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. We constrain the efficiency and stability of thermal timescale mass transfer in massive binary evolution using the observed population of massive interacting binaries on the Main Sequence (`Algols') in the Milky Way, Large and Small Magellanic Clouds. Assuming the present-day mass of the donor star represents its initial convective core mass at Zero-Age Main Sequence, we estimate its initial mass using detailed stellar evolution models. From the initial donor mass, we calculate the range of initial accretor masses (for different mass transfer efficiencies). By imposing physical constraints on the above initial parameter ranges, we derive the mass transfer efficiency, stability and angular momentum loss that can reproduce the current properties of each Algol binary. 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\%. The current sample of massive Algols does not require mass transfer to be efficient at the shortest orbital periods (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 $\sim 0.6$. The massive Algols in the SMC seem to have undergone less efficient mass transfer than those in the LMC and Milky Way. (Abridged)
Alex: Welcome to another episode of ResearchPod. Sam, I've come across this work on massive stars in pairs—what's the main idea here?
Sam: This paper looks at 62 observed pairs of massive stars called massive Algols, in our Milky Way galaxy and its neighboring clouds, the Large and Small Magellanic Clouds. These are close pairs where one star loses mass to the other while both still burn hydrogen steadily on the main sequence. The key finding is that this mass transfer is mostly inefficient—the receiving star keeps no more than half of what the donor loses, across galaxies with different metal contents.
Alex: So they're using these real star pairs to test how much mass actually sticks to the gaining star?
Sam: Yes. In close binary systems, the less massive star can swell up and spill its outer layers onto its partner. The puzzle is how much of that spilled mass the partner keeps. That efficiency matters because uncertain answers lead to predictions differing by up to ten times for how many gravitational wave signals we'll detect from the remnants of these stars.
Alex: Gravitational waves come from those compact remnants colliding. Why do these Algols give such a clear view of that early spilling phase?
Sam: These are semi-detached binaries with stars at least eight times our Sun's mass, caught right after a fast initial mass transfer called Case A, while both burn hydrogen stably. This early phase needs few assumptions, so their current masses and orbit sizes let researchers work backward to the starting setup using mass budgets and angular momentum conservation—like piecing together a car's speed before a crash from the wreckage and skid marks. Purely conservative transfer, where the gainer keeps everything, or fully non-conservative models don't match about 28 percent of the Small Magellanic Cloud cases.
Alex: Huh. So observations rule out the extremes, giving a solid benchmark for modeling supernova progenitors and wave sources.
Sam: Precisely. It sharpens predictions for stripped-envelope supernovae and gravitational wave merger rates by bounding the earliest binary evolution phase.
Alex: Walk me through how it pins down the range for that efficiency in something like LZ Cep.
Sam: In LZ Cep, the donor now weighs about 6.5 times our Sun's mass, orbiting a 16-solar-mass partner every 3 days. Researchers assume the donor's current mass matches its original central core—the dense hydrogen-burning heart that survives when the outer envelope strips away fast. That sets the initial donor mass around 13.5 solar masses, meaning it lost about 7 solar masses.
Alex: So the mass budget gives a ceiling on how much the gainer could have picked up. But why does a lopsided starting mass ratio cause stability trouble?
Sam: If the future gainer starts too light compared to the donor—say a mass ratio below about 0.6—their response times don't sync. Think of it like two dancers: the donor shrinks fast on its short timescale, but the gainer lags and risks unstable overflow that merges them instead of steady transfer. Models show stable transfer holds down to that ratio threshold, narrowing efficiencies to half or less.
Alex: Huh—so no system across these galaxies demands more than 50% efficiency. That caps early transfer for supernova progenitors and wave mergers.
Sam: Yes, detailed models for LMC and SMC populations confirm this bound holds, independent of metallicity.
Alex: But what about outliers—do any demand tweaking those physics boundaries?
Sam: Take O026631 in the Small Magellanic Cloud: donor at 11 solar masses, gainer at 11.5, orbit 1.4 days. Mass budget and stability limits leave no room unless the minimum initial mass ratio relaxes to about 0.56—where models predict steady transfer might just hold. That's the point where the donor contracts quicker than the gainer expands, leaking material uncontrollably through the L2 point, a weak spot in their gravity. It caps efficiency around 45% at most.
Alex: So stability sets the tightest limits. How does that play out across the full sample?
Sam: Across Milky Way, LMC, and SMC Algols, stability forces efficiencies below 0.5, especially at short orbits. The least massive donors, around 10 to 15 solar masses initially, need steadier stability down to ratios near 0.6—evidence that real transfers hold steadier than some older models predict.
Alex: Huh. So the population confirms inefficiency rules, sharpening merger forecasts.
Sam: Yes. Mass budget alone rules out zero efficiency in about half the LMC and Milky Way systems. Angular momentum limits exclude full efficiency in roughly a quarter of SMC Algols.
Alex: Mass budget sets a floor, orbit rules cap the ceiling, and stability tightens it most.
Sam: Right—when the gainer starts too light, it overflows through the L2 point, that saddle-shaped weak spot where material leaks unstably. Plots cluster solutions below half efficiency.
Alex: Models predict conservative transfer at tight orbits from spin-up limits, yet real stars don't. Is there a role for disks?
Sam: Disks could funnel mass while siphoning spin back to the orbit. But L2 overflow still caps them, especially at low mass ratios under two, where most SMC systems sit—suggesting inefficiency dominates. The paper notes SMC Algols underwent less efficient transfer on average than LMC or Milky Way ones.
Alex: One thing that's unclear—how do they nail down the donor's original mass from its shrunken state?
Sam: They look at the central region, where hydrogen burns hottest and material mixes like a boiling pot. During rapid mass loss, outer layers peel away cleanly, leaving that core as the new surface—so its current mass approximates the original core size, often with a bit of extra mixing called overshooting.
Alex: Like the wreckage reveals the engine block after the shell strips. But models show variation—some donors aren't fully peeled to that core?
Sam: Yes, at LMC metallicity, most cluster near the initial convective core with overshooting. Real observations fit deeper stripping better—shallower assumptions push efficiencies higher, but make some systems unphysical.
Alex: Huh—so even optimistic cases keep SMC Algols under half?
Sam: Yes. Surface nitrogen levels from spectra could test this further, as mixing exposes processed material.
Alex: Those uncertainties in core size and stripping add scatter. Pulling it together, what does the paper conclude?
Sam: Neither fully conservative nor fully non-conservative transfer fits all observed massive Algols, regardless of metallicity. Most point to inefficient transfer, with the gainer keeping half or less, even at shortest orbits around two days. Stability holds down to initial mass ratios near 0.6 for donors under 20 solar masses.
Alex: And SMC ones average even less efficient. What limitations does the paper highlight?
Sam: The sample is heterogeneous—masses from old studies without error bars or modern follow-ups. Few have surface abundances or rotational velocities. The framework assumes fast initial transfer strips to the zero-age main sequence core, but models suggest minor variation from overshooting or winds.
Alex: Huh, so patchy data and assumptions add uncertainty, but bounds hold. How does this sharpen forecasts for supernovae and gravitational waves?
Sam: These Algols benchmark early mass transfer across metallicities, anchoring models for stripped-envelope supernovae and gravitational wave mergers. It cuts uncertainties in population predictions. Future surveys with rotation and abundance data, plus better simulations, will refine it.
Alex: That's a clear, empirical step forward for binary evolution. Thanks, Sam—this has been a solid dive into how real stars constrain the models.
Sam: My pleasure, Alex. Thanks for listening to ResearchPod.