due to the very small diamond opacity compared to that of amorphous carbon. In both cases, however, the main effect of the dust was a 400 K heating of the surface layers. The dust itself is not clearly visible in the synthetic spectrum, but the heating and correspondingly reduced molecular partial pressures cause a weakeningof spectral features in the 3μm region (due mainly to reduced C2H2 abundance in the upper layers) and reduced CO fundamental and first overtone band intensities.