Mass Transfer in Binaries Philipp 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 (0.5M ) 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 Ṁ > 10 3 M Edd 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 Ṁ 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 R RL depends on mass ratio and angular-momentum loss Mass-driving mechanisms Evolutionary-driven mass loss 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) nuclear evolution (slow phases) thermal evolution (Hertzsprung gap; donors forced out of thermal equilibrium) irradiation-driven evolution (mass-transfer cycles in L/IMXBs?)
convective radiative radiative convective Podsiadlowski (2002)
Podsiadlowski et al. (2002)
Podsiadlowski et al. (2002)
The role of non-conservative mass transfer 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 > q crit = M donor /M accretor = 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: q crit 1.1 1.3 for (non-conservative; much smaller q crit for conservative case [Chen & Han 2008]) tidally enhanced mass loss (CRAP) (Eggleton, Tout) break-down of mixing-length theory before mass transfer becomes dynamical (Paczyński & Sienkiewicz 1972; Pavlovskii)
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Common-envelope evolution and ejection dynamical mass transfer leads to a CE and spiral-in phase if envelope is ejected short-period binary (Paczyński 1976) CE ejection criterion? qualitatively: α CE E orb > E env 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) Ṁ exp[ (R RL R)/R atm ] (e.g. R atm = H P ; Ritter 1988) symbiotic phase real giants: R atm H P RLOF of extended atmosphere (e.g. Pastetter & Ritter 1989) short-lived phase (up to 10 5 yr) important to understand for estimating rates of symbiotics Chen et al. (2010) M RG = 1.5M, M WD = 0.75M P in orb = 300d
The Orbital Period Distribution of S-Type Symbiotics with WDs orbital period range: 200 1400d 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 > q crit : temporary ( 10 4 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)
The Early Case B Problem mass transfer in the Hertzsprung gap (radiative envelopes) is dynamically stable for large mass ratios: q crit 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? Pols (1994)
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?
The Role of the Accreting Star Kippenhahn & Meyer-Hofmeister (1977) the accreting star expands if t acc > t env therm (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. Paczyński; Marsh) Petrovic, Langer & van der Hucht (2005)
The Symbiotic Binary Mira AB wide binary (P orb 400yr), consisting of Mira A (P puls 330d) and an accreting white dwarf Ṁ 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 envelopeof Mira is resolvedin X-rays and the mid-ir (Marengo et al. 2001) the slow wind from Mira A fills its Roche lobe (R RL 25AU) but: radius of Mira A: 1 2AU a new mode of mass transfer(?): wind Roche-lobe overflow important implications for D-type symbiotics
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