Introduction

If binary stars simply executed their orbits according to Newtonian theory for point masses, then interest in their properties would have waned long ago, save for the need to improve determinations of stellar masses. The universe is rather more exciting, however, and at least the close binary stars (as defined in Chapter 1) display all manner of perturbations and interactions that guarantee that they will continue to provide an abundance of astrophysical phenomena that will require explanation. In this chapter we consider a sequence of progressively greater departures from the point-mass, spherical-star model that we used in Chapters 2 and 3.

We consider, firstly, a theory of mild perturbations, or deviations from the idealized spherical shape for a star, which theory can fully explain the observed phenomena of apsidal motion, the circularization of orbits, and the synchronization of stellar axial-rotation periods and orbital periods. The stars in such binary systems become tidally locked, such that two stellar hemispheres face each other, and two are permanently averted. The logical extension of these perturbations is to the Roche model for binary stars that is applicable to tidally locked systems in circular orbits. Here the stars can be virtually spherical in shape when their radii (R) are small relative to their separation (a)(R/a < 0.10), and they appear no different from those in the earlier point-mass theory. But the Roche model also permits stars to become seriously distorted from spherical shape, with R/a > 0.20, far beyond the limitations of the earlier perturbation theory.

Introduction

For many observational astronomers who study the properties of binary stars, the ultimate goal of their work is to make direct determinations of the masses, radii, shapes, temperatures, and luminosities of the component stars, often referred to as the astrophysical parameters. The term absolute dimensions has been used to indicate that analyses of the radial-velocity curves and light curves for binaries really do provide descriptions of the stars in SI units, regardless of the distances of the binaries from us. As noted in Chapter 1, because the luminosities of the stars in binaries are determined directly, they act, potentially, as excellent standard candles for distance determinations amongst nearby galaxies. Much effort has been devoted to finding ways of ensuring that such data are free from systematic errors and have the smallest possible random errors, so that direct comparisons can be made between these empirical results and the predictions from stellar-structure and stellar-evolution theories applied to binary stars. The main theme underlying Chapters 3–5 in this text has been to demonstrate the ways in which systematic errors can be overcome, and random errors minimized, by making use of spectroscopy and photometry at the best spectral and temporal resolution consistent with the observational task at hand. This chapter will summarize the progress that has been achieved in these directions amongst the different subclasses of binary stars.

The subject of binary stars is always discussed in introductory texts in astronomy and astrophysics. The usual prescription involves the distinctions between visual (or resolved) binaries and the spectroscopic and eclipsing binaries, as well as schematic examples of resolved orbits, radial-velocity curves, and light curves. Examples of interacting binaries are discussed, and there are artists' impressions of Roche-lobe-filling stars sending gas streams across to impact an accretion disc surrounding a black hole, with jets of ejected matter from the inner regions of a thick accretion disc interacting with the local interstellar medium. A brief discussion usually emphasizes the importance of binaries for the determination of stellar masses and other parameters and their central role in explaining the properties and evolutionary states of many unusual stellar objects, such as novae, symbiotic stars, and x-ray binaries.

I have assumed that the reader of this text has already benefited from an introductory course in astronomy, including a careful reading of one of the many excellent introductory texts currently available. The basic ideas of astrophysics, including stellar evolution and the essential ideas about binary stars, should be well understood. I have assumed also that the reader has studied physics and mathematics to a similar level. Beyond these assumptions, I have tried to write a text that will be readily understood by an intermediate-to-advanced-Ievel undergraduate in astrophysics who is interested in the more practical, observational, and data-analysis aspects of studies of close binary stars.

Introduction

Measurement of the brightness of astronomical sources is a fundamental part of all astronomy. The first detections of variations in brightness levels led to the beginning of the recognition of the existence of eclipsing binary stars, thanks to the work of Goodricke (1783), as noted in Chapter 1. Since that time, systematic searches for photometrically variable stars have been conducted by visual, photographic, and photoelectric techniques, and many eclipsing, or photometrically variable, binary stars have been discovered in the process, again as discussed in general terms in Chapter 1. It is therefore no accident that the observational technique of photometry has been the mainstay of studies of binary stars in general, at least in part because photometry can be conducted with very modest equipment and relatively small telescopes. Recent developments in CCD technology that have made it possible to record digital images of small areas of the sky with remarkable photometric precision have further enhanced the value of telescopes of modest apertures in conducting front-line research – for example, the recent discoveries of substantial numbers of eclipsing binaries in the nearby galaxy M31 by Kaluzny et al. (1998, 1999) and Stanek et al. (1998, 1999), who used a telescope of 1.3-m aperture. The current prospects for setting up a global network of programmable robotic telescopes to conduct continuous photometric monitoring of variable sources, including binary stars, are very encouraging, and that will herald a new era in our understanding of the properties of binary stars – magnetic-activity cycles, outbursts, changes in accretion structures, for example.

Chapter 1

1.1 Use Kepler's third law and the small-angle formula to obtain a = 0.051 AU and α = 2.5 mas, still below the currently attainable spatial resolution.

1.2 Use Kepler's third law to obtain a = 19.87 AU, or a = 4270.9 R⊙. Thus both stars have space to evolve independently. The present age of Sirius A is t = 3.28 × 108 years. Sirius B must be massive enough to evolve to a white dwarf in that time. Hence mB = 2.86 M⊙ is the minimum mass for the progenitor of Sirius B, and it must have lost 1.92 M⊙ through the redgiant wind-driven mass-loss phase and the planetary-nebula phase. Discuss whether or not these figures are in accordance with our knowledge of mass loss at different evolutionary stages.

1.3 A CV is composed of a white dwarf and a low-mass main-sequence star. The white dwarf is the degenerate core remnant of a star that was once a red giant. Hence the need for enough space in the binary to allow evolution through the red-giant phase undisturbed, requiring Roche lobes greater than about 100 R⊙. Thus the initial orbital period must have been years, rather than a few as hours as for W UMa systems.

1.4 High-mass x-ray binary (HMXB): 0 star's main-sequence lifetime about 2 × 106 years; A star's, about 100 times longer. 0 star evolves to red-supergiant stage, losing mass to companion through RLOF and mass-ratio reversal.

Introduction

The fundamental equations, relationships, and definitions that we considered in Chapter 2 can be applied directly to interpretation of observational data on binary stars from four types of experiments. The first is spectroscopy, which yields measurements of line-of-sight (or radial) velocities, followed by derivation of the elements of the orbits from those observed velocities. These data furnish the quantities related to the absolute sizes of the orbits and to the masses of the stars in binary systems. The second is pulse timing: measurements of the times of arrival of short pulses of radiation from x-ray and radio pulsars that are found to be members of binary systems, followed by derivation of the relevant orbital elements. Nature has been kind enough to provide us with the kinds of binary stars that will permit both of these independent types of observations to be carried out, with the result that quite complete descriptions of the systems are possible, and observational astronomy can yield directly determined masses for the intriguing end states of stellar evolution: neutron stars and black holes. The third experiment is astrometry: accurate determination of the positions of the components of resolved binaries, both relative to each other and relative to a fundamental astrometric reference frame over the whole sky. Once again, we find some binary systems for which both astrometric data and radial-velocity data are available, so that complete descriptions can be established.

I review the two main aspects of convection modeling important for the stellar structure: i) the determination of the temperature gradient in the stellar interior, and in particular in the superadiabatic part of the envelope, which plays a key role for the determination of the stellar Teff; ii) the description of chemical mixing –mainly in the presence of nuclear burning. I discuss these two aspects in general, and their importance for low and very low mass stars and brown dwarfs structures.

In particular, I discuss the uncertainty (of ∼ 200K) in the Teff of masses M ≲ 0.1 M⊙ in the phase of Deuterium burning, and the role of mixing in the problem of Lithium burning in very low masses. For this latter problem, I show that the relation between the age of a cluster and the luminosity of the lithium depletion edge is not only independent of the mixing timescale, but also independent of the metallicity, in the population I range, so that the Lithium test can be safely used as an age indicator.

Modeling convection: MLT and FST models

A convection model for general use in stellar structure relies on the computation of two main quantities: the fluxes and the scale length ∧. As the models presently available are all local, one can not expect that the description be unique, so there will be also one or more tuning parameters.

Photometric surveys in nearby, young open clusters have provided a large amount of very low-mass stars and brown dwarfs over the last two decades. These clusters offer a number of advantages like known distance, metallicity and age, which make feasible the identification of such objects. Furthermore, deep searches do constitute one of the most direct means for measuring the mass function through the whole stellar (and brown dwarf) mass range. In this paper it will be reviewed the progress of recent work on several young open clusters leading to the findings of unambiguous brown dwarfs and very low mass stars approaching the substellar mass limit. These discoveries, particularly in the Pleiades, imply a rising mass function (α = 0.75 ± 0.25, dN/dM ∼ M−α) in the very low mass stellar and substellar domains down to 0.04 M⊙. The detection of reliable free-floating candidate members with estimated masses of only 0.04−0.015 M⊙ does provide substantial evidence on the formation of such low mass objects and thus, on the extension of the initial mass function down to the deuterium burning mass limit.

Introduction

Our knowledge of the low mass stellar content in open clusters has increased considerably during the last decade. For a relatively large amount of nearby young clusters, like α Per, Pleiades, Praesepe and Hyades, membership lists extending down to the hydrogen-burning limit (∼0.08 M⊙) are now available (see the reviews by Stauffer 1996, and Hambly 1998).

Introduction

This paper has three parts. First will be an estimate of how many brown dwarfs there ought to be in globular clusters, by following their observed mass functions as close as possible to the hydrogen-burning limit, and then naïvely extrapolating the mass function beyond that. Next will be a discussion of the H-burning limit and how we can try to locate it observationally, by pushing luminosity functions as faint as possible. This part will conclude with a demonstration of how the observations can guide the theoreticians toward more accurate models in that region, by telling us something about how the MLR must go. And finally we will give a brief description of a microlensing experiment that some one else has underway, that may actually tell us how many brown dwarfs one particular globular cluster contains.

Introduction

The next few years will be a marvellous time for X-ray astronomy, with the launch of AXAF (Advanced X-ray Astrophysics Facility) in spring 1999 and of XMM (X-ray Multi Mirror Mission) and ASTRO-E (the new Japanese X-ray mission) in early 2000. These new powerful missions will produce a great leap forward in all fields of X-ray astronomy, from nearby stars to the most distant objects in the Universe. They will be far more sensitive than past and ongoing X-ray missions and will be equipped with new detectors (CCD and microchannel plate cameras, transmission and reflection gratings, and X-ray microcalorimeters) that will allow detection of fainter objects as well as detailed medium to high-resolution spectroscopy of the brightest sources.

Introduction

We have been carrying out large surveys of M dwarfs in the field (Reid et al. 1995, hereafter PMSU1, Hawley, Gizis & Reid 1996, hereafter PMSU2) and in nearby open clusters (Hawley, Tourtellot & Reid 1998, hereafter HTR98). Although these stars, on the whole, might not qualify as “very low mass” (VLM) stars for this conference, they are interesting to study in order to understand the properties that might affect stars even further down the main sequence.

Introduction

After waiting three decades since Kumar (1963) proposed their existence, we are gratified to see literally dozens of candidates probably or definitely below the stellar mass limit being found in young clusters and associations. Here one has the big advantages that the age, the distance and luminosity of a cluster member are generally known. In this presentation, complementary to the topic of this meeting, we report the finding of a large number of candidates in one of the first infrared surveys of the field population.

We review the current theory of very low mass stars model atmospheres including the coolest known M dwarfs, M subdwarfs, and brown dwarfs, i.e. Teff ≤ 5,000K and −2.0 ≤ [M/H] ≤ +0.0. We discuss ongoing efforts to incorporate molecular and grain opacities in cool stellar spectra, as well as the latest progress in deriving the effective temperature scale of M dwarfs. We especially present the latest results of the models related to the search for brown dwarfs.

Very low mass star models and the Teff scale

Very Low Mass stars (VLMs) with masses from about 0.3 M⊙ to the hydrogen burning minimum mass (0.075 M⊙, Baraffe et al. 1995) and young substellar brown dwarfs share similar atmospheric properties. Most of their photospheric hydrogen is locked in H2 and most of the carbon in CO, with the excess oxygen forming important molecular absorbers such as TiO, VO, and H2O. They are subject to an efficient convective mixing often reaching the uppermost layers of their photosphere. Their energy distribution is governed by the millions of absorption lines of TiO, VO, CaH, and FeH in the optical to near-infrared, and H2O and CO in the infrared, which leave no window of true continuum. But as brown dwarfs cool with age, they begin to differentiate themselves with the formation of methane (CH4) in the infrared (Tsuji et al. 1995; Allard et al. 1996).

In this paper we review the results of the denis survey on very low mass stars and brown dwarfs. The analysis of denis catalogs for 1500 square degrees has produced a sample of ∼ 100 very-late M dwarfs and 15 L dwarfs. Spectroscopy of these objects has established a spectroscopic classification sequence for L dwarfs, and determined the underlying effective temperature scale.

We use this sample to obtain the local luminosity function of the very low mass stars and brown dwarfs, with particular attention to correcting possible error sources and Malmquist-like biases. This first denis luminosity function has good statistical accuracy down to the limit between M and L dwarfs.

Introduction

Very low mass stars and brown dwarfs can be looked for around known brighter stars, in clusters, or in the general field, with advantages and disadvantages which have been repeatedly discussed in detail (for instance, Hambly 1998). Companion searches have historically identified the coolest object known at any given time, though usually not the least massive (which are found in clusters, where they haven't yet cooled much). Companion searches in the immediate solar neighbourhood also provide the information needed to correct cluster and field samples for the contribution of unresolved companions to more distant objects, and as such they are an essential complement to both field and cluster surveys. Cluster searches benefit both from an increased source density and from the much larger luminosity of younger brown dwarfs, and as a consequence they are sensitive to much lower mass objects (e.g. Zapatero-Osorio et al. 1999).

The first of the “Three-Island” Euroconferences on Stellar Clusters and Associations was dedicated to Very Low-Mass Stars and Brown Dwarfs. It was held in the island of La Palma (May 11–15, 1998) where the Observatory of Roque de los Muchachos is located. These series of Euroconferences, an initiative led by Roberto Pallavicini (co-ordinator), Thierry Montmerle and Rafael Rebolo, are aimed to cover a very broad range of astrophysical problems where research on Stellar Clusters and Associations is crucial. In the first Euroconference, we reviewed, in a beautiful location, problems related to the formation, evolution and characterization of objects at the bottom of the Main Sequence and beyond. The first discoveries of brown dwarfs in 1995 have been followed by numerous detections in stellar clusters and in the solar vicinity. The drastic increase in the number of known examples of these fascinating objects, which suggests they are indeed very numerous in the Galaxy, has allowed a better comparison with theoretical predictions and a better and faster development of our knowledge about their physical conditions.

Some of the questions addressed in the papers compiled in this volume and delivered by active researchers in the field are: how very low-mass stars and brown dwarfs form, how many there are in the Galaxy, how they evolve, what the physical conditions of their atmospheres and interiors are, how magnetic activity develops in fully convective objects, if they generate magnetic fields, if brown dwarfs are chromospherically active and show coronae.