Early-type Be stars form via nonconservative mass transfer in close binaries

Astronomers have argued for decades about how the fastest-spinning ordinary stars in the Galaxy get that way, and a new computational study offers a strikingly forgiving answer. According to Evgeny Staritsin of the Astronomical Observatory at B.N. Yeltsin Ural Federal University in Ekaterinburg, writing in Astrophysics and Space Science on 28 April 2026, a star that gains mass from a bloated companion in a close binary needs to accrete an amount equal to only about 30 percent of its own mass to be spun up to the rotation rates that define the classical Be stars. The conclusion holds even when the binary is wasteful, ejecting a large share of the transferred gas into space instead of letting it settle, a scenario long suspected among interacting binaries but difficult to model, because every gram that leaks away carries angular momentum that can never spin the accretor. Staritsin’s calculations follow the spin history of a mass-gaining star that ends the exchange with roughly 16 solar masses, the mass typical of early-subclass Be stars, and they show that the outcome barely depends on the messy details of how the arriving gas delivers its angular momentum.

Classical Be stars are the showpieces of the B-type family: hot, luminous stars spinning so fast that centrifugal flattening brings the effective gravity at their equators close to zero, the so-called critical or break-up rate at which matter can barely remain bound. At such speeds material drifts outward into a gaseous decretion disk, and it is the disk — not the photosphere — that brands the object with its defining signature: bright emission in the hydrogen Balmer lines, most famously H-alpha, along with an infrared excess from the warm circumstellar gas. Angelo Secchi recorded such emission lines as early as the 1860s on Gamma Cassiopeiae, and the phenomenon has been catalogued ever since as one of the puzzles of early-type stars. The earliest subclasses, B0 through B3, host the most extreme examples, and it is stars near 16 solar masses that the new study targets. Because statistical work shows that disks form only at a large fraction of the critical rotation rate, the formation question reduces to a precise one: how does a B star acquire such rotation in the first place?

Two rival answers dominate that debate. The single-star channel holds that some B stars are simply born rotating close to the critical limit, a picture complicated by surveys such as the VLT-FLAMES Tarantula Survey, which found a puzzlingly bimodal distribution of projected rotational velocities among otherwise ordinary early-B stars. The binary channel is older and, to many eyes, more persuasive: when the heavier member of a close pair evolves off the main sequence and swells into a giant, it overfills its Roche lobe and pours gas through the inner Lagrange point onto its companion, and that stream arrives carrying substantial orbital angular momentum. A landmark 1981 calculation showed that under conservative exchange an accreting star is spun to critical rotation after absorbing only a small fraction of its own mass. The binary route gained observational teeth when the Be star Phi Persei was shown to orbit a stripped helium subdwarf, the remnant of the very donor that once fed it, and population-synthesis studies have since argued over how many Be stars such channels can supply, with some analyses imposing stringent upper limits on the binary-made fraction. What remained contested was the hard case: transfer that is not conservative.

The new work confronts precisely that case. In the modelled scenario, a donor crossing the Hertzsprung gap — a star expanding for the first time after exhausting hydrogen in its core — overfills its Roche lobe and hands mass to its companion on a rapid, thermal timescale. Real exchanges are demonstrably leaky: studies of Algol-type systems and of Be X-ray binaries in the Small Magellanic Cloud indicate that a substantial fraction of the donor’s envelope escapes the system entirely, removing both mass and angular momentum from the binary. Staritsin therefore treats the accretion as nonconservative and asks how much mass the gainer must actually retain for spin-up to succeed. The accretor’s mass increase was scanned across a broad range, from 5 to 100 percent, while the star was steered to finish the episode with a mass of 16 solar masses, the value characteristic of early-subclass Be stars. The central quantity is the angular momentum the accreting component receives, which depends directly on how much mass it gains during the exchange — so the answer hinges on where, along that range, Be-star rotation becomes attainable.

The physics splits the problem in two. Upstream, the transferred gas arrives either as a direct stream or through an accretion disk, carrying a specific angular momentum set by the orbital geometry; between the disk and the stellar surface lies a boundary layer whose efficiency at transmitting torque into the star is uncertain, and the disk’s angular velocity may even fall below the Keplerian value close to the star. Downstream, whatever angular momentum is deposited in the outermost layers must be redistributed through the interior, since a Be star is not a shell spinning over a sluggish core but a body rotating rapidly as a whole. The accreted mass is the lever: each increment of accreted material adds angular momentum in proportion to its share of the transfer, so a leaky system, which loses most of the donor’s envelope, delivers correspondingly little spin. The question was whether the lever remains long enough to matter, and whether fine adjustments at the disk’s inner edge could compensate for a wasteful exchange.

Inside the accreting star, Staritsin follows the redistribution of angular momentum through the two hydrodynamic mechanisms that modern stellar-evolution theory regards as dominant in radiative envelopes: meridional circulation and shear turbulence. Meridional circulation arises because rotation distorts the star’s thermal balance, driving large-scale currents that transport angular momentum vertically through the interior, with a direction and strength that respond to the angular-velocity gradients created as fresh, spinning material is added. Shear turbulence, fed by instabilities wherever adjacent layers rotate at different speeds, diffuses momentum down those gradients and carries the spin acquired at the surface into the deeper interior. The computations track the internal rotation profile continuously as the mass grows, so the redistribution of momentum and the growth of the star are treated as a single coupled process rather than separate stages. That coupling matters because the model must deliver a specific verdict: whether, at the end of the exchange, the accretor’s surface rotates fast enough to sustain the decretion disk that gives Be stars their emission-line signature.

The verdict is a blunt threshold: if the accreted mass accounts for more than 30 percent of the accreting component’s mass, the accretor obtains rotation typical of early Be stars; below that share, it emerges as an ordinary, moderately rotating B star. What makes the result striking is its stubbornness. Staritsin tested it against the four complications most likely to overturn it — the rotation of the accreting component before mass transfer began, the amount of angular momentum supplied by the boundary layer between the star and its accretion disk, a possible drop of the disk’s angular velocity below the Keplerian value near the stellar surface, and the efficiency of turbulence inside the accretor. None of them changed the outcome. Once the star has swallowed more than roughly a third of its mass in fresh material, the angular-momentum budget is large enough that plausible adjustments at the surface or within the interior cannot prevent the spin-up, and the star arrives at the near-critical rotation from which a decretion disk can be launched.

For researchers who model Be-star demographics, the threshold is immediately usable. Binary population synthesis must decide, star by simulated star, how efficiently mass is exchanged, and the result supplies a robust criterion: a close binary qualifies as a Be-star factory whenever the accretor’s mass grows by more than about 30 percent, regardless of how much of the donor’s envelope the system squanders. That widens the pool of viable progenitors, because observations of Algol-type systems and of Be X-ray binaries in the Small Magellanic Cloud indicate that real transfers are markedly nonconservative, and it aligns with evidence reported in 2025 that stripped donors hand over mass efficiently and leave their companions spinning rapidly. It also bears on Be X-ray binaries, in which the Be star’s disk feeds a neutron-star companion, since the gainer’s ability to reach disk-launching rotation under wasteful transfer helps set how many such systems a galaxy can produce. A criterion insensitive to fine details at the accretion interface is exactly what population codes need, because those details are the hardest to constrain observationally.

The study is deliberately economical: it is a hydrodynamic evolution model with parameterized treatments of the boundary layer and of interior turbulence, applied to a single final accretor mass of 16 solar masses, not a three-dimensional simulation of the gas flow, and it examines one donor stage — the Hertzsprung gap — rather than the full spread of binary configurations. Within those limits, the author’s series of papers has built the argument step by step, from spin-up during conservative exchange and transfer on the thermal timescale to the common-envelope stage, and the present work completes the sequence by tackling the nonconservative case that observers consider the realistic one. Testing the prediction against nature will require sharper statistics on binarity among early Be stars, interferometric images of their disks, and rotation censuses of young clusters, where the model’s most distinctive claim can be checked: because the outcome ignores the accretor’s initial spin and the fine print of the angular-momentum budget, binary-made early Be stars should cluster tightly at the same rotation rates no matter how their exchanges unfolded.

The upshot is a number that population modellers can insert directly into their codes: thirty percent. A star that retains mass equal to about a third of its own during an episode of Roche-lobe overflow is spun to the rotation characteristic of the early Be stars, while most of the transferred gas and angular momentum escapes into interstellar space. In that sense, the Galaxy’s most flamboyant rotators are manufactured from lopsided bargains in which the accretor keeps only a minority stake — and still ends up, quite literally, spinning the deal to its advantage.