Common-envelope Ejection Efficiency Research Articles

The Common Envelope Evolution Outcome. II. Short-orbital-period Hot Subdwarf B Binaries Reveal a Clear Picture

Common envelope evolution (CEE) is vital for forming short-orbital-period compact binaries. It covers many objects, such as double compact merging binaries, Type Ia supernovae progenitors, binary pulsars, and X-ray binaries. Knowledge of the common envelope (CE) ejection efficiency still needs to be improved, though progress has been made recently. Short-orbital-period hot subdwarf B star (sdB) plus white dwarf (WD) binaries are the most straightforward samples with which to constrain CEE physics. We apply the known orbital period–WD mass relation to constrain the sdB progenitors of seven sdB+WD binaries with a known inclination angle. The average CE efficiency parameter is 0.32. This is consistent with previous studies. However, the CE efficiency need not be constant, but a function of the initial mass ratio, based on well-constrained sdB progenitor mass and evolutionary stage. Our results can be used as physical inputs for binary population synthesis simulations of related objects. A similar method can also be applied to study other short-orbital-period WD binaries.

Influence of a mass transfer stability criterion on double white dwarf populations

Context. Mass transfer stability is a key issue in studies of binary evolution. Critical mass ratios for dynamically stable mass transfer have been analyzed on the basis of an adiabatic mass loss model, finding that the donor stars on the giant branches tend to be more stable than that based on the composite polytropic stellar model. Double white dwarfs (DWDs) are of great importance in many fields and their properties would be significantly affected under the new mass transfer stability criterion. Aims. We seek to investigate the influence of mass transfer stability on the formation and properties of DWD populations and discuss the implications in supernova Type Ia (SN Ia) and gravitational wave (GW) sources. Methods. We performed a series of binary population synthesis, adopting the critical mass ratios from the adiabatic mass loss model (i.e., Ge’s model) and that of the composite polytropic model, respectively. In each simulation, 5 × 106 binaries were included and evolved from zero-age main sequence to the end of their evolution and the DWDs were gradually obtained. Results. For Ge’s model, most of the DWDs are produced from the stable non-conservative Roche lobe (RL) overflow, along with a common-envelope (CE) ejection channel (RL+CE channel), regardless of the CE ejection efficiency, αCE. Conversely, the results of the polytropic model strongly depend on the adopted value of αCE. We find DWDs produced from the RL+CE channel have comparable WD masses and the mass ratio distribution peaks at around 1. Based on the magnitude-limited sample of DWDs, the space densities for the detectable DWDs and those with extremely low-mass WD (ELM WD) companions in Ge’s model is: 1347 kpc−3 and 473 kpc−3, respectively, which is close to what has been shown in observations. On the other hand, the polytropic model overpredicts space density of DWDs by a factor of about 2−3. We also find that the results of DWD merger rate distribution per Galaxy in Ge’s model reproduce the observations better than that of the polytropic model, and the merger rate of DWDs with ELM WD companions in the Galaxy is about 1.8 × 10−3 yr−1 in Ge’s model. This result is comparable to the observation estimation of 2 × 10−3 yr−1. The findings from Ge’s model predict a Galactic SN Ia rate of ∼6 × 10−3 yr−1 from DWDs, supporting observations of (5.4 ± 1.2)×10−3 yr−1. For the fiducial model of αCE = 1, the number of detectable GW sources in the polytropic model is larger than that in Ge’s model by about 35%. Conclusions. We confirm that mass transfer stability plays an important role in the formation and properties of DWD populations as well as in the progenitors of SNe Ia and detectable GW sources. The results of Ge’s model support the observational DWD merger rate distribution per Galaxy and the space density of DWDs in the Galaxy.

Detectability of Black Hole Binaries with Gaia: Dependence on Binary Evolution Models

Abstract The astrometric satellite Gaia is expected to observe noninteracting black hole (BH) binaries with luminous companions (LCs; hereafter BH-LC binaries), a different population from BH X-ray binaries previously discovered. The detectability of BH-LC binaries with Gaia might be dependent on binary evolution models. We investigated the Gaia's detectability of BH-LC binaries formed through isolated binary evolution by means of the binary population synthesis technique and examined its dependence on single and binary star models: supernova models, common envelope (CE) ejection efficiency α, and BH natal kick models. We estimated that 1.1–46 BH-LC binaries can be detected within the five-year observation, and found that α has the largest impact on the detectable number. In each model, observable and intrinsic BH-LC binaries have similar distributions. Therefore, we found three important implications: (1) if the lower BH mass gap is not intrinsic (i.e., 3–5 M ⊙ BHs exist), Gaia will observe ≤5 M ⊙ BHs; (2) we may observe short orbital period binaries with light LCs if CE efficiency is significantly high; and (3) we may be able to identify the existence of natal kick from eccentricity distribution.

Formation and evolution of binary neutron stars: mergers and their host galaxies

ABSTRACT In this paper, we investigate the properties of binary neutron stars (BNSs) and their mergers by combining population synthesis models for binary stellar evolution (BSE) with cosmological galaxy formation and evolution models. We obtain constraints on BSE model parameters by using the observed Galactic BNSs and local BNS merger rate density (R0) inferred from gravitational wave (GW) observations, and consequently estimate the host galaxy distributions of BNS mergers. We find that the Galactic BNS observations imply efficient energy depletion in the common envelope (CE) phase, a bimodal kick velocity distribution, and low mass ejection during the secondary supernova explosion. However, the inferred R0 does not necessarily require an extremely high CE ejection efficiency and low kick velocities, different from the previous claims, mainly because the latest inferred R0 is narrowed to a lower value ($320_{-240}^{+490}\, \rm Gpc^{-3}\, yr^{-1}$). The BNS merger rate density resulting from the preferred model can be described by R($z$) ∼ R0(1 + $z$)ζ at low redshift ($z$ ≲ 0.5), with R0 ∼ 316–$784\, \rm Gpc^{-3}\, yr^{-1}$ and ζ ∼ 1.34–2.03, respectively. Our results also show that R0 and ζ depend on settings of BSE model parameters, and thus accurate estimates of these parameters by future GW detections will put strong constraints on BSE models. We further estimate that the fractions of BNS mergers hosted in spiral and elliptical galaxies at $z$ ∼ 0 are ∼81–84 and ∼16–19 per cent, respectively. The BNS merger rate per galaxy can be well determined by the host galaxy stellar mass, star formation rate, and metallicity, which provides a guidance in search for most probable candidates of BNS host galaxies.

WD mass and orbital period relation of sdB + He WD binaries

ABSTRACT Most subdwarf B (sdB) + Helium white dwarf (He WD) binaries are believed to be formed from a particular channel. In this channel, the He WDs are produced first from red giants (RGs) with degenerate cores via stable mass transfer and sdB stars are produced from RGs with degenerate cores via common-envelope (CE) ejection. They are important for the studies of CE evolution, binary evolution, and binary population synthesis. However, the relation between WD mass and orbital period of sdB + He WD binaries has not been specifically studied. In this paper, we first use a semi-analytic method to follow their formation and find a WD mass and orbital period relation. Then we use a detailed stellar evolution code to model their formation from main-sequence binaries. We find a similar relation between the WD mass and orbital period, which is in broad agreement with observations. For most sdB + He WD systems, if the WD mass (orbital period) can be determined, the orbital period (WD mass) can be inferred with this relation and then the inclination angle can be constrained with the binary mass function. In addition, we can also use this relation to constrain the CE ejection efficiency and find that a relative large CE ejection efficiency is favoured. If both the WD and sdB star masses can be determined, the critical mass ratios of dynamically unstable mass transfer for RG binaries can also be constrained.

Hot subdwarf B stars with neutron star components

Context. Subdwarf B stars (sdBs) play a crucial role in stellar evolution, asteroseismology, and far-UV radiation of early-type galaxies, and have been intensively studied with observation and theory. It has theoretically been predicted that sdBs with neutron star (NS) companions exist in the Galaxy, but none have been discovered yet. This remains a puzzle in this field. In a previous study (hereafter Paper I), we have studied the formation channels of sdB+NS binaries from main-sequence (MS) stars plus NS binaries by establishing a model grid, but it is still unclear how these binaries consisting of MS stars and NS binaries came to be in the first place. Aims. We systematically study the formation of sdB+NS binaries from their original zero-age main-sequence progenitors. We bridge the gap left by our previous study in this way. We obtain the statistical population properties of sdB+NS binaries and provide some guidance for observational efforts. Methods. We first used Hurley’s rapid binary evolution code BSE to evolve 107 primordial binaries to the point where the companions of NS+MS, NS+Hertzsprung gap star, and NS+Giant Branch star binaries have just filled their Roche lobes. Next, we injected these binaries into the model grid we developed in Paper I to obtain the properties of the sdB+NS populations. We adopted two prescriptions of NS natal kicks: the classical Maxwellian distribution with a dispersion of σ = 265 km s−1, and a linear formula that assumes that the kick velocity is associated with the ratio of ejected to remnant mass. Different values of αCE, where αCE is the common-envelope ejection efficiency, were chosen to examine the effect of common-envelope evolution on the results. Results. In the Galaxy, the birthrate of sdB+NS binaries is about 10−4 yr−1 and there are ∼7000 − 21 000 such binaries. This contributes 0.3−0.5% of all sdB binaries in the most favorable case. Most Galactic sdB+NS binaries (≳60%) arise from the channel of stable mass transfer. The value of αCE has little effect on the results, but when we use the linear formula prescription of NS natal kick, the number and birthrate doubles in comparison to the results we obtained with the Maxwellian distribution. The orbital periods of sdB+NS binaries from different formation channels differ significantly, as expected. This results in two peaks in the radial velocity (RV) semi-amplitude distribution: 100 − 150 km s−1 for stable mass transfer, and 400 − 600 km s−1 for common-envelope ejection. However, the two sdB+NS binary populations exhibit similar delay-time distributions, which both peak at about 0.2 Gyr. This indicates that Galactic sdB+NS binaries are born in very young populations, probably in the Galactic disk. The sdB+NS binaries produced from the common-envelope ejection channel are potential sources of strong gravitational wave radiation (GWR), and about ∼100 − 300 could be detected by the Laser Interferometer Space Antenna (LISA) with a signal-to-noise ratio of 1. Conclusions. Most sdB+NS binaries are located in the Galactic disk with small RV semi-amplitudes. SdB+NS binaries with large RV semi-amplitudes are expected to be strong GWR sources, some of which could be detected by LISA in the future.

The impact of electron-capture supernovae on merging double neutron stars

Natal kicks are one of the most debated issues about double neutron star (DNS) formation. Several observational and theoretical results suggest that some DNSs have formed with low natal kicks ($\lesssim{}50$ km s$^{-1}$), which might be attributed to electron-capture supernovae (ECSNe). We investigate the impact of ECSNe on the formation of DNSs by means of population synthesis simulations. In particular, we assume a Maxwellian velocity distribution for the natal kick induced by ECSNe with one dimensional root-mean-square $\sigma_{\rm ECSN} = 0,7,15,26,265$ km s$^{-1}$. The total number of DNSs scales inversely with $\sigma_{\rm ECSN}$ and the number of DNS mergers is higher for relatively low kicks. This effect is particularly strong if we assume low efficiency of common-envelope ejection (described by the parameter $\alpha=1$), while it is only mild for high efficiency of common-envelope ejection ($\alpha{}=5$). In most simulations, more than 50 per cent of the progenitors of merging DNSs undergo at least one ECSN and the ECSN is almost always the first SN occurring in the binary system. Finally, we have considered the extreme case in which all neutron stars receive a low natal kick ($\lesssim{}50$~km~s$^{-1}$). In this case, the number of DNSs increases by a factor of ten and the percentage of merging DNSs which went through an ECSN is significantly suppressed ($<40$ per cent).

The cosmic merger rate of neutron stars and black holes

Six gravitational wave detections have been reported so far, providing crucial insights on the merger rate of double compact objects. We investigate the cosmic merger rate of double neutron stars (DNSs), neutron star-black hole binaries (NSBHs) and black hole binaries (BHBs) by means of population-synthesis simulations coupled with the Illustris cosmological simulation. We have performed six different simulations, considering different assumptions for the efficiency of common envelope (CE) ejection and exploring two distributions for the supernova (SN) kicks. The current BHB merger rate derived from our simulations spans from $\sim{}150$ to $\sim{}240$ Gpc$^{-3}$ yr$^{-1}$ and is only mildly dependent on CE efficiency. In contrast, the current merger rates of DNSs (ranging from $\sim{}20$ to $\sim{}600$ Gpc$^{-3}$ yr$^{-1}$) and NSBHs (ranging from $\sim{}10$ to $\sim{}100$ Gpc$^{-3}$ yr$^{-1}$) strongly depend on the assumptions on CE and natal kicks. The merger rate of DNSs is consistent with the one inferred from the detection of GW170817 only if a high efficiency of CE ejection and low SN kicks (drawn from a Maxwellian distribution with one dimensional root mean square $\sigma{}=15$ km s$^{-1}$) are assumed.

Super-Eddington wind scenario for the progenitors of type Ia supernovae: binary population synthesis calculations

The super-Eddington wind scenario has been proposed as an alternative way for producing type Ia supernovae (SNe Ia). The super-Eddington wind can naturally prevent the carbon--oxygen white dwarfs (CO WDs) with high mass-accretion rates from becoming red-giant-like stars. Furthermore, it works in low-metallicity environments, which may explain SNe Ia observed at high redshifts. In this article, we systematically investigated the most prominent single-degenerate WD+MS channel based on the super-Eddington wind scenario. We combined the Eggleton stellar evolution code with a rapid binary population synthesis (BPS) approach to predict SN Ia birthrates for the WD+MS channel by adopting the super-Eddington wind scenario and detailed mass-accumulation efficiencies of H-shell flashes on the WDs. Our BPS calculations found that the estimated SN Ia birthrates for the WD+MS channel are ~0.009-0.315*10^{-3}{yr}^{-1} if we adopt the Eddington accretion rate as the critical accretion rate, which are much lower than that of the observations (<10% of the observed SN Ia birthrates). This indicates that the WD+MS channel only contributes a small proportion of all SNe Ia. The birthrates in this simulation are lower than previous studies, the main reason of which is that new mass-accumulation efficiencies of H-shell flashes are adopted. We also found that the critical mass-accretion rate has a significant influence on the birthrates of SNe Ia. Meanwhile, the results of our BPS calculations are sensitive to the values of the common-envelope ejection efficiency.

THE BIRTH RATE OF SNe Ia FROM HYBRID CONe WHITE DWARFS

Considering the uncertainties of the C-burning rate (CBR) and the treatment of convective boundaries, Chen et al. (2014) found that there is a regime where it is possible to form hybrid CONe white dwarfs (WDs), i.e. ONe WDs with carbon-rich cores. As these hybrid WDs can be as massive as 1.30 $M_{\odot}$, not much mass needs to be accreted for these objects to reach the Chandrasekhar limit and to explode as Type Ia supernovae (SNe Ia). We have investigated their contribution to the overall SN Ia birth rate and found that such SNe Ia tend to be relatively young with typical time delays between 0.1 and 1 Gyr, where some may be as young as 30 Myr. SNe Ia from hybrid CONe WDs may contribute several percent to all SNe Ia, depending on the common-envelope ejection efficiency and the CBR. We suggest that these SNe Ia may produce part of the 2002cx-like SN Ia class.

MODELING X-RAY BINARY EVOLUTION IN NORMAL GALAXIES: INSIGHTS FROM SINGS

We present the largest-scale comparison to date between observed extragalactic X-ray binary (XRB) populations and theoretical models of their production. We construct observational X-ray luminosity functions (oXLFs) using Chandra observations of 12 late-type galaxies from the Spitzer Infrared Nearby Galaxy Survey (SINGS). For each galaxy, we obtain theoretical XLFs (tXLFs) by combining XRB synthetic models, constructed with the population synthesis code StarTrack, with observational star formation histories (SFHs). We identify highest-likelihood models both for individual galaxies and globally, averaged over the full galaxy sample. Individual tXLFs successfully reproduce about half of oXLFs, but for some galaxies we are unable to find underlying source populations, indicating that galaxy SFHs and metallicities are not well matched and/or XRB modeling requires calibration on larger observational samples. Given these limitations, we find that best models are consistent with a product of common envelope ejection efficiency and central donor concentration ~=0.1, and a 50% uniform -- 50% "twins" initial mass-ratio distribution. We present and discuss constituent subpopulations of tXLFs according to donor, accretor and stellar population characteristics. The galaxy-wide X-ray luminosity due to low-mass and high-mass XRBs, estimated via our best global model tXLF, follows the general trend expected from the L_x - star formation rate and L_x - stellar mass relations of Lehmer et al 2010. Our best models are also in agreement with modeling of the evolution both of XRBs over cosmic time and of the galaxy X-ray luminosity with redshift.

ON THE RARITY OF X-RAY BINARIES WITH NAKED HELIUM DONORS

The paucity of known High-Mass X-Ray Binaries (HMXB) with naked He donor stars (hereafter He star) in the Galaxy has been noted over the years as a surprising fact, given the significant number of Galactic HMXBs containing H-rich donors, which are expected to be their progenitors. This contrast has further sharpened in light of recent observations uncovering a preponderance of HMXBs hosting loosely bound Be donors orbiting neutron stars (NS), which would be expected to naturally evolve into He-HMXBs through dynamical mass transfer onto the NS and a common-envelope (CE) phase. Hence, reconciling the large population of Be-HMXBs with the observation of only one He-HMXB can help constrain the dynamics of CE physics. Here, we use detailed stellar structure and evolution models and show that binary mergers of HMXBs during CE events must be common in order to resolve the tension between these observed populations. We find that, quantitatively, this scenario remains consistent with the typically adopted energy parameterization of CE evolution, yielding expected populations which are not at odds with current observations. However, future observations which better constrain the underlying population of loosely bound O/B-NS binaries are likely to place significant constraints on the efficiency of CE ejection.

POPULATION SYNTHESIS OF HOT SUBDWARFS: A PARAMETER STUDY

Binaries that contain a hot subdwarf (sdB) star and a main sequence companion may have interacted in the past. This binary population has historically helped determine our understanding of binary stellar evolution. We have computed a grid of binary population synthesis models using different assumptions about the minimum core mass for helium ignition, the envelope binding energy, the common envelope ejection efficiency, the amount of mass and angular momentum lost during stable mass transfer, and the criteria for stable mass transfer on the red giant branch and in the Hertzsprung gap. These parameters separately and together can significantly change the entire predicted population of sdBs. Nonetheless, several different parameter sets can reproduce the observed subpopulation of sdB + white dwarf and sdB + M dwarf binaries, which has been used to constrain these parameters in previous studies. The period distribution of sdB + early F dwarf binaries offers a better test of different mass transfer scenarios for stars that fill their Roche lobes on the red giant branch.

Is the common envelope ejection efficiency a function of the binary parameters?

We reconstruct the common envelope (CE) phase for the current sample of observed white dwarf-main sequence post-common envelope binaries (PCEBs). We apply multi-regression analysis in order to investigate whether correlations exist between the CE ejection efficiencies, alpha_CE, inferred from the sample, and the binary parameters: white dwarf mass, secondary mass, orbital period at the point the CE commences, or the orbital period immediately after the CE phase. We do this with and without consideration for the internal energy of the progenitor primary giants' envelope. Our fits should pave the first steps towards an observationally motivated recipe for calculating alpha_CE using the binary parameters at the start of the CE phase, which will be useful for population synthesis calculations or models of compact binary evolution. If we do consider the internal energy of the giants' envelope, we find a statistically significant correlation between alpha_CE and the white dwarf mass. If we do not, a correlation is found between alpha_CE and the orbital period at the point the CE phase commences. Furthermore, if the internal energy of the progenitor primary envelope is taken into account, then the CE ejection efficiencies are within the canonical range 0<alpha_CE<=1, although PCEBs with brown dwarf secondaries still require alpha_CE>=1.

The birth rate of subluminous and overluminous type Ia supernovae

Based on the results of Chen & Li (2009) and Pakmor et al. (2010), we carried out a series of binary population synthesis calculations and considered two treatment of common envelope (CE) evolution, i.e. $\alpha$-formalism and $\gamma$-algorithm. We found that the evolution of birth rate of these peculiar SNe Ia is heavily dependent on how to treat the CE evolution. The over-luminous SNe Ia may only occur for $\alpha$-formalism with low CE ejection efficiency and the delay time of the SNe Ia is between 0.4 and 0.8 Gyr. The upper limit of the contribution rate of the supernovae to all SN Ia is less than 0.3%. The delay time of sub-luminous SNe Ia from equal-mass DD systems is between 0.1 and 0.3 Gyr for $\alpha$-formalism with $\alpha=3.0$, while longer than 9 Gyr for $\alpha=1.0$. The range of the delay time for $\gamma$-algorithm is very wide, i.e. longer than 0.22 Gyr, even as long as 15 Gyr. The sub-luminous SNe Ia from equal-mass DD systems may only account for no more than 1% of all SNe Ia observed. The super-Chandrasekhar mass model of Chen & Li (2009) may account for a part of 2003fg-like supernovae and the equal-mass DD model developed by Pakmor et al. (2010) may explain some 1991bg-like events, too. In addition, based on the comparison between theories and observations, including the birth rate and delay time of the 1991bg-like events, we found that the $\gamma$-algorithm is more likely to be an appropriate prescription of the CE evolution of DD systems than the $\alpha$-formalism if the equal-mass DD systems is the progenitor of 1991bg-like SNe Ia.

How many cataclysmic variables are crossing the period gap? A test for the disruption of magnetic braking

We apply population synthesis techniques to calculate the present-day number of two types of white-dwarf main-sequence star (WDMS) binaries within the cataclysmic variable 2 to 3 h period gap. The first are post-common envelope binaries with secondary stars that have masses 0.17 <= M-2/M-circle dot <= 0.36 gap-post common envelope binaries (gPCEBs), such that they will commence mass transfer within the period gap. The second type are systems that were cataclysmic variables (CVs) at some point in their past, but detached once they evolved down in orbital period to approximate to 3 h as a consequence of disrupted magnetic braking, and are crossing the period gap via gravitational radiation detached cataclysmic variables (dCVs). Full population synthesis calculations are performed where we either assume constant, global values of the common envelope ejection efficiency, alpha CE, or consider alpha CE as a function of secondary mass. Several forms of magnetic braking are also considered. We predict an excess of dCVs over gPCEBs within the period gap of similar to 4 to similar to 13 assuming alpha(CE) = 0.1-0.6, and an initial mass ratio distribution of the form n(q) = 1. This excess is revealed as a prominent peak at the location of the period gap in the orbital period distribution of the combined gPCEB and dCV population. We suggest that if such a feature is observed in the orbital period distribution of an observed sample of short orbital periodWDMS binaries, this would strongly corroborate the disruption of magnetic braking.

Evolutionary models of short-period soft X-ray transients: comparison with observations

We consider evolutionary models for the population of short-period (Porb h) low-mass black-hole binaries (LMBHBs) and compare them with observations of soft X-ray transients (SXTs). We show that assuming strongly reduced magnetic braking (as suggested by us before for low-mass semidetached binaries) the calculated masses and effective temperatures of secondaries are encouragingly close to the observed masses and effective temperatures (as inferred from their spectra) of donor stars in short-period LMBHBs. Theoretical mass-transfer rates in SXTs are consistent with the observed ones if one assumes that accretion discs in these systems are truncated (“leaky”). We find that the population of short-period SXTs is formed mainly by systems which had unevolved or slightly evolved main-sequence donors () with a hydrogen abundance in the center at the Roche-lobe overflow (RLOF). Longer period (Porb day) SXTs might descend from systems with initial donor masses of about 1 and . Thus, one can explain the origin of short period LMBHB without invoking donors with cores almost totally depleted of hydrogen. Our models suggest that, unless the currently accepted empirical estimates of mass-loss rates by winds for massive O-stars and Wolf-Rayet stars are significantly over-evaluated, a very high efficiency of common-envelope ejection is necessary to form short-period LMBHBs.

A possible solution for the lack of EHB binaries in globular clusters

Context. The binary fraction among extreme horizontal branch (EHB) stars in Galactic globular clusters (GCs) is an order of magnitude lower than the binary fraction among their counterparts, field hot subdwarfs. This casts serious doubt on their formation channels. Aims. In this Letter, I explain the difference between the field and the cluster EHB stars with the binary model of Han et al. (2002, MNRAS, 336, 449; 2003, MNRAS, 341, 669) for the formation of EHB stars. Methods. With the binary population synthesis code of Han et al. (2002, 2003), I follow the evolution of simple stellar populations resulting from single star bursts (note that Han et al. 2002, 2003, adopted a constant star formation rate over the last 15 Gyr for the production of field EHB stars), and obtain EHB stars at different stellar population ages. Results. I found that the binary fraction among EHB stars decreases with the stellar population age. The fraction of EHB binaries with orbital periods P < 5d is similar to 2.5% for a stellar population of 10Gyr from the standard simulation set. Conclusions. The binary model of Han et al. (2002, 2003) is able to explain the lack of EHB binaries in globular clusters. I also propose that the precise determination of the physical parameters of close EHB binaries in GCs can lead to the strictest constraint on common-envelope ejection efficiency.

Inclusion of binaries in evolutionary population synthesis

Using evolutionary population synthesis we present integrated colours, integrated spectral energy distributions and absorption-line indices defined by the Lick Observatory image dissector scanner (referred to as Lick/IDS) system, for an extensive set of instantaneous burst binary stellar populations with and without binary interactions. The ages of the populations are in the range $1-15 $Gyr and the metallicities are in the range $0.0001-0.03$. By comparing the results for populations with and without binary interactions we show that the inclusion of binary interactions makes the integrated $\rm U-B$, $\rm B-V$, $\rm V-R$ and $\rm R-I$ colours and all Lick/IDS spectral absorption indices (except for $\rm H_\beta$) substantially smaller. In other words binary evolution makes a population appear bluer. This effect raises the derived age and metallicity of the population. We calculate several sets of additional solar-metallicity binary stellar populations to explore the influence of input parameters to the binary evolution algorithm (the common-envelope ejection efficiency and the stellar wind mass-loss rate) on the resulting integrated colours. We also look at the dependence on the choice of distribution functions used to generate the initial binary population. The results show that variations in the choice of input model parameters and distributions can significantly affect the results. However, comparing the discrepancies that exist between the colours of various models, we find that the differences are less than those produced between the models with and those without binary interactions. Therefore it is very necessary to consider binary interactions in order to draw accurate conclusions from evolutionary population synthesis work.

Detached white dwarf main-sequence star binaries

We initiated a comprehensive state of the art binary population synthesis study of white dwarf main-sequence star (WDMS) binaries to serve as a foundation for subsequent studies on pre-cataclysmic variables, double white dwarfs, and white dwarf + B-star binaries. We considered seven distinct formation channels subdivided into three main groups according to the evolutionary process that gives rise to the formation of the white dwarf or its helium-star progenitor: dynamically stable Roche- lobe overflow (Algol-type evolution), dynamically unstable Roche-lobe overflow (common-envelope evolution), or stellar winds (single star evolution). For each formation channel, we examine the sensitivity of the population to changes in the amount of mass lost from the system during dynamically stable Roche-lobe overflow, the common-envelope ejection efficiency, and the initial mass ratio or initial secondary mass distribution. In the case of a flat initial mass ratio distribution, the local space density of WDMS binaries is of the order of ∼10 −3 pc −3 . This number decreases to ∼10 −4 pc −3 when the initial mass ratio distribution is approximately proportional to the inverse of the initial mass ratio. More than 75% of the WDMS binary population originates from wide systems in which both components essentially evolve as if they were single stars. The remaining part of the population is dominated by systems in which the white dwarf is formed in a common-envelope phase when the primary ascends the first giant branch or the asymptotic giant branch. When dynamically stable mass transfer proceeds highly conservative and the common-envelope ejection process is very efficient, the birthrate of WDMS binaries forming through a common-envelope phase is about 10 times larger than the birthrate of WDMS binaries forming through a stable Roche-lobe overflow phase. The ratio of the number of helium white dwarf systems to the number of carbon/oxygen or oxygen/neon/magnesium white dwarf systems derived from large samples of observed WDMS binaries by, e.g., future planet-search missions such as SuperWASP, COROT, and Kepler may furthermore constrain the common-envelope ejection efficiency.