Using self-organizing maps to identify potential halo white dwarfs

Abstract

We present the results of an unsupervised classification of the disk and halo white dwarf populations in the solar neighborhood. The classification is done by merging the results of detailed Monte Carlo (MC) simulations, which reproduce very well the characteristics of the white dwarf populations in the solar neighborhood, with a catalogue of real stars. The resulting composite catalogue is analyzed using a competitive learning algorithm. In particular we have used the so-called self-organized map. The MC simulated stars are used as tracers and help in identifying the resulting clusters. The results of such an strategy turn out to be quite satisfactory, suggesting that this approach can provide an useful framework for analyzing large databases of white dwarfs with well determined kinematical, spatial and photometric properties once they become available in the next decade. Moreover, the results are of astrophysical interest as well, since a straightforward interpretation of several recent astronomical observations, like the detected microlensing events in the direction of the Magellanic Clouds, the possible detection of high proper motion white dwarfs in the Hubble Deep Field and the discovery of high velocity white dwarfs in the solar neighborhood, suggests that a fraction of the baryonic dark matter component of our galaxy could be in the form of old and dim halo white dwarfs.

Introduction

White dwarfs are the most common end-point of stellar evolution. Moreover, white dwarfs are well-studied objects. In fact, the relative simplicity of their constitutive physics allows us to obtain very detailed evolutionary models (Salaris, Garcı́a-Berro, Hernanz, Isern, & Saumon, 2000, and references therein). Although these evolutionary models can be extremely sophisticated, it can be said that their evolution is essentially a cooling process—see, for instance, the recent review of Fontaine, Brassard, and Bergeron (2001)—during which the degenerate and almost isothermal core releases gravothermal energy which is evacuated through the partially degenerate atmosphere, whereas the hydrostatic equilibrium is achieved mostly by the pressure of the nearly degenerate electrons. This atmosphere, in turn, controls the rate at which the energy is radiated away. Additionally, white dwarfs have very long evolutionary time scales, which are comparable to the age of our galaxy. Due to these facts, white dwarfs provide us with an invaluable tracer of the early evolution of our galaxy and, consequently, allow us to explore how our galaxy, and other galaxies, formed and evolved (both chemically and kinematically).

Given their intrinsic faintness, white dwarfs are difficult to detect at large distances and, thus, the currently available surveys reach modest distances, at most 300 pc. In fact, a large fraction of white dwarfs has been found in proper motion surveys. Thus, the vast majority of known white dwarfs belong to the solar neighborhood. Whether these white dwarfs are members of the known galactic disk populations (namely the thin and the thick disk) or are halo members is a crucial issue. There is now a widespread consensus that the distribution of faint white dwarfs in the solar neighborhood is in good agreement with the expectations of the standard old thick disk population, being their space density of about 0.005 pc⁻³, with possibly a small fraction of halo white dwarfs present in the sample.

The observational situation has improved dramatically in the last few years with the advent of the Hubble Space Telescope and large ground based telescopes. For instance, faint white dwarfs have been already detected in several open and globular galactic clusters, and there are some evidences that the galactic halo white dwarf population has been already detected, although this particular topic is still the subject of large controversies. To be more specific, halo white dwarfs have received a continuous interest during almost one decade from both the theoretical (Isern et al., 1998, Mochkovitch et al., 1990, Tamanaha et al., 1990) and the observational points of view. From this last point of view it is important to stress the big effort of Liebert, Dahn, and Monet (1989) who studied a high proper motion sample and from it derived the very first (although severely incomplete) halo white dwarf luminosity function. Later Flynn et al., 1996, Méndez et al., 1996 studied the white dwarf content of the Hubble deep field. Moreover, the MACHO team reported the discovery of microlenses towards the large Magellanic cloud and claimed that about 20% of the dark matter in the Galaxy could be in the form of white dwarfs (Alcock et al., 1997). However, recent analyses (Alcock, 2000) have shown that the fraction of dark matter in the form of white dwarfs is smaller, of the order of ≤10%, in good agreement with the theoretical expectations of Isern et al. (1998). More recently, Ibata, Irwin, Bienaymé, Scholz, and Guibert (2000) have reported the discovery of two extremely cool white dwarfs in the solar neighborhood with very high proper motion, making them very likely observational counterparts of a putative ancient halo white dwarf population. Other faint white dwarfs with extremely large proper motions have been also discovered recently (Hambly et al., 1997, Hambly et al., 1999, Hodgkin et al., 2000) making use of stacked photographic plates. Increasing attention has been paid to this topic since the very recent discovery (Oppenheimer, Hambly, Digby, Hodgkin, & Saumon, 2001) of 38 new, nearby and old white dwarfs with large space velocities. Whether these white dwarfs belong to the thick disk or to the halo is still the subject of a strong debate. In summary, although there are evidences of a possible detection of the halo white dwarf population, given the scarce number of halo white dwarfs it is difficult to ascertain whether a small sample of these objects remains hidden in the current catalogs and how this putative population could be identified. In this paper we describe how to identify the population of halo white dwarfs in the existing white dwarf catalogues.