Binary stars

Giannis Dellis�&�Manos Zapartas

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AstroFriday�9/1/2026

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Mass transfer

Roche potential

test particle around the binary system

Coriolis

Euler

centrifugal

• Circular orbit
• co-rotating frame of reference
• non-moving test particle

Roche potential

Source - Marc van der Sluys (2006)

q = M1/M2 = 2

Roche lobe

for

Eggleton 1983

Stars tend to expand during their evolution (and so they fill their Roche lobe)

Mass transfer

Mass transfer rate calculation

eq. (7.1-7.6) Pols notes

Hydro simulations of mass transfer rate

• e.g. taking into account the Coriolis force

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• Quite close to the analytical forms

Ryu et al. 2025

Orbital evolution during stable MT

Newtonian �two-body problem

Orbital evolution during stable MT

Conservative MT:

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• When the donor is more massive 🡪 orbit shrinks
• When the donor is less massive 🡪 orbit widens

Stability of mass transfer

Stellar radius vs Roche lobe radius

(M_total= 2 M_sun)

unstable expected when :

• mass ratio is extreme
• convective envelope donor

Common envelope evolution

Succesful envelope ejection:�short orbit binary

Merging of the two stars in one

vs

or better:

Impact in �stellar �evolution

mass�stripping

Stripped star

Evolution of a �stripped star in a binary

Götberg et al (2017)

mass gaining

Mass transfer

mass gaining

Merging

Credits: (ESO) / L. Calçada

70% of O-type stars are expected to interact with a close binary companion!

Adapted figure from Sana+2012, courtesy of S.E. de Mink

Kobulnicky+Fryer 2007; Eggleton+Tokovinin2008; Chini +2012; Kiminki+Kobulnicky 2012; Sana+2012; Dunstall +2015; Moe+DiStefano 2017; Almeida+al. 2017

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3-body system

Tidal forces

• Circularization
• Synchronization
• Co-rotation

Summary until now

• Binaries are common, especially for massive stars
• Powerful tool to infer stellar properties.
• Various observational techniques

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• Affects the evolution of both stars:
• Mass transfer
• mass stripping and mass and angular momentum gaining
• potentially unstable → common envelope and maybe merger
• Tidal forces

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Explosions in binary systems

Core collapse of �massive stars

White dwarf �thermonuclear explosion

Will the companion survive?

Hirai+2018

Supernova in binaries? �Possible binary disruption

For e>1:

eq. (2.27) Verbunt notes

eq. (2.28) Verbunt notes �for periastron

eq. (10.2) Pols notes

eq. (10.3) Pols notes

α_i

M₁

M₂

if no intrinsic kick at the compact object during the collapse

M₁-ΔΜ

periastron distance

Velocity in eccentric orbit

But intrinsic kicks �during the supernova explosion

α_i

M₁

M₂

If binary survives the supernova:�Potentially X-ray binary

If binary survives the supernova:�Potentially X-ray binary

If binary survives the supernova:�Potentially X-ray binary

Low mass X-ray binary

• Low mass donor
• Roche lobe overflow

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High mass X-ray binary

• High mass donor
• Wind-fed accretion

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Mass accretion onto compact object

Gravitational waves from coalescing compact objects!

Laser interferometer

Laser interferometer

First detection of binary black holes merging

GW150914

Two important �observational constraints

Chirp mass

How do we find compact objects �in close orbits?

How do we find compact objects �in close orbits?

time

Stellar black holes are observed�in binary systems!

Else they are invisible

Stellar black holes are observed�in binary systems!

Else they are invisible

Summary

• Binaries (and multiple systems) are common, especially for massive stars
• They affect the evolution of both stars:
• Mass transfer
• potentially unstable → common envelope and maybe merger
• Tidal forces

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• Core-collapse supernovae in binaries leads to compact object binaries
• X-ray binaries
• compact object mergers → gravitational wave sources

Questions?