List of Figures

View Image Figure 1:
Descendants of components of close binaries depending on the radius of the star at RLOF. The boundary between progenitors of He and CO-WDs is uncertain by several 0.1 M ⊙, the boundary between WDs and NSs by ∼ 1M ⊙, while for the formation of BHs the lower mass limit may be even by ∼ 10M ⊙ higher than indicated.
View Image Figure 2:
Sensitivity limits of GW detectors and the regions of the fh diagram occupied by some of the potential GW sources. (Courtesy G. Nelemans.)
View Image Figure 3:
The maximum initial orbital period (in hours) of two point masses which will coalesce due to gravitational wave emission in a time interval shorter than 1010 yr, as a function of the initial eccentricity e0. The lines are calculated for 10 M ⊙ + 10 M ⊙ (BH + BH), 10 M ⊙ + 1.4M ⊙ (BH + NS), and 1.4 M ⊙ + 1.4M ⊙ (NS + NS).
View Image Figure 4:
Evolutionary scenario for the formation of neutron stars or black holes in close binaries.
View Image Figure 5:
Formation of close binary dwarfs and their descendants (scale and colour-coding are arbitrary).
View Image Figure 6:
The age of merging pairs of helium WDs. Two components of the distribution correspond to the systems that experienced in the course of formation two or one common envelope episodes, respectively.
View Image Figure 7:
Known close binaries with two WD components, or a WD and a sd component. Green circles mark systems known prior to the SPY project. Black filled symbols mark the positions of DDs and WD + sd systems detected in the SPY project. A blue triangle marks the positions of the WD component of the binary planetary nebula nucleus PN G135.9+55.9 detected by Tovmassian et al. [404]. (Courtesy R. Napiwotzki.)
View Image Figure 8:
The position of the primary components of known DDs in the “orbital-period–mass” diagram. The underlying gray scale plot is a model prediction from Nelemans et al. [286]. (Figure from [277].)
View Image Figure 9:
Mass-loss rate vs. orbital period for “typical” AM CVn-stars: an interacting double degenerate system with initial masses of donor and accretor 0.2M ⊙ and 0.6 M ⊙ (red line) and a “semidegenerate” low-mass helium star donor plus white dwarf accretor of the same initial masses (blue line). Black dots on the red curve mark positions of the system at log T (yr) = 5,6,7,8,9,10 from Roche-lobe overflow; on the blue curve they mark logT (yr) = 5,6, 7,8. Green lines mark lower and upper limits of the disk instability region according to Tsugawa and Osaki [406]. Below the magenta circles q < 0.02 and conventional evolutionary computations may be not adequate for description of mass-transfer process (see the text).
View Image Figure 10:
Dependence of the dimensionless strain amplitude for a WD + WD detached system with initial masses of the components of 0.6M ⊙ + 0.6 M ⊙ (red line), a WD + WD system with 0.6M ⊙ + 0.2M ⊙ (blue line) and a WD + NS system with 1.4M ⊙ + 0.2 M ⊙ (green line). All systems have an initial separation of components 1 R ⊙ and are assumed to be at a distance of 1 kpc (i.e. the actual strength of the signal has to be scaled with factor 1 ∕d, with d in kpc). For the DD system the line shows an evolution into contact, while for the two other systems the upper branches show pre-contact evolution and lower branches – a post-contact evolution with mass exchange. The total time-span of evolution covered by the tracks is 13.5 Gyr. Red dots mark the positions of systems with mass-ratio of components q = 0.02 below which the conventional picture of evolution with a mass exchange may be not valid. The red dashed line marks the position of the confusion limit as determined in [287].
View Image Figure 11:
GWR background produced by detached and semidetached double white dwarfs as it would be detected at the Earth. The assumed integration time is 1 yr. The ‘noisy’ black line gives the total power spectrum, the white line the average. The dashed lines show the expected LISA sensitivity for a S ∕N of 1 and 5 [212]. Semidetached double white dwarfs contribute to the peak between logf ≃ − 3.4 and − 3.0. (Figure from [286].)
View Image Figure 12:
The number of systems per bin on a logarithmic scale. Semidetached double white dwarfs contribute to the peak between log f ≃ − 3.4 and − 3.0. (Figure from [286].)
View Image Figure 13:
Fraction of bins that contain exactly one system (solid line), empty bins (dashed line), and bins that contain more than one system (dotted line) as function of the frequency of the signals. (Figure from [286].)
View Image Figure 14:
Gravitational waves background formed by the Galactic population of white dwarfs and signal amplitudes produced by some of the most compact binaries with white dwarf components ([273]). The green line presents results from [286], the black one from [287], while the red one presents a model with all assumptions similar to [287], but with the γ-formalism for the treatment of common envelopes [285284] (see also Section 3.5). The blue line shows the background derived in [28]. (Figure from [275].)
View Image Figure 15:
Strain amplitude h as a function of the frequency for the model populations of resolved DDs (left panel, ≃ 10,700 objects) and AM CVn systems (right panel, ≃ 11,000 objects.). The gray shades give the density distribution of the resolved systems normalized to the maximum density in each panel (1,548 and 1,823 per “cell” for the double white dwarfs and AM CVn-stars panels, respectively). The 200 strongest sources in each sample are shown as dots to enhance their visibility. In the AM CVn panel the periods of several observed short period systems are indicated by the vertical dotted lines. The solid line shows the average background noise due to detached white dwarfs. The LISA sensitivities for an integration time of one year and a signal-to-noise ratio of 1 and 5 are indicated by the dashed lines [212]. (Figure from [287].)
View Image Figure 16:
Distribution of short period AM CVn-type systems detectable in soft X-rays and as optical sources as a function of orbital period and distance. Top panel: systems detectable in X-rays only (blue pluses), direct impact systems observable in X-ray and V -band (red filled circles), systems detectable in X-ray with an optically visible donor (green squares), and systems detectable in X-rays and with an optically visible disc (large filled triangles). Bottom panel: direct impact systems (red open circles), systems with a visible donor (green squares), and systems with a visible accretion disc (small open triangles). The overlap of these systems with systems observable in gravitational waves is shown in Figure 17. (Updated figure from [287], see also [274].)
View Image Figure 17:
Short-period AM CVn systems, subdivided in different types. Each panel shows the total population as the white histogram. The top left panel shows 11,000 systems that can be resolved by LISA in gray, and they are subdivided into the ones that have optical counterparts (GWR + Opt), X-ray counterparts (GWR + X), and both (GWR + Opt + X). The top right panel shows the systems that are in the direct impact phase of accretion in gray, and they are subdivided in GWR and X-ray sources. The bottom two panels show (again in gray) the populations that are detectable in the optical band (left panel) and the X-ray band (right panel). The distribution of sources detectable both in optical and X-ray bands is shown as hatched bins in both lower panels (Opt + X). (Figure from [287].)
View Image Figure 18:
Effects of a finite entropy of donors on the properties of AM CVn-stars. The left panel shows the relation between Porb and M˙ along tracks for a system with initial masses of components 0.2 M ⊙ and 0.6 M ⊙ (like in Figure 9). The solid lines show the evolution for donors with Tc = 104 K, 106 K, 5 × 106 K, and 107 K (left to right). The symbols show the positions of models with M2 = 0.01 M ⊙ (triangles), 0.02 M ⊙ (squares), and 0.05M ⊙ (pentagons). The disk stability criteria (for q = 0.05) are shown by the dashed lines (after [406]). The right panel compares the numbers of systems as a function of Porb for the model with a T = 0 WD (dot-dashed line) and the model with “realistic” cooling (solid lines, RWDC). The smooth curves show the percentage of each population laying above a given Porb. (Figures from [77].)