Context. There is still considerable debate over the progenitors of type Ia supernovae (SNe Ia). Likewise, it is not agreed how single white dwarfs with masses 0.5 M can be formed in the field, even though they are known to exist. Aims. We consider whether single low-mass white dwarfs (LMWDs) could have been formed in binary systems where their companions have exploded as an SN Ia. In this model, the observed single LMWDs are the remnants of giant-branch donor stars whose envelopes have been stripped off by the supernova explosion. Methods. We investigate the likely remnants of SNe Ia, including the effects of the explosion on the envelope of the donor star. We also use evolutionary arguments to examine alternative formation channels for single LMWDs. In addition, we calculate the expected kinematics of the potential remnants of SNe Ia. Results. SN Ia in systems with giant-branch donor stars can naturally explain the production of single LMWDs. It seems difficult for any other formation mechanism to account for the observations, especially for those single LMWDs with masses 0.4 M . Independent of those results, we find that the kinematics of one potentially useful population containing single LMWDs is consistent with our model. Studying remnant white-dwarf kinematics seems to be a promising way to investigate SN Ia progenitors. Conclusions. The existence of single LMWDs appears to constitute evidence for the production of SNe Ia in binary systems with a red-giant donor star. Other single white dwarfs with higher space velocities support a second, probably dominant, population of SN Ia progenitors which contained main-sequence or subgiant donor stars at the time of explosion. The runaway stars LP 400-22 and US 708 suggest the possibility of a third formation channnel for some SNe Ia in systems where the donor stars are hot subdwarfs.

The nature of the progenitors of Type Ia supernovae (SNe Ia) is still unclear. In this paper, by considering the effect of the instability of accretion disk on the evolution of white dwarf (WD) binaries, we performed binary evolution calculations for about 2400 close WD binaries, in which a carbon--oxygen WD accretes material from a main-sequence star or a slightly evolved subgiant star (WD + MS channel), or a red-giant star (WD + RG channel) to increase its mass to the Chandrasekhar (Ch) mass limit. According to these calculations, we mapped out the initial parameters for SNe Ia in the orbital period--secondary mass ($\log P^{\rm i}-M^{\rm i}_2$) plane for various WD masses for these two channels, respectively. We confirm that WDs in the WD + MS channel with a mass as low as $0.61 M_\odot$ can accrete efficiently and reach the Ch limit, while the lowest WD mass for the WD + RG channel is $1.0 \rm M_\odot$. We have implemented these results in a binary population synthesis study to obtain the SN Ia birthrates and the evolution of SN Ia birthrates with time for both a constant star formation rate and a single starburst. We find that the Galactic SN Ia birthrate from the WD + MS channel is $\sim$$1.8\times 10^{-3} {\rm yr}^{-1}$ according to our standard model, which is higher than previous results. However, similar to previous studies, the birthrate from the WD + RG channel is still low ($\sim$$3\times 10^{-5} {\rm yr}^{-1}$). We also find that about one third of SNe Ia from the WD + MS channel and all SNe Ia from the WD + RG channel can contribute to the old populations ($\ga$1 Gyr) of SN Ia progenitors.Comment: 11 pages, 9 figures, 1 table, accepted for publication in MNRA

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 the 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 U-B, B-V, V-R and R-I colours and all Lick/IDS spectral absorption indices (except for H β ) 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 the binary evolution algorithm input parameters (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.

Using evolutionary population synthesis, we present high-resolution (0.3 Å) integrated spectral energy distributions from 3000 to 7000 Å and absorption-line indices defined by the Lick Observatory Image Dissector Scanner (Lick/IDS) system, for an extensive set of instantaneousburst binary stellar populations with binary interactions. The ages of the populations are in the range 1-15 Gyr and the metallicities are in the range 0.004-0.03. These high-resolution synthesis results can satisfy the needs of modern spectroscopic galaxy surveys, and are available on request.By comparing the synthetic continuum of populations at high and low resolution, we show that there is good agreement for solar metallicity and tolerable disagreement for non-solar metallicity. The strength of the Balmer lines at high spectral resolution is greater than that at low resolution for all metallicities. The comparison of Lick/IDS absorption-line indices at low and high resolution, both of which are obtained by the fitting functions, shows that the discrepancies in all indices except for TiO 1 and TiO 2 are insignificant for populations with Z = 0.004 and 0.02. The high-resolution Ca4227, Fe5015 and Mg b indices are redder than the corresponding low-resolution ones for populations with Z = 0.01 and 0.03; this effect lowers the derived age and metallicity of the population. The high-resolution Mg 1 , Fe5709 and Fe5782 indices are bluer than those at low resolution; this effect raises the age and metallicity. The discrepancy in these six indices is greater for populations with Z = 0.03 in comparison to Z = 0.01.At high resolution we compare the Lick/IDS spectral absorption indices obtained by using the fitting functions with those measured directly from the synthetic spectra. We find that the Ca4455, Fe4668, Mg b and Na D indices obtained by the use of the fitting functions are redder for all metallicities, Fe5709 is redder at Z = 0.03 and becomes bluer at Z = 0.01 and 0.004, and the other indices are bluer for all metallicities than the corresponding values measured directly from the synthetic spectra.

Binary interactions lead to the formation of intriguing objects, such as compact binaries, supernovae, gamma ray bursts, X-ray binaries, pulsars, novae, cataclysmic variables, hot subdwarf stars, barium stars and blue stragglers. To study the evolution of binary populations and the consequent formation of these objects, many methods have been developed over the years, for which a robust approach named binary population synthesis (BPS) warrants special attention. This approach has seen widespread application in many areas of astrophysics, including but not limited to analyses of the stellar content of galaxies, research on galactic chemical evolution and studies concerning star formation and cosmic re-ionization. In this review, we discuss the role of BPS, its general picture and the various components that comprise it. We pay special attention to the stability criteria for mass transfer in binaries, as this stability largely determines the fate of binary systems. We conclude with our perspectives regarding the future of this field.