List of Figures
![]() |
Figure 1:
Endpoints of evolution of moderate-mass nonrotating single stars depending on initial mass and metallicity. Image reproduced with permission from [709], copyright by IAU. |
![]() |
Figure 2:
Sensitivity limits of GW detectors and the regions of the ![]() ![]() |
![]() |
Figure 3:
The maximum initial orbital period (in hours) of two point masses that will coalesce due to gravitational wave emission in a time interval shorter than 1010 yr, as a function of the initial eccentricity ![]() ![]() ![]() ![]() |
![]() |
Figure 4:
A 3-D representation of a dimensionless Roche potential in the co-rotating frame for a binary with a mass ratio of components ![]() |
![]() |
Figure 5:
Descendants of components of close binaries depending on the radius of the star at RLOF. The upper solid line separates close and wide binaries (after [293]). The boundary between progenitors of He- and CO-WDs is uncertain by several ![]() ![]() ![]() ![]() ![]() |
![]() |
Figure 6:
Relation between ZAMS masses of stars ![]() ![]() |
![]() |
Figure 7:
Evolutionary scenario for the formation of neutron stars or black holes in close binaries. T is the typical time scale of an evolutionary stage, N is the estimated number of objects in the given evolutionary stage. |
![]() |
Figure 8:
Upper panel: the probability distribution for the orbital parameters of the NS + NS binaries with ![]() ![]() ![]() ![]() |
![]() |
Figure 9:
Formation of close dwarf binaries and their descendants (scale and color-coding are arbitrary). |
![]() |
Figure 10:
Limits of different burning regimes of accreted hydrogen onto a CO WD as a function of mass of the WD and accretion rate ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() |
Figure 11:
Possible combinations of masses and chemical compositions of components in a close WD binary [461]. Solid curves are lines of constant chirp mass (see Sections 3.1.2 and 10). Image reproduced with permission from [461], copyright by IOP. |
![]() |
Figure 12:
The total masses of binaries in the simulated population of WD binaries with ![]() ![]() ![]() |
![]() |
Figure 13:
Constraints on mass, effective temperature, radius and average density of the primary star of SN 2011fe. The shaded red region is excluded by non-detection of an optical quiescent counterpart in the Hubble Space Telescope imaging. The shaded green region is excluded from considerations of the non-detection of a shock breakout at early times. The blue region is excluded by the non-detection of a quiescent counterpart in the Chandra X-ray imaging. The location of the H, He, and C main-sequence is shown, with the symbol size scaled for different primary masses. Several observed WDs and NSs are shown. The primary radius in units of ![]() ![]() |
![]() |
Figure 14:
Limits on different burning regimes of helium accreted onto a CO WD as a function of the WD mass and accretion rate [590], Piersanti, Tornambé & Yungelson (in prep.). Above the “RG Configuration” line, accreted He forms an extended red-giant–like envelope. Below ![]() |
![]() |
Figure 15:
The accumulation efficiency of helium as a function of the accretion rate for CO WD models of 0.6, 0.7, 0.81, 0.92, ![]() ![]() |
![]() |
Figure 16:
Upper panel: model light curve of a SN Ia having collided with a red giant companion separated by ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() |
Figure 17:
Estimates of regimes of mass transfer in WD binaries. Instantaneous tidal coupling is assumed. For longer time scales of tidal coupling, the stability limit in the plot shifts down [464]. The filled squares mark initial positions of the models studied in the quoted paper. Image reproduced with permission from [129], copyright by AAS. |
![]() |
Figure 18:
Outcomes of merger of WD binaries depending on the mass and chemical composition of the components. Systems in the hatched region are expected to experience He-detonations during mass transfer or at the time of merger. The numbers near the arrows indicate relevant timescales. Image reproduced with permission from Figure 1 of [128], copyright by the authors. |
![]() |
Figure 19:
Known close binaries with two WD components, or a WD and a sd component. Red circles mark double-line WDs found by SPY. Green diamonds are single-line WDs found by SPY. Blue asterisks mark double-line WD discovered in surveys other than SPY. Magenta squares are sd + WD systems from SPY. Black crosses and small squares are single-line WD and sd found by different authors. Filled black circles are extremely low-mass WD (ELM) for which, typically, only one spectrum is observed. For single-line systems from SPY we assume inclination of the orbit ![]() |
![]() |
Figure 20:
Mass ratios of ELM WD. Vertical lines separate binaries which will, upon RLOF, exchange mass definitely stably (possible progenitors of AM CVn stars), WD for which stability of mass-exchange will depend on the efficiency of tidal interaction, and definitely unstable stars. The latter systems may be progenitors of SNe Ia, as discussed in Section 7.3.2. Courtesy T. Marsh [459]. |
![]() |
Figure 21:
Sketch of the period – mass transfer rate evolution of the binaries in the three proposed formation channels of AM CVn stars (the dashed line shows the detached phase of the white dwarf channel). For comparison, the evolutionary path of an ordinary hydrogen-rich CV or low-mass X-ray binary is shown. Image reproduced with permission from Figure 1 of [521], copyright by the authors. |
![]() |
Figure 22:
Birthrates and stability limits for mass transfer between close WD binaries. The shaded areas show the birth probability of progenitors of AM CVn stars in double-degenerate channel scaled to the maximum birth rate per bin of ![]() ![]() ![]() |
![]() |
Figure 23:
Examples of the evolution of AM CVn systems. Left panel: The evolution of the orbital period as a function of the mass of the donor star. Right panel: The change of the mass transfer rate during the evolution. The solid and dashed lines are for zero-temperature white dwarf donor stars with initial mass ![]() ![]() ![]() ![]() ![]() |
![]() |
Figure 24:
Left panel: the ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() |
Figure 25:
Mass-loss rate vs. orbital period dependence for semidetached systems with He-star donors and WD accretors, having post-common envelope ![]() ![]() |
![]() |
Figure 26:
An overview of the evolution and chemical abundances in the transferred matter for helium star donors in ultra-compact binaries. We show abundances (top), mass-transfer rate (middle) and donor mass (bottom) as a function of time since the start of the Roche lobe overflow. The binary period is indicated by the solid circles in the bottom panels for ![]() |
![]() |
Figure 27:
Abundance ratios (by mass) N/C for He-WD (the solid line) and He-star donors (the shaded region with dashed lines) as a function of the orbital period. For the helium star donors we indicate the upper part of the full range of abundances which extends to 0. The dashed lines are examples of tracks shown in detail in Figure 26. The helium white dwarfs are descendants of 1, 1.5 and ![]() |
![]() |
Figure 28:
Accreted mass as a function of the accretion rate for models experiencing a dynamical He-flash. The lines refer to WD with different initial masses — 0.6, 0.7, 0.81, 0.92, 1.02 ![]() |
![]() |
Figure 29:
Simulated time-series of the DD Galactic foreground signal of 3 years of data. “Noise” is the instrumental LISA noise. Based on computations in [519]. Image reproduced with permission from [170], copyright by ASP. |
![]() |
Figure 30:
Dependence of the dimensionless strain amplitude for a WD + WD detached system with initial masses of the components of ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() |
Figure 31:
The distribution of Galactic detached WD + WD binaries and interacting WD (AM CVn stars) as a function of the gravitational wave frequency and chirp mass. From [170], based on computations in [519]. |
![]() |
Figure 32:
GWR foreground produced by detached and semidetached WD binaries as it was expected to be detected by LISA. The assumed integration time is 1 yr. The ‘noisy’ black line gives the total power spectrum, the white line shows the average. The dashed lines show the expected LISA sensitivity for a ![]() ![]() ![]() |
![]() |
Figure 33:
The number of systems per bin on a logarithmic scale. Semidetached WD binaries contribute to the peak between ![]() ![]() |
![]() |
Figure 34:
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 a function of the signal frequency. From [518], copyright by ESO. |
![]() |
Figure 35:
Strain amplitude spectral density (in Hz–1/2) versus frequency for the verification binaries and the brightest binaries in the simulated Galactic population of ultra-compact binaries [519]. The solid line shows the sensitivity of eLISA. The assumed integration time is 2 yrs. 100 simulated binaries with the largest strain amplitude are shown as red squares. Observed ultra-compact binaries are shown as blue squares, while the subsample of them that can serve as verification binaries is marked as green squares. Image reproduced with permission from [11], copyright by the authors. |
![]() |
Figure 36:
The number density as a function of GW-strain amplitude ![]() ![]() |
![]() |
Figure 37:
The frequency-space density and GW foreground of DD and AM CVn systems for two scenarios. In each subplot, the bottom panel shows the power spectral density of the unsubtracted (blue) and partially subtracted (red) foreground, compared to instrumental noise (black). The open white circles indicate the frequency and amplitude of the “verification binaries”. The green dots show the individually-detectable DD systems; the red dots show the detectable AM CVn systems formed from DD progenitors and the blue dots show the detectable AM CVn systems that arise from the He-star–WD channel. The top panel shows histograms of the detected sources in the frequency space. Image reproduced with permission from [531], copyright by AAS. |
![]() |
Figure 38:
The histogram of apparent magnitudes of the WD binaries that are estimated to be individually detected by LISA. The black-and-white line shows the distribution in the ![]() ![]() ![]() ![]() |
![]() |
Figure 39:
Distribution of short period AM CVn-type systems detectable in soft X-ray and as optical sources as a function of the orbital period and distance. Top panel: systems detectable in X-ray only (blue pluses), direct impact systems observable in X-ray and ![]() ![]() |