The Evolution of Binary Star Systems

Core Concepts

The Roche lobe

Around each star in a binary is a teardrop-shaped region called its Roche lobe — the volume within which material is gravitationally bound to that star. Between them lies a gravitational saddle point, the inner Lagrange point (L1). As long as both stars fit inside their lobes, no matter is exchanged and they evolve like isolated stars. But when a star expands — as red giants do — and fills its Roche lobe, gas spills through L1 onto the companion.

Accretion disks

Gas transferred to the companion cannot fall straight down; it has angular momentum, so it spirals into a flat accretion disk around the receiving star. Friction heats the disk, converting gravitational potential energy into radiation. Around a compact object (white dwarf, neutron star, or black hole), infalling gas reaches millions of kelvin and shines in X-rays — a disk can outshine its own star. The disk also feeds mass and angular momentum onto the accreting star.

The Algol paradox

The star Algol (β Persei) seemed to defy stellar evolution: its more massive star is an unremarkable main-sequence star, while its less massive star is a more-evolved subgiant. Since massive stars evolve sooner, the more evolved star should be the more massive one. The paradox dissolves once mass transfer is included: the originally massive star evolved first, swelled, and dumped much of its mass onto its companion. The star we now see as massive is the gainer; the subgiant is the loser that gave away its mass. In interacting binaries, current mass does not reveal original mass.

Four classic outcomes

• White dwarf + ordinary star → nova and Type Ia supernova. Hydrogen from the companion accumulates on the white dwarf and detonates in a nova — a surface flash that does not destroy the star and can repeat. But if the white dwarf accretes enough mass to approach the Chandrasekhar limit (~1.4 solar masses), carbon fusion ignites throughout and the star is completely destroyed in a Type Ia supernova. Because these explosions all occur at nearly the same mass, they share nearly the same peak luminosity — making them standard candles for measuring distance.
• Neutron star or black hole + star → X-ray binary. Gas pulled from the companion (by a stellar wind or Roche-lobe overflow) forms a hot accretion disk around the compact object, emitting X-rays. Cygnus X-1, a black hole candidate paired with a blue supergiant, was the first widely accepted example.
• Neutron star + low-mass star → millisecond pulsar. Accretion transfers angular momentum to an old neutron star, spinning it up to hundreds of rotations per second — the millisecond pulsars of the previous topic.
• Two compact objects merge. If both stars become compact remnants and the orbit shrinks via gravitational-wave emission, they spiral together. The 2017 event GW170817 — gravitational waves from a neutron-star merger followed 1.7 seconds later by a gamma-ray burst and a "kilonova" — confirmed this channel; mergers also forge heavy elements like gold.

Unstable mass transfer: the common envelope

Mass transfer is not always gentle. If the donor expands faster than the companion can absorb gas, the pair becomes engulfed in a common envelope — a shared outer atmosphere. Drag makes the cores spiral inward, ejecting the envelope. The outcome is a much closer binary or a merger — the origin of the tightest binaries.

Common Confusions