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White dwarfs are the final remnants of low- and intermediate-mass stars. Their evolution is essentially a cooling process that lasts for ∼ 10 Gyr. Their observed properties provide information about the history of the Galaxy, its dark matter content and a host of other interesting astrophysical problems. Examples of these include an independent determination of the past history of the local star formation rate, identification of the objects responsible for the reported microlensing events, constraints on the rate of change of the gravitational constant, and upper limits to the mass of weakly interacting massive particles. To carry on these tasks the essential observational tools are the luminosity and mass functions of white dwarfs, whereas the theoretical tools are the evolutionary sequences of white dwarf progenitors, and the corresponding white dwarf cooling sequences. In particular, the observed white dwarf luminosity function is the key manifestation of the white dwarf cooling theory, although other relevant ingredients are needed to compare theory and observations. In this review we summarize the recent attempts to empirically determine the white dwarf luminosity function for the different Galactic populations. We also discuss the biases that may affect its interpretation. Finally, we elaborate on the theoretical ingredients needed to model the white dwarf luminosity function, paying special attention to the remaining uncertainties, and we comment on some applications of the white dwarf cooling theory. Astrophysical problems for which white dwarf stars may provide useful leverage in the near future are also discussed. [ABSTRACT FROM AUTHOR]

Context. Detached white dwarf + main sequence (WD+MS) systems represent the simplest population of post-common envelope binaries (PCEBs). Since the ensemble properties of this population carries important information about the characteristics of the common-envelope (CE) phase, it deserves close scrutiny. However, most population synthesis studies do not fully consider the effects of the observational selection biases of the samples used to compare with the theoretical simulations. Aims. Here we present the results of a set of detailed Monte Carlo simulations of the population of WD+MS binaries in the Sloan Digital Sky Survey (SDSS) Data Release 7. Methods. We used up-to-date stellar evolutionary models, a complete treatment of the Roche lobe overflow episode, and a full implementation of the orbital evolution of the binary systems. Moreover, in our treatment we took the selection criteria and all the known observational biases into account. Results. Our population synthesis study allowed us to make a meaningful comparison with the available observational data. In particular, we examined the CE efficiency, the possible contribution of internal energy, and the initial mass ratio distribution (IMRD) of the binary systems. We find that our simulations correctly reproduce the properties of the observed distribution of WD+MS PCEBs. In particular, we find that once the observational biases are carefully considered, the distribution of orbital periods and of masses of the WD and MS stars can be correctly reproduced for several choices of the free parameters and different IMRDs, although models in which a moderate fraction (≤10%) of the internal energy is used to eject the CE and in which a low value of CE efficiency is used (≤0.3) seem to fit the observational data better. We also find that systems with He-core WDs are over-represented in the observed sample, because of selection effects. Conclusions. Although our study represents an important step forward in modeling the population of WD+MS PCEBs, the still scarce observational data preclude deriving a precise value of the several free parameters used to compute the CE phase without ambiguity or ascertaining which the correct IMRD might be. [ABSTRACT FROM AUTHOR]

The disc white dwarf luminosity function is an important tool for studying the solar neighbourhood, since it allows the determination of several Galactic parameters, the most important one being the age of the Galactic disc. However, only the method has been employed so far for observationally determining the white dwarf luminosity function, whereas for other kind of luminosity functions several other methods have been frequently used. Moreover, the procedures to determine the white dwarf luminosity function are not free of biases. These biases have two different origins: they can either be of statistical nature or a consequence of the measurement errors. In a previous paper we carried out an in-depth study of the first category of biases for several luminosity function estimators. In this paper we focus on the biases introduced by the measurement errors and on the effects of the degree of contamination of the input sample used to build the disc white dwarf luminosity function by different kinematical populations. To assess the extent of these biases we use a Monte Carlo simulator to generate a controlled synthetic population and analyse the behaviour of the disc white dwarf luminosity function for several assumptions about the magnitude of the measurement errors and for several degrees of contamination, comparing the performances of the most robust luminosity function estimators under such conditions. [ABSTRACT FROM AUTHOR]

The white dwarf luminosity function is an important tool for the study of the solar neighbourhood, since it allows the determination of the age of the Galactic disc. Over the years, several methods have been proposed to compute galaxy luminosity functions, from the most simple ones – counting sample objects inside a given volume – to very sophisticated ones – like the C− method, the STY method or the Choloniewski method, among others. However, only the method is usually employed in computing the white dwarf luminosity function and other methods have not been applied so far to the observational sample of spectroscopically identified white dwarfs – in sharp contrast with the situation when galaxy luminosity functions are derived from a large variety of samples. Moreover, the statistical significance of the white dwarf luminosity function has also received little attention and a thorough study still remains to be done. In this paper, we study, using a controlled synthetic sample of white dwarfs generated using a Monte Carlo simulator, which is the statistical significance of the white dwarf luminosity function and which are the expected biases. We also present a comparison between different estimators for computing the white dwarf luminosity function. We find that for sample sizes large enough the method provides a reliable characterization of the white dwarf luminosity function, provided that the input sample is selected carefully. Particularly, the method recovers well the position of the cut-off of the white dwarf luminosity function. However, this method turns out to be less robust than the Choloniewski method when the possible incompletenesses of the sample are taken into account. We also find that the Choloniewski method performs better than the method in estimating the overall density of white dwarfs, but misses the exact location of the cut-off of the white dwarf luminosity function. [ABSTRACT FROM AUTHOR]

One of the most promising space missions of the European Space Agency is the astrometric satellite Gaia, which will provide very precise astrometry and multicolour photometry, for all 1.3 billion objects to , and radial velocities with accuracies of a few km s−1 for most stars brighter than . Consequently, full homogeneous six-dimensional phase-space information for a huge number of stars will become available. Our Monte Carlo simulator has been used to estimate the number of white dwarfs potentially observable by Gaia. From this we assess the white dwarf luminosity functions that Gaia will obtain and discuss in depth the scientific returns of Gaia in the specific field of white dwarf populations. Scientifically attainable goals include, among others, a reliable determination of the age of the Galactic disc, a better knowledge of the halo of the Milky Way and the reconstruction of the star formation history of the Galactic disc. Our results also demonstrate the potential impact of a mission such as Gaia within the context of current understanding of white dwarf cooling theory. [ABSTRACT FROM AUTHOR]

Abstract The interpretation of the old, cool white dwarfs recently found by Oppenheimer et al. is still controversial. Whereas these authors claim that they have finally found the elusive ancient-halo white dwarf population that contributes significantly to the mass budget of the galactic halo, there have been several other contributions that argue that these white dwarfs are not genuine halo members but, instead, thick-disc stars. We show here that the interpretation of this sample is based on the adopted distances, which are obtained from a colour–magnitude calibration, and we demonstrate that when the correct distances are used a sizeable fraction of these putative halo white dwarfs belong indeed to the disc population. We also perform a maximum likelihood analysis of the remaining set of white dwarfs and we find that they most probably belong to the thick-disc population. However, another possible explanation is that this sample of white dwarfs has been drawn from a 1:1 mixture of the halo and disc white dwarf populations. [ABSTRACT FROM AUTHOR]

In this paper we analyse the consequences in the white dwarf population of a hypothetical merger episode in our Galactic disc. We have studied several different merging scenarios with our Monte Carlo simulator. For each one of these scenarios we have derived the main characteristics of the resulting white dwarf population and we have compared them with the available observational data, namely the white dwarf luminosity function and the kinematic properties of the white dwarf population. Our results indicate that very recent (less than ∼6 Gyr ago) and massive (∼16 per cent of the mass of our Galaxy) merger episodes are quite unlikely in view of the available kinematical properties of the disc white dwarf population. Smaller merger episodes (of the order of ∼4 per cent of the mass of our Galaxy) are, however, compatible with our current knowledge of those kinematical properties. Finally, we prove that the white dwarf luminosity function is quite insensitive to such a merger episode. [ABSTRACT FROM AUTHOR]