Binary Star Model Research Articles

Improved Period Variations of 32 Contact Binaries with Rapidly Decreasing Periods in the Galactic Bulge

We present detailed analyses of updated eclipse timing diagrams for 32 contact binary merger candidates in the Galactic bulge. The photometric data was obtained from 2016 to 2021 using the Korea Microlensing Telescope Network with the 1.6 m telescopes located at three southern sites (CTIO, SAAO, and SSO). The times of minimum lights were determined by applying the binary-star model to full light curves created at half-year intervals from the observations. The orbital period variations of the binary systems were analyzed using the O − C diagrams from our new timings with the others published in the literature, which are based on the OGLE observations from 2001 to 2015. As results, the orbital periods and period-decreasing rates of 32 binary systems were located to be in the ranges of 0.370 to 1.238 days and from −3.0 to −13.1 × 10−6 day yr−1, respectively. Out of these stars, 24 systems show a combination effect of a parabola and a light travel time caused by a third body, and their outer orbital periods are in the range of 9.1–26.5 yr. We propose that all of our merger candidates need additional monitoring observations to study a luminous-red nova progenitor.

A multimessenger model for neutron star–black hole mergers

ABSTRACT We present a semi-analytic model for predicting kilonova light curves from the mergers of neutron stars with black holes (NSBH). The model is integrated into the mosfit platform, and can generate light curves from input binary properties and nuclear equation-of-state considerations, or incorporate measurements from gravitational wave (GW) detectors to perform multimessenger parameter estimation. The rapid framework enables the generation of NSBH kilonova distributions from binary populations, light curve predictions from GW data, and statistically meaningful comparisons with an equivalent binary neutron star (BNS) model in mosfit. We investigate a sample of kilonova candidates associated with cosmological short gamma-ray bursts, and demonstrate that they are broadly consistent with being driven by NSBH systems, though most have limited data. We also perform fits to the very well sampled GW170817, and show that the inability of an NSBH merger to produce lanthanide-poor ejecta results in a significant underestimate of the early (≲2 d) optical emission. Our model indicates that NSBH-driven kilonovae may peak up to a week after merger at optical wavelengths for some observer angles. This demonstrates the need for early coverage of emergent kilonovae in cases where the GW signal is either ambiguous or absent; they likely cannot be distinguished from BNS mergers by the light curves alone from ∼2 d after the merger. We also discuss the detectability of our model kilonovae with the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST).

MoBiDICT: New 3D static models of close synchronised binaries in hydrostatic equilibrium

Context. In close binary systems, tidal interactions and rotational effects can strongly influence stellar evolution as a result of mass transfer and common envelope phases. These aspects can only be treated following improvements of theoretical models to take into account the breaking of spherical symmetry occurring in close binaries. Current models of binary stars rely on either the so-called Roche model or the perturbative approach, both of which result in several assumptions concerning the gravitational, tidal, and centrifugal potentials. Aims. Our aim is to develop a precise 3D model of stellar deformations and to study the robustness of the Roche and perturbative models in different deformation regimes. Methods. We developed a new non-perturbative method to compute the precise structural deformation of a binary system in three dimensions that is valid even in the most distorted cases. We then compared our new method to the Roche and perturbative models for different orbital separations and binary components. Results. We found that in the most distorted cases, both the Roche and perturbative models significantly underestimate the deformation of binaries. The effective gravity and the overall structural deformations are also noticeably different in the most distorted cases, leading to modifications of the usual gravity darkening generally obtained through the Roche model when interpreting the observations. Moreover, we found that the dipolar term of the gravitational potential, usually neglected by the perturbative theory, has the same order of magnitude as the leading tidal term in the most distorted cases. Conclusions. We developed a new method that is capable of precisely computing the deformations of a binary system composed of any type of stars, even compact objects. For all the stars we studied, the differences in deformation with respect to the Roche or perturbative models are significant in the most distorted cases, which impacts both the interpretation of observations and the theoretical structural depiction of these distorted bodies. In the weaker deformation regimes, the Roche model is a viable option for studying the surface properties of binaries, while the perturbative model is strongly favoured when evaluating structural deformations.

POSYDON: A General-purpose Population Synthesis Code with Detailed Binary-evolution Simulations

Most massive stars are members of a binary or a higher-order stellar system, where the presence of a binary companion can decisively alter their evolution via binary interactions. Interacting binaries are also important astrophysical laboratories for the study of compact objects. Binary population synthesis studies have been used extensively over the last two decades to interpret observations of compact-object binaries and to decipher the physical processes that lead to their formation. Here, we present POSYDON, a novel, publicly available, binary population synthesis code that incorporates full stellar structure and binary-evolution modeling, using the MESA code, throughout the whole evolution of the binaries. The use of POSYDON enables the self-consistent treatment of physical processes in stellar and binary evolution, including: realistic mass-transfer calculations and assessment of stability, internal angular-momentum transport and tides, stellar core sizes, mass-transfer rates, and orbital periods. This paper describes the detailed methodology and implementation of POSYDON, including the assumed physics of stellar and binary evolution, the extensive grids of detailed single- and binary-star models, the postprocessing, classification, and interpolation methods we developed for use with the grids, and the treatment of evolutionary phases that are not based on precalculated grids. The first version of POSYDON targets binaries with massive primary stars (potential progenitors of neutron stars or black holes) at solar metallicity.

ATOMIUM: ALMA tracing the origins of molecules in dust forming oxygen rich M-type stars

This overview paper presentsATOMIUM, a Large Programme in Cycle 6 with the Atacama Large Millimeter/submillimeter Array (ALMA). The goal ofATOMIUMis to understand the dynamics and the gas phase and dust formation chemistry in the winds of evolved asymptotic giant branch (AGB) and red supergiant (RSG) stars. A more general aim is to identify chemical processes applicable to other astrophysical environments. Seventeen oxygen-rich AGB and RSG stars spanning a range in (circum)stellar parameters and evolutionary phases were observed in a homogeneous observing strategy allowing for an unambiguous comparison. Data were obtained between 213.83 and 269.71 GHz at high (∼0″​​.025–0″​​.050), medium (∼0″​​.13–0″​​.24), and low (∼1″) angular resolution. The sensitivity per ∼1.3 km s−1channel was 1.5–5 mJy beam−1, and the line-free channels were used to image the millimetre wave continuum. Our primary molecules for studying the gas dynamics and dust formation are CO, SiO, AlO, AlOH, TiO, TiO2, and HCN; secondary molecules include SO, SO2, SiS, CS, H2O, and NaCl. The scientific motivation, survey design, sample properties, data reduction, and an overview of the data products are described. In addition, we highlight one scientific result – the wind kinematics of theATOMIUMsources. Our analysis suggests that theATOMIUMsources often have a slow wind acceleration, and a fraction of the gas reaches a velocity which can be up to a factor of two times larger than previously reported terminal velocities assuming isotropic expansion. Moreover, the wind kinematic profiles establish that the radial velocity described by the momentum equation for a spherical wind structure cannot capture the complexity of the velocity field. In fifteen sources, some molecular transitions other than12COv = 0J = 2 − 1 reach a higher outflow velocity, with a spatial emission zone that is often greater than 30 stellar radii, but much less than the extent of CO. We propose that a binary interaction with a (sub)stellar companion may (partly) explain the non-monotonic behaviour of the projected velocity field. TheATOMIUMdata hence provide a crucial benchmark for the wind dynamics of evolved stars in single and binary star models.

Detectability of Black Hole Binaries with Gaia: Dependence on Binary Evolution Models

Abstract The astrometric satellite Gaia is expected to observe noninteracting black hole (BH) binaries with luminous companions (LCs; hereafter BH-LC binaries), a different population from BH X-ray binaries previously discovered. The detectability of BH-LC binaries with Gaia might be dependent on binary evolution models. We investigated the Gaia's detectability of BH-LC binaries formed through isolated binary evolution by means of the binary population synthesis technique and examined its dependence on single and binary star models: supernova models, common envelope (CE) ejection efficiency α, and BH natal kick models. We estimated that 1.1–46 BH-LC binaries can be detected within the five-year observation, and found that α has the largest impact on the detectable number. In each model, observable and intrinsic BH-LC binaries have similar distributions. Therefore, we found three important implications: (1) if the lower BH mass gap is not intrinsic (i.e., 3–5 M ⊙ BHs exist), Gaia will observe ≤5 M ⊙ BHs; (2) we may observe short orbital period binaries with light LCs if CE efficiency is significantly high; and (3) we may be able to identify the existence of natal kick from eccentricity distribution.

Cloud Computing Bayesian Approach to Study Effects of Binary Stars on Ages of Star Clusters

We apply bayesian algorithms to studying the effects of binary stellar population models on the age determination of 46 new star clusters in Gaia DR2. The ages of star clusters are obtained via color-magnitude diagram (CMDs). The data are selected from two works. Our analysis focus on exploring the potential of bayesian algorithm to estimate the effects of binary stars on the parameter determination of star clusters. Our work is based on simple stellar population models of binary stars and single stars. As a result, the bayesian analysis shows that binary stars have significant effects on the determination of ages of star clusters. The models with binary stars report older ages for most star clusters. The age difference between binary-star models and single-star models follows a Gaussian distribution with mean of 1.2 Gyr.

Hubble spectroscopy of LB-1: Comparison with B+black-hole and Be+stripped-star models

Context. LB-1 (alias ALS 8775) has been proposed as either an X-ray dim B-type star plus black hole (B+BH) binary or a Be star plus an inflated stripped star (Be+Bstr) binary. The latter hypothesis contingent upon the detection and characterization of the hidden broad-lined star in a composite optical spectrum. Aims. Our study is aimed at testing the published B+BH (single star) and Be+Bstr (binary star) models using a flux-calibrated UV-optical-IR spectrum. Methods. The Space Telescope Imaging Spectrograph (STIS) on board the Hubble Space Telescope (HST) was used to obtain a flux-calibrated spectrum with an accuracy of ∼1%. We compared these data with non-local thermal equilibrium (non-LTE) spectral energy distributions (SED) and line profiles for the proposed models. The Hubble data, together with the Gaia EDR3 parallax and a well-determined extinction, were used to provide tight constraints on the properties and stellar luminosities of the LB-1 system. In the case of the Be+Bstr model we adopted the published flux ratio for the Be and Bstr stars, re-determined the Teff of the Bstr using the silicon ionization balance, and inferred Teff for the Be star from the fit to the SED. Results. The UV data strongly constrain the microturbulence velocity to ≲2 km s−1 for the stellar components of both models. We also find stellar parameters consistent with previous results, but with greater precision enabled by the Hubble SED. For the B+BH single-star model, we find the parameters (Teff, log(L/L⊙), Mspec/M⊙) of the B-type star to be (15 300 ± 300 K, 3.23−0.10+0.09, 5.2−1.4+1.8). For the Bstr star we obtain (12 500 ± 100 K, 2.70−0.09+0.09, 0.8−0.3+0.5), and for the Be star (18 900 ± 200 K, 3.04−0.09+0.09, 3.4−1.8+3.5). While the Be+Bstr model is a better fit to the He I lines and cores of the Balmer lines in the optical, the B+BH model provides a better fit to the Si IV resonance lines in the UV. The analysis also implies that the Bstr star has roughly twice the solar silicon abundance, which is difficult to reconcile with a stripped star origin. The Be star, on the other hand, has a rather low luminosity and a spectroscopic mass that is inconsistent with its possible dynamical mass. Conclusions. We provide tight constraints on the stellar luminosities of the Be+Bstr and B+BH models. For the former, the Bstr star appears to be silicon-rich, while the notional Be star appears to be sub-luminous for a classical Be star of its temperature and the predicted UV spectrum is inconsistent with the data. This latter issue can be significantly improved by reducing the Teff and radius of the Be star, at the cost, however, of a different mass ratio as a result. In the B+BH model, the single B-type spectrum is a good match to the UV spectrum. Adopting a mass ratio of 5.1 ± 0.1, from the literature, implies a BH mass of ∼21−8+9 M⊙.

A cool and inflated progenitor candidate for the Type Ib supernova 2019yvr at 2.6 yr before explosion

ABSTRACT We present Hubble Space Telescope imaging of a pre-explosion counterpart to SN 2019yvr obtained 2.6 yr before its explosion as a type Ib supernova (SN Ib). Aligning to a post-explosion Gemini-S/GSAOI image, we demonstrate that there is a single source consistent with being the SN 2019yvr progenitor system, the second SN Ib progenitor candidate after iPTF13bvn. We also analysed pre-explosion Spitzer/Infrared Array Camera (IRAC) imaging, but we do not detect any counterparts at the SN location. SN 2019yvr was highly reddened, and comparing its spectra and photometry to those of other, less extinguished SNe Ib we derive $E(B-V)=0.51\substack{+0.27\\ -0.16}$ mag for SN 2019yvr. Correcting photometry of the pre-explosion source for dust reddening, we determine that this source is consistent with a log (L/L⊙) = 5.3 ± 0.2 and $T_{\mathrm{eff}} = 6800\substack{+400\\ -200}$ K star. This relatively cool photospheric temperature implies a radius of 320$\substack{+30\\ -50}~\mathrm{ R}_{\odot}$, much larger than expectations for SN Ib progenitor stars with trace amounts of hydrogen but in agreement with previously identified SN IIb progenitor systems. The photometry of the system is also consistent with binary star models that undergo common envelope evolution, leading to a primary star hydrogen envelope mass that is mostly depleted but still seemingly in conflict with the SN Ib classification of SN 2019yvr. SN 2019yvr had signatures of strong circumstellar interaction in late-time (>150 d) spectra and imaging, and so we consider eruptive mass-loss and common envelope evolution scenarios that explain the SN Ib spectroscopic class, pre-explosion counterpart, and dense circumstellar material. We also hypothesize that the apparent inflation could be caused by a quasi-photosphere formed in an extended, low-density envelope, or circumstellar matter around the primary star.

Inferring the maximum and minimum mass of merging neutron stars with gravitational waves

We show that the maximum and the minimum mass of merging neutron stars can be estimated with upcoming gravitational wave observations. We simulate populations of binary neutron star signals and model their mass distribution including upper and lower cutoffs. The lower(upper) limit can be measured to $\sim 0.2(0.1)\text{M}_{\odot}$ with $50$ detections if the mass distribution supports neutron stars with masses close to the cutoffs. The upper mass limit informs about the high density properties of the neutron star equation of state, while the lower limit signals the divide between neutron stars and white dwarfs.

Close Binary Perspectives

Development of analytic binary star models is discussed in historical and on-going perspective, beginning with an overview of paradigm shifts, the merits of direct (rectification-free) models, and fundamental four-type binary system morphology. Attention is called to the likelihood that many or even most cataclysmic variables may be of the double contact morphological type. Eclipsing binary distance estimates differ from those of standard candles in being individually measurable—without reliance on (usually nearby) objects that are assumed similar. Recent progress on circumstellar accretion disk models is briefly summarized, with emphasis on the separate roles of fluid dynamic, structural, and analytic models. Time-related parameters (ephemeris, apsidal motion, and light travel time) now can be found with a unified algorithm that processes light curves, velocity curves, and pre-existing eclipse timings together, without need to compute any new timings. Changes in data publication practices are recommended and logical errors and inconsistencies in terminology are noted. Parameter estimation strategies are discussed.

TESS photometry of the eclipsing δ Scuti star AI Hydrae

Abstract AI Hya has been known as an eclipsing binary with a monoperiodic $\delta$ Sct pulsator. We present the results from its TESS (Transiting Exoplanet Survey Satellite) photometry observed during Sector 7. Including our five minimum epochs, the eclipse timing diagram displays the apsidal motion with a rate of $\dot{\omega } = 0.075 \pm 0.031\:$deg$\:$yr$^{-1}$, which corresponds to an apsidal period of $U = 4800\pm 2000\:$yr. The binary star model represents that the smaller, less massive primary component is $427\:$K hotter than the pulsating secondary, and our distance of $612\pm 36\:$pc is in good agreement with the Gaia distance of $644\pm 26\:$pc. We subtracted the binary effects from the observed TESS data and applied a multifrequency analysis to these residuals. The result reveals that AI Hya is multiperiodic in its pulsation. Of 14 signals detected, four ($f_1$, $f_2$, $f_3$, $f_6$) may be considered independent pulsation frequencies. The period ratios of $P_{\rm pul}/P_{\rm orb} = 0.012$–0.021 and the pulsation constants of $Q = 0.30$–0.52 d correspond to $\delta$ Sct pulsations in binaries. We found that the secondary component of AI Hya pulsates in both radial fundamental $F$ modes ($f_2$ and $f_3$) and non-radial $g_1$ modes with a low degree of $\ell = 2$ ($f_1$ and $f_6$).

Progenitors of Type IIb Supernovae. I. Evolutionary Pathways and Rates

Abstract Type IIb supernovae (SNe) are important candidates to understand mechanisms that drive the stripping of stripped-envelope (SE) supernova (SN) progenitors. While binary interactions and their high incidence are generally cited to favor them as SN IIb progenitors, this idea has not been tested using models covering a broad parameter space. In this paper, we use non-rotating single- and binary-star models at solar and low metallicities spanning a wide parameter space in primary mass, mass ratio, orbital period, and mass transfer efficiencies. We find that our single- and binary-star models contribute to roughly equal, however small, numbers of SNe IIb at solar metallicity. Binaries only dominate as progenitors at low metallicity. We also find that our models can account for less than half of the observationally inferred rate for SNe IIb at solar metallicity, with computed rates ≲4% of core-collapse (CC) SNe. On the other hand, our models can account for the rates currently indicated by observations at low metallicity, with computed rates as high as 15% of CC SNe. However, this requires low mass transfer efficiencies (≲0.1) to prevent most progenitors from entering contact. We suggest that the stellar wind mass-loss rates at solar metallicity used in our models are too high. Lower mass-loss rates would widen the parameter space for binary SNe IIb at solar metallicity by allowing stars that initiate mass transfer earlier in their evolution to reach CC without getting fully stripped.

Parameter Estimation STAR (1;1) Model Using Binary Weight

Space Time Auto Regressive(1;1) Model or STAR(1;1) model is a form of model that involves location and time. The STAR(1;1) model is a stationary space time model in mean and variance. The STAR model can be used to forecast future observations at these locations by involving the effects of observations at other nearby locations in spatial lag 1 and lag time 1 [2]. The STAR model can be written as a linear model assuming that error is normally distributed with zero mean and constant variance. In this research, the parameter estimation procedure for STAR model using binary weight, MKT method and STAR model for the estimation of petroleum production in 3 wells is assumed to be in a homogeneous reservoir.

Improving the NRTidal model for binary neutron star systems

Accurate and fast gravitational waveform (GW) models are essential to extract information about the properties of compact binary systems that generate GWs. Building on previous work, we present an extension of the NRTidal model for binary neutron star (BNS) waveforms. The upgrades are: (i) a new closed-form expression for the tidal contribution to the GW phase which includes further analytical knowledge and is calibrated to more accurate numerical relativity data than previously available; (ii) a tidal correction to the GW amplitude; (iii) an extension of the spin-sector incorporating equation-of-state-dependent finite size effects at quadrupolar and octupolar order; these appear in the spin-spin tail terms and cubic-in-spin terms, both at 3.5PN. We add the new description to the precessing binary black hole waveform model IMRPhenomPv2 to obtain a frequency-domain precessing binary neutron star model. In addition, we extend the SEOBNRv4_ROM and IMRPhenomD aligned-spin binary black hole waveform models with the improved tidal phase corrections. Focusing on the new IMRPhenomPv2_NRTidalv2 approximant, we test the model by comparing with numerical relativity waveforms as well as hybrid waveforms combining tidal effective-one-body and numerical relativity data. We also check consistency against a tidal effective-one-body model across large regions of the BNS parameter space.

A progenitor candidate for the type II-P supernova SN 2018aoq in NGC 4151

We present our findings based on pre- and post-explosion data of the type II-Plateau SN 2018aoq that exploded in NGC 4151. As distance estimates to NGC 4151 vary by an order of magnitude, we utilised the well-known correlation between ejecta velocity and plateau brightness, i.e. the standard candle method, to obtain a distance of 18.2 ± 1.2 Mpc, which is in very good agreement with measurements based on geometric methods. The above distance implies a mid-plateau absolute magnitude of MV50 = − 15.76 ± 0.14 suggesting that it is of intermediate brightness when compared to IIP SNe such as SN 2005cs at the faint end, and more typical events such as SN 1999em. This is further supported by relatively low expansion velocities (Fe IIλ5169 ∼ 3000 km s−1 at +42 d). Using archival HST/WFC3 imaging data, we find a point source coincident with the supernova position in the F350LP, F555W, F814W, and F160W filters. This source shows no significant variability over the ∼2 month time span of the data. From fits to the spectral energy distribution of the candidate progenitor, we find log(L/L⊙) ∼ 4.7 and Teff ∼ 3.5 kK, implying an M-type red supergiant progenitor. From comparisons to single and binary star models, we find that both favour the explosion of a star with a zero-age main sequence mass of ∼10 M⊙.

Dust Attenuation, Star Formation, and Metallicity in z ∼ 2–3 Galaxies from KBSS-MOSFIRE

Abstract We present a detailed analysis of 317 2.0 ≤ z ≤ 2.7 star-forming galaxies from the Keck Baryonic Structure Survey. Using complementary spectroscopic observations with Keck/LRIS and Keck/MOSFIRE, as well as spectral energy distribution (SED) fits to broadband photometry, we examine the joint rest-UV and rest-optical properties of the same galaxies, including stellar and nebular dust attenuation, metallicity, and star formation rate (SFR). The inferred parameters of the stellar population (reddening, age, SFR, and stellar mass) are strongly dependent on the details of the assumed stellar population model and the shape of the attenuation curve. Nebular reddening is generally larger than continuum reddening, but with large scatter. Compared to local galaxies, high-redshift galaxies have lower gas-phase metallicities (and/or higher nebular excitation) at fixed nebular reddening, and higher nebular reddening at fixed stellar mass, consistent with gas fractions that increase with redshift. We find that continuum reddening is correlated with 12 + log(O/H)O3N2 at 3.0σ significance, whereas nebular reddening is correlated with only 1.1σ significance. This may reflect the dependence of both continuum reddening and O3N2 on the shape of the ionizing radiation field produced by the massive stars. Finally, we show that Hα-based and SED-based estimates of SFR exhibit significant scatter relative to one another, and on average agree only for particular combinations of spectral synthesis models and attenuation curves. We find that the SMC extinction curve predicts consistent SFRs if we assume the subsolar (0.14 Z ⊙) binary star models that are favored for high-redshift galaxies.

Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions

We consider a class of systems where $N$ identical particles with positions ${\bf q}_1,...,{\bf q}_N$ and momenta ${\bf p}_1,...,{\bf p}_N$ are enclosed in a box of size $L$, and exhibit the scaling $\mathcal{U}(L{\bf r}_1,...,L{\bf r}_N)=\alpha(L)\, \mathcal{U}({\bf r}_1,...,{\bf r}_N)$ for the associated potential energy function $\mathcal{U}({\bf q}_1,...,{\bf q}_N)$. For these systems, we propose an efficient implementation of the Wang-Landau algorithm for evaluating thermodynamic observables involving energy and volume fluctuations in the microcanonical description, and temperature and volume fluctuations in the canonical description. This requires performing the Wang-Landau simulation in a scaled box of unit size and evaluating the density of states corresponding to the potential energy part only. To demonstrate the efficacy of our approach, as example systems, we consider Padmanabhan's binary star model and an ideal gas trapped in a harmonic potential within the box.

Core-collapse supernovae ages and metallicities from emission-line diagnostics of nearby stellar populations

Massive stars are the main objects that illuminate H II regions and they evolve quickly to end their lives in core-collapse supernovae (CCSNe). Thus it is important to investigate the association between CCSNe and H II regions. In this paper, we present emission line diagnostics of the stellar populations around nearby CCSNe, that include their host H II regions, from the PMAS/PPAK Integral-field Supernova hosts COmpilation (PISCO). We then use BPASS stellar population models to determine the age, metallicity and gas parameters for H II regions associated with CCSNe, contrasting models that consider either single star evolution alone or incorporate interacting binaries. We find binary-star models, that allow for ionizing photon loss, provide a more realistic fit to the observed CCSN hosts with metallicities that are closer to those derived from the oxygen abundance in O3N2. We also find that type II and type Ibc SNe arise from progenitor stars of similar age, mostly from 7 to 45 Myr, which corresponds to stars with masses < 20 solar mass . However these two types SNe have little preference in their host environment metallicity measured by oxygen abundance or in progenitor initial mass. We note however that at lower metallicities supernovae are more likely to be of type II.

Discovery and characterisation of long-period eclipsing binary stars from Kepler K2 campaigns 1, 2, and 3

Context. The Kepler K2 mission now makes it possible to find and study a wider variety of eclipsing binary stars than has been possible to-date, particularly long-period systems with narrow eclipses. Aims. Our aim is to characterise eclipsing binary stars observed by the Kepler K2 mission with orbital periods longer than P ≈ 5.5 days. Methods. The ellc binary star model has been used to determine the geometry of eclipsing binary systems in Kepler K2 campaigns 1, 2 and 3. The nature of the stars in each binary is estimated by comparison to stellar evolution tracks in the effective temperature – mean stellar density plane. Results. 43 eclipsing binary systems have been identified and 40 of these are characterised in some detail. The majority of these systems are found to be late-type dwarf and sub-giant stars with masses in the range 0.6–1.4 solar masses. We identify two eclipsing binaries containing red giant stars, including one bright system with total eclipses that is ideal for detailed follow-up observations. The bright B3V-type star HD 142883 is found to be an eclipsing binary in a triple star system. We observe a series of frequencies at large multiples of the orbital frequency in BW Aqr that we tentatively identify as tidally induced pulsations in this well-studied eccentric binary system. We find that the faint eclipsing binary EPIC 201160323 shows rapid apsidal motion. Rotational modulation signals are observed in 13 eclipsing systems, the majority of which are found to rotate non-synchronously with their orbits. Conclusions. The K2 mission is a rich source of data that can be used to find long period eclipsing binary stars. These data combined with follow-up observations can be used to precisely measure the masses and radii of stars for which such fundamental data are currently lacking, e.g., sub-giant stars and slowly-rotating low-mass stars.