Subdwarf B (sdB) stars (and related sdO/sdOB stars) are believed to be helium‐core‐burning objects with very thin hydrogen‐rich envelopes. In recent years it has become increasingly clear from observational surveys that a large fraction of these objects are members of binary systems. To understand their formation better, we present the results of a detailed investigation of the three main binary evolution channels that can lead to the formation of sdB stars: the common‐envelope (CE) ejection channel, the stable Roche lobe overflow (RLOF) channel, and the double helium white dwarfs (WDs) merger channel. The CE ejection channel leads to the formation of sdB stars in short‐period binaries with typical orbital periods between 0.1 and 10 d, very thin hydrogen‐rich envelopes and a mass distribution sharply peaked around ∼0.46 M⊙. On the other hand, under the assumption that all mass transferred is soon lost, the stable RLOF channel produces sdB stars with similar masses but long orbital periods (400–1500 d) and with rather thick hydrogen‐rich envelopes. The merger channel gives rise to single sdB stars whose hydrogen‐rich envelopes are extremely thin but which have a fairly wide distribution of masses (0.4−0.65 M⊙). We obtained the conditions for the formation of sdB stars from each of these channels using detailed stellar and binary evolution calculations where we modelled the detailed evolution of sdB stars and carried out simplified binary population synthesis simulations. The observed period distribution of sdB stars in compact binaries strongly constrains the CE ejection parameters. The best fits to the observations are obtained for very efficient CE ejection where the envelope ionization energy is included, consistent with previous results. We also present the distribution of sdB stars in the Teff−log g diagram, the Hertzsprung–Russell diagram and the distribution of mass functions.

In this paper, the second of a series, we study the stellar dynamical and evolutionary processes leading to the formation of compact binaries containing neutron stars (NSs) in dense globular clusters. For this study, 70 dense clusters were simulated independently, with a total stellar mass ∼2 × 107 M⊙, exceeding the total mass of all dense globular clusters in our Galaxy. We find that, in order to reproduce the empirically derived formation rate of low‐mass X‐ray binaries (LMXBs), we must assume that NSs can be formed via electron‐capture supernovae with typical natal kicks smaller than in core‐collapse supernovae. Our results explain the observed dependence of the number of LMXBs on ‘collision number’ as well as the large scatter observed between different globular clusters. We predict that the number of quiescent LMXBs in different clusters should not have a strong metallicity dependence. We compare the results obtained from our simulations with the observed population of millisecond pulsars (MSPs). We find that in our cluster model the following mass‐gaining events create populations of MSPs that do not match the observations (either they are inconsistent with the observed LMXB production rates, or the inferred binary periods or companion masses are not observed among radio bMSPs): (i) accretion during a common‐envelope event with a NS formed through electron‐capture supernovae (ECSNe), and (ii) mass transfer (MT) from a white dwarf donor. Some processes lead only to a mild recycling – physical collisions or MT in a post‐accretion‐induced collapse system. In addition, for MSPs, we distinguish low magnetic field (long‐lived) and high magnetic field (short‐lived) populations, where in the latter NSs are formed as a result of accretion‐induced collapse or merger‐induced collapse. With this distinction and by considering only those mass‐gaining events that appear to lead to NS recycling, we obtain good agreement of our models with the numbers and characteristics of observed MSPs in 47 Tuc and Terzan 5, as well as with the cumulative statistics for MSPs detected in globular clusters of different dynamical properties. We find that significant production of merging double NSs potentially detectable as short γ‐ray bursts occurs only in very dense, most likely core‐collapsed clusters.

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficientWe obtain new interesting cases of such equations with the density f localized in space, which have non-trivial invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local transformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.

This paper completes investigation of symmetry properties of nonlinear variable coefficient -11]. Potential symmetries of equations from the considered class are found and the connection of them with Lie symmetries of diffusion-type equations is shown. Exact solutions of the Fujita-Storm equation u t = (u −2 u x ) x are constructed.

Articles you may be interested inOn twistor transformations and invariant differential operator of simple Lie group G2 (2)

The stability of mass transfer in binaries with convective giant donors remains an open question in modern astrophysics. There is a significant discrepancy between what the existing methods predict for a response to mass loss of the giant itself, as well as for the mass transfer rate during the Roche lobe overflow. Here we show that the recombination energy in the superadiabatic layer plays an important and hitherto unaccounted-for role in the donor's response to mass loss, in particular on its luminosity and effective temperature. Our improved optically thick nozzle method to calculate the mass transfer rate via L 1 allows us to evolve binary systems for a substantial Roche lobe overflow. We propose a new, strengthened criterion for the mass transfer instability, basing it on whether the donor experiences overflow through its outer Lagrangian point. We find that with the new criterion, if the donor has a well-developed outer convective envelope, the critical initial mass ratio for which a binary would evolve stably through the conservative mass transfer varies from 1.5 to 2.2, which is about twice as large as previously believed. In underdeveloped giants with shallow convective envelopes this critical ratio may be even larger. When the convective envelope is still growing, and in particular for most cases of massive donors, the critical mass ratio gradually decreases to this value, from that of radiative donors.

We present a new mechanism for the ejection of a common envelope in a massive binary, where the energy source is nuclear energy rather than orbital energy. This can occur during the slow merger of a massive primary with a secondary of 1–3  M⊙ when the primary has already completed helium core burning. We show that in the final merging phase, hydrogen‐rich material from the secondary can be injected into the helium‐burning shell of the primary. This leads to a nuclear runaway and the explosive ejection of both the hydrogen and the helium layers, producing a close binary containing a CO star and a low‐mass companion. We argue that this presents a viable scenario to produce short‐period black‐hole binaries and long‐duration gamma‐ray bursts (LGRBs). We estimate an LGRB rate of ∼ 10−6 yr−1 at solar metallicity, which implies that this may account for a significant fraction of all LGRBs and that this rate should be higher at lower metallicity.

We carry out an extensive investigation of conservation laws and potential symmetries for the class of linear (1+1)-dimensional second-order parabolic equations. The group classification of this class is revised by employing admissible transformations, the notion of normalized classes of differential equations and the adjoint variational principle. All possible potential conservation laws are described completely. They are in fact exhausted by local conservation laws. For any equation from the above class the characteristic space of local conservation laws is isomorphic to the solution set of the adjoint equation. Effective criteria for the existence of potential symmetries are proposed. Their proofs involve a rather intricate interplay between different representations of potential systems, the notion of a potential equation associated with a tuple of characteristics, prolongation of the equivalence group to the whole potential frame and application of multiple dual Darboux transformations. Based on the tools developed, a preliminary analysis of generalized potential symmetries is carried out and then applied to substantiate our construction of potential systems. The simplest potential symmetries of the linear heat equation, which are associated with single conservation laws, are classified with respect to its point symmetry group. Equations possessing infinite series of potential symmetry algebras are studied in detail.Comment: 67 pages, minor correction