Binary Evolution in the Light of Barium and Related Stars
Tyl Dermine
Thesis submitted for the degree of Ph.D. in Sciences
Binary Evolution in the Light of Barium and Related Stars
Tyl Dermine
Thesis submitted for the degree of Ph.D. in Sciences
Binary Evolution in the Light of Barium and Related Stars
Tyl Dermine
Promotor: Prof. Alain Jorissen Co-promotor: Dr. Lionel Siess
Thesis submitted for the degree of Ph.D. in Sciences
Brussels 2011
Hopefully, nobody turned on the light of the Universe.
Dermine T.
Résumé 1
Preface 3
1. Evolution of Low- and Intermediate-mass Single Stars 5
1.1. Pre-AGB stellar evolution . . . 5
1.1.1. From birth to main sequence . . . 5
1.1.2. The red giant branch and the horizontal branch . . . 7
1.2. The asymptotic giant branch . . . 7
1.2.1. The early asymptotic giant branch . . . 7
1.2.2. The thermally pulsing asymptotic giant branch . . . 8
1.2.3. From the superwind phase to white dwarf stage . . . 10
1.3. Nucleosynthesis during the TPAGB . . . 10
2. Physics of Interacting Binary Stars 13 2.1. The "binary_c" population synthesis code . . . 13
2.2. Roche lobe overow . . . 15
2.2.1. The Roche Model . . . 15
2.2.2. Roche lobe overow . . . 16
2.2.3. Stability . . . 17
2.3. Common envelope evolution . . . 18
2.3.1. Theα formalism . . . 20
2.3.2. Theγ formalism . . . 21
2.4. Wind mass transfer . . . 21
2.5. Tidal eects . . . 24
3. Evolution of low- and intermediate-mass Binary Stars 25 3.1. Barium star formation . . . 25
3.2. A binary evolutionary sequence . . . 29
3.2.1. Carbon stars . . . 29
3.2.2. Post-AGB stars . . . 32
3.2.5. CH stars . . . 34
3.2.6. Carbon enhanced metal poor stars . . . 35
3.2.7. S stars . . . 35
3.2.8. Yellow symbiotic stars . . . 36
3.3. Frequencies of extrinsic stars . . . 37
3.4. Outline of the Thesis . . . 38
4. Orbits of Barium and Related Stars 39 4.1. Introduction . . . 39
4.2. Radial-velocity monitoring with the HERMES spectrograph . . . 40
4.3. Individual radial velocities . . . 43
4.4. New orbits from the HERMES survey . . . 44
4.4.1. Barium stars . . . 44
4.4.2. Barium dwarfs . . . 49
4.4.3. S stars . . . 51
4.4.4. S symbiotics . . . 52
4.4.5. CH stars . . . 54
4.5. Period-eccentricity diagrams and remaining problems . . . 56
4.5.1. Population I stars . . . 59
4.5.2. Population II stars . . . 64
4.5.3. Discussion . . . 66
5. Radiation Pressure and Pulsation Eects on the Roche lobe 67 5.1. Introduction . . . 67
5.2. The dierent modes of wind mass loss . . . 68
5.3. The eective potential . . . 69
5.4. How to correctly account for radiation pressure . . . 71
5.5. Typical f values . . . 73
5.6. The modied Roche equipotentials . . . 75
5.7. The RLOF criterion . . . 78
5.7.1. The modied Roche radius . . . 78
5.7.2. RLOF stability . . . 79
5.7.3. Critical period . . . 80
5.7.4. Radiation pressure eect on chemically peculiar stars . . . 81
5.7.5. No RLOF forf >1 . . . 81
5.7.6. Pulsation-driven winds: The case of Mira stars . . . 83
5.8. Conclusions . . . 87
6. White-Dwarf Kicks and Implications for Barium Stars 89 6.1. Introduction . . . 89
6.2. Modelling Ba stars with white-dwarf kicks . . . 91
6.3.2. White-dwarf kicks . . . 93
6.3.3. Common envelope evolution . . . 93
6.3.4. Orbital angular momentum . . . 94
6.4. Discussion . . . 96
6.4.1. Fast and slow kicks and in which direction? . . . 96
6.4.2. Disrupted systems . . . 97
6.4.3. Mass loss, the angular momentum budget and Mira . . . 97
6.4.4. Mild vs strong barium stars . . . 98
6.4.5. Implications for planetary nebulae . . . 99
6.5. Conclusions . . . 99
7. Circumbinary Discs: from Post-AGB to Barium Stars 101 7.1. Introduction . . . 101
7.2. Circumbinary discs . . . 102
7.2.1. Formation . . . 103
7.2.2. Evolution . . . 103
7.2.3. Resonant interaction . . . 105
7.2.4. Eccentricity gap . . . 106
7.3. Modelling binaries with circumbinary discs . . . 107
7.3.1. Circumbinary disc model . . . 107
7.4. Simulated post-AGB and Ba-star populations . . . 110
7.4.1. Common envelope evolution . . . 110
7.5. Binary evolution with CB disc . . . 111
7.5.1. Typical evolutionary tracks for CB disc models . . . 111
7.5.2. Synthetice−logP diagrams following CB interaction . . . 112
7.5.3. Ecient angular momentum loss . . . 118
7.6. Uncertainties of the model . . . 119
7.7. Discussion . . . 120
7.7.1. Orbital parameters of post-AGB and Ba progenitor systems . . . . 120
7.7.2. Post-AGB stars as Ba star progenitors? . . . 122
7.7.3. CB disc vs white dwarf kicks . . . 122
7.8. Conclusions . . . 123
8. Conclusions 125 A. Appendix 131 A.1. A complete set of orbital elements . . . 131
A.2. Radial velocities . . . 138
A.2.1. Ba stars . . . 138
A.2.2. Ba dwarf . . . 143
A.2.3. S stars . . . 144
A.2.4. CH stars . . . 146
Bibliography 151
List of Acronyms 165
Si l'évolution des étoiles simples est relativement bien comprise, l'étude des étoiles bi- naires, qui représentent la majorité des étoiles, nécessite encore des progrès majeurs, par- ticulièrement en ce qui concerne leurs diérents modes d'interactions. Dans ces systèmes, la composition de surface d'une étoile peut être altérée non seulement par l'accrétion d'éléments synthétisés au sein de l'étoile compagnon, mais également par des proces- sus de mélanges internes induits par les forces de marées et d'un transport du moment angulaire. Plusieurs classes d'étoiles post-transfert de masse (les étoiles à baryum, CH et S) possèdent eectivement des compositions de surface caractérisées par la présence d'éléments lourds, tel que le baryum. Ces systèmes sont présumés se former au sein de systèmes binaires incluant une étoile de la branche asymptotique des géantes (appelé étoile AGB). Ces dernières sont des étoiles remarquables qui représentent l'unique site d'une nucléosynthèse particulière. En eet, elles constituent les contributeurs essentiels de la production de uor ou de baryum. Les étoiles AGB sont également caractérisées par une importante perte de masse par vent qui ejecte progressivement leur enveloppe en- richie en ces éléments. Au sein d'un système binaire, une partie de ce vent est accretée par l'étoile compagnon et pollue ainsi sa surface, laissant une signature spectrale distincte qui subsistera longtemps après que l'étoile AGB ait disparu. Ce scénario est suggeré comme étant responsable de la formation d'une grande variété d'étoiles chimiquement particulières, tels que les étoiles à baryum.
Cependant, plusieurs propriétés clés de ces systèmes, en particulier leurs distribu- tions de périodes orbitales et d'excentricités, demeurent inexpliquées depuis des décen- nies. L'incapacité de nos modèles à reproduire ces propriétés orbitales met en évidence notre compréhension limitée des mécanismes d'interaction qui gouvernent l'évolution des systèmes binaires. Plus particulièrement, des mécanismes qui génèrent des orbites ex- centriques au sein des étoiles à baryum et des systèmes analogues sont requis. Nous examinons ainsi la possibilité qu'à sa naissance l'étoile naine blanche subisse un kick ou que la présence d'un disque entourant le système binaire soit à l'origine des fortes excen- tricités observées chez les étoiles à baryum. Ces deux mécanismes permettent pour la première fois depuis l'étude de ces systèmes d'apporter une solution à ces problèmes.
Il est montré comment comprendre les signatures induites par un compagnon étoile
travail.
If the evolution of single stars seems to be fairly well understood, our knowledge of the evolution of binaries, which represent the majority of stars, still needs major improvements, especially concerning their multiple ways of interacting. In these systems, the star surface composition may be altered not only by accretion of nucleosynthesis products from a companion, but also by internal mixing processes induced by tidal forces and angular momentum transport. Several classes of post-mass-transfer binary stars (like barium, extrinsic S, CH and many carbon-enriched metal-poor stars) indeed exhibit peculiar surface compositions characterized by overabundances of heavy elements. These classes of stars are believed to form in binary systems involving a star on the asymptotic giant branch (AGB). The latter are very interesting objects as they present a unique site for a rich nucleosynthesis. They are indeed the main contributors to the production of elements such as uorine (essential in our lives as needed in toothpaste) or barium. AGB stars are also characterised by strong mass loss that ejects their envelope enriched by these heavy elements. A fraction of this wind is accreted by the companion star and thus pollutes its surface with heavy elements that will remain apparent long after the AGB star has disappeared.
Several key properties of these systems, in particular their eccentricity and orbital- period distributions still remain unexplained despite decades of research and challenge our basic understanding of binary-star physics. The inability of models to reproduce these orbital parameters highlights our limited knowledge of the binary interaction mechanisms.
They call for mechanisms which generate eccentricity in barium and related systems. We thus investigate the possibility that kicks imparted to the white dwarfs at their birth and the presence of a disc surrounding the binary system are the cause of their high eccentricities. These mechanisms are key ingredients that have to be taken into account in binary evolution and represent the rst reasonable solution of this problem.
Understanding the signatures imprinted by an AGB companion and correlate them with the orbital properties of the binary will be shown to be very important to test and improve our understanding of binary star evolution; the aim of this work.
they are responsible for the formation of chemically peculiar stars. We also identify the main interactions which take place in binary systems (Chap. 2) and nally describe the evolution of binaries (Chap. 3). This introduction is followed by an outline of the thesis, presented in Sect. 3.4. In this thesis, we focus more particularly on the evolution of systems which lead to the formation of chemically peculiar stars such as the barium stars as its maingoal is to explain their orbital properties. We then collect their orbital elements completed by newly derived orbits (Chap. 4). It is shown how binary evolution models fail to reproduce their orbital properties. We then try to solve this problem by considering improved or additional mechanisms. Namely, a mass transfer mechanism is improved to take into account the eects of radiation pressure and stellar pulsations (Chap. 5) and we investigate the possibility that white-dwarf kicks (Chap. 6) or the presence of a circumbinary disc (Chap. 7) are the cause of the high eccentricities of chemically peculiar stars.
Chapter 1
Evolution of Low- and Intermediate-mass Single Stars
The evolution of stars is primarily governed by their mass and chemical composition.
Therefore one can dene dierent classes of stars based on their initial mass. The stars studied in this thesis are the low- and intermediate-mass stars, i.e. with masses ranging from about0.9to 6.0 M. A qualitative picture of the main phases of evolution of these stars is sketched in the following sections and their evolution in the Hertzsprung-Russell (HR) diagram is illustrated in Fig. 1.1. Lower mass stars (M .0.9M) basically evolve on lifetimes longer than the age of the universe. At higher masses (M &10 M), stars are considered to be massive and end up as supernovae, leaving a neutron star or black hole remnant. In the intermediate range (6.0 . M/M . 10), stars are referred to as super-AGB stars. Massive stars follow a very dierent evolution and are not related to classes of stars studied here. They are thus not considered in this work.
The next sections are inspired from Van Eck (1999).
1.1. Pre-AGB stellar evolution
1.1.1. From birth to main sequence
The life of a star begins with the gravitational collapse of an interstellar molecular cloud.
The star reaches the zero-age main-sequence (MS) when the contraction of the star brings its core to reach high enough temperatures to convert hydrogen into helium through nuclear fusion (T &107 K). This energy production allows the star to be in thermal and hydrostatic equilibrium, when outward thermal pressure from the core is balancing the inward gravitational pull from the overlying layers. At this stage, the star evolves on a nuclear timescale (∼11×109 years for the Sun), that encompasses about 70 to 90% of its lifetime.
1.1 Pre-AGB stellar evolution
1 2C ( p ,g )1 3N (b + )1 3C ( a , n )1 6O . . .
c e n t e r
t i m e
L m(r)
H e b u r n i n g H b u r n i n g
p u l s e i n t e r p u l s e
s e m i - c o n v e c t i o n
c o r eH e
convective envelope
Hs h e l l R G B c o r eC O
c onv ec ti ve
envelope
H
s h e l l T P A G B
H e s h e l l
m a i n s e q u
e n c e c o r e H e b u r n i n g
s h e l l H e b u r n i n g
1 s t t h e r m a l p u l s e
EAGB TPAGB
T e f f p o s t - A G B
d r e d g e - u p h e a v y e l e m e n t s p r o d u c t i o n
o f h e a v y e l e m e n t s
c o r e H b u r n i n g
Figure 1.1.: Schematic evolution of a sun-like star in the Hertzsprung-Russell diagram, i.e. a graph showing the relationship between the stars luminosity and its eective temperature. With the courtesy of Sophie Van Eck (Van Eck, 1999).
1.1.2. The red giant branch and the horizontal branch
When hydrogen is exhausted in the core, nuclear reactions stop at the centre but continue in a burning shell surrounding a contracting core. The higher energy production of the hydrogen burning shell produces an expansion of the envelope, resulting in a lower surface temperature and a fast migration through the Hertzsprung gap towards the red (see Fig. 1.1). As the star reaches the Hayashi limit, convection primarily limited to the outer layers extends deeply inward from the surface and penetrates into the region where partial H-burning has occurred previously. This material enriched by the products of CNO cycling, primarily14N and13C are mixed in the convective envelope, reducing the surface12C/13C ratio. The phase characterising the deepening of the convective envelope is known as the rst dredge-up.
Stars spend about 5% to 12% of their life as red giants. Most red giant branch (RGB) stars are classied as G and K giants (in the Harvard classication), corresponding to eective temperatures in the range 3620 ≤ Teff/K ≤ 5150 (Jaschek & Jaschek, 1995).
Note that the stellar evolutionary phase is dicult to determine because at the same eective temperature two stars of distinct mass may have the same luminosity (e.g. pre- MS and RGB stars).
As the star ascends the giant branch the helium core continues to contract. If the star is less massive than∼2.2M, the helium core becomes electron-degenerate and helium combustion starts o-centre at the point of maximum temperature. Since in this plasma, temperature and density are decoupled, the triple-α ignition of helium is explosive. It is referred to as the (core) helium ash. Following this, the star quickly moves in the HR diagram on the horizontal branch, where it burns helium hydrostatically in a convective core. This phase represents ∼7.5×108 years for a solar-metallicity 1 M star.
The intermediate-mass stars (1.8−2.2.M .6 M) ignite He under non-degenerate conditions at the centre and avoid a runaway situation, such as the core helium ash in low-mass stars.
1.2. The asymptotic giant branch
Understanding the evolution of binaries involving an asymptotic giant branch (AGB) star obviously requires a knowledge of its structure and evolution, which is the aim of this section. Binary systems involving an AGB star may produce remarkable signatures on their companion long after it has turned into a white dwarf. Peculiar classes of objects, like barium, CH, carbon-enhanced metal-poor and S stars are thought to originate from such an evolution (see Sect. 3.2) which explains the importance of describing it.
1.2.1. The early asymptotic giant branch
When the central helium is exhausted, the star starts burning helium in a shell sur- rounding a degenerate carbon-oxygen core and ascends the giant branch for the second time. Its path in the HR diagram (see Fig. 1.1) is almost aligned with its previous red
giant track, hence the name asymptotic giant branch or AGB. These stars are usually associated to M-type stars, showing eective temperatures lower than 3620 K (Jaschek
& Jaschek, 1995).
The structural readjustment to helium-shell burning results in a strong expansion of the envelope, and for stars with masses greater than ∼4 M, the hydrogen shell is temporarily extinguished as the star begins its ascent on the AGB. The inner edge of the convective envelope is thus free to penetrate the extinct hydrogen shell, and mix to the surface the products of complete hydrogen burning. This is the second dredge-up, that further reduces the12C/13C ratio, enhances the14N abundance, and slightly reduces the
16O abundance.
Following this, the hydrogen shell re-ignites. Due to the core contraction, the he- lium and hydrogen burning shells narrow and get closer to each other (Iben, 1967).
At this stage the structure is qualitatively similar for all masses: (i) a very compact CO core (Mcore ∼ 0.5 to 1 M, Rcore ∼ 10−4R∗) which grows in mass by accreting nuclear-processed matter from the H and He burning shells; (ii) a thin radiative layer (∼ 10−2 M) occupied by the helium and hydrogen burning shells separated by the intershell (Fig. 1.2), and (iii) an extended convective envelope (several 10 or 100 of R).
1.2.2. The thermally pulsing asymptotic giant branch
The thin helium burning shell becomes thermally unstable and experiences periodic out- bursts called thermal pulses (see Fig. 1.2). Since the emergence of the rst thermal pulse, the remaining evolution on the AGB is referred to as the thermally-pulsing AGB (or TPAGB) phase, and former evolution on the AGB as the early AGB (or EAGB). To give an idea, for a 1 M star the EAGB lasts for about5×106 years, and the TPAGB
∼ 5×105 years. This evolutionary phase is crucial as it is when heavy elements are produced (see Sect. 1.3) and does account for the formation of chemically peculiar stars (see Sect. 3.1).
Thermal pulses are instabilities resulting from the high temperature sensitivity of the rate of helium burning combined with the thinness of the shell in which it occurs (Schwarzschild & Härm, 1965). When energy is dumped into a shell within a star, this shell expands and thus lifts the above layers upward. Being pushed further away from the centre of the star, those layers will have a decreasing weight. Since the pressure in the considered shells is directly caused in hydrostatic equilibrium by the weight of the overlying layers, the pressure will drop. Now if the shell in question is thin (like the burning shells in low- and intermediate-mass stars), it can undergo a substantial expansion with a large fractional drop in density, but only lift the overlying layers by a small fraction of their radial distance to the centre. Consequently, the pressure drop within the shell will be small compared to the density drop. Then, according to the classical gas law, the temperature will actually rise. If this shell contains a substantial source of nuclear energy whose production rate is very temperature dependent, the rise in temperature will cause a further energy gain. Provided the shell has a high enough optical thickness, the energy loss will be smaller than the gain.
Hence an energy gain leads to a thermal runaway in a shell that is (1) suciently
Figure 1.2.: Stellar structure during thermal pulses. The top panels describe the struc- ture of the intershell during thermal pulses, where the dashed region are convective, the green and blue lines are respectively the H and He burning shells. The middle and lower panels represent the changes in radius and in luminosity from the H (black line) and He burning shell (red line).
thin that perturbations in it do not aect the hydrostatic structure of the star, and (2) suciently optically thick that it does not lose easily the excess thermal energy.
This instability becomes a thermal pulse if it is strong enough to require a convective transport of the energy in the helium shell (i.e. if the radiative gradient exceeds the adiabatic gradient).
The thermally-pulsing AGB may be seen as a succession of four phases (see e.g. Pols
& Tout, 2001), and this cycle goes on until mass loss has left an envelope of∼10−2 M: 1. the quiescent helium-hydrogen double-shell burning: This phase refers to the inter- pulse in the right panel of Fig. 1.2. Almost all of the surface luminosity is provided by the hydrogen shell. This phase lasts for 103 to 105 years, depending on the core mass (the smaller the core mass, the longer the phase). In stars more massive than ∼ 4 M, non-negligible hydrogen-burning can take place at the base of the convective envelope: this phenomenon is called hot bottom burning (e.g. Lattanzio et al., 1997). In this situation, the processed matter is immediately convected to the stellar surface.
2. the thermal-pulse phase: the thermal instability develops in the helium-burning shell, producing a convective zone that extends from the helium shell almost to the hydrogen-shell and lasts for a few102 years (referred to as a pulse in the left panel of Fig. 1.2). This convective zone is made of helium and12C.
3. the hydrogen-o phase: the helium shell dies down and the convection is shut-o.
The energy released previously during the pulse drives a substantial expansion,
pushing the hydrogen-shell to such low temperatures and densities that it is ex- tinguished. A phase of slow helium burning starts, that will last a few thousand years.
4. dredge-up phase: the convective envelope after being pushed to larger radii extends inward and may, after a certain number of pulses, penetrate into the formerly convective helium-burning zone. This phenomenon is called third dredge-up (3DUP, see Fig. 1.2). It results in freshly produced 4He, 12C and heavy elements (see Sect. 1.3) being mixed to the surface by envelope convection (Iben & Renzini, 1983; Boothroyd & Sackmann, 1988; Mowlavi, 1999). The star contracts back and the hydrogen-shell is re-ignited, re-starting at step 1. Note that the third dredge-up is expected to be ecient for stars more massive than ∼ 1.5 M and stops when the envelope becomes less massive than∼0.5 M.
1.2.3. From the superwind phase to white dwarf stage
A superwind is activated in the last∼104 yr of the high-luminosity AGB phase. During that stage the star ejects its remaining envelope through a heavy mass loss (i.e., a super- wind of ∼10−4 M/year). The asymptotic giant branch evolution is terminated when the mass of the envelope decreases below∼0.01 M.
At this stage the star evolves o the AGB toward higher temperatures at constant luminosity (see Fig. 1.1); it is called the post-AGB phase or equivalently proto-planetary nebula phase. This phase is believed to be short with respect to the previous TPAGB phase and strongly dependent on the core mass of the star (see Eq. 4.3). From single star model, predicted lifetimes of post-AGB stars are of the order 103 to 105 years. There is however no observation which constrain these lifetimes.
When the eective temperature of the central star reaches ∼ 30,000 K, the circum- stellar material ejected during the superwind phase is ionised and becomes a planetary nebula (PN). When the nebula is dispersed, the central star turns into a white dwarf (WD). Single white dwarfs in the solar neighbourhood present the interesting property that their mass distribution is strongly peaked around0.6±0.2M (Weidemann, 1990).
1.3. Nucleosynthesis during the TPAGB
Many observations have demonstrated that AGB stars are enriched with carbon and specic heavy elements (like Sr, Y, Zr, Tc, Ba), implying that these elements have been synthesized in the interiors of the stars and dredged up to the stellar surface.
Carbon: The repeated operation of the third dredge-up after each thermal pulse is responsible for the periodic envelope enrichment in12C. If enough dredge-ups have time to occur before the stellar envelope is entirely stripped, an AGB star whose initial surface C/O ratio is less than 1, will turn into a carbon-rich star, with C/O>1.
Note also that as the amount of 12C initially present in the envelope decreases with the metallicity, less third dredge-ups are needed at low metallicity for the star to become C-rich (i.e. C/O> 1). We then naturally expect more C-rich TPAGB stars at low metallicity (see Fig. 8.1).
s-process elements: In AGB stars, the heavy elements observed to be overabun- dant are known to be produced by the s-process nucleosynthesis (where "s" stands for slow). The s-process involves a neutron-capture reactions starting on iron seed nuclei that requires low neutron densities so that neutron captures occur on timescales that are long enough to enable unstable nuclei toβ-decay before absorbing another neutron. The s-process nucleosynthesis produces nuclides along the valley of beta-stability. In fact it imprints a very clear signature on its product nuclei, in the form of overabundance peaks for nuclei with a closed neutron shell (i.e. which have a smaller neutron-capture cross section), one around strontium (Sr), another around barium (Ba), a third one around lead (Pb), which are precisely those observed as overabundant in carbon stars (Smith &
Lambert, 1985, 1990).
Technetium (Tc) is a particularly interesting element, all isotopes being unstable. 99Tc, the only technetium isotope produced by the s-process, has a half-life of∼213,000years, which is short compared to the star's lifetime. Hence technetium plays a key diagnostic role in identifying recent s-processing stars, serving as a marker of TPAGB stars (see Sect. 3.2.7).
In AGB stars, the neutrons required for the s-process are mainly produced by α- captures on13C in a thin layer below the convective envelope. The13C can be synthesised through
12C(p, γ)13N(β+)13C,
when at the time of the deepest extent of the envelope during the third dredge-up, protons are injected in the C-rich layers of the pulse. However the physical mechanism responsible for injecting protons is still largely unknown. The amount of protons has also to be small enough not to complete the CN cycle through 13C(p, γ)14N, so that the amount of 14N, a neutron poison, remains small compared to 13C. In evolutionary codes, the amount of 13C, called the 13C pocket, represents the main uncertainty in the prediction of the production of s-process elements.
After the proton injection, when the temperature in the mixed layers reaches ∼ 9× 107 K, neutrons are released by
13C(α,n)16O.
See Goriely & Siess (2004) for more details.
The s-process eciency is expected to increase with decreasing metallicity because the number of neutrons available per seed iron nucleus is larger at lower metallicities. This leads to the prediction that at very low metallicity ([Fe/H].−1 or Z .0.002)1 most of
1The metallicity,[Fe/H]≡log(NFe/NH)−log(NFe/NH), whereNi is the number ofiatoms per unit of volume.
We also have, [Fe/H]≈log(Z/0.02)≈log(Z) + 1.7.
the seed nuclei are transformed into Pb and Bi, the heaviest nuclei possibly produced by the s-process. Observations seem to conrm the tendency that the s-process eciency (given e.g. by [Pb/Ba]) is increasing from Ba, CH, to carbon-enhanced metal-poor stars (see Sect. 3.2), these families representing a sequence of decreasing metallicity. This was also conrmed by the observation of metal-poor s-rich Pb stars (Van Eck et al., 2001).
Hot bottom burning: In stars more massive than∼3−4M, hydrogen burns at the base of the convective envelope. This phenomenon is called hot bottom burning (HBB) and is responsible for changes in stellar surface abundances. C/O and12C/13C decrease as the dredged-up12C is processed into14N via the CN cycle, and the 12C/13C drops to its CN equilibrium value of∼3.
Chapter 2
Physics of Interacting Binary Stars
This chapter describes our binary population synthesis code, binary_c, and some of the main interaction processes that may occur in a binary system. If the orbital semi-major axis becomes suciently small with respect to the stellar radius, either because of the expansion of a star (due to its own evolution) or by orbital contraction due to angular momentum losses, interaction may occur. The interaction may be radiative, as in the heating of the surface of one component by the hot companion, tidally driven, resulting in the distortion of both components, or matter can be transferred from one star to its companion.
2.1. The "binary_c" population synthesis code
In this thesis, binary-star evolution is performed with the population synthesis code binary_c (Hurley et al., 2002) with nucleosynthesis as described by Izzard et al. (2004, 2006, 2009). Stellar evolution is achieved by analytical ts (Hurley et al., 2000), which do not need to resolve the internal structure of the star and make the simulations much faster. In addition to all aspects of single star evolution, binary interactions are also included. The main interaction mechanisms that govern the evolution of binary systems, i.e. the Roche lobe overow, the common-envelope evolution, the wind-mass transfer and the tidal eects, are described in the following sections, which also highlight their major uncertainties.
Binary population synthesis codes are very interesting tools that simulate the evolution of a huge number of systems (tcpu/system≈0.01−0.1 second), and give the possibility to explore the whole parameter space. A grid of systems can then be computed with dierent initial parameters in order to simulate the evolution of a group of stars. It is then a very suitable tool to study classes of single, or (even more interesting) binary stars (see Sect. 4.5).
When computing a grid of systems, the general idea is to give a probability of existence for each system depending on the initial distribution of mass Ψ (the initial mass func- tion -IMF- from Kroupa et al., 1993), the initial distribution of mass ratio (q≡M1/M2
assumed to be at), the initial distribution in separationχ (assumed to be at in log a, usually chosen in binary population synthesis although it diers from the ndings of Eggleton et al., 1989) and the initial distribution in eccentricityΞ(from a thermal distri- bution, i.e. a Maxwellian velocity distribution for stars in a cluster, Ξ(e) = 2e; Heggie, 1975). Given these distributions, a logarithmic grid is set up in the 4D M1M2ae space. The grid is split into n stars per dimension such that each star represents the centre of a logarithmic grid-cell of sizeδV, the phase volume where
δV =δlnM1δlnM2δlna δlne (2.1) and
δlnx= lnxmax−lnxmin
n , (2.2)
where x represents M1, M2, a or e and xmax and xmin are the grid limits. The total number of stars is denoted by N such that N = n4. Given a set of stellar parameters M1,M2,aandeand phase volumes δlnM1,δlnM2,δlnaandδlne, the probability of existence of stariis calculated from
pi = Ψ(M1)Φ(M2)χ(a) Ξ(e)δlnM1δlnM2δlna δlne
= Ψ ΦχΞδlnV (2.3)
where P
pi = 1 and ´
Ψ(M1)dM1 = ´
Ψ(M2)dM2 = ´
χ(a)da = ´
Ξ(e)de = 1. Note however, that the probabilities used in this thesis areδpi×δtwhereδtis the time spent in the phase of interest.
In this thesis (except where stated otherwise), binary systems have an initial period ranging from 100 to 105 days, an initial mass of the primary and secondary ranging between 0.9 to 7 M and 0.5 to 7 M, respectively, and an initial eccentricity of 0 to 1. We assume all stars to be formed in binaries, and our models have a grid resolution N =NM1×NM2×Na×Ne= 304 = 8.1×105.
We model tides (see Sect. 2.5) following Hurley, Tout, & Pols (2002) who base their models on the Zahn (1977) and Hut (1981) formalisms. The tidal circularisation timescale during the TPAGB is given by τcirc∼104(a/3R)8 years (e.g. Soker, 2000). This implies that tides rapidly circularise any binary containing an AGB star with a separation less than a few stellar radii.
Our nucleosynthesis model includes third dredge-ups with an eciency given by Karakas et al. (2002) ands-process abundances based on the models of Busso et al. (2001). Our initial metallicity is Z = 0.008 for Population I stars and Z = 0.0002 for Population II stars with an abundance mixture according to Anders & Grevesse (1989). The 13C pocket eciency,13ξ, is a multiplicative factor used to change the amount of13Crelative to the 2.8×10−6M in the standard pocket of Gallino et al. (1998). We set it to 1 in order to make sucient barium stars atZ = 0.008(about 1%of GK giants).
Mass loss during the TPAGB is parametrised by the formula of Vassiliadis & Wood (1993) and mass is accreted onto the secondary at a rate given by Bondi & Hoyle (1944) as
Figure 2.1.: Roche potential surface (upper part) and section in the orbital plane of the Roche equipotentials (lower part). L1,L2, andL3are the Lagrangian points where forces cancel out. From van der Sluys (2006).
described in Hurley, Tout, & Pols (2002, Eq. 6) with an eciency parameterαwind= 1.5 and an accretion rate limited by
M˙2 <0.8
M˙1
(where star 1 is the donor and star 2 the accretor).
2.2. Roche lobe overow
2.2.1. The Roche Model
The Roche model considers the two components of a binary system as point sources in a circular orbit and in synchronous rotation with the orbital motion. It is then possible to dene a reference frame in uniform rotation about the centre of mass of the system in which the two stars are at rest. When distances are expressed in units of the or- bital separation (a), time in units of the orbital period and masses in units of the total mass (M1+M2), the eective potential of the system, including the gravitational and centrifugal potentials, is given by
Φ =−µ
r1 −1−µ
r2 − x2+y2
2 (2.4)
where
µ= M1
M1+M2
and
r1 = (x+ 1−µ)2+y2+z21/2
r2 = (x−µ)2+y2+z21/2
are respectively the distance of a test particle located at (x, y, z) to the primary star (located atx1 =µ−1) and to the companion (located at x2 =µ). The centre of mass is located at the origin of the coordinate system. The mass of the test particle is supposed to be small enough not to disturb the potential.
The Roche equipotentials in the orbital plane are shown in Fig. 2.1. The Lagrangian points L1,L2, and L3 are dened as the positions where forces cancel out.
As stellar surfaces coincide with equipotential surfaces, close to each star, surfaces of equal gravitational potential are approximately spherical. Far from each stellar compo- nent, the equipotentials are distorted by the gravitational attraction of the companion and centrifugal force and become ellipsoidal and elongated along the line joining the stellar centres. A critical equipotential intersects itself at theL1 Lagrangian point of the system, forming a two-lobed gure with a star at the centre of each lobe. This critical equipotential denes the Roche lobes of each star.
Binaries are named detached if neither component lls its Roche lobe, and semi- detached or contact if respectively one or the two component(s) are lling their Roche lobe. In detached systems, mass transfer can occur through wind accretion, while semi- detached systems experience Roche lobe overow.
2.2.2. Roche lobe overow
When one of the components lls its Roche lobe, either because of the expansion of its radius (due to its own evolution) or by orbital contraction due to angular momentum losses, material is transferred to the companion through L1 in the so-called Roche lobe overow (RLOF) model.
RLOF takes place when the radius of the star is greater than the Roche radius (RR), dened as the radius of a sphere that has the same volume as the Roche lobe. Several approximation formulae for the Roche radius are available in the literature and relate RR to the orbital separation a and to the mass ratio q. For instance Eggleton (1983) suggests
RR
a = 0.49q2/3
0.6q2/3+ ln(1 +q1/3). (2.5) A generalisation of this formula has been obtained in the present thesis (for cases when radiation pressure or pulsation add to the gravitational and centrifugal forces), as given in Eq. 5.12.
When a star lls its Roche lobe, gas falls towards the secondary star. Because of the angular momentum of this matter, it may not directly impact the star but forms an accretion disc inside the Roche lobe of the gainer. As more and more gas gets accreted into the ring, friction causes the outward transport of angular momentum allowing the matter in the disc to spiral in and to be accreted onto the secondary.
2.2.3. Stability
In order to evaluate the stability of mass transfer, one needs to take into account how the radii of the donor star and of its Roche lobe react to mass changes. In the Roche model, the stability condition imposes that, when mass is transferred the Roche lobe expands faster than the star or shrink less rapidly than the star. This is expressed by the conditionζR< ζ, where
ζR≡ d lnRR
d lnM1 (2.6)
and
ζ ≡ d lnR1
d lnM1 (2.7)
are the Roche-lobe mass-radius exponent and the mass-radius exponent of the donor, respectively. A star responds to mass loss on two timescales. The immediate response is on the adiabatic (or dynamical) time scale,
τdyn≡ r R3
GM,
after which hydrostatic equilibrium is restored but negligible heat transport has occurred.
The mass-radius exponent characterising this adiabatic readjustment is denoted byζad. On the other hand, thermal equilibrium is recovered on the Kelvin-Helmholtz time scale,
τKH ≡ GM2 2RL,
and the response of the star on this timescale is characterised by the exponentζth. The adiabatic and thermal stability conditions become respectively
ζR< ζad (2.8)
and
ζR< ζth . (2.9)
IfζR<min(ζad, ζth), the mass transfer is stable upon a further expansion of the star. If ζth < ζR < ζad, the mass transfer is unstable on a thermal timescale, i.e. with a mass loss rate limited by M˙ = M1/τKH, and if neither of these conditions is satised, mass transfer proceeds on the dynamical timescale.
In binary_c, the mass transfer rate is determined such that the star remains on its Roche lobe, i.e. R∗ ≈ RR∗. This is achieved by increasing the mass transfer rate
depending on how much the Roche lobe is overlled, M˙ ∝ln
R RR
3
.
See Hurley et al. (2002) for more details about the mass transfer prescriptions.
Note that an AGB star is well characterised by an adiabatic polytrope (i.e. a fully convective star). The corresponding adiabatic mass-radius exponent is ζad = −1/3 (Soberman et al., 1997). In addition, the thermal mass-radius exponent is also nega- tive,ζth≈ −0.3. Thus the adiabatic and thermal response to mass loss of an AGB star is an increase of its radius. RLOF involving an AGB star will then proceed on a dynam- ical timescale which leads the system into a common envelope unless the donor star is rather less massive than the accretor, so thatζR is less negative thanζad. Thus dynam- ical mass transfer occurs for giant stars when q > qcrit, where qcrit is given from models of condensed polytropes under the assumption that mass is transferred conservatively (Hjellming & Webbink, 1987).
The eect of additional forces such as the radiation pressure or pulsation on the RLOF stability is studied in Sect. 5.7.2.
2.3. Common envelope evolution
In the case of dynamically unstable RLOF, the companion star cannot usually accrete matter at the imposed rate, and the companion eventually lls its Roche lobe as well.
This is referred to as the common envelope (CE, see Fig. 2.2).
During a CE phase, the envelope does not corotate with the stellar cores. This asyn- chronicity leads to energy and angular momentum transfer between the orbit and the CE, potentially expelling the CE, and reducing the orbital separation of the binary (Web- bink, 1976; Livio & Soker, 1988). Ejecting the envelope may extract a large fraction of the orbital energy and leave the system with very short orbital periods (e.g. a few hours) or even lead to coalescence (e.g. blue stragglers, see Sect. 3.2.3). Interestingly, post-CE systems are observed in a large range of orbital periods: systems with periods ranging from hours to days (cataclysmic variables, so-called CVs and related systems), to systems with orbital periods as long as a few103 days (like some post-AGB, CH, Ba, or carbon-enhanced metal-poor stars, see Sect. 3.2).
Note that the CE evolution represents one of the most uncertain phase in binary evolution. For example, the mass accreted by the companion during the CE evolution is usually not considered in binary evolution code. However, it has been shown that accretion remains small but may not be completely negligible (Ricker & Taam, 2008).
When considering the formation of chemically peculiar stars (see Sect. 3.1), the amount of s-process-rich matter accreted is of major importance. The mass accretion rate estimated in Ricker & Taam (2008) is however only indicative due to the lack of a detailed inner boundary treatment for the companion. We then do not consider accretion during the CE evolution. The prescriptions used in our models are described in the following sections.
(a) A binary system initially consisting of a ZAMS primary and secondary star of mass M1 and M2 respectively. Note that the binary is detached.
(b) BecauseM1> M2, the primary evolves o the main sequence rst. Depending on the orbital separation, the primary will ll its Roche lobe on either the giant or asymptotic giant branch for a CE to oc- cur.
(c) Due to the dynamical timescale mass transfer, the accreting layers on the sec- ondary do not have sucient time to cool, and instead expand. The secondary sub- sequently lls its own Roche lobe.
(d) The envelope of the giant primary sur- rounds both the secondary star and the core of the giant. Friction between the stellar components and the envelope pro- vides a torque.
(e) The torque removes angular momen- tum and energy from the orbit, greatly re- ducing the binary separation. If enough energy is imparted onto the CE it may be ejected from the system leaving a white dwarf-main sequence system.
2.3.1. The α formalism
The original formulation of CE evolution assumes transfer of orbital energy to gravita- tional binding energy of the envelope at some (constant) transfer eciency,αCE (Iben &
Tutukov, 1984; Webbink, 1984),
αCE= ∆Ebind
∆Eorb
, (2.10)
whereαCE = 1is used in our models. A parameter λwas introduced by de Kool (1990) as a numerical factor (of order unity) which depends on the structure of the envelope, such that the real binding energy of the envelope can be expressed as:
Eenv =−GM1M1,env
λR1
. (2.11)
This parameter has however been re-evaluated to account for the contribution of the ionisation energy to the binding energy of the envelope, leading to much higher values (λ >5, Dewi & Tauris, 2000).
Eq. 2.10 may be written explicitly (Webbink, 1984; Nelemans et al., 2000) as M1,envM1
λR1 =αCE
M1,coreM2
2af −M1M2 2ai
, (2.12)
whereai and af are the initial and nal orbital separations, respectively. Alternatively the parameter λ may be absorbed into the uncertainty factor αCE (e.g. Nelemans &
Tout, 2005). Given this process of energy transfer, the ratio of initial to nal orbital separations is
af
ai = M1,core
M1
1 + 2ai
αCEλR1 M1,env
M2 −1
, (2.13)
whereai/R1 may be approximated by Eq. 2.5.
The value of αCE may be aected by several factors. Of particular importance is the three-dimensional structure of the CE. It has been shown that mass is preferentially ejected from the CE in the orbital plane (Livio & Soker, 1988; Terman et al., 1994;
Sandquist et al., 2000). This material reaches velocities greater than the escape velocity of the system. This means that more energy is used to eject this material than is necessary and so there is less energy available to eject additional material. Besides if energy is transported to the surface of the CE and radiated away quickly, then less energy is available to unbind the envelope and the eciency factor is reduced. The value of αCE may also vary in numerical simulations due to the one-dimensional approximation. The thermal and magnetic energy of the envelope material can also aectαCE. These sources are thought to represent only a small contribution to the total energy and their eect on αCE could be small. However, a potentially signicant amount of energy may be produced due to recombination within the envelope as it is expelled (Han et al., 1994;
Dewi & Tauris, 2000).
2.3.2. The γ formalism
An alternative to the α-formalism is the mechanism which considers the transfer of angular momentum rather than energy between the orbit and the envelope (Paczy«ski
& Zióªkowski, 1967; Nelemans et al., 2000):
∆Jb
Jb,i =γ∆M
M . (2.14)
Here ∆Jb is the change in orbital angular momentum during CE evolution, Jb,i is the initial angular momentum, ∆M is the mass lost from the system and M is the total mass of the binary. Once again we may formulate Eq. 2.14 with the same variables as in Eq. 2.12 (Nelemans & Tout, 2005):
af ai
=
M1
M1,core
2
M2,core+M1,core
M2+M1,core
1−γ M1,env
M2+M1,core
2
. (2.15) Nelemans & Tout (2005) investigated the ability of theα and γ formalisms to correctly account for the observed properties of double white-dwarf, sub-dwarf and pre-CV binary systems. By inferring the mass of the progenitor stars using stellar evolution models, they were able to determine the possible initial masses, radii and hence orbital separation when Roche Lobe overow started. We see from Eq. 2.12 and 2.15 that this determines the values ofλαCE andγ for each system. Theαformalism typically produces a wide spread of possible values forαCE.0.5, but there is not any typical value which is able to describe all systems. On the other hand, a value of γ = 1.5 is able to satisfactorily describe all of the systems considered, but such a formalism is less straightforward as it provides less constraints on the orbital energy. Indeed, angular momentum can be lost from the system without the orbital energy having necessarily decreased. Therefore energy conservation constrains the system more tightly than angular momentum conservation.
Our simulations are then using the α formalism.
We nally refer to Taam & Ricker (2010) for a recent descriptive review on CE hydro- dynamical simulations.
2.4. Wind mass transfer
A simple model of wind mass transfer as been proposed by Hoyle & Lyttleton (1939). The Hoyle-Lyttleton model describes how the supersonic motion of a point mass is focused by the gravitational attraction of a star and nally accreted. The geometry is sketched in Fig. 2.3. For a review of this model we refer the reader to Edgar (2004).
Basically, the material is accreted if bound to the star, i.e. if 1
2v∞2 − GM r <0,
Figure 2.3.: Sketch of the Bondi-Hoyle-Lyttleton accretion geometry (from Edgar, 2004).
or similarly material with an impact parameter σ < σHL= 2GM
v∞2 , (2.16)
which denes the critical impact parameter σHL, known as the Hoyle-Lyttleton radius.
The accreted mass ux satises Eq. 2.16, writes
M˙HL=πσHL2 v∞ρ∞= 4πG2M2ρ∞
v∞3 . (2.17)
Simulations of pressure-dominated spherically symmetric accretion onto a point mass led Bondi & Hoyle (1944) to suggest the addition of an extra term such that
M˙BH = 4πG2M2ρ∞
(c2∞+v2∞)3/2, (2.18)
known as the Bondi-Hoyle accretion rate, where c∞ is the sound speed. In binary_c, the accretion rate is parametrised as follows (replacing v∞ by the relative wind-orbital velocity(vwind2 +v2orb)1/2; Hurley et al., 2002),
M˙2,acc= −1
√ 1−e2
GM2 vwind2
2
αwind 2a2
1
1 +vv2orb2 wind
3/2M˙1,wind, (2.19) withαwind(an empirical factor to match predictions from detailed hydrodynamical calcu- lations; see below) taken to be 3/2. This model gives a simple and very useful prescription for the fraction of mass lost by a star that is accreted by its companion. In the context of binary stars, it is however only valid for fast (with respect to the orbital velocity) winds, which is not the case for AGB stars, where the wind velocity is ∼15 km/s. However, without any better prescription, the BH prescription is used in all cases in the population synthesis code binary_c to treat wind accretion. Hydrodynamical simulations of slow
winds have been performed by several authors (see e.g. Theuns & Jorissen, 1993; Theuns et al., 1996; Mastrodemos & Morris, 1998; de Val-Borro et al., 2009) and show that mat- ter is strongly focused toward the orbital plane. In the Hoyle-Lyttleton model, matter is accreted from a column on theθ= 0axis (see Fig. 2.3) and no angular momentum is transferred to the companion.
In binary_c, changes of the spin angular momentum through wind mass transfer are computed as follows (Hurley et al., 2002): The change in eccentricity and separation averaged over an orbit are expressed as
hδei
e =− hδM2i 1
M + 1
2M2
, (2.20)
and hδai
a =−hδM1i
M −
2−e2 M2
+1 +e2 M
hδM2i
1−e2, (2.21)
whereh i indicates the averaged value of a parameter over one orbit. The change in the orbital angular momentum is given by
J˙orb= Jorb
M1+M2
M˙1,wind−M2
M1M˙2,acc
. (2.22)
whereM˙i,wind (<0) and M˙i,acc (>0) are the rates of mass lost by wind and accreted by star i, respectively. Note that Eq. 2.22 is only valid for |M˙2| |M˙1|, which might not be the case when RLOF occurs though.
Finally, it has also been suggested (Tout & Eggleton, 1988) that wind mass loss is tidally enhanced by the gravitational attraction of the companion,
M˙ = ˙Mwind
"
1 +B min 1
2, R RR
6#
, (2.23)
with B a free parameter (in our simulations this eect is not taken into account, so B = 0) and where the extra term represents a saturation at R = 12RR when complete corotation is expected to take place.
The accretion of material onto the companion star determines the resulting amount of pollution by s-process elements at its surface. Usually, the mean molecular weight (µ) of the accreted material (e.g. enriched in C-rich material) is greater than the material in the atmosphere of the accretor so an instability occurs, the thermohaline mixing. As µ increases towards the surface, it results in mixing that occurs on a thermal timescale until the molecular weight dierence has disappeared. Due to this mixing mechanism and as the thermal timescale is relatively fast compared to the evolution timescale of the accretor (usually a MS star), we assume that the accreted material is instantaneously mixed into the entire envelope of the accretor. This is in agreement with recent studies of Stanclie et al. (2007) which have shown this process to be very ecient.
2.5. Tidal eects
Tides arise due to the dierential gravitational attraction of a star by its companion.
Tidal forces cause strains that elongate the stars along the line between the centres of mass, producing tidal bulges. When a viscous body rotates while subject to tidal forces, internal friction results in the gradual dissipation of its rotational kinetic energy. The resulting torque exchanges angular momentum between the orbit and the rotation of each star. This ultimately results in a rotation which is tidally locked to the orbital motion, a situation called synchronisation.
In eccentric orbits, tidal forces are stronger at periastron (the point at which the distance between the two stars is minimum) compared to apoastron (point of maximum distance). This leads to energy dissipation that brings the system to the equilibrium state, characterised by co-rotation in a circular orbit.
Tidal synchronisation and circularisation induced by convective or radiative damping have been investigated by Zahn (1977) and Hut (1981), and are associated to timescales expressed as
1
τsynch. = 1 (ω−Ω)
dΩ dt ∝
R a
6
,
whereω and Ωare the rotational and orbital velocities, respectively and 1
τcirc. = 1 e
|de|
dt ∝ R
a 8
.
We refer to Hurley et al. (2002) for the exact expressions of τsynch. and τcirc. for the dierent physical mechanisms responsible for the tidal dissipation, e.g. convective or radiative damping.
As a > R, τsynch. < τcirc., the synchronisation is achieved before the orbit is cir- cularised. Note that the most ecient form of dissipation corresponds to tides in the extended convective envelope, e.g. stars in the RGB or AGB phase. To give an idea, the circularisation timescale can be as short as ∼104 yr in the AGB phase. The changes of the binary parameters (a,eand ω) due to tides are described by Hut (1981).
Chapter 3
Evolution of low- and intermediate-mass Binary Stars
3.1. Barium star formation
The two dierent channels for barium star formation are the wind and the CE chan- nels (Fig. 3.1). For each formation channel, a typical evolutionary track in the period- eccentricity diagram, computed with our canonical model (described in Sect. 2.1, which corresponds to the set of parameters given in Table 3.1) is presented in Fig. 3.2. The evolution starts with both stars on the MS. The most massive of the two evolves faster and rst ascends the RGB, settles on the core He-burning phase and then starts to as- cend the AGB phase. At that stage, successive third dredge-ups gradually pollute the AGB envelope with s-process elements (such as barium, see Sect. 1.2). At the same time, s-process-rich matter expelled by the strong AGB wind is accreted by the companion, thus imprinting a clear signature on its surface.
Because of the very large radius of the AGB star, strong energy dissipation by tides
Table 3.1.: Set of initial distributions and key parameters used in our canonical model (see Chap. 2 for a complete description of the code).
Parameter value/range Comment/ref
Initial distributions M1 0.9 - 7 M Kroupa et al. (1993)
q=M1/M2 1 - 14 Flat
a 100 - 105 R Flat in loga
e 0 - 1 ∝e(Heggie, 1975)
CE evolution αCE 1 No accretion during CE evolution.
Wind accretion αwind 1.5
B 0 Tout & Eggleton (1988)
Nucleosynthesis 13ξ 1 Gallino et al. (1998)
AGB phase Mass transfer Main sequence
Production of heavy elements (Sr,Ba,Tc,...)
Barium star
2 1
RGB phase
White Dwarf
Figure 3.1.: Main Ba star formation channels: once on the AGB, s-process-rich material is transferred by wind-accretion onto the companion. The system may then either avoid CE evolution (case 1: the wind channel), or not (case 2: the CE channel), and nally becomes a barium star when the polluted companion ascends the RGB.
0 0.2 0.4 0.6 0.8 1
102 103 104 105
Period/days
Eccentricity
0 0.2 0.4 0.6 0.8 1
Eccentricity
Figure 3.2.: Typical evolutionary tracks (black lines) in thee−logP diagram of a binary system with stars of mass 2 M and 1 M, compared with the observations of Ba stars (+++ symbols are from Jorissen et al., 1998, without the triple system BD +38◦ 118; 56 UMa symbol is from Grin, 2008, HR 5692 is from Stefanik et al., 2011 and××× are the new orbits from the HERMES survey see Chap. 4). In the upper panel the system with an initial period of8,000days and e= 0.5avoids common envelope, contrarily to the system in the lower panel (with an initial period of 4,000 days). Note the small post-CE track aroundP = 50days.
occurs, which progressively decreases the eccentricity of the system and shortens the orbital period due to angular momentum losses (see Fig. 3.2). Depending on the orbital separation, two dierent evolutionary paths are possible:
1. At large orbital separations, the system avoids a CE phase (channel 1 in Fig. 3.1).
In this case, the AGB wind progressively removes the envelope, nally revealing its CO core (i.e. the future CO white dwarf). This leads to long-period systems. Note that the orbit may avoid complete circularisation as shown in the upper panel of Fig. 3.2.
2. At smaller orbital separation, the TPAGB star may overll its Roche lobe. As described in Sect. 2.3, the reaction to mass loss of a star with a convective envelope is to expand. In this conguration, mass is transferred on a dynamical timescale, leading the system to a CE evolution (Hjellming & Webbink, 1987). A substantial fraction of the orbital energy is removed from the binary to eject the CE, leaving the system with a CO white dwarf and a MS companion (channel 2 in Fig. 3.1). Note that no mass is assumed to be accreted by the companion star inside a common envelope. This process rapidly circularises the orbit and shortens the orbital period to about50 days (lower panel of Fig. 3.2).
In both cases (1 and 2), the AGB terminates and the post-AGB phase starts. The very hot white dwarf becomes less luminous as it cools, which progressively reveals its s-process-enriched MS companion (a barium dwarf). While ascending the RGB, the companion becomes a barium star and nally a S star. A similar evolution is thought to be responsible for the formation of some blue stragglers, CH, carbon-enhanced metal-poor stars and yellow symbiotic stars (see Sect. 3.2).
Note that stable RLOF channel is encountered if the mass ratio of the two stars is inverted before RLOF takes place. This may happen in a limited range of orbital periods (to give an idea, for a 2 M and a 1 M stars, stable RLOF is encountered when the initial period ranges between3150and3300days). Stable RLOF is included in our wind channel (case 1), and we refer to Han et al. (1995) for a detailed study of the orbital period distribution of this specic formation channel as well as the wind and CE channels. These authors have shown that the orbital period distribution associated with the dierent formation channels heavily depends on the wind tidal-enhancement parameter B (see Eq. 2.23), the maximum AGB mass for s-processing, the core mass at which thermal pulses are initiated, the stellar formation history, the mass ratio distribution and the wind velocity. Their best model for Ba stars also requires a strongly enhanced wind (B = 500), which leads a large fraction of systems to lose most of their envelope by the time they ll their Roche lobe so their mass ratio is notably decreased. This results in many systems with stable RLOF which populate the orbital period around103days when they become a Ba star. However, a more recent study by Pols et al. (2003) including a better treatment of the TPAGB phase (Hurley et al., 2002) has shown that the stable RLOF formation channel is not signicant compared to the main formation channel, i.e.
wind accretion. Moreover, tidally-enhanced wind shortens the AGB lifetime, so that less s-process material is produced and the pollution on the companion is reduced. He has
also shown that eccentric systems are only produced at periods longer than 3000 days and post-CE systems are mostly predicted at periods between 100 and 1000 days which disagrees with the observations (see Fig. 3.2).
3.2. A binary evolutionary sequence
The evolution of a binary system can be characterised by the evolutionary stage of each components, which gives rise to numerous classes of objects. In this thesis we focus on the evolution of binaries involving low- or intermediate-mass stars for which the primary star reaches the AGB phase, as only those are leading to the formation of stars polluted in carbon and s-process elements (called chemically-peculiar stars, see 3.1). The successive families of chemically-peculiar stars formed during binary evolution is sketched in Fig. 3.3 (Van Eck, 1999). In the left column are represented the spectral families not requiring binarity. In this section we focus on classes of peculiar stars requiring binarity. Detailed information on these families as well as their observational counterparts is presented in the following sections.
3.2.1. Carbon stars
The rst families of interest for this thesis are encountered when the primary reaches the TPAGB phase. The repeated dredge-ups lead the AGB star to enrich its envelope in carbon1, which may ultimately become C-rich (C/O>1), as observed in N, J and Early R stars described below. However, carbon stars are not necessarily binaries. For the fraction which is member of a binary system, note that a WD companion may not always be distinguished from a MS companion, so these carbon stars may belong to either phase 4 or 11.
N stars (phases 4 - 11)
They are C-rich stars, i.e. exhibit strong C2, CN and CH bands and no metallic oxide bands. They were soon separated in groups R and N. N stars exhibit a very strong depression in the violet part of their spectrum, while R stars have warmer temperatures.
N stars have temperatures comparable to normal giants of spectral type M3 or later;
many are variable. Both their s-process enhancements (Lambert et al., 1986) and their HIPPARCOS absolute magnitudes (Wallerstein & Knapp, 1998) are compatible with their TPAGB status (and do not require to belong to a binary system), except for the few which do not have s-process enhancements and which are also J stars (e.g. Lloyd Evans, 1986).
Technetium has been searched for in carbon stars (e.g. Smith & Wallerstein, 1983) but due to the very faintness in the region of resonance lines of technetium, the fraction of Tc-rich to Tc-poor carbon stars still remains very uncertain. As explained in Sect. 1.3,
1Note that carbon star and carbon-rich (C-rich) star do not dene the same class of objects and need to be distinguished. The former exhibits C2, CN and CH bands and does not necessarily have C/O>1, when the latter does.
