Mass Transfer in BinariesPhilipp Podsiadlowski (Oxford)

• Understanding the physics of mass transfer is essential

for understanding binary evolution

• Simplest assumption: stable, “conservative” mass

transfer in a circular system from a synchronized,

Roche-lobe-filling donor with a ‘sharp’ surface boundary

I. Observational Constraints

II. Some basic principles

III. Key Issues

Observational Constraints

Symbiotic Binaries (S-type)

• should not exist

⊲ orbital periods are not explained

by simple binary evolution

⊲ tend to have mass ratios that

should lead to dynamically

unstable mass transfer

Hot Subdwarfs (sdBs)

• H-deficient, He-core burning,

low-mass stars (0.5 M⊙) with

well-defined history

→ ideal for testing both stable (wide

sdBs) and unstable (short-periods

sdBs) mass transfer

X-ray binaries

• observed X-ray luminosities much larger

than expected (irradiation effects?)

• the case of Cygnus X-2: an

intermediate-mass X-ray binary that

survived mass transfer with M ∼> 103 ˙MEdd

• the origin of low-mass black-hole binaries

• Super-Eddington accretion

Mass transfer in eccentric binaries

• VV Cephei systems: stable mass transfer

from red to blue supergiants with e ∼> 0.5

• recent: wide sdB binaries (post-RLOF

systems) have moderate eccentricities

(Østensen & Van Winckel [2012]; Deca

[2012]; Wade, Barlow [2012])

Some Basic Principles

The radius evolution

• M is determined by the relative evolution

of the donor’s radius and the Roche-lobe

radius (or equivalent)

⊲ difference between stars with radiative

and convective envelopes → different

response to rapid mass loss

⊲ RRL depends on mass ratio and

angular-momentum loss

Mass-driving mechanisms

• Evolutionary-driven mass loss

⊲ nuclear evolution (slow phases)

⊲ thermal evolution (Hertzsprung gap;

donors forced out of thermal

equilibrium)

⊲ irradiation-driven evolution

(mass-transfer cycles in L/IMXBs?)

• Evolution driven by systemic

angular momentum loss

⊲ gravitational radiation (well

understood)

⊲ magnetic braking (poorly

understood)

Angular Momentum

• accounting for the angular

momentum of all the components

(donor, accretor, disk, systemic mass

loss) is essential for understanding

the evolution of binaries (orbital

evolution, stability of mass transfer)

convective

radiative

radiative

convective

Podsiadlowski (2002)

Podsiadlowski et al. (2002)

Podsiadlowski et al. (2002)

The role of non-conservative masstransfer

• mass transfer is often very

non-conservative

• angular-momentum loss affects orbital

evolution

⊲ different prescriptions give very

different outcomes (e.g. can

stabilize/destabilize mass transfer)

⊲ no good theoretical model, weak

observational constraints

• sdB binaries: mass transfer in stable

systems has to be very non-conservative

to produce short-period sdB binaries

with WD companions (Han et al.

2002/2003)

• observed mass loss modes:

⊲ bipolar mass loss from the accreting

component (also Cyg X-2)

⊲ disk-like outflow (from accretion disk

or system?)

The criterion for dynamical mass transfer

• dynamical mass transfer is caused by a

mass-transfer runaway (giant expands, Roche lobe

shrinks)

⊲ for n = 1.5 polytrope:

q > qcrit = Mdonor/Maccretor = 2/3

• real stars have core-envelope structures

(Hjellming & Webbink 1987; Ge et al. 2010)

• the outer layer is non-adiabatic (e.g., Tauris,

Podsiadlowski, Han, Chen, Passy)

⊲ real stars: qcrit ≃ 1.1 − 1.3 for

(non-conservative; much smaller qcrit for

conservative case [Chen & Han 2008])

• tidally enhanced mass loss (CRAP) (Eggleton,

Tout)

• break-down of mixing-length theory before mass

transfer becomes dynamical (Paczynski &

Sienkiewicz 1972; → Pavlovskii)

.

Common-envelope evolution and ejection

• dynamical mass transfer leads to a CE and

spiral-in phase

• if envelope is ejected → short-period binary

(Paczynski 1976)

• CE ejection criterion?

• qualitatively: αCE |∆Eorb| > Eenv

• energy criterion (necessary, but not sufficient)

• other possible energies

⊲ recombination energy

⊲ accretion energy

⊲ nuclear energy (possibility of explosive CE

ejection)

• long-lived initial phase in synchronized binary

→ pre-expansion?

Sawada et al. (1984)

Atmospheric RLOF

• some symbiotics show ellipsoidal light

curve variations (Miko lajewska,

Gromadzki)

→ Roche-lobe filling (or at least close)

despite large mass ratio (∼> 3)

• M ∝ exp[−(RRL − R)/Ratm] (e.g.

Ratm = HP; Ritter 1988)

• real giants: Ratm ≫ HP

• RLOF of extended atmosphere (e.g.

Pastetter & Ritter 1989)

• short-lived phase (up to 105 yr)

• important to understand for estimating

rates of symbiotics

symbiotic phase

Chen et al. (2010)

⊲ MRG = 1.5 M⊙, MWD = 0.75 M⊙

⊲ Pinorb = 300 d

The Orbital Period Distribution of S-TypeSymbiotics with WDs

• orbital period range: 200 – 1400 d

Problem:

⊲ these systems must have experienced a previous

mass-transfer phase

⊲ most likely dynamically unstable mass transfer

(common-envelope [CE] phase) → spiral-in phase →

much closer orbits expected

⊲ or stable mass transfer, which should led to a

widening of the systems

• need stable mass transfer with a lot of mass loss and

little orbital shrinkage (Webbink 1986)

• the role of circumbinary disks (formation?)

Main Goal:

• understand the evolutionary connection between

different types of binaries

e.g.: AGB mass transfer → circumbinary disks → post-AGB

binaries (pre-symbiotics) → S-type symbiotics → Type

Ia supernovae?

Quasi-dynamical mass transfer?

• need a different mode of mass

transfer (Webbink, Podsiadlowski)

• very non-conservative mass transfer

but without significant spiral-in

• also needed to explain the properties

of double degenerate binaries

(Nelemans), υ Sgr, etc.

• transient CE phase or circumbinary

disk (Frankowski, Dermine)?

Transient Common-Envelope Phase

(Podsiadlowski et al. 1992)

• q ∼> qcrit: temporary (∼ 104 yr) CE phase

with moderate spiral-in (no differential

rotation!) (similar to γ-mechanism

proposed by Nelemans)

⊲ moderate shrinking of orbit (as implied

by observations; Miko lajewska)

⊲ accretion of RG/AGB material?

(observations!)

⊲ formation of circumbinary disk (→

eccentric post-AGB binaries, barium

stars [Dermine & Jorissen]) (outflow

from L2/L3 or left-over CE)

Pols (1994)

The Early Case B Problem

• mass transfer in the Hertzsprung

gap (radiative envelopes) is

dynamically stable for large mass

ratios: qcrit ∼ 3 − 4 (e.g., Eggleton,

Han, Podsiadlowski, . . .)

• but: the accretor cannot ‘accept’

transferred mass (Pols 1994;

Wellstein & Langer 2001, . . .) →

contact phase even for q quite close

to 1

• → transient contact phase or

merger?

Non-Synchronicity

• for large mass ratio, synchronization

is impossible

• origin of the Darwin instability

• modified ‘Roche-lobe’ radius (e.g.

Avni 1982)

• but: depends on angular momentum

transport inside the tidally forced

star

Eccentricity

• post-RLOF sdBs have moderate

eccentrities

• incomplete circularization even for

q ∼< 2?

Kippenhahn & Meyer-Hofmeister (1977)

Petrovic, Langer & van der Hucht (2005)

The Role of the Accreting Star

• the accreting star expands if

tacc > tenvtherm (depends on entropy of

the accreted material; e.g. Shaviv;

Stahler [80s])

• a star only has to accrete a few % of

its total mass to be spun up to

critical surface rotation (Packet

1981)

• what happens to the angular

momentum?

⊲ angular momentum transport

inside accretor

⊲ mass loss from the system

(Langer et al.)

⊲ feedback to the orbit: the role of

the disk (e.g. Paczynski; Marsh)

The Symbiotic Binary Mira AB

• wide binary (Porb ∼ 400 yr), consisting of

Mira A (Ppuls ≃ 330 d) and an accreting

white dwarf

• M ∼ 10−7 M⊙ yr−1

Observations:

• soft X-rays (Chandra, Karovska et al.

2005) from both components (shocks in

the wind of Mira A and from accretion

disk)

• the envelope of Mira is resolved in X-rays

and the mid-IR (Marengo et al. 2001)

⊲ the slow wind from Mira A fills its

Roche lobe (RRL ∼ 25 AU)

⊲ but: radius of Mira A: 1 – 2 AU

• a new mode of mass transfer(?): wind

Roche-lobe overflow

• important implications for D-type sym-

biotics

Wind Roche-Lobe Overflow

• a new mass-transfer mode for wide

binaries

• high mass-transfer fraction (compared

to Bondi-Hoyle wind accretion) → more

efficient accretion of s-process elements

for the formation of barium stars

(without circularization)

• accretion rate in the regime where WDs

can accrete? → increase the range for

SN Ia progenitors (but may not be

efficient enough)

• asymmetric system mass loss →

formation of circumstellar disks and

bipolar outflows from accreting

component (e.g. OH231.8+4.2)

→ shaping of (proto-)planetary nebulae

⊲ binaries with longer orbital periods

important

Case D Mass Transfer

• extension of case C mass transfer,

but potentially more important

(possibly larger orbital period range)

• also: massive, cool supergiants with

dynamically unstable envelopes (e.g.

Yoon & Langer)

• large mass loss just before the

supernova?

• possible implications for Type II-L,

IIb supernovae (increases rate

estimates), SN 2002ic

• delays onset of dynamical mass

transfer

→ produces wider S-type

symbiotic binaries (i.e. solve

orbital period problem)

→ solve the problem of black-hole

binaries with low-mass

companions