The white dwarf luminosity function – II. The effect of the measurement errors and other biases

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.     

Simulating Gaia performances on white dwarfs

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   V ∼ 20  , and radial velocities with accuracies of a few km s⁻¹ for most stars brighter than   V ∼ 17  . 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.     

Galactic models and white dwarf populations

We make use of a previous well-tested Galactic model, but describing the observational behaviour of the various stellar components in terms of suitable assumptions on their evolutionary status. In this way we are able to predict the expected distribution of Galactic white dwarfs (WDs), with results which appear in rather good agreement with recent estimates of the local WD luminosity function. The predicted occurrence of WDs in deep observations of selected Galactic fields is presented, and we discuss the role played by WDs in star counts. The effects on the theoretical predictions of different white dwarf evolutionary models, ages, initial mass functions and relations between progenitor mass and WD mass are also discussed.     

On the parallax of WD 0346++246: a halo white dwarf candidate

We present a parallax measurement for the very cool degenerate WD 0346+246, the serendipitous discovery of which was reported by Hambly et al. We find an absolute parallax of 36±5 mas, yielding a distance estimate of 28±4 pc. The resulting absolute visual magnitude of the object is M _V =16.8±0.3, making it the second-lowest luminosity white dwarf currently known. We use the distance estimate and measured proper motion to show that the object has kinematics consistent with membership of the Galactic halo. WD 0346+246 is therefore by far the coolest and least luminous of only a handful of plausible halo white dwarf candidates. As such, the object has relevance to the ongoing debate concerning the results of microlensing experiments and the nature of any baryonic dark matter component to the Galactic halo residing in stellar remnants.     

The field of NGC 6397 as a test for Galactic models

Taking advantage of recent Hubble Space Telescope ( HST ) data for field stars in the region of the Galactic globular cluster NGC 6397, we tested the predictions of several Galactic models with star counts reaching a largely unexplored range of magnitudes, down to V ∼26.5. After updating the input stellar ( V − I ) colours, we found that the two-component Bahcall–Soneira (B&S) model can be put into satisfactory agreement with observations for suitable choices of disc/spheroid luminosity functions (LFs). However, if one assumes the disc LF of Gould, Bahcall and Flynn together with the spheroid LF of Gould, Flynn and Bahcall, there is no way to reconcile the predicted and observed V -magnitude distribution. We also analysed the agreement between observed and predicted magnitude and colour distributions for two selected models with a thick disc component. Even in this case there are suitable combinations of model parameters and faint-magnitude LFs that can give a reasonable agreement with observational star counts in both magnitude and colour. However, the above-quoted combination of Gould et al. LFs again gives predictions in clear disagreement with observations.     

Theoretical model of a magnetic white dwarf

In this paper a theoretical model of a magnetic white dwarf is studied. All numerical calculations are performed under the assumption of a spherically symmetric star. The obtained equation of state is stiffer with the increase of value of the magnetic field (B). Numerical values of the maximum mass and radius are presented. The influence of the magnetic field on the results is evident. Finally the departure from the condition of isothermality of a degenerate electron gas in the gravitational field is discussed.     

The initial–final mass relationship of white dwarfs revisited: effect on the luminosity function and mass distribution

The initial–final mass relationship connects the mass of a white dwarf with the mass of its progenitor in the main sequence. Although this function is of fundamental importance to several fields in modern astrophysics, it is not well constrained either from the theoretical or from the observational points of view. In this work, we revise the present semi-empirical initial–final mass relationship by re-evaluating the available data. The distribution obtained from grouping all our results presents a considerable dispersion, which is larger than the uncertainties. We have carried out a weighted least-squares linear fit of these data and a careful analysis to give some clues on the dependence of this relationship on some parameters such as metallicity or rotation. The semi-empirical initial–final mass relationship arising from our study covers the range of initial masses from 1.0 to  6.5 M_⊙  , including in this way the low-mass domain, poorly studied until recently. Finally, we have also performed a test of the initial–final mass relationship by studying its effect on the luminosity function and on the mass distribution of white dwarfs. This was done by using different initial–final mass relationships from the literature, including the expression derived in this work, and comparing the results obtained with the observational data from the Palomar Green Survey and the Sloan Digital Sky Survey. We find that the semi-empirical initial–final mass relationship derived here gives results in good agreement with the observational data, especially in the case of the white dwarf mass distribution.     

Diffusion in helium white dwarf stars

This paper is aimed at exploring the effects of diffusion on the structure and evolution of low-mass helium white dwarfs. To this end, we solve the multicomponent flow equations describing gravitational settling and chemical and thermal diffusion. The diffusion calculations are coupled to an evolutionary code in order to follow the cooling of low-mass, helium core white dwarf models having envelopes made up of a mixture of hydrogen and helium, as recently suggested by detailed evolutionary calculations for white dwarf progenitors in binary systems. We find that diffusion causes hydrogen to float and the other elements to sink over time-scales shorter than evolutionary time-scales. This produces a noticeable change in the structure of the outer layers, making the star inflate. Thus, in order to compute accurately the mass–radius relation for low-mass helium white dwarfs we need to account for the diffusion processes during (at least) the white dwarf stages of the evolution of these objects. This should be particularly important when studying the general characteristics of binary systems containing a helium white dwarf and a pulsar.
In addition, we present an analytic, approximate model for the outer layers of the white dwarf aimed at interpreting the physical reasons for the change in the surface gravity for low-mass white dwarfs induced by diffusion.     

Discovery of a widely separated ultracool dwarf–white dwarf binary

We present the discovery of the widest known ultracool dwarf–white dwarf binary. This binary is the first spectroscopically confirmed widely separated system from our target sample. We have used the Two-Micron All-Sky Survey (2MASS) and SuperCOSMOS archives in the southern hemisphere, searching for very widely separated ultracool dwarf–white dwarf binaries, and find one common proper motion system, with a separation of 3650–5250 au at an estimated distance of 41–59 pc, making it the widest known system of this type. Spectroscopy reveals 2MASS J0030−3740 is a DA white dwarf with   T _eff= 7600 ± 100 K, log( g ) = 7.79–8.09  and   M _WD= 0.48–0.65 M_⊙  . We spectroscopically type the ultracool dwarf companion (2MASS J0030−3739) as M9 ± 1 and estimate a mass of  0.07–0.08 M_⊙,  T _eff= 2000–2400 K  and  log( g ) = 5.30–5.35  , placing it near the mass limit for brown dwarfs. We estimate the age of the system to be >1.94 Gyr (from the white dwarf cooling age and the likely length of the main-sequence lifetime of the progenitor) and suggest that this system and other such wide binaries can be used as benchmark ultracool dwarfs.     

Hidden subluminous stars among the FAUST UV sources towards Ophiuchus

We present results of an analysis of a UV image in the direction of Ophiuchus, obtained with the FAUST instrument. The image contains 228 UV sources. Most of these are identified as normal early-type stars through correlations with catalogued objects. For the first time in this project we identify UV sources as such stars by selecting suitable candidates in crowded fields as the bluest objects in colour–colour diagrams using observations from the Wise Observatory. These candidates are then studied using low-resolution spectroscopy, which allows the determination of spectral types to an accuracy of about one-half class, for 60 stars.
Synthetic photometry of spectral data is performed in order to predict the expected UV emission, on the basis of the photometric information. These results are used along with the Hipparcos /Tycho information, to search for subluminous stars. The comparison of the predicted emission with the FAUST measured magnitudes allows us to select 12 stars as highly probable evolved hot stars. High signal-to-noise spectra are obtained for nine of these stars, and Balmer line profiles are compared with the prediction of atmosphere models and with the spectrum of real stellar atmospheres. Among the nine candidates, six are classified as previously unrecognized sdB stars, and two as white dwarfs. Our result indicates that indeed more bright subluminous stars are still unrecognized in the existing samples.