When a core-collapse supernova explodes in a binary star system, the ejecta might encounter an overdense shell, where the stellar winds of the two stars previously collided. In this work, we investigate effects of such interactions on supernova light curves on time-scales from the early flash ionization signatures to approximately one year after the explosion. We construct a model of the colliding-wind shell in an orbiting binary star system and we provide an analytical expression for the shell thickness and density, which we calibrate with three-dimensional adaptive mesh refinement hydrodynamical simulations probing different ratios of wind momenta and different regimes of radiative cooling efficiency. We model the angle-dependent interaction of supernova ejecta with the circumstellar medium and estimate the shock radiative efficiency with a realistic cooling function. We find that the radiated shock power exceeds typical Type IIP supernova luminosity only for double red supergiant binaries with mass ratios $q \gtrsim 0.9$, wind mass-loss rates $\dot{M} \gtrsim 10^{-4} M_\odot\,\text{yr}^{-1}$, and separations between about 50 and 1500 AU. The required $\dot{M}$ increases for binaries with smaller $q$ or primaries with faster wind. We estimate that $\ll 1\%$ of all collapsing massive stars satisfy the conditions on binary mass ratio and separation. Recombination luminosities due to colliding wind shells are at most a factor of 10 higher than for an otherwise unperturbed constant-velocity wind, but higher densities associated with wind acceleration close to the star provide much stronger signal.
Massive systems made of two or more stars are known to be the site for interesting physical processes -- including at least in some cases -- particle acceleration. Over the past decade, this topic motivated a particular effort to unveil the properties of these systems and characterize the circumstances responsible for the acceleration of particles and the potential role of pre-supernova massive stars in the production of high energy particles in our Galaxy. Although previous studies on this topic were mostly devoted to processes in general, or to a few individual objects in particular, a unifi…
The dynamics of colliding wind binary systems and conditions for efficient particle acceleration therein have attracted multiple numerical studies in the recent years. These numerical models seek an explanation of the thermal and non-thermal emission of these systems as seen by observations. In the non-thermal regime, radio and X-ray emission is observed for several of these colliding-wind binaries, while gamma-ray emission has so far only been found in $η$ Carinae and possibly in WR 11. Energetic electrons are deemed responsible for a large fraction of the observed high-energy photons in thes…
In colliding-wind binaries, shocks accelerate a fraction of the electrons up to relativistic speeds. These electrons then emit synchrotron radiation at radio wavelengths. Whether or not we detect this radiation depends on the size of the free-free absorption region in the stellar winds of both components. One expects long-period binaries to be detectable, but not the short-period ones. It was therefore surprising to find that Cyg OB2 No. 8A (P = 21.9 d) does show variability locked with orbital phase. To investigate this, we developed a model for the relativistic electron generation (including…
Gamma-ray binaries emit most of their radiated power beyond ~10 MeV. The non-thermal emission is thought to arise from the interaction of the relativistic wind of a rotation-powered pulsar with the stellar wind of its massive (O or Be) companion star. A powerful pulsar creates an extended cavity, filled with relativistic electrons, in the radiatively-driven wind of the massive star. As a result, the observed P Cyg profiles of UV resonant lines from the stellar wind should be different from those of single massive stars. We propose to use UV emission lines to detect and constrain the colliding …
Gamma-ray binaries are colliding wind binaries (CWB) composed of a massive star a non-accreting pulsar with a highly relativistic wind. Particle acceleration at the shocks results in emission going from extended radio emission to the gamma-ray band. The interaction region is expected to show common features with stellar CWB. Performing numerical simulations with the hydrodynamical code RAMSES, we focus on their structure and stability and find that the Kelvin-Helmholtz instability (KHI) can lead to important mixing between the winds and destroy the large scale spiral structure. To investigate …
Colliding wind binaries (CWBs) are unique laboratories for X-ray astrophysics. The massive stars in these systems possess powerful stellar winds with speeds up to $\sim$3000 km s$^{-1}$, and their collision leads to hot plasma (up to $\sim10^8$K) that emit thermal X-rays (up to $\sim$10 keV). Many X-ray telescopes have observed CWBs, including Suzaku, and our work aims to model these X-ray observations. We use 3D smoothed particle hydrodynamics (SPH) to model the wind-wind interaction, and then perform 3D radiative transfer to compute the emergent X-ray flux, which is folded through X-ray tele…
Many early-type stars are in binary systems. A number of them shows radio emissivity with periodic variability. This variability is associated with non-thermal synchrotron radiation emitted by relativistic electrons. The strong shocks necessary to accelerate the electrons up to high energies are produced by the collision of the radiatively-driven stellar winds. A study of the non-thermal emission is necessary in order to investigate O-star colliding wind binaries. Here preliminary results of our modeling of the colliding winds in Cyg OB2 No.9 are presented.
Some OB stars show variable non-thermal radio emission. The non-thermal emission is due to synchrotron radiation that is emitted by electrons accelerated to high energies. The electron acceleration occurs at strong shocks created by the collision of radiatively-driven stellar winds in binary systems. Here we present results of our modelling of two colliding wind systems: Cyg OB2 No. 8A and Cyg OB2 No. 9.
Colliding wind binaries (CWBs) have been considered as a possible high energy $γ$-ray sources for some time, however no system other than $η$ Car has been detected. In the paper a sample of seven CWBs (WR 11, WR 70, WR 137, WR 140, WR 146, WR 147) which, by means of theoretic modelling, were deemed most promising candidates, was analyzed using almost 7 years of the Fermi-LAT data. WR 11 ($γ^2$ Vel) was detected at 6.1$σ$ confidence level with a photon flux in 0.1-100 GeV range $(1.8\pm0.6)\times10^{-9}~\mathrm{ph~cm^{-2}~s^{-1}}$ and an energy flux $(2.7\pm0.5)\times10^{-12}~~\mathrm{erg~cm^{-…
Several colliding-wind massive binaries are known to be non-thermal emitters in the radio domain. This constitutes strong evidence for the fact that an efficient particle acceleration process is at work in these objects. The acceleration mechanism is most probably the Diffusive Shock Acceleration (DSA) process in the presence of strong hydrodynamic shocks due to the colliding-winds. In order to investigate the physics of this particle acceleration, we initiated a multiwavelength campaign covering a large part of the electromagnetic spectrum. In this context, the detailed study of the hard X-ra…
Particle-accelerating colliding-wind binaries (PACWBs) are multiple systems made of early-type stars able to accelerate particles up to relativistic velocities. The relativistic particles can interact with different fields (magnetic or radiation) in the colliding-wind region and produce non-thermal emission. In many cases, non-thermal synchrotron radiation might be observable and thus constitute an indicator of the existence of a relativistic particle population in these multiple systems. To date, the catalogue of PACWBs includes about 40 objects spread over many stellar types and evolutionary…
The influence of free-free absorption on the radio spectrum of Particle-Accelerating Colliding-Wind Binaries
University of Liège（列日大学）；Indian Institute for Space science and Technology (IIST)（印度空间科学与技术学院）；Instituto Argentino de Radioastronomía（阿根廷射电天文学研究所）；Peking University（北京大学）；Chalmers University of Technology（查尔姆斯理工大学）
We have compiled a list of 36 O+O and 89 Wolf-Rayet binary candidates in the Milky Way and Magellanic clouds detected with the Chandra, XMM-Newton and ROSAT satellites to probe the connection between their X-ray properties and their system characteristics. Of the WR binaries with published parameters, all but two have kT > 0.9 keV. The most X-ray luminous WR binaries are typically very long period systems. The WR binaries show a nearly four-order of magnitude spread in X-ray luminosity, even among among systems with very similar WR primaries. Among the O+O binaries, short-period systems genera…
We present high resolution simulations with RAMSES of supersonic colliding stellar winds. The collision results in a double shock structure which is subject to different instabilities. The Kelvin-Helmholtz instability (KHI) introduces some mixing and variability. For isothermal winds, the Non-linear Thin Shell Instability violently affects the interaction region. Properly modelling these instabilities requires a high enough resolution and an adapted numerical method, especially when one of the winds strongly dominates the other one. At large scale, orbital motion is expected to turn the shocke…
We carry out a numerical experiment of ejecting winds in a massive colliding wind binary system, and quantifying the accretion onto the secondary star under different primary mass loss rates. We set a binary system comprising a Luminous Blue Variable (LBV) as the primary and a Wolf-Rayet (WR) star as the secondary, and vary the mass loss rate of the LBV to obtain different values of wind momentum ratio $η$. Our simulations include two sets of cases: one where the stars are stationary, and one that includes the orbital motion. As $η$ decreases the colliding wind structure moves closer to the se…
Binary systems formed by early-type stars with strong winds are known to display variable non-thermal radio emission, thermal X-rays, and, at least in one case (Eta Carina), $γ$ rays. Some of these systems are quite eccentric and the conditions for efficient particle acceleration and $γ$-ray production might manifest only occasionally. In this paper I briefly review the physics of colliding wind binaries with emphasis on the observational signatures of non-thermal particle acceleration. I discuss, in particular, the case of the system HD 93129A which is made up by an O2 If* star (the primary) …
In addition to gamma-ray binaries which contain a compact object, high-energy and very high-energy gamma rays have also been detected from colliding-wind binaries. The collision of the winds produces two strong shock fronts, one for each wind, both surrounding a shock region of compressed and heated plasma, where particles are accelerated to very high energies. Magnetic field is also amplified in the shocked region on which the acceleration of particles greatly depends. In this work, we performed full three-dimensional magnetohydrodynamic simulations of colliding winds coupled to a code that e…
The interaction between the strong winds of the stars in colliding-wind binary (CWB) systems produces two shock fronts, delimiting the wind collision region (WCR). There, particles are expected to be accelerated mainly via diffusive shock acceleration, and to produce $γ$-rays, in processes involving relativistic electrons and/or protons. We investigate the injection and the acceleration of protons in typical CWB systems by means of Monte Carlo simulations, with a test-particle approach. We use magnetohydrodynamic simulations to determine the background conditions in the wind collision region. …
The number of binaries containing black holes or neutron stars depends critically on the fraction of binaries that survive supernova explosions. We searched for surviving star plus remnant binaries in a sample of 49 supernova remnants (SNR) containing 23 previously identified compact remnants and three high mass X-ray binaries (HMXB), finding no new interacting or non-interacting binaries. The upper limits on any main sequence stellar companion are typically <0.2Msun and are at worst <3Msun. This implies that f<0.1 of core collapse SNRs contain a non-interacting binary, and f=0.083 (0.032<f<0.…
We perform binary evolution calculations on helium star - carbon-oxygen white dwarf (CO WD) binaries using the stellar evolution code MESA. This single degenerate channel may contribute significantly to thermonuclear supernovae at short delay times. We examine the thermal-timescale mass transfer from a 1.1 - 2.0 $M_{\odot}$ helium star to a 0.90 - 1.05 $M_{\odot}$ CO WD for initial orbital periods in the range 0.05 - 1 day. Systems in this range may produce a thermonuclear supernova, helium novae, a helium star - oxygen-neon WD binary, or a detached double CO WD binary. Our time-dependent calc…
We perform 3D hydrodynamical simulations of new-born neutron stars (NSs) colliding with main-sequence binary companions after supernova explosions. Based on those hydrodynamical models, we construct a semi-analytical formula that describes the drag force inside stars with steep density gradients. We then compute the outcome of NS--companion collisions over a wide range of parameters using the semi-analytical formula. Depending on the direction and magnitude of the natal kick, we find that the collision may lead to various outcomes. For relatively fast kicks and high impact parameters, the NS m…
Context. Particle-accelerating colliding-wind binaries (PACWBs) are systems that are formed by two massive and hot stars and produce nonthermal (NT) radiation. The key elements of these systems are fast winds and the shocks that they create when they collide. Binaries with nonaccreting young pulsars have also been detected as NT emitters, again as a consequence of the wind-wind interaction. Black holes (BHs) might produce NT radiation by this mechanism if they accrete at super-Eddington rates. In such cases, the disk is expected to launch a radiation-driven wind, and if this wind has an equato…
Massive stars play an important role in explaining the cosmic ray spectrum below the knee, possibly even up to the ankle, i.e. up to energies of 1e15 eV or 1e18.5 eV, respectively. In particular, Supernova Remnants are discussed as one of the main candidates to explain the cosmic ray spectrum. Even before their violent deaths, during the stars' regular life times, cosmic rays can be accelerated in wind environments. High-energy gamma-ray measurements indicate hadronic acceleration binary systems, leading to both periodic gamma-ray emission from binaries like LSI+60~303 and continuous emission …
In the single degenerate scenario for the progenitors of type Ia supernovae (SNe Ia), a white dwarf rapidly accretes hydrogen- or helium-rich material from its companion star, and appears as a supersoft X-ray source. This picture has been challenged by the properties of the supersoft X-ray sources with very low-mass companions and the observations of several nearby SNe Ia. It has been pointed out that, the X-ray radiation or the wind from the accreting white dwarf can excite wind or strip mass from the companion star, thus significantly influence the mass transfer processes. In this paper we p…
The fraction of stars which are in binaries or triples at the time of stellar death and the fraction of these systems which survive the supernova (SN) explosion are crucial constraints for evolution models and predictions for gravitational wave source populations. These fractions are also subject to direct observational determination. Here we search 10 supernova remnants (SNR) containing compact objects with proper motions for unbound binaries or triples using Gaia EDR3 and new statistical methods and tests for false positives. We confirm the one known example of an unbound binary, HD 37424 in…
We carry out a systematic study of the response of companion stars in massive binaries after being impacted by supernova ejecta. A total of 720 1D stellar evolution calculations are performed to follow the inflation and contraction of the star in response to the energy injection and how it depends on various parameters. We find that the maximum luminosity achieved during the inflated phase is only dependent on the stellar mass and we derive an analytic formula to describe the relation. There is also a tight correlation between the duration of expansion and the intersected energy. These correla…
Massive stars in binary systems (as WR140, WR147 or $η$ Carinae) have long been regarded as potential sources of high-energy $γ$-rays. The emission is thought to arise in the region where the stellar winds collide and produce relativistic particles which subsequently might be able to emit $γ$-rays. Detailed numerical hydrodynamic simulations have already offered insight in the complex dynamics of the wind collision region (WCR), while independent analytical studies, albeit with simplified descriptions of the WCR, have shed light on the spectra of charged particles. In this paper, we describe a…
The long-term (over more than one decade) X-ray emission from two massive stellar systems known to be particle accelerators is investigated using XMM-Newton. Their X-ray properties are interpreted taking into account recent information about their multiplicity and orbital parameters. The two targets, HD168112 and HD167971 appear to be overluminous in X-rays, lending additional support to the idea that a significant contribution of the X-ray emission comes from colliding-wind regions. The variability of the X-ray flux from HD168112 is interpreted in terms of varying separation expected to follo…
Evolution of binaries containing a hot subdwarf and a white dwarf to double white dwarfs, and double detonation supernovae with hypervelocity runaway stars
We have analysed the X-ray emission from a sample of close WR+O binaries using data from the public Chandra and XMM-Newton archives. Global spectral fits show that two-temperature plasma is needed to match the X-ray emission from these objects as the hot component (kT > 2 keV) is an important ingredient of the spectral models. In close WR+O binaries, X-rays likely originate in colliding stellar wind (CSW) shocks driven by the massive winds of the binary components. CSW shocks in these objects are expected to be radiative due to the high density of the plasma in the interaction region. Opposite…
We present results of new Chandra High-Energy Transmission Grating (HETG) observations (2019 November - December) of the massive Wolf-Rayet (WR) binary WR 48a. Analysis of these high-quality data showed that the spectral lines in this massive binary are broadened (FWHM = 1400 km/s) and marginally blushifted (~ -100 km/s). A direct modelling of these high-resolution spectra in the framework of the standard colliding stellar wind (CSW) picture provided a very good correspondence between the shape of the theoretical and observed spectra. Also, the theoretical line profiles are in most cases an ac…
We investigate the structure and X-ray emission from the colliding stellar winds in massive star binaries. We find that the opening angle of the contact discontinuity (CD) is overestimated by several formulae in the literature at very small values of the wind momentum ratio. We find also that the shocks in the primary (dominant) and secondary winds flare by approx 20 degrees compared to the CD, and that the entire secondary wind is shocked when the wind momentum ratio < 0.02. Analytical expressions for the opening angles of the shocks, and the fraction of each wind that is shocked, are provide…
Context: Colliding wind binaries (CWBs) are thought to give rise to a plethora of physical processes including acceleration and interaction of relativistic particles. Observation of synchrotron radiation in the radio band confirms there is a relativistic electron population in CWBs. Accordingly, CWBs have been suspected sources of high-energy gamma-ray emission since the COS-B era. Theoretical models exist that characterize the underlying physical processes leading to particle acceleration and quantitatively predict the non-thermal energy emission observable at Earth. Aims: We strive to find e…
With the increasing number of observed magnetic white dwarfs (WDs), the role of magnetic field of the WD in both single and binary evolutions should draw more attentions. In this study, we investigate the WD/main-sequence star binary evolution with the Modules for Experiments in Stellar Astrophysics (MESA code), by considering WDs with non-, intermediate and high magnetic field strength. We mainly focus on how the strong magnetic field of the WD (in a polar-like system) affects the binary evolution towards type Ia supernovae (SNe Ia). The accreted matter goes along the magnetic field lines and…
High-mass binary systems involve extreme environments that produce non-thermal emission from radio to gamma rays. Only three types of these systems are known to emit persistent gamma-ray emission: colliding-wind binaries, high-mass X-ray binaries and gamma-ray binaries. This thesis is focused on the radio emission of high-mass binary systems through interferometric observations, and we have explored several of these sources with low- and high-frequency radio observations, and very high-resolution VLBI ones. We have studied two gamma-ray binaries, LS 5039 and LS I +61 303, at low frequencies. W…
The interaction between the strong winds in stellar colliding-wind binary (CWB) systems produces two shock fronts, delimiting the wind collision region (WCR). There, particles are expected to be accelerated mainly via diffusive shock acceleration (DSA). We investigate the injection and the acceleration of protons in typical CWB systems by means of Monte Carlo simulations, with both a test-particle approach and a non-linear method modelling a shock locally modified by the backreaction of the accelerated protons. We use magnetohydrodynamic simulations to determine the background plasma in the WC…
We perform smoothed-particle hydrodynamical simulations of the explosion of a helium star in a close binary system, and study the effects of the explosion on the companion star as well as the effect of the presence of the companion on the supernova remnant. By simulating the mechanism of the supernova from just after core bounce until the remnant shell passes the stellar companion, we are able to separate the various effects leading to the final system parameters. In the final system, we measure the mass stripping and ablation from, and the velocity kick imparted to, the companion star, as wel…
Context. The companions of the exploding carbon-oxygen white dwarfs (CO WDs) for producing type Ia supernovae (SNe Ia) are still not conclusively confirmed. A red-giant (RG) star has been suggested to be the mass donor of the exploding WD, named as the symbiotic channel. However, previous studies on the this channel gave a relatively low rate of SNe Ia. Aims. We aim to systematically investigate the parameter space, Galactic rates and delay time distributions of SNe Ia from the symbiotic channel by employing a revised mass-transfer prescription. Methods. We adopted an integrated mass-transfer …
The "Scenario Machine" (a computer code designed for studies of the evolution of close binaries) was used to carry out a population synthesis for a wide range of merging astrophysical objects: main-sequence stars with main-sequence stars; white dwarfs with white dwarfs, neutron stars, and black holes; neutron stars with neutron stars and black holes; and black holes with black holes.We calculate the rates of such events, and plot the mass distributions for merging white dwarfs and main-sequence stars. It is shown that Type Ia supernovae can be used as standard candles only after approximately …
LS I +61 303 and LS 5039 are exceptionally rare examples of HMXBs with MeV-TeV emission, making them two of only five known or proposed "gamma-ray binaries". There has been disagreement within the literature over whether these systems are microquasars, with stellar winds accreting onto a compact object to produce high energy emission and relativistic jets, or whether their emission properties might be better explained by a relativistic pulsar wind colliding with the stellar wind. Here we present an attempt to detect radio pulsars in both systems with the Green Bank Telescope. The upper limits …
Pair-instability and pulsational pair-instability supernovae (PPISN) have not been unambiguously observed so far. They are, however, promising candidates for the progenitors of the heaviest binary black hole (BBH) mergers detected. If these BBHs are the product of binary evolution, then PPISNe could occur in very close binaries. Motivated by this, we discuss the implications of a PPISN happening with a close binary companion, and what impact these events have on the formation of merging BBHs through binary evolution. For this, we have computed a set of models of metal-poor ($Z_\odot/10$) singl…
The most commonly accepted progenitor system for Type Iax supernovae (SNe Iax) is the partial deflagration of a near-Chandrasekhar-mass white dwarf (WD) accreting from a non-degenerate helium donor star, leaving a bound remnant following the explosion. In this paper, we investigate whether the WD remant can undergo multiple SNe during the system's lifetime. We use Modules for Experiments in Astrophysics (MESA) to evolve various single-degenerate binaries to determine which could plausibly undergo multiple SNe Iax due to multiple helium accretion phases. We also investigate the possibility for …
We explore the ability of high energy observations to constrain orbital parameters of long period massive binary systems by means of an inverse Compton model acting in colliding wind environments. This is particular relevant for (very) long period binaries where orbital parameters are often poorly known from conventional methods, as is the case e.g. for the Wolf-Rayet (WR) star binary system WR 147 where INTEGRAL and MAGIC upper limits on the high-energy emission have recently been presented. We conduct a parameter study of the set of free quantities describing the yet vaguely constrained geom…
The $η$ Carinae binary system is the first $γ$-ray binary ever observed which does not contain a compact object. The dense wind of the primary star shocks against the fast light wind coming from the companion star, creating the conditions to accelerate particles up to relativistic energies via Fermi mechanisms. These relativistic particles subsequently dissipates non-thermal radiation. Fermi-LAT and H.E.S.S. detection of $η$ Carinae confirm such hypotheses. Hydrodynamic simulations provide a convincing match to the observations if a few percent of the wind mechanical energy dissipated in the s…
Several tens of massive binary systems display indirect, or even strong evidence for non-thermal radio emission, hence their particle accelerator status. These objects are referred to as particle-accelerating colliding-wind binaries (PACWBs). WR 133 is one of the shortest period Wolf-Rayet + O systems in this category, and is therefore critical to characterize the boundaries of the parameter space adequate for particle acceleration in massive binaries. Our methodology consists in analyzing JVLA observations of WR 133 at different epochs to search for compelling evidence for a phase-locked vari…
[Abridged]We investigate the long-term secular dynamics and Lidov-Kozai(LK) eccentricity oscillations of quadruple systems composed of two binaries at quadrupole and octupole order in the perturbing Hamiltonian. We show that the fraction of systems reaching high eccentricities is enhanced relative to triple systems, over a broader range of parameter space. We show that this fraction grows with time, unlike triple systems evolved at quadrupole order. This is fundamentally because with their additional degrees of freedom, quadruple systems do not have a maximal set of commuting constants of the …
The double-detonation explosion scenario of Type Ia supernovae has gained increased support from the SN Ia community as a viable progenitor model, making it a promising candidate alongside the well-known single degenerate and double degenerate scenarios. We present delay times of double-detonation SNe, in which a sub-Chandrasekhar mass carbon-oxygen white dwarf accretes non-dynamically from a helium-rich companion. One of the main uncertainties in quantifying SN rates from double-detonations is the (assumed) retention efficiency of He-rich matter. Therefore, we implement a new prescription for…
Massive stars in binary systems have long been regarded as potential sources of high-energy gamma rays.The emission is principally thought to arise in the region where the stellar winds collide and accelerate relativistic particles which ubsequently emit gamma rays. On the basis of a three-dimensional distribution function of high-energy particles in the wind collision region - as obtained by a numerical hydrodynamics and particle transport model - we present the computation of the three-dimensional nonthermal photon emission for a given line of sight. Anisotropic inverse Compton emission is m…
Some binary systems composed of a white dwarf (WD) and a hot subdwarf (sdB) helium star will make contact within the helium burning lifetime of the sdB star. The accreted helium on the WD inevitably undergoes a thermonuclear instability, causing a detonation that is expected to transition into the WD core and lead to a thermonuclear supernova while the donor orbits nearby with high velocity. Motivated by the recent discovery of fast-moving objects that occupy unusual locations on the HR diagram, we explore the impact of the thermonuclear supernovae on the donors in this specific double detonat…
Neutron stars receive velocity kicks at birth in supernovae. Those formed in electron-capture supernovae from super asymptotic giant branch stars -- the lowest mass stars to end their lives in supernovae -- may receive significantly lower kicks than typical neutron stars. Given that many massive stars are members of wide binaries, this suggests the existence of a population of low-mass ($1.25 < M_\mathrm{psr} / $M$_\odot < 1.3$), wide ($P_\mathrm{orb} \gtrsim 10^{4}$\,day), eccentric ($e \sim 0.7$), unrecycled ($P_\mathrm{spin} \sim 1$\,s) binary pulsars. The formation rate of such binaries is…
