Compact Objects Research Articles

Measuring the Lense–Thirring Orbital Precession and the Neutron Star Moment of Inertia with Pulsars

Neutron stars (NSs) are compact objects that host the densest forms of matter in the observable universe, providing unique opportunities to study the behaviour of matter at extreme densities. While precision measurements of NS masses through pulsar timing have imposed effective constraints on the equation of state (EoS) of dense matter, accurately determining the radius or moment of inertia (MoI) of an NS remains a major challenge. This article presents a detailed review on measuring the Lense–Thirring (LT) precession effect in the orbit of binary pulsars, which would give access to the MoI of NSs and offer further constraints on the EoS. We discuss the suitability of certain classes of binary pulsars for measuring the LT precession from the perspective of binary star evolution and highlight five pulsars that exhibit properties promising to realise these goals in the near future. Finally, discoveries of compact binaries with shorter orbital periods hold the potential to greatly enhance measurements of the MoI of NSs. The MoI measurements of binary pulsars are pivotal to advancing our understanding of matter at supranuclear densities, as well as improving the precision of gravity tests, such as the orbital decay due to gravitational wave emission, and of tests of alternative gravity theories.

Gravitational waves with dark matter minispikes: Fourier-domain waveforms of eccentric intermediate-mass-ratio-inspirals

Abstract An intermediate mass black hole (IMBH) may have a dark matter (DM) minihalo around it and develop a spiky structure called DM minispike. Gravitational waves (GWs) can be produced if a stellar compact object, such as a black hole (BH) or neutron star, inspirals into the IMBH. This kind of systems are known as itermediate-mass-ratio-inspirals (IMRIs) and may be observed by space-based gravitational wave detectors including LISA, Taiji and Tianqin. In this paper, we lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waves produced by eccentric IMRIs with DM minispikes in a post-circular or small-eccentricity approximation (e < 0.4). We take the effect of dynamical friction from the DM as a perturbation, and decompose the dynamical equations into perturbed part and unperturbed part. The equations are solved in a series expansion form about zero initial eccentricity to eighth order. The time-dependent, “plus” and “cross” polarizations are expanded in Bessel functions, which are then self-consistently reexpanded in a power series about zero initial eccentricity. The stationary-phase approximation is then employed to obtain the explicit DM-modified analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify this framework by considering a typical IMRI with a DM minispike and find the GW detectability strongly depends on the radial profile of the DM distribution. When the density of DM is large enough, the signal to noise ratio (SNR) will be degraded significantly and a detection loss may occur if we use a template without the effect of DM to treat a signal including the DM effect. With the Fourier-domain gravitational waveforms we also estimate the accuracy of the measurement of the DM minispike parameters in our reference model. Our framework hold the promise to construct a “ready-to-use” Fourier-domain waveforms for data analysis of eccentric IMRIs with DM minispikes.

Asteroseismology of Compact Stars

Compact stars have been perceived as natural laboratories of matter at an extremely high density. The uncertainties of the equation of state (EOS) of matter can be constrained by observing compact stars. In this review, we investigate the EOSs, global structure, and elastic properties of compact stars. We focus in detail on how to constrain the above properties of compact stars via asteroseismology. Observations that include studies of quasi-periodic oscillations from giant flares of soft gamma-ray repeaters and gravitational waves provide information about the elastic properties and internal compositions of compact stars.

A comprehensive study of massive compact star admitting conformal motion under bardeen geometry

This article primarily investigates the existence of the charged compact star under the conformal motion treatment within the context of f(Q) gravity. We have developed two models by implementing the power-law and linear form of conformal factor, enabling an in-depth comparison in our study. We have selected the MIT Bag model equation of state to describe the connection between pressure and energy density and matched the interior spherically symmetric space-time with the Bardeen space-time. In addition, the present research examines various physically valid characteristics of realistic stars, such as PSR J1614−2230, PSR J1903+327, Vela X-1, Cen X-3, and SMC X-1. We compare two constructed models by attributing the behavior of density, pressure, equilibrium conditions, and the adiabatic index. We have additionally included a brief analysis of the scenario involving Reissner-Nordstrom spacetime as an external geometry for the matching condition. In contrast to the Reissner-Nordstrom instance, the Bardeen model with the extra term in the asymptotic representations yields a more intriguing and viable result. The current analysis reveals that the resulting compact star solutions are physically acceptable and authentic when considering the presence of charge with conformal motion in f(Q) gravity.

Charged Spherical Solution in Torsion and Matter Coupling Gravity and Influence of Torsion Parameter and Electric Charge on Compact Stars in Lower Mass Gap

Abstract In this study, we explore a new exact solution for a charged spherical model as well as the astrophysical implications of the torsion parameter χ1 and electric charge Q on compact stars in lower mass gaps in the $f(\mathcal {T})$ gravity framework. Commencing with the field equations that describe anisotropic matter distributions, we select a well-behaved ansatz for the radial component of the metric function, along with an appropriate formulation for the electric field. The resulting model undergoes rigorous testing to ensure its qualification as a physically viable compact object within the $f(\mathcal {T})$ gravity background. We extensively investigate two factors: χ1 and Q, carefully analyzing their impacts on the mass, radius, and stability of the star. Our analyses demonstrate that our models exhibit well-behaved behavior, free from singularities, and can successfully explain the existence of a wide range of observed compact objects. These objects have masses ranging from $0.85^{+0.15}_{-0.15}$ to 2.67 M⊙, with the upper value falling within the mass gap regime observed in gravitational events like GW190814. A notable finding of this study has two aspects: we observe significant effects on the maximum mass (Mmax) and the corresponding radii of these objects. Increasing values of χ1 lead to higher Mmax (approximately $2.64^{+0.13}_{-0.14}$) and smaller radii (approximately $10.40^{+0.16}_{-0.60}$), suggesting the possibility of the existence of massive neutron stars within the system. Conversely, increasing values of Q result in a decrease in Mmax (approximately $1.70^{+0.05}_{-0.03}$) and larger radii (approximately $13.71^{+0.19}_{-0.20}$). Furthermore, an intriguing observation arises from comparing the results: for all values of χ1, nonrotating stars possess higher masses compared to slow-rotating stars, whereas this trend is reversed when adjusting Q.

Dark matter reconstruction from stellar orbits in the Galactic centre

Current constraints on distributed matter in the innermost Galactic centre (such as a cluster of faint stars and stellar remnants, dark matter, or a combination thereof) based on the orbital dynamics of the visible stars closest to the central black hole typically assume simple functional forms for the distributions. We aim to take a general model-agnostic approach in which the form of the distribution is not constrained by prior assumptions on the physical composition of the matter. This approach yields unbiased, entirely observation-driven fits for the matter distribution and places constraints on our ability to discriminate between different density profiles (and consequently between physical compositions) of the distributed matter. We constructed a spherical shell model with the flexibility to fit a wide variety of physically reasonable density profiles by modelling the distribution as a series of concentric mass shells. We tested this approach in an analysis of mock observations of the star S2. For a sufficiently large and precise data set, we find that it is possible to discriminate among several physically motivated density profiles. However, for data coming from current and expected next generation observational instruments, the potential for profile distinction will remain limited by the precision of the instruments. Future observations will still be able to constrain the overall enclosed distributed mass within the apocentre of the probing orbit in an unbiased manner. We interpret this in the theoretical context of constraining the secular versus non-secular orbital dynamics. Our results show that while stellar data over multiple orbits of currently known stars will eventually yield model-agnostic constraints for the overall amount of distributed matter within the probe's apocentre in the innermost Galactic centre, an unbiased model distinction made by determining the radial density profile of the distribution is, in principle, out of the measurement accuracy of the current and next-generation instruments. Constraints on dark matter models will therefore remain subject to model assumptions and will not be able to significantly downsize the zoo of candidate models.

Cracking and complexity of self-gravitating dissipative compact objects

Cracking and complexity of self-gravitating dissipative compact objects

Non-radial oscillations in newly born compact star considering effects of phase transition

Abstract The massive stars end their lives by supernova explosions leaving central compact objects that may evolve into neutron stars. Initially, after birth, the star remains hot and gradually cools down. We explore the matter and star properties during this initial stage of the compact stars considering the possibility of the appearance of deconfined quark matter in the core of the star. At the initial stage after the supernova explosion, the occurrence of non-radial oscillation in the newly born compact object is highly possible. Non-radial oscillations are an important source of GWs. There is a high chance for GWs from these oscillations, especially the nodeless fundamental (f-) mode to be detected by next-generation GW detectors. We study the evolution in frequencies of non-radial oscillation after birth considering phase transition and predicting the possible signature for different possibilities of theoretical compact star models.

Observational signatures of Rotating compact objects in Plasma space–time

We have investigated the characteristics of shadows cast by the Kerr black hole in the presence of plasma and compared them to those of a rotating wormhole in a uniform plasma space–time for an observer at infinity. Interestingly, for the same uniform plasma density, the apparent shadow size of the rotating wormhole is always greater than that of the Kerr black hole. To further distinguish the two compact objects we studied the deflection angle and did a comparative study in the presence of the uniform and non-uniform plasma profiles. The goal of this whole exercise is to deepen our understanding of the observational phenomena of these astrophysical objects. The analysis reveals the importance of specific plasma distribution profiles, the impact of plasma on the shadow diameter, and the behavior of deflection angles in different plasma scenarios. We have calculated constraints on the plasma parameters by considering observational data and employing analytical formulations. Our work therefore provides valuable insights into the behavior of light rays near compact objects in plasma space–time.

Sustainable development insights: synergizing publishing and academic research to propel SDGs Forward

Objective: To explore the integral roles of the publishing industry and Scopus, an academic research tool, in supporting and advancing the United Nations Sustainable Development Goals (SDGs). Method: Qualitative analysis focusing on the impact of publishing on SDG awareness, the evolution of the SDG Publishers Compact, Scopus's role in integrating SDGs, and the broader implications of these initiatives. Results: Identification of challenges and opportunities in implementing the Compact's objectives, highlighting the importance of collaborative research efforts to tackle complex global challenges, with special emphasis on Scopus's inclusion of SDGs. Practical Implications: Highlights the synergistic impact of publishing and academic tools in advancing the sustainable development agenda, suggesting the need for collaboration among publishers, researchers, policymakers, and other stakeholders. Conclusions: The integration of SDGs into the publishing industry and academic tools represents a significant step forward in the global effort to achieve sustainable development, emphasizing the importance of information and knowledge in fostering a more informed, engaged, and proactive global community.

Compact white dwarf binaries in the combined SRG/eROSITA/SDSS eFEDS survey

X-ray surveys combined with optical follow-up observations are used to generate complete flux-limited samples of the main X-ray emitting source classes. on the Spectrum-Roentgen-Gamma (SRG) mission provides sufficient sensitivity to build significantly enhanced samples of rare X-ray emitting sources. We strive to identify and classify compact white dwarf binaries, cataclysmic variables (CVs), and related objects, which were detected in the sky area of eFEDS, the Final Equatorial Depths Survey, and they were observed in the plate program of SDSS-V. Compact white dwarf binaries were selected from spectra obtained in the early SDSS-V plate program. A dedicated set of SDSS plate observations were carried out in the eFEDS field, providing spectroscopic classifications for a significant fraction of the optically bright end ($r<22.5$) of the X-ray sample. The identification and subclassification rests on visual inspections of the SDSS spectra, spectral variability, color-magnitude and color-color diagrams involving optical and X-ray fluxes, optical variability, and literature work. Upon visual inspection of SDSS spectra and various auxiliary data products, we have identified 26 accreting compact white dwarf binaries (aCWDBs) in eFEDS, of which 24 are proven X-ray emitters. Among those 26 objects, there are 12 dwarf novae, three WZ Sge-like disk-accreting nonmagnetic CVs with low accretion rates, five likely nonmagnetic high accretion rate nova-like CVs, two magnetic CVs of the polar subcategory, and three double degenerates (AM CVn objects). Period bouncing candidates and magnetic systems are rarer than expected in this sample, but it is too small for a thorough statistical analysis. Fourteen of the systems are new discoveries, of which five are fainter than the magnitude limit. Thirteen aCWDBs have measured or estimated orbital periods, of which five were presented here. Through a Zeeman analysis, we revise the magnetic field estimate of the polar system J0926$+0105$, which is likely a low-field polar at $B=16$\,MG. We quantified the success of X-ray versus optical/UV selection of compact white dwarf binaries which will be relevant for the full SDSS-V survey. We also identified six white dwarf main sequence (WDMS) systems, among them there is one confirmed pre-CV at an orbital period of 17.6 hours and another pre-CV candidate. This work presents successful initial work in building large samples of all kinds of accreting and X-ray emitting compact white dwarf binaries that will be continued over the full hemisphere in the years to come.

Excluded volume effects in the quark-mass density-dependent model: Implications for the equation of state and compact star structure

Excluded volume effects in the quark-mass density-dependent model: Implications for the equation of state and compact star structure

Electromagnetic field on the complexity of minimally deformed compact stars

In the context of this endeavor, we establish a simple protocol for formulating interior stellar solutions that exhibit spherically symmetric configurations against the backdrop of relativistic gravitational decoupling through radial metric deformation (minimal geometric deformation scheme). In this pursuit, we make use of the vanishing complexity factor (Y~TF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{Y}_{TF}$$\\end{document}) condition, based on Herrera’s (Phys Rev D 97, 044010, 2018) innovative concept regarding the complexity of static or slowly evolving spherical matter configurations. The idea of a complexity factor emerges as the outcome of the orthogonal splitting of the Riemann–Christoffel tensor, which yields different scalar functions, known as structure scalars. The protocol is demonstrated by employing the Buchdahl and Tolman relativistic stellar ansatzes as isotropic seeds. Both of these ansatzes exhibit similar physical features, with a minor variation in their magnitudes in the case of Y~TF≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{Y}_{TF}\ e 0$$\\end{document}, where 0≤α<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\\le \\alpha <1$$\\end{document}, and α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} represents a coupling parameter. However, when Y~TF=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{Y}_{TF}=0$$\\end{document}, the Buchdahl stellar ansatz exhibits a uniform density matter configuration, while the Tolman model features an increasing pressure profile. The obtained relativistic stellar models satisfy the basic viability constraints required for the physically realistic configurations.

Comparison of magnetized thick disks around black holes and boson stars

Boson stars are considered as promising candidates for black hole mimickers. Similar to other compact objects they can form accretion disks around them. The properties of these disks could possibly distinguish them from other compact objects like black holes in future observations. Retrograde thick disks around boson stars and the influence of strong magnetic fields on them were already studied and it was shown that they can harbor very distinct features compared to black hole disks. However, the case of prograde thick disks is mostly unexplored, since they may appear much more similar to black hole disks. In this work we will investigate similarities and differences regarding prograde thick disks around non-selfinteracting rotating boson stars and rotating black holes. We assume thereby a polytropic equation of state and a constant specific angular momentum distribution of the disks. We classify the various conceivable boson star and black hole solutions by a dimensionless spin parameter a and compare their corresponding disk solutions. The influence of toroidal magnetic fields on the disks is analyzed by selected disk properties, as the rest-mass density distribution and the Bernoulli parameter. Disk solutions are characterized by their degree of magnetization represented by the magnetization parameter βmc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _{mc}$$\\end{document}. We found that strong magnetic fields can strengthen the differences of disk solutions or oppositely even lead to a correlation in disk properties, depending on the spin parameter of the boson star and black hole solutions. We identify the vertical thickness of the boson star disks as the main differentiating factor, since for most solutions the vertical density distribution is far more outreaching for boson star disks compared to black hole disks.

Scattering of spinning compact objects from a worldline EFT

We study the EFT of a spinning compact object and show that with appropriate gauge fixing, computations become amenable to worldline quantum field theory techniques. We use the resulting action to compute Compton and one-loop scattering amplitudes at fourth order in spin. By matching these amplitdes to solutions of the Teukolsky equations, we fix the values of Wilson coefficients appearing in the EFT such that it reproduces Kerr black hole scattering. We keep track of the spin supplementary condition throughout our computations and discuss alternative ways to ensure its preservation.

A sequence of Type Ib, IIb, II-L, and II-P supernovae from binary-star progenitors with varying initial separations

Over the last decade, evidence has accumulated that massive stars do not typically evolve in isolation but instead follow a tumultuous journey with a companion star on their way to core collapse. While Roche-lobe overflow appears instrumental for the production of a large fraction of Type Ib and Ic supernovae (SNe), variations in the initial orbital period, $P_ init $, of massive interacting binaries may also produce a wide diversity of case B, BC, or C systems, with pre-SN stars endowed from minute to massive H-rich envelopes. Focusing here on the explosion of the primary donor star, originally 12.6\ we used radiation hydrodynamics and nonlocal thermodynamic equilibrium time-dependent radiative transfer to document the gas and radiation properties of such SNe, covering Types Ib, IIb, II-L, and II-P. Variations in init $ are the root cause of the wide diversity of our SN light curves, which present single-peak, double-peak, fast-declining, or plateau-like morphologies in the $V$ band. The different ejecta structures, expansion rates, and relative abundances (e.g., H, He, and can lead to a great deal of diversity in terms of spectral line shapes (absorption versus emission strength and width) and evolution. We emphasize that Halpha is a key tracer of these modulations, and that He is an enduring optical diagnostic for the presence of He. Our grid of simulations fares well against representative Type Ib, IIb, and II-P SNe, but interaction with circumstellar material, which is ignored in this work, is likely at the origin of the tension between our Type II-L SN models and observations (e.g., of SN\,2006Y). Remaining discrepancies in the rise time to bolometric maximum of our models call for a proper account of both small-scale and large-scale structures in core-collapse SN ejecta. Discrepant Type II-P SN models, with a high plateau brightness but small spectral line widths, can be fixed by adopting more compact red-supergiant star progenitors.

Probing the emission mechanism and nature of the pulsating compact object in the X-ray binary SAX J1324.4-6200

Recently, there has been renewed interest in the Be X-ray binary (Be/XRB) because of its spatial coincidence with a variable gamma -ray source detected by To explore more thoroughly its properties, new X-ray observations were carried out in 2023 by and satellites, jointly covering the energy range from $0.2-79$ keV. was caught at an X-ray flux of $ $ erg cm$^ $ s$^ $. The X-ray spectrum fits well with an absorbed power law with a high energy cutoff. Other acceptable fits require an additional blackbody component ($kT_ bb 1.1$ keV) or a Gaussian in absorption gabs keV). We measured a spin period of $175.8127 and an spin period of $175.862 We show that all the available spin period measurements of spanning 29 years, are highly correlated with time, resulting in a remarkably stable spin-down of $ P $ s s$^ $. We find that if hosts an accretion-powered pulsar, accretion torque models indicate a surface magnetic field of $ $ G. The X-ray properties emerging from our analysis strenghten the hypothesis that belongs to the small group of persistent Be/XRBs. We also performed radio observations with the Parkes Murriyang telescope, to search for radio pulsations. However, no radio pulsations compatible with the rotational ephemeris of were detected. We rule out the hypothesis that is a gamma -ray binary where the emission is produced by interactions between the pulsar and the companion winds. Other models commonly used to account for the production of $ in accreting pulsars cannot reproduce the bright emission from We examined other possible mechanisms behind the $ emission and note that there is a $ 0.5$&lt;!PCT!&gt; chance probability that an unknown extragalactic active galactic nucleus (AGN) observed through the Galactic plane may coincidentally fall within the error circle of the source and be responsible for the $ emission.

Significance of Fabry-Perot Cavities for Space Gravitational Wave Antenna DECIGO

DECIGO is a future Japanese project for the detection of gravitational waves in space. To conduct various scientific missions, including the verification of cosmic inflation through the detection of primordial gravitational waves as the main objective, DECIGO is designed to have high sensitivity in the frequency band from 0.1 to 10 Hz, with arms of length 1000 km. Furthermore, the use of the Fabry-Perotcavity in these arms has been established for the DECIGO project. In this paper, we scrutinize the significance of the Fabry-Perot cavity for promoting this project, with a focus on the possibility of observing gravitational waves from cosmic inflation and binary compact star systems as indicators. The results show that using the Fabry-Perot cavity is extremely beneficial for detecting them, and it is anticipated to enable the opening of a new window in gravitational wave astronomy.

Testing alternative spacetimes by high-frequency quasi-periodic oscillations observed in microquasars and active galactic nuclei

In this article, we try to capture the influence of deviation from standard Kerr black hole (BH) spacetime on observed high-frequency quasi-periodic oscillations (QPOs) signal. We explore the dynamics of test particles in the field of rotating compact objects governed by the various modifications of the standard Kerr BH spacetime and apply the model of epicyclic oscillations of Keplerian discs to the observed microquasars and active galactic nuclei high-frequency QPOs data. We present a generalized formalism for fitting two well-known high-frequency QPO models: the epicyclic resonance model and the relativistic precession model. This is done assuming stationary, axisymmetric, and asymptotically flat spacetimes. Recently, we have used the same set of stationary, axisymmetric, and asymptotically flat spacetimes, and estimated the restrictions of spacetime parameters with the help of hot-spot data of three flares observed at Sgr A* by GRAVITY instrument (Misbah Shahzadi et al 2022 Eur. Phys. J. C 82 407). The aim of this work is not to test a particular theoretical model or to determine and constrain its parameters, but to map a set of well-astrophysically motivated deviations from classical Kerr BH spacetime and demonstrate which ones provide the best fit for high-frequency QPOs data and could be fruitful for future exploration.

Flares during eclipses of high-mass X-ray binary systems Vela X-1, 4U 1700−37, and LMC X-4

ABSTRACT In eclipsing X-ray binary systems, the direct X-ray emission is blocked by the companion star during the eclipse. We observe only reprocessed emission that contains clues about the environment of the compact object and its chemical composition, ionization levels, etc. We have found flares in some X-ray binaries during their eclipses. The study of eclipse flares provides additional clues regarding the size of the reprocessing region and helps distinguish between different components of the X-ray spectrum observed during the eclipse. In the archival data, we searched for flares during eclipses of high-mass X-ray binaries and found flares in three sources: Vela X-1, LMC X-4, and 4U 1700−37. Comparing spectral properties of the eclipse flare and non-flare data, we found changes in the power-law photon index in all three sources and multiple emission lines in Vela X-1 and 4U 1700-37. The fluxes of prominent emission lines showed a similar increase as the overall X-ray flux during the eclipse flare, suggesting the lines originate in the binary environment and not in the interstellar medium. We also observed a soft excess in 4U 1700-37 that remains unchanged during both eclipse flare and non-flare states. Our analysis suggests that this emission originates from the extremely thin shell of the stellar wind surrounding the photosphere of its companion star. The detection of short (100–200 s) count-rate doubling time-scale in 4U 1700−37 and LMC X-4 indicates that the eclipse reprocessing occurs in a region larger than, but comparable to the size of the companion star.