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Many aspects of the evolution of stars, and in particular the evolution of binary stars, remain beyond our ability to model them in detail. Instead, we rely on observations to guide our often phenomenological models and pin down uncertain model parameters. To do this statistically requires population synthesis. Populations of stars modelled on computers are compared to populations of stars observed with our best telescopes. The closest match between observations and models provides insight into unknown model parameters and hence the underlying astrophysics. In this brief review, we describe the impact that modern big-data surveys will have on population synthesis, the large parameter space problem that is rife for the application of modern data science algorithms, and some examples of how population synthesis is relevant to modern astrophysics.
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The carbon-enhanced metal-poor (CEMP) stars constitute approximately one fifth of the metal-poor ([Fe/H] ~< -2) population but their origin is not well understood. The most widely accepted formation scenario, invokes mass-transfer of carbon-rich material from a thermally-pulsing asymptotic giant branch (TPAGB) primary star to a less massive main-sequence companion which is seen today. Recent studies explore the possibility that an initial mass function biased toward intermediate-mass stars is required to reproduce the observed CEMP fraction in stars with metallicity [Fe/H] < -2.5. These models also implicitly predict a large number of nitrogen-enhanced metal-poor (NEMP) stars which is not seen. We investigate whether the observed CEMP and NEMP to extremely metal-poor (EMP) ratios can be explained without invoking a change in the initial mass function. We confirm earlier findings that with current detailed TPAGB models the large observed CEMP fraction cannot be accounted for. We find that efficient third dredge up in low-mass (less than 1.25Msun), low-metallicity stars may offer at least a partial explanation to the large observed CEMP fraction while remaining consistent with the small observed NEMP fraction.
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 Hurleys rapid binary evolution code BSE to evolve 10^7 primordial binaries to the point where the companions of NS+MS, NS+Hertzsprung gap (HG) star, and NS+Giant Branch (GB) 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. Different values of common-envelope ejection efficiency were chosen to examine the effect of common-envelope evolution on the results. 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 stellar population in the Galactic halo is characterised by a large fraction of CEMP stars. Most CEMP stars are enriched in $s$-elements (CEMP-$s$ stars), and some of these are also enriched in $r$-elements (CEMP-$s/r$ stars). One formation scenario proposed for CEMP stars invokes wind mass transfer in the past from a TP-AGB primary star to a less massive companion star which is presently observed. We generate low-metallicity populations of binary stars to reproduce the observed CEMP-star fraction. In addition, we aim to constrain our wind mass-transfer model and investigate under which conditions our synthetic populations reproduce observed abundance distributions. We compare the CEMP fractions and the abundance distributions determined from our synthetic populations with observations. Several physical parameters of the binary stellar population of the halo are uncertain, e.g. the initial mass function, the mass-ratio and orbital-period distributions, and the binary fraction. We vary the assumptions in our model about these parameters, as well as the wind mass-transfer process, and study the consequent variations of our synthetic CEMP population. The CEMP fractions calculated in our synthetic populations vary between 7% and 17%, a range consistent with the CEMP fractions among very metal-poor stars recently derived from the SDSS/SEGUE data sample. The results of our comparison between the modelled and observed abundance distributions are different for CEMP-$s/r$ stars and for CEMP-$s$ stars. For the latter, our simulations qualitatively reproduce the observed distributions of C, Na, Sr, Ba, Eu, and Pb. Contrarily, for CEMP-$s/r$ stars our model cannot reproduce the large abundances of neutron-rich elements such as Ba, Eu, and Pb. This result is consistent with previous studies, and suggests that CEMP-$s/r$ stars experienced a different nucleosynthesis history to CEMP-$s$ stars.
Binary population synthesis (BPS) modelling is a very effective tool to study the evolution and properties of close binary systems. The uncertainty in the parameters of the model and their effect on a population can be tested in a statistical way, which then leads to a deeper understanding of the underlying physical processes involved. To understand the predictive power of BPS codes, we study the similarities and differences in the predicted populations of four different BPS codes for low- and intermediate-mass binaries. We investigate whether the differences are caused by different assumptions made in the BPS codes or by numerical effects. To simplify the complex problem of comparing BPS codes, we equalise the inherent assumptions as much as possible. We find that the simulated populations are similar between the codes. Regarding the population of binaries with one WD, there is very good agreement between the physical characteristics, the evolutionary channels that lead to the birth of these systems, and their birthrates. Regarding the double WD population, there is a good agreement on which evolutionary channels exist to create double WDs and a rough agreement on the characteristics of the double WD population. Regarding which progenitor systems lead to a single and double WD system and which systems do not, the four codes agree well. Most importantly, we find that for these two populations, the differences in the predictions from the four codes are not due to numerical differences, but because of different inherent assumptions. We identify critical assumptions for BPS studies that need to be studied in more detail.
We present a comparison of the frequencies of carbon-enhanced metal-poor (CEMP) giant and main-sequence turnoff stars, selected from the Sloan Digital Sky Survey and the Sloan Extension for Galactic Understanding and Exploration, with predictions from asymptotic giant-branch (AGB) mass-transfer models. We consider two initial mass functions (IMFs)-a Salpeter IMF, and a mass function with a characteristic mass of 10 solar mass. These comparisons indicate good agreement between the observed CEMP frequencies for stars with [Fe/H] > -1.5 and a Salpeter IMF, but not with an IMF having a higher characteristic mass. Thus, while the adopted AGB model works well for low-mass progenitor stars, it does not do so for high-mass progenitors. Our results imply that the IMF shifted from high- to low-mass dominated in the early history of the Milky Way, which appears to have occurred at a chemical time between [Fe/H] = -2.5 and [Fe/H] = -1.5. The corrected CEMP frequency for the turnoff stars with [Fe/H] < -3.0 is much higher than the AGB model prediction from the high-mass IMF, supporting the previous assertion that one or more additional mechanisms, not associated with AGB stars, are required for the production of carbon-rich material below [Fe/H] = -3.0. [abridged]
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