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To be observed and analyzed by the network of current gravitational-wave detectors (LIGO, Virgo, KAGRA), and in anticipation of future third generation ground-based (Einstein Telescope, Cosmic Explorer) and space-borne (LISA) detectors, inspiralling compact binaries—binary star systems composed of neutron stars and/or black holes in their late stage of evolution prior the final coalescence—require high-accuracy predictions from general relativity. The orbital dynamics and emitted gravitational waves of these very relativistic systems can be accurately modelled using state-of-the-art post-Newtonian theory. In this article we review the multipolar-post-Minkowskian approximation scheme, merged to the standard post-Newtonian expansion into a single formalism valid for general isolated matter system. This cocktail of approximation methods (called MPM-PN) has been successfully applied to compact binary systems, producing equations of motion up to the fourth-post-Newtonian (4PN) level, and gravitational waveform and flux to 4.5PN order beyond the Einstein quadrupole formula. We describe the dimensional regularization at work in such high post-Newtonian calculations, for curing both ultra-violet and infra-red divergences. Several landmark results are detailed: the definition of multipole moments, the gravitational radiation reaction, the conservative dynamics of circular orbits, the first law of compact binary mechanics, and the non-linear effects in the gravitational-wave propagation (tails, iterated tails and non-linear memory). We also discuss the case of compact binaries moving on eccentric orbits, and the effects of spins (both spin-orbit and spin–spin) on the equations of motion and gravitational-wave energy flux and waveform.

We review the phenomenology of classical Cepheids (CCs), Anomalous Cepheids (ACs) and type II Cepheids (TIICs) in the Milky Way (MW) and in the Magellanic Clouds (MCs). We also examine the Hertzsprung progression in different stellar systems by using the shape of I-band light curves (Fourier parameters) and observables based on the difference in magnitude and in phase between the bump and the minimum in luminosity. The distribution of Cepheids in optical and in optical–near infrared (NIR) color–magnitude diagrams is investigated to constrain the topology of the instability strip. The use of Cepheids as tracers of young (CCs), intermediate (ACs) and old (TIICs) stellar populations are brought forward by the comparison between observations (MCs) and cluster isochrones covering a broad range in stellar ages and in chemical compositions. The different diagnostics adopted to estimate individual distances (period–luminosity, period–Wesenheit, period–luminosity–color relations) are reviewed together with pros and cons in the use of fundamental and overtones, optical and NIR photometric bands, and reddening free pseudo magnitudes (Wesenheit). We also discuss the use of CCs as stellar tracers and the radial gradients among the different groups of elements (iron, α, neutron-capture) together with their age-dependence. Finally, we briefly outline the role that near-future space and ground-based facilities will play in the astrophysical and cosmological use of Cepheids.

Tidal synchronization plays a fundamental role in the evolution of binary star systems. However, key details such as the timescale of synchronization, efficiency of tidal dissipation, rotation period, and dependence on stellar mass are not well constrained. We present a catalog of rotation periods, orbital periods, and eccentricities from eclipsing binaries (EBs) that can be used to study the role of tides in the rotational evolution of low-mass dwarf (FGKM spectral type) binaries. This study presents the largest catalog of EB orbital and rotational periods (Porb and Prot) measured from the Transiting Exoplanet Satellite Survey (TESS). We first classify 4584 light curves from the TESS EB catalog according to out-of-eclipse stellar variability type: starspot modulation, ellipsoidal variability, nonperiodic variability, and “other” variability (e.g., pulsations). We then manually validate each light curve’s classification, resulting in a sample of 1039 candidates with 584 high-confidence EBs that exhibit detectable starspot modulation. From there, we measure and compare the rotation period of each starspot-modulated EB using three methods: a Lomb–Scargle periodogram, autocorrelation function, and phase dispersion minimization. We find that our period distributions are consistent with previous work that used a sample of 816 starspot EBs from Kepler to identify two populations: a synchronous population (with Porb ≈ Prot), and a subsynchronous population (with 8Porb ≈ 7Prot). Using Bayesian model comparison, we find that a bimodal distribution is a significantly better fit than a unimodal distribution for the Kepler and TESS samples, both individually or combined, confirming that the subsynchronous population is statistically significant.

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Mergings of compact-star binaries are expected to be the most important sources for forthcoming gravitational-wave (GW) astronomy. In the first part of the review, we discuss observational manifestations of close binaries with NS and/or BH components and their merger rate, crucial points in the formation and evolution of compact stars in binary systems, including the treatment of the natal kicks, which NSs and BHs acquire during the core collapse of massive stars and the common envelope phase of binary evolution, which are most relevant to the merging rates of NS-NS, NS-BH and BH-BH binaries. The second part of the review is devoted mainly to the formation and evolution of binary WDs and their observational manifestations, including their role as progenitors of cosmologically-important thermonuclear SN Ia. We also consider AM CVn-stars, which are thought to be the best verification binary GW sources for future low-frequency GW space interferometers.

Stellar mergers are a brief but common phase in the evolution of binary star systems 1 , 2 . These events have many astrophysical implications; for example, they may lead to the creation of atypical stars (such as magnetic stars 3 , blue stragglers 4 and rapid rotators 5 ), they play an important part in our interpretation of stellar populations 6 and they represent formation channels of compact-object mergers 7 . Although a handful of stellar mergers have been observed directly 8 , 9 , the central remnants of these events were shrouded by an opaque shell of dust and molecules 10 , making it impossible to observe their final state (for example, as a single merged star or a tighter, surviving binary 11 ). Here we report observations of an unusual, ring-shaped ultraviolet (‘blue’) nebula and the star at its centre, TYC 2597-735-1. The nebula has two opposing fronts, suggesting a bipolar outflow of material from TYC 2597-735-1. The spectrum of TYC 2597-735-1 and its proximity to the Galactic plane suggest that it is an old star, yet it has abnormally low surface gravity and a detectable long-term luminosity decay, which is uncharacteristic for its evolutionary stage. TYC 2597-735-1 also exhibits Hα emission, radial-velocity variations, enhanced ultraviolet radiation and excess infrared emission—signatures of dusty circumstellar disks 12 , stellar activity 13 and accretion 14 . Combined with stellar evolution models, the observations suggest that TYC 2597-735-1 merged with a lower-mass companion several thousand years ago. TYC 2597-735-1 provides a look at an unobstructed stellar merger at an evolutionary stage between its dynamic onset and the theorized final equilibrium state, enabling the direct study of the merging process. Observations and stellar evolution models of a blue ring nebula and its central star (TYC 2597-735-1) suggest that the remnant star merged with a lower-mass companion several thousand years ago.

We study the formation of Population III stars by performing radiation hydrodynamic simulations for three different initial clouds extracted from cosmological hydrodynamic simulations. Starting from the cloud collapse stage, we follow the growth of protostars by accretion for ∼105 yr until the radiative feedback from the protostars suppresses the accretion and the stellar properties are nearly fixed. We find that Population III stars form in massive and wide binary/small-multiple stellar systems, with masses >30 M ⊙ and separations >2000 au. We also find that the properties of the final stellar system correlate with those of the initial clouds: the total mass increases with the cloud-scale accretion rate, and the angular momentum of the binary orbit matches that of the initial cloud. While the total mass of the system in our simulations is consistent with our previous single-star formation simulations, individual masses are lower due to mass sharing, suggesting potential modification in the extent of feedback from Population III stars in the subsequent evolution of the Universe. We also identify such systems as mini-binaries embedded in a wider outer multiple-star system, which could evolve into progenitors for observed gravitational wave events.

The fate of planets around rapidly evolving stars is not well understood. Previous studies have suggested that, relative to the main-sequence population, planets transiting evolved stars (P < 100 days) tend to have more eccentric orbits. Here we present the discovery of TOI-4582 b, a 0.94−0.12+0.09 R J , 0.53 ± 0.05 M J planet orbiting an intermediate-mass subgiant star every 31.034 days. We find that this planet is also on a significantly eccentric orbit (e = 0.51 ± 0.05). We then compare the population of planets found transiting evolved (log g < 3.8) stars to the population of planets transiting main-sequence stars. We find that the rate at which median orbital eccentricity grows with period is significantly higher for evolved star systems than for otherwise similar main-sequence systems. In general, we observe that mean planet eccentricity 〈e〉 = a+blog10(P) for the evolved population with significant orbital eccentricity where a = −0.18 ± 0.08 and b = 0.38 ± 0.06, significantly distinct from the main-sequence planetary system population. This trend is seen even after controlling for stellar mass and metallicity. These systems do not appear to represent a steady evolution pathway from eccentric, long-period planetary orbits to circular, short-period orbits, as orbital model comparisons suggest that inspiral timescales are uncorrelated with orbital separation or eccentricity. Characterization of additional evolved planetary systems will distinguish effects of stellar evolution from those of stellar mass and composition.

In close binary star systems, common envelope evolution (CEE) may occur after a previous phase of mass transfer. Some isolated formation channels for double neutron star binaries suggest that the donor of CEE was the accretor of a previous phase of stable mass transfer. Accretion should substantially alter the structure of the donor, particularly by steepening the density gradient at the core-envelope interface and rejuvenating the star. We study the CEE of a donor that was the accretor of a previous phase of stable mass transfer and has a rejuvenated structure. We perform 3D hydrodynamics simulations of the CEE of an 18 M⊙ supergiant with a 1.4 M⊙ companion using rejuvenated and non-rejuvenated 1D stellar models for the donor. We compare the two simulations to characterize the effect of the rejuvenation on the outcome of the common envelope phase and the shape of the ejecta. We find that accounting for a previous phase of mass transfer reduces the duration of the inspiral phase by a factor of two, likely due to the different structures in the outer layers of the donor. In the rejuvenated case, the simulations show more equatorially concentrated and asymmetric ejecta, though both cases display evidence for the formation of a pressure-supported thick circumbinary disk. During the dynamical inspiral phase, the impact of rejuvenation on the unbinding of the envelope is unclear; we find that rejuvenation decreases the amount of unbound mass by 20%–40% depending on the energy criterion used.

Galactic globular clusters are old, dense star systems typically containing 104–106 stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution that leads to relativistic binaries, and current and possible future observational evidence for this population. Our discussion of globular cluster evolution will focus on the processes that boost the production of tight binary systems and the subsequent interaction of these binaries that can alter the properties of both bodies and can lead to exotic objects. Direct N-body integrations and Fokker-Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.

In this work, we investigate an alternative channel for the formation of fast-spinning black hole–neutron star (BHNS) binaries, in which super-Eddington accretion is expected to occur in accreting BHs during the stable mass transfer phase within BH-stripped helium (BH–He-rich) star binary systems. We evolve intensive MESA grids of close-orbit BH–He-rich star systems to systematically explore the projected aligned spins of BHs in BHNS binaries, as well as the impact of different accretion limits on the tidal disruption probability and electromagnetic (EM) signature of BHNS mergers. Most of the BHs in BHNS mergers cannot be effectively spun up through accretion if the accretion rate is limited to ≲10ṀEdd , where ṀEdd is the standard Eddington accretion limit. In order to reach high spins (e.g., χ BH ≳ 0.5), the BHs are required to be born less massive (e.g., ≲3.0 M ⊙) in binary systems with initial periods of ≲0.2–0.3 days and accrete material at ∼100ṀEdd . However, even under this high accretion limit, ≳6 M ⊙ BHs are typically challenging to significantly spin up and generate detectable associated EM signals. Our population simulations suggest that different accretion limits have a slight impact on the ratio of tidal disruption events. However, as the accretion limit increases, the EM counterparts from the cosmological BHNS population can become bright overall.