arXiv subjects

Norbert Langer

Publications and source records attributed to Norbert Langer.

At least 19 recordsLinked to original sources

arXiv2026

Chemical fingerprints of binary mass transfer in massive stars

The majority of massive stars are born in close binary systems. As stars expand when they age, mass transfer or even a merger with their companion is inevitable. However, most binary interaction products appear as single stars, such that the main evidence of their exciting past is lost. In a comprehensive grid of detailed massive binary evolution models we find systematic trends in chemical surface abundances that allow identifying the past mass gainers. We develop an analytic framework which is independent of specific evolutionary models, to constrain the amount and composition of the accreted material from their observed surface abundances. This yields tight constraints on the uncertain mass transfer physics in massive binary stars and allows us to reconstruct the past evolutionary history of the progenitor binary system. This method, which is shown to also constrain binary mergers (for example, SN 1987A), is applied to some of the best-studied OB stars so far. For {\gamma} Columbae, suggested to be an envelope-stripped star, we show that it is a mass gainer instead, whose companion star likely formed a stripped-envelope supernova. Our results highlight surface abundance measurements as a powerful tool to improve our understanding of massive binary systems evolving towards supernovae and compact object binaries.

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arXiv2026

Binary-induced mass increase and helium enrichment of the envelopes of Type~IIP supernova progenitors

Binary interactions are expected to play a major role in shaping the progenitor population of core-collapse supernovae, particularly in the era of deep, high-cadence transient surveys. Using ComBinE, a rapid binary population synthesis code combining tabulated stellar structure models with physically motivated mass-transfer stability criteria, we find that ~40% of Type II supernova progenitors at Milky Way metallicity originate from mergers between a post-main-sequence star and a main-sequence companion following unstable mass transfer. Compared to single-star progenitors with the same helium-core mass, these merger products have more massive hydrogen-rich envelopes and broader envelope-mass distributions. Their envelopes are helium-enriched, with relative enhancements of up to 80% and helium mass fractions reaching 0.4. These differences are expected to affect Type IIP light curves and should be considered in future progenitor and explosion models. Constraining the merger-induced Type IIP fraction with facilities such as LSST, Roman, and the ELT will provide insights into binary evolution physics.

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arXiv2026

Neutron star-companion interaction in core collapse supernovae. Population synthesis based on detailed binary evolution models

Most massive stars live in binary systems. When the first supernova (SN) in a binary occurs, the ejecta hit the companion, which may inflate as a consequence, and then interacts with the newly formed compact object. The recent Type Ic SN2022jli shows a periodic modulation in its emission, which is interpreted as evidence for such interaction. We derive predictions for the occurrence rate and observables of SNe exhibiting these companion - compact-object interactions (CCIs). We analyze a comprehensive, state-of-the-art grid of detailed binary stellar evolution models, and implement analytic prescriptions for the expansion of the companion star following its interaction with the SN ejecta. We employ the newly developed population synthesis code SN-ORACLE to derive the distribution functions of the properties of the SNe affected by CCI and their companions, where we use different explodability and neutron star birth kick distributions. We find that periodic CCI is expected to occur in more than half of the binary systems that produce a hydrogen-poor core collapse SN and are not disrupted, while the occurrence rate in systems producing hydrogen-rich SNe is small. We find broad period ranges, peaking around 20-50 days, with the interaction lasting for 0.5-10 years. We identify specific binary evolution models that reproduce the observed period of the light curve undulations of SN2022jli, SN2015ap, and SN2022esa. The inflation of the companion also increases its luminosity and brightness, increasing its detectability with current instruments. For SN2022jli, our best fitting models predict a J-band magnitude of 21-23 for up to 10 years. We find that up to 27% of H-poor SNe could show periodicity in their light curves, while only a few such events have been identified so far. Our results may help find periodic CCI features in future and archival SN observations.

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arXiv2026

Binarity at LOw Metallicity (BLOeM): massive star variability revealed using a novel software tool for point-spread function fitting of TESS images

Massive stars, the progenitors of neutron stars and black holes, play a crucial role in shaping the chemical and radiative properties of entire galaxies through their winds and explosive deaths. Stellar pulsations are a common phenomenon in massive stars and asteroseismology -- the study of such pulsations -- provides crucial constraints on the physics of massive star interiors. The excitation of heat-driven pulsations in massive stars is expected to depend on a star's metallicity, but this remains largely uncalibrated in evolution models due to a lack of a sufficient observations. While TESS has dramatically improved the statistics for Galactic massive stars, obtaining TESS light curves for low-metallicity massive stars beyond the Milky Way is challenging, due to their faintness and heavy crowding. In this paper, we present a novel point-spread function (PSF) based light curve extraction method called {\sc Lemons}, which overcomes these challenges. We also demonstrate the limitations of the often-used simple aperture photometry (SAP) method that can provide heavily contaminated light curves. With this new technique, accurate light curves of 91 SMC massive stars in the BLOeM sample are extracted. They reveal a variety of variability types including indications of binarity (e.g. eclipses and ellipsoidal modulation) and stellar pulsations. They also enable us to investigate stochastic low-frequency (SLF) variability for massive stars in the SMC. Furthermore we demonstrate how the morphology of SLF variability probes a star's location in the Hertzsprung--Russell diagram, which appears similar to Galactic massive stars thus indicating that the underlying physical mechanism could be insensitive to metallicity.

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arXiv2026

Evolution of wide O star binaries through their LBV stage. Population synthesis with mass-ejection-driven orbital evolution

Context. Long-period Wolf-Rayet (WR) star binaries produced by mass transfer are predicted to be abundant, but are observationally rare. This yields constraints on the evolution of initially wide O star binaries, including those potentially leading to the formation of gravitational-wave sources through the Common Envelope Channel. Aims. We investigate this issue in the light of a new type of orbital evolution for initially wide O star binaries, which is driven by mass ejection at periastron passage during the Luminous Blue Variable (LBV) phase. Methods. The assumption that the mass ejection occurs instantly at periastron passage allows us to analytically describe the orbital evolution. This approach is motivated by our understanding of an Eddington-limit driven LBV phase. We perform population synthesis calculations for the WR stars in the Small Magellanic Cloud (SMC), and compare them to the observed SMC WR star population. Results. Different from mass transfer, our mass ejection scenario leads to increased orbital periods and eccentricities. The Galactic system WR 140 (orbital period 2895 d, eccentricity 0.9) could be a typical result of this evolution scenario. Our models predict measurable binary space velocities, and allow for the disruption of the binary. Our SMC population synthesis model predicts statistically 5.3 close, 3.7 long-period, and further 2 runaway single WR stars. With largely increased orbital periods and eccentricities, such WR+O star binaries may not be ruled out by past radial-velocity searches. Applying our scenario to the Gaia BH1 and BH2 systems, we find that it provides viable progenitor evolution models. Conclusions. The mass-ejection-driven orbital evolution could explain why so few wide WR binaries are observed, and why some of the apparently single WR stars have high space velocities. We discuss implications for gravitational-wave sources.

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arXiv2026

Thermal-timescale accretion does not always yield critical rotation in mass gainers

Binary evolution plays a central role in producing rapidly rotating stars. Previous studies have shown that mass gainers in binaries can reach critical rotation after accreting only modest amounts of material, particularly during thermal-timescale Case B mass transfer, where tidal spin-down is ineffective due to wide orbits. However, such rapid accretion often drives the mass gainer out of thermal equilibrium, and its subsequent spin evolution during thermal relaxation has not been analysed in depth. In this study, we construct a suite of accreting detailed single-star models with different accretion prescriptions, which inflate and spin up to critical rotation during the accretion. After the accretion has ended, the models relax thermally and deflate. We find that the ratio of surface to critical angular velocity decreases to subcritical values during thermal contraction, with the magnitude of this decrease correlating with the degree of thermal disequilibrium at the end of accretion. This reduction in fractional critical rotation is even stronger when internal angular momentum transport is inefficient. Detailed binary models show the same trend, indicating that the results from our toy single-star models also apply to real binary evolution. Our results highlight that binary mass transfer does not always produce critically rotating stars, but instead may yield a wide range of spin rates depending on the mass transfer and accretion history. Our findings offer new insights into the rotational properties of mass gainers in binaries, stellar merger products, and newly formed massive stars following accretion.

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arXiv2025

Stable mass transfer in massive binaries leading to merging black holes

The vast majority of massive binary systems in the universe is evidently unsuited to produce merging binary black holes. However, several narrow evolutionary paths of isolated massive binaries towards this goal have recently been identified. Due to the high degree of simplification and assumptions applied in previous modelling of these paths, conclusions remained vague so far. For one of these paths, the stable mass transfer channel, we now construct detailed binary evolution models which include internal differential rotation as well as mass and angular momentum transfer between the stars, all the way from the zero-age main sequence to the formation of the black holes, only skipping the rapid late burning stages. This allows us to follow the mass and chemical structure evolution of the mass accreting component, which turns out to have a key influence on the phase of reverse mass transfer, that allows the obtained black hole spins and mass ratios to naturally fall into the regime observed for the gravitational-wave source in the 10--25$M_\odot$ primary black hole mass range. As for this channel, also a large number of progenitor binaries are known, we conclude that it likely contributes to the observed population of gravitational wave sources.

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arXiv2025

Interacting binaries on the Main Sequence as in-situ tracers of mass transfer efficiency and stability

Understanding the transfer of mass and angular momentum in binary interactions is crucial for modelling the evolution of any interacting binary after the first mass transfer phase. Mass transfer physics assumptions shape the predictions for later stages of binary evolution, such as the immediate progenitors of stripped-envelope supernovae and gravitational wave mergers. We constrain the efficiency and stability of thermal timescale mass transfer in massive binary evolution using the observed population of 62 massive interacting binaries on the Main Sequence (`Algols') in the Milky Way, Large and Small Magellanic Clouds. We find that purely conservative or non-conservative mass transfer cannot explain the current mass ratio and orbital period of all massive Algols. Angular momentum conservation rules out conservative mass transfer in $\sim$28\,\% of massive Algols in the SMC. About three-quarters of all massive Algols are consistent with having undergone inefficient mass transfer ($\lesssim$\,50\,\%), while the remaining systems, mostly residing in the LMC and Milky Way, require mass transfer to have been more efficient than 25\%. For our fiducial assumption on the extent of envelope stripping, the current sample of massive Algols does not require mass transfer to be efficient at the shortest orbital periods ($\sim$2\,d) at any metallicity. We find evidence that mass transfer on the Main Sequence needs to be stable for initial accretor-to-donor mass ratios as unequal as $\sim 0.6$. Unless biased by observational selection effects, the massive Algols in the SMC seem to have undergone less efficient mass transfer than those in the LMC and Milky Way.

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arXiv2025

A comprehensive grid of massive binary evolution models for the Galaxy - Surface properties of post-mass transfer stars

Massive stars often evolve in binary systems, in which binary interactions significantly affect their evolution. Massive stars in the Galaxy serve as valuable testbeds for this due to their proximity. We computed the evolution of more than 38000 galactic binary systems with initial primary star masses of 5...100 Msun. In this paper, we aim to investigate the surface properties of post-mass transfer mass donor and mass gainer stars through core hydrogen burning, core helium burning, and for the pre-supernova stage. The models are computed with MESA, incorporating detailed stellar and binary physics, including internal differential rotation, magnetic angular momentum transport, mass-dependent overshooting, stellar wind mass-loss, mass and angular momentum transfer and tidal interaction. They incorporate a new extensive nuclear network for hydrogen burning, which allows us to track the full range of hydrogen burning nucleosynthesis products, from the light elements to aluminum. The widest, non-interacting binary models in our grid effectively serve as single star models. We find that mass gainers and mass donors may evolve through long-lived blue and yellow supergiant stages during core helium burning where single stars of the same mass remain red supergiants. Furthermore, some of our gainers evolve into more luminous yellow and blue supergiants prior to core collapse than single stars, while some donors end their life as red or yellow supergiants, showing a rich diversity in supernova progenitors. We show that the surface elemental and isotopic abundances carry valuable information about a star's evolutionary history and can be used to distinguish binary interaction products from single stars. Our binary model grid may serve as a tool for identifying post-mass transfer stars and supernovae, and holds potential for population studies, supernova modeling, and guidance of future observations.

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arXiv2025

A constant upper luminosity limit of cool supergiant stars down to the extremely low metallicity of I Zw 18

Stellar wind mass loss is often assumed to depend on their metallicity $Z$. Therefore, evolutionary models of massive stars at lower $Z$ are able to retain more of their H-rich layers and evolve into brighter cool supergiants (cool SGs; $T_\mathrm{eff} < 7$ kK). Surprisingly, in galaxies in the range $0.2 \lesssim Z / Z_\odot \lesssim 1.5$ previous studies did not find a $Z$-dependence of the upper luminosity limit $L_\mathrm{max}$ of cool SGs. Here, we study four extra galaxies with HST and JWST. Observations of the extremely low-$Z$ dwarf galaxy I Zw 18 from JWST allow us to go down to $Z / Z_\odot \approx 1/40$. For cool SGs in all studied galaxies including I Zw 18, we find a constant $L_\mathrm{max} \approx 10^{5.6}$L$_\odot$, similar to literature results for $0.2 \lesssim Z / Z_\odot \lesssim 1.5$. In I Zw 18 and the other studied galaxies, the presence of Wolf-Rayet stars has been claimed. Although we cannot rule out that some of them become intermediate-temperature objects, this paints a picture in which evolved stars with $L>10^{5.6}$L$_\odot$ burn He as hot He-rich stars down to extremely low $Z$. We argue that $Z$-independent late-phase mass loss would be the most likely mechanism responsible. Regardless of the exact stripping mechanism, for the Early Universe our results imply a limitation on black hole masses and a contribution of stars born with $M\gtrsim 30$M$_\odot$ to its surprisingly strong nitrogen enrichment. We propose a scenario in which single stars at low $Z$ emit sufficiently hard ionizing radiation to produce lines of He II and C IV. In this scenario, late-phase $Z$-independent mass loss produces hot He-rich stars. Due to the well-understood $Z$-dependence of radiation-driven winds of hot stars, a window of opportunity would open below 0.2Z$_\odot$, where self-stripped He-rich stars can exist without dense WR winds that absorb hard ionizing radiation.

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arXiv2025

The demographics of core-collapse supernovae. The role of binary evolution and CSM interaction

The observational properties of core-collapse supernovae (CC-SNe) are shaped by the envelopes of their progenitors. In massive binary systems, mass-transfer alters the pre-SN structures compared to single stars, leading to a diversity in SN explosions. Aims. We compute the distribution of CC-SN properties based on comprehensive detailed grids of single and binary stellar evolution models. We conduct a grid-based population synthesis to produce a synthetic population of CC-SNe, and compare it to observed SN samples. We also apply various explodability and merger criteria to our models. In line with earlier results, we identify interacting SN progenitors as those stars that undergo CC during or shortly after a Roche-lobe overflow phase. With an interacting binary fraction of 68%, our models predict two-thirds of all CC-SNe to be of Type IIP/L, and one third of Type Ibc, in agreement with recent volume-limited SN surveys. We find that 76% of the Type Ibc SN progenitors took part in a previous binary mass transfer (mostly as mass donor), but also 63% of the Type IIP/L SN progenitors (mostly as mass gainers), yielding a much broader envelope mass distribution than expected from single stars. We find that mass-transfer induced interacting SNe make up ~5% of all CC-SNe, which is close to the observed fractions of Type IIn and Type Ibn SNe. When assuming a disk or toroidal CSM geometry for Type IIn SNe, our models predict a bimodal distribution of the radiated energies, similar to that deduced from observations. While we find the effect of binary evolution on the relative number of Type Ibc and Type IIP/L SNe to be moderate, it leads to lower average ejecta masses in Type Ibc and Type IIb SNe, and can lead to higher pre-SN masses in Type IIP/L SNe than single stars. Binary models are also able to reproduce the number and properties of interacting SNe.

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arXiv2025

Evidence of polar and ultralow supernova kicks from the orbits of Be X-ray binaries

Supernovae, the explosive deaths of massive stars, create heavy elements and form black holes and neutron stars. These compact objects often receive a velocity at formation, a "kick" whose physical origin remains debated. We investigate kicks in Be X-ray binaries, containing a neutron star and a rapidly spinning companion. We identify two distinct populations: one with kicks below $10\,\rm{km}\,\rm{s}^{-1}$, much lower than theoretical predictions, and another with kicks around $100\,\rm{km}\,\rm{s}^{-1}$, that shows evidence for being aligned within 5 degrees of the progenitor's rotation axis. The distribution of progenitor masses for the two populations have medians around $2.3\,\rm{M}_\odot$ and $4.9\,\rm{M}_\odot$, corresponding to stars with birth masses of about $10\,\rm{M}_\odot$ and $15\,\rm{M}_\odot$. The second component matches the low-velocity mode observed in isolated pulsars. Combined with the known high-velocity component, which dominates isolated pulsars, this suggests three distinct kick modes. These results reveal previously unrecognized diversity in neutron-star formation.

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arXiv2025

A fundamental limit to how close binary systems can get via stable mass transfer shapes the properties of binary black hole mergers

Mass transfer in binary systems is the key process in the formation of various classes of objects, including merging binary black holes (BBHs) and neutron stars. Orbital evolution during mass transfer depends on how much mass is accreted and how much angular momentum is lost $-$ two of the main uncertainties in binary evolution. Here, we demonstrate that, despite these unknowns, a fundamental limit exists to how close binary systems can get via stable mass transfer (SMT), that is robust against uncertainties in orbital evolution. Based on detailed evolutionary models of interacting systems with a BH accretor and a massive star companion, we show that the post-interaction orbit is always wider than $\sim10R_{\odot}$, even with extreme shrinkage due to L2 outflows. Systems evolving towards tighter orbits become unstable and result in stellar mergers. This separation limit has direct implications for the properties of BBH mergers: long delay times ($\gtrsim1 \rm Gyr$), and no high BH spins from the tidal spin-up of helium stars. At high metallicity, the SMT channel may be severely quenched due to Wolf-Rayet winds. The reason for the separation limit lies in the stellar structure, not in binary physics. If the orbit gets too narrow during mass transfer, a dynamical instability is triggered by a rapid expansion of the remaining donor envelope due to its near-flat entropy profile. The closest separations can be achieved from core-He burning ($\sim8-15R_{\odot}$) and Main Sequence donors ($\sim15-30R_{\odot}$), while Hertzsprung Gap donors lead to wider orbits ($\gtrsim30-50R_{\odot}$) and non-merging BBHs. These outcomes and mass transfer stability are governed by the internal composition profiles of donor stars. Thus, the formation of compact binaries is a sensitive probe of chemical mixing in stars. We propose a simple treatment of mass transfer stability to reproduce the detailed results.

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arXiv2025

Using detailed single star and binary evolution models to probe the large observed luminosity spread of red supergiants in young open star clusters

Red supergiants (RSGs) represent a late evolutionary stage of massive stars. Recent observations reveal that the observed luminosity range of RSGs in young open clusters is wider than expected from single star evolution models. Binary evolution effects have been suggested as a possible explanation. Here, we analyse 3670 detailed binary-evolution models, as well as corresponding single-star models, to probe the contribution of binary mass transfer and binary mergers on the luminosity distribution of RSGs in star clusters with ages up to 100 Myr. We confirm that the expected luminosity range of RSGs in a coeval population can span a factor of ten, as a consequence of mergers between two main-sequence stars, which reproduces the observed red supergiant luminosity ranges in rich clusters well. While the luminosity increase as consequence of mass transfer is more limited, it may help to increase the number of overluminous RSGs. However, our results also demonstrate that binary effects alone are insufficient to account for the number of RSGs found with luminosities of up to three times those predicted by current single-star models. We discuss observational accuracy, rotational mixing, age spread, and intrinsic RSG variability as possible explanations. Further observations of RSGs in young open clusters, in particular studies of their intrinsic brightness variability, appear crucial for disentangling these effects.

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arXiv2024

Mass-transferring binary stars as progenitors of interacting hydrogen-free supernovae

Stripped-envelope supernovae (SNe) are H-poor transients produced at the end of the life of massive stars that previously lost their H-rich envelope. Their progenitors are thought to be donor stars in mass-transferring binary systems, which were stripped of their H-rich envelopes some $10^6$yr before core collapse. A subset of the stripped-envelope SNe exhibit spectral and photometric features indicative of interaction between their ejecta and nearby circumstellar material (CSM). We examine whether mass transfer during, or shortly before, core collapse in massive binary systems can produce the CSM inferred from the observations of interacting H-poor SNe. We select 44 models from a comprehensive grid of detailed binary evolution models in which the mass donors are H-free and explode while transferring mass to a main-sequence companion. We find that in these models, mass transfer starts less than $\sim20$kyr before, and often continues until the core collapse of the donor star. Up to $0.8M_\odot$ of H-free material are removed from the donor star during this phase, which may produce a He-rich circumbinary material. We explore plausible assumptions for its spatial distribution at the time of explosion. When assuming that the CSM accumulates in a circumbinary disk, we find qualitative agreement with the supernova and CSM properties inferred from observed Type Ibn SNe, and to a lesser extent with constraints from Type Icn SNe. We find that our mass transferring stripped envelope SN progenitor models may produce up to $\sim$10% of all stripped envelope supernovae. The binary channel proposed in this work can qualitatively account for the observed key properties and rate of interacting H-poor SNe. Models for the evolution of the circumbinary material and the spectral evolution of exploding progenitors from this channel are needed to further test its significance.

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arXiv2024

Standing torsional Alfv\'en waves as the source of the rotational period variation in magnetic early-type stars

Context. The influence of magnetic fields on stellar evolution remains unresolved. It has been proposed that if there is a large-scale magnetic field in the stellar interior, torsional waves could arise, efficiently transporting angular momentum. In fact, the observed variations in the rotation periods of some magnetic stars may be attributed to these torsional waves' standing waves. Aims. To demonstrate the existence of torsional waves through modeling of the rotational period variations. Method. We conduct an eigenmode analysis of standing waves based on one-dimensional magnetohydrodynamic equations. The internal magnetic field structures are parametrically represented to treat poloidal fields with different degrees of central/surface concentration. The obtained frequencies are compared with the observed frequencies of the rotational period variations, thereby constraining the internal magnetic field structures. Results. The 67.6 years exhibited by CU Vir is reproduced for surface-concentrated magnetic field structures. The rotational period variations of all ten magnetic stars analyzed in this study are inconsistent with a centrally concentrated magnetic field. Conclusions. Torsional waves can reproduce the observations of rotational period variations. The large-scale magnetic fields within magnetic stars would be concentrated on the surface.

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arXiv2024

Modeling contact binaries, III. Properties of a population of close, massive binaries

Among massive stars, binary interaction is the rule rather than the exception. The closest binaries, those with periods of less than about 10 days, undergo mass transfer during core-hydrogen burning, with many of them experiencing a nuclear-timescale contact phase. Current binary population synthesis models predict the mass-ratio distribution of contact binaries to be heavily skewed toward a mass ratio of unity, which is inconsistent with observations. It has been shown that effects of tidal deformation due to the Roche potential, as well as energy transfer in the common layers of a contact binary, alter the internal structure of close binary components. However, previous population studies neglected these effects. We model a population of massive binary stars that undergo mass transfer during core-hydrogen burning, while consistently considering the effects of tidal deformation and energy transfer in contact phases. We use the MESA binary-evolution code to compute large grids of models with primary star masses of $8\,M_\odot$ to $70\,M_\odot$ at Solar metallicity. We then perform a population synthesis study to predict distribution functions of the observational properties of close binary systems, focusing in particular on the mass and luminosity ratio distribution. We find that the effects of tidal deformation and energy transfer have a limited effect on the predicted mass-ratio distribution of massive contact binaries. Only a small fraction of the population has their mass ratio significantly shifted toward a more unequal configuration. However, we suggest that orbital hardening could affect the evolution of contact binaries and their progenitors, and we advocate for a homogeneous set of observed contact binary parameters.

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arXiv2024

A new sample of massive B-type contact binary candidates from the OGLE survey of the Magellanic Clouds

Massive contact binaries (CBs) are key to understanding close-binary evolution and stellar mergers, yet their study has been limited by the scarcity of observed systems, particularly of B-type binaries expected to dominate this class. We bridge this gap by mining a large sample of massive CB candidates from the OGLE-IV database, increasing their known numbers in the Magellanic Clouds by nearly an order of magnitude. Using main-sequence colour-magnitude limits, an observationally informed period-luminosity-colour relation for CBs, and a high morph-parameter cut ($c\geq0.7$), we identified 68 O- and B-type binaries that exhibit smooth, sinusoidal light curves with nearly equal eclipse depths. We then isolated a bona fide sample of 37 CB candidates (28 in the LMC and 9 in the SMC) that match theoretical colour-magnitude and period distributions derived from an extensive grid of MESA binary models. The bona fide sample, dominated by B-type systems with $P\approx0.6-1$ d, agrees with the predicted population and may contain many $q\approx1$ binaries, as expected from models showing mass equalization preceding temperature equalization during nuclear-timescale contact. Synthetic PHOEBE light curves of contact and near-contact phases of MESA models reveal a degeneracy between these configurations, suggesting possible misidentifications among these systems. Spectroscopic follow-up is required to test these predictions and refine the evolutionary framework of massive CBs.

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