12.2 Going further

The major issue concerning compact binaries – DDs, IDDs, UCXBs – is their number. Theoretical predictions strongly depend on the assumed parameters and range within an order of magnitude (see references in Section 10). The treatment of common envelopes and the distribution of stars over q are, perhaps, the crux. On the other hand, observational estimates suffer from numerous selection effects. For instance, the estimates of the local space density of white dwarfs may be uncertain by a factor of ∼ 5: cf. 4.2 × 10–3 pc–3 [195], (5 ± 0.7) × 10–3 pc–3 [151], or (20 ± 7) × 10–3 pc–3 [104]. The problem with AM CVn-stars is their deficiency by a factor of several compared even to the most pessimistic predictions, but in this case the situation improves: about half of the known and candidate systems were found within the past decade, while for another half it took about 30 years. In contrast to DDs, systematic searches for AM CVn-stars started only recently; in fact, the majority of known objects were found serendipitously. Rather successful was the search for AM CVn-candidates in the SDSS catalogue and follow-up observations which brought two confirmed and three candidate stars [3548]. Further progress may be expected from dedicated surveys with wide-field cameras. “RApid Temporal Survey” (RATS) by Ramsey and Hakala [339] is aimed at discovering objects with periodicities down to 2 min and is sensitive to V ∼ 22.5. Preliminary results [337] yielded no new AM CVn-stars, though several objects were expected in the 6 square degrees of the sky covered so far. This may be related to the fact that initially the interstellar extinction for these objects, which have to be located predominantly in the Galactic plane, was underestimated.

Another promising project is “OmegaWhite” (with PI P. Groot, University of Nijmegen in the Netherlands); see [125].

This project is also aimed at compact binaries, it will cover 400 square degrees of the sky, and will provide broad-band and narrow band photometric information down to 21st magnitude or equivalent line fluxes.

Another key issue in the studies of detached and interacting binary white dwarfs is the determination of their distances. In this aspect, the Gaia space probe which is aimed at the creation of a three-dimensional chart of our Galaxy by providing positional and radial velocity measurements for about one billion stars (see [116]) may appear the most promising source of information.

A failure to discover a significant number of detached and interacting double degenerates or to confirm current ideas on their structure and evolution will mean that serious drawbacks exist either in the implementation of known stellar evolution physics and observational statistical data in the population synthesis codes or in our understanding of the processes occurring in compact binaries or in the treatment of selection effects. Special attention in theoretical studies has to be paid to the onset of mass-transfer.

Above, we presented some of the current ideas on formation and compact binaries that may be interesting for general relativity and cosmology and on signals that may be expected from them in the LISA waveband. There is another side of the problem – the analysis of the signal, would it be detected. This topic is out of the scope of this brief review. We refer the reader only to several papers discussing methods for detecting and subtracting individual binary signals from a data stream with many overlapping signals [64], inferring properties of the distribution of white-dwarf binaries [90], the accuracy of parameter estimation of low-mass binaries [396356], and the discussion of the quality of information that may be provided by LISA [391].

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