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Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles Docteur en sciences de l’Université Libre de Bruxelles

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Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Université Libre de Bruxelles Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Faculty of sciences — Physics department Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique Institut d’Astronomie et d’Astrophysique

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Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile Chile — Siantago de Chile

Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars Evolution of low and intermediate mass stars

in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems: in binary systems:

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A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems A new look at Algol systems

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President of the Jury: President of the Jury: President of the Jury: President of the Jury: Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K Prof. Bernard K NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN ^NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN ^NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN NAEPEN

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Jury - exterior: Jury - exterior: Jury - exterior: Jury - exterior: Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre Prof. Jean-Pierre DE DE DE DE DE DE DE DE DE DE DE ^DE DE DE DE DE DE DE DE DE DE DE DE ^DE DE DE DE DE DE DE DE DE DE G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE ^RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE ^RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE RÈVE

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© 2015 All Rights Reserved Romain DESCHAMPS

Contents

Acknowledgements v

List of Figures ix

List of Tables xi

Preface xiii

1 INTRODUCTION TO BINARY STAR EVOLUTION ANDALGOLS 1

1.1 A brief introduction to stellar evolution . . . 2

1.1.1 Stellar evolution seen through Hertzsprung-Russell and Kippenhahn Diagrams . 2 1.1.2 The birth of stars: from Pre-Main Sequence to Zero Age Main Sequence stars . . . 4

1.1.3 Main Sequence stars . . . 5

1.1.4 Ascending the Red Giant branch . . . 6

1.1.5 The helium core flash . . . 6

1.1.6 Horizontal Branch . . . 6

1.1.7 Asymptotic Giant Branch and latter stages . . . 7

1.1.8 Evolution of the stellar radius . . . 7

1.2 Binarity . . . 7

1.2.1 Classification of binary stars . . . 8

1.2.2 The importance of the initial periods and stellar masses . . . 9

1.2.3 The two-body system . . . 9

1.2.4 Mass and angular-momentum transfer between two stars . . . 11

1.2.5 Stellar winds . . . 11

1.2.6 Mass loss via Roche lobe overflow . . . 13

1.2.7 Mass accretion due to Roche lobe overflow . . . 13

1.2.8 The effects of mass transfer and mass loss on the orbital parameters . . . 14

1.3 Algols among interacting binaries . . . 14

1.3.1 First limitation of our understanding of Algols: non-conservative evolution . . . . 15

1.3.2 Second limitation of our understanding of Algols: the spin up of the gainer star . 18 1.3.3 Accretion discs in Algols . . . 19

1.4 Sub-types of Algol systems . . . 20

1.4.1 βLyræ . . . 20

1.4.2 W Ser systems . . . 21

1.4.3 The B[e] stars case . . . 22

1.4.4 Contact systems — W UMa type star . . . 22

1.4.5 Symbiotic Algols . . . 23

1.5 Tackling the “critical rotation” and “systemic mass loss” problems . . . 24

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2 THEBINSTAR CODE: IMPLEMENTATION OF THE PHYSICS 25

2.1 Binary physics . . . 26

2.1.1 Binary parameters evolution . . . 26

2.2 Ballistic approach . . . 28

2.2.1 Equations of motion . . . 28

2.2.2 Specific angular momentum of the stream . . . 29

2.3 Accretion discs . . . 30

2.3.1 Standard accretion discs . . . 30

2.3.2 Decretion disc around critically rotating accretors . . . 30

2.3.3 Accretion disc and star-disc boundary layer . . . 30

2.4 Magnetic fields effects . . . 33

2.5 Tides . . . 34

2.5.1 Tidal timescale for radiative stars . . . 35

2.5.2 Tidal timescale for stars with a convective envelope . . . 36

2.5.3 Summary . . . 36

2.6 Non-conservative evolution . . . 36

2.6.1 Hotspots and critical mass-transfer rate . . . 36

2.6.2 Angular-momentum losses during non-conservative evolution . . . 41

2.7 Canonical simulations with the BINSTARcode . . . 42

2.7.1 Subclasses of Algol systems . . . 42

2.7.2 Comparison with another stellar code . . . 46

2.7.3 Roche and stellar radii evolution diagram . . . 46

3 ON THE EVOLUTION OF CRITICALLY ROTATING ACCRETORS INA^LGOLS 49 3.1 On the spin up of the gainer . . . 50

3.2 Magnetic field effects . . . 50

3.3 Tidal effects . . . 53

3.4 Star-disc boundary layer treatment . . . 53

3.5 General evolution with different spin down mechanisms . . . 54

3.6 On the rotation of Algols . . . 57

3.7 Discs around critically rotating stars . . . 58

3.8 On a new theoretically based classification of Algol systems . . . 58

3.8.1 Class I—Pre-Algol systems . . . 60

3.8.2 Class II—Active Algols . . . 60

3.8.3 Class III—Quiescent Algols . . . 60

3.9 Conclusion . . . 60

4 NON-CONSERVATIVE EVOLUTION INALGOLS 61 4.1 Hotspot . . . 62

4.2 Hotspot and magnetic braking . . . 65

4.3 Following the mass ejected from the hotspot . . . 67

4.4 The model system . . . 68

4.4.1 Density profile of the out-flowing matter . . . 68

4.4.2 Spiral structure . . . 69

4.4.3 Chemistry of the outflow: gas composition and dust formation . . . 70

4.4.4 Stellar parameters . . . 71

4.4.5 Setup of CLOUDYand SKIRT . . . 74

4.5 Results . . . 75

4.5.1 Temperature and emissivity profiles . . . 75

4.5.2 Synthetic SEDs . . . 76

4.5.3 Models with strong ionisation . . . 82

4.5.4 Parameter study: geometry - SKIRTsimulations - dust-to-gas ratio . . . 83

4.6 Confrontation to observations . . . 84

4.6.1 Stellar samples . . . 84

4.6.2 Constraint on the dust formation: IR diagnostics . . . 86

4.6.3 Constraint on Strömgren photometry and weakly ionised emission lines . . . 90

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4.7 Conclusions . . . 90

Perspectives 93 Bipolar jets . . . 94

Hydro-dynamical simulation of a disc around a critically rotating accretor . . . 94

Impact of the RLOF stream on the gainer’s surface . . . 94

3D Hydro-dynamical simulation of the outflow . . . 95

Contact systems . . . 95

Observations . . . 95

Appendices 97

A The BINSTARcode: numerical description 97 A.1 The Origin of BINSTAR: STAREVOL . . . 97

A.2 Stellar structure computation . . . 97

A.3 Numerics . . . 99

A.4 Procedure . . . 100

A.5 Time-step . . . 100

A.5.1 Stellar time-step . . . 101

A.5.2 Binary interactions time-step . . . 103

A.5.3 Global time-step . . . 103

A.6 Parallelisation with OPENMP . . . 103

A.7 Parameter card and initial model . . . 103

A.8 A BINSTARcomputation in numbers . . . 103

A.9 Calibration with other codes . . . 104

B Analytical derivations 105 B.1 Mass losses by RLOF . . . 105

B.2 Initial width of the accretion stream . . . 106

B.3 Specific angular momentum of the stream . . . 106

B.4 Critical accretion in solid rotation . . . 107

B.5 Boundary layer treatment . . . 108

B.6 Wind bracking . . . 109

B.7 Disc-locking . . . 110

B.8 tides . . . 112

B.8.1 Hut prescription . . . 112

B.8.2 Zahn 1977 time-scale for radiative stars . . . 113

B.8.3 Convective stars . . . 113

C Mass outflows in Algols 115 C.1 Estimation of the opening angle of the outflow . . . 115

C.2 Calculation of the effective flux . . . 116

C.3 UV continuum and line variability in W Ser . . . 117

C.4 Chemical composition of the outflow . . . 118

Bibliography 120

Personal bibliography 135

Acknowledgements

I

t would not have been possible to write this thesis without the support of many persons. I would like to start by acknowledging everyone who helped me along my years as a PhD. student.

First of all, I acknowledge financial support from an ARC found (Coordinated Research Action 2008-2013) and from a European Southern Observatory - Vitacura studentship grant.

I also want to thank the promotors that lead me during my thesis, Lionel Siess and Alain Jorissen from the Institut d’Astronomie et d’Astrophysique of Brussels, and, later on, Henri Boffin from the European Southern Observatory. I am grateful for their patience and advice.

I would like to thank the people who directly worked with me, Philip Davis and Kilian Braun from IAA and Walter Van Rensbergen and Jean-Pierre De Greve from the Vrije Universiteit Brussels. I would like to thank all the staff at the IAA.

There were also those who taught me how to enjoy my thesis, Ioannis (C’est la vie, oπως λǫνǫ καιoι γαλλoι), Andrea, Thomas, Ester (some says they still hear laughs in the IAA corridors), Andreas, Tyl, Christos, Anthea, Stéven...

I also had the chance to move one year to Chile. There, a dream-team took the relay and I would like to thank all the ESO members (scientists and staffs) I met, especially Claudio Melo who has always been there when needed.

I also thanks all the students that share my experience: Paul (still taking it for the team!), Julien (probably run- ning somewhere right now), Jos (probably climbing somewhere right now), Mirjam (probably exploding rockets somewhere right now) and all the others.

I am also thankful to all my Master colleagues: Christophe (we still need to buy a dart game), Damien and the others.

This thesis has also been four years far from home, from my family, the ones that probably did the most and largest sacrifices to allow me to accomplish it. I owe a huge thanks to my parents. Thanks to my brother who did the smart choice staying right on the ground more than wandering off along the stars. I am also grateful to all the people I consider to be part of my family for their support.

Finally, there are all these people I met during this thesis, these people I can’t name here, but that helped me at some point along this thesis. Thank you all.

List of Figures

1 Algol andβLyræ images. . . xv

1.1 Hertzsprung Russell diagram of nearby stars. . . 3

1.2 Hertzsprung-Russell diagrams for several masses . . . 3

1.3 Kippenhahn diagrams for star of different masses. . . 4

1.4 Schematic evolution of low- and intermediate mass stars in the mass range 0.4 to 8 M_⊙. . 5

1.5 Evolution of the radius of a 1.5M_⊙(left) and a 4M_⊙(right) star. . . 8

1.6 Binary fraction as a function of the spectral type of the primary star. . . 9

1.7 Gravitational potential of a binary system. . . 10

1.8 Binary systems configurations. . . 11

1.9 Top: Light-curve of the typical Algol-like star BH Virgo (Giuricin et al.,1984). Bottom: Sketch illustrating the corresponding configuration. . . 15

1.10 Schematic evolution for Algol systems. . . 16

1.11 Period histogram for Algol systems. . . 17

1.12 Final mass ratio histogram for Algol systems. . . 18

1.13 Distribution of the rotation rate for the gainer in Algol systems. . . 19

1.14 Left:Light-curve for two different eclipses of the W Ser prototype (Guinan,1989).Right: Averytentative model proposed byGuinan(1989). . . 21

1.15 Top:Light-curve of the contact system (W UMa-like star) AP Leonis (Snyder and Lapham, 2007).Bottom:Geometric structure of AP Leonis. . . 23

2.1 Ballistic trajectories of a matter stream. . . 28

2.2 Geometry for the computation of the specific angular momentum of the RLOF-stream. . . 29

2.3 Structure of a critically rotating accretor disc . . . 31

2.4 Magnetic field lines configuration. . . 33

2.5 Configuration of an accretion disc surrounding a magnetic star. . . 34

2.6 Scheme representing the tidal mechanism in a binary system. . . 35

2.7 Modes of mass transfer between the two stars and systemic mass loss. . . 39

2.8 Angular-momentum budget for the gainer. . . 39

2.9 Typical mass-transfer rate for a case A system with initial masses 12 + 7.2 M_⊙and initial periodP= 4 d. . . 42

2.10 Kippenhahn diagram for the donor star of the case A system with initial masses 12 + 7.2 M_⊙ and initial periodP= 4 d. . . 43

2.11 HR diagram for a case A system with initial masses 12 + 7.2 M_⊙and initial periodP= 4 d. 43 2.12 Typical mass-transfer rate for a case B system with initial masses 6 + 3.6 M_⊙ and initial periodP= 3.5 d. . . 44

2.13 HR diagram for a case B system with initial masses 6 + 3.6 M_⊙and initial periodP= 3.5 d. 45 2.14 Kippenhahn diagram for the donor star of our case B systems with initial masses 6 + 3.6 M_⊙ and initial periodP= 3.5 d. . . 45

2.15 Comparison of the HR diagrams and mass transfer rates for the case A (12 + 7.2 M_⊙, P_orb=4d) and case B (6 + 3.6 M_⊙,P_orb=3.5d). . . 47

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2.16 Roche and stellar radii evolution diagram for a case B system with initial masses 6 + 3.6 M_⊙

and initial periodP= 3.5 d. . . 48

3.1 Evolution of the mass-transfer rate (top), stellar masses (middle), surface velocity (bot- tom) for a 6 M_⊙donor (dotted red line) and 3.6 M_⊙gainer (Solid black line) system with initial period P_init= 2.5 days. . . 50

3.2 Impact of the magnetic field on the evolution of the gainer’s surface velocity for different spin-down mechanisms for a 6 + 3.6 M_⊙system with initial period P_init= 2.5 d . . . 51

3.3 Same as Fig. 3.2 but comparing the disc-locking and wind braking impact. . . 51

3.4 Same as Fig. 3.2 but for the effect of tides. . . 52

3.5 Evolution of the torque on the gainer star ˙J_acc,g^RLOF. . . 53

3.6 Same as Fig. 3.2 but for the impact of the boundary-layer mechanism. . . 54

3.7 Evolution of the orbital separation for our 6 + 3.6 M_⊙system with different braking mech- anisms. . . 55

3.8 Evolution of the mass-accretion rate for our 6 + 3.6 M_⊙ system with different braking mechanisms. . . 55

3.9 Binary section evolution of our 6 + 3.6 M_⊙system with different braking mechanisms. . . 56

3.10 Same as Fig. 3.8 but for the HR diagram. . . 56

3.11 A new classification of Algol system. . . 58

4.1 Evolution of the luminosities for our 6 + 3.6 M_⊙,P=2.5 d, system with hotspot formation. 62 4.2 Evolution ofβ. . . 63

4.3 Evolution of the masses. . . 63

4.4 Same that Fig. 4.1 but for the orbital separation. . . 64

4.5 Evolution of the surface spin-angular velocity for our 6 + 3.6 M_⊙system with P_init= 2.5 days with hotspot and different magnetic field strengths: surface spin-angular velocity. . . 65

4.6 Same as Fig. 4.5 but for the evolution of the orbital separation. . . 66

4.7 Same as Fig. 4.5 but for the evolution of the parameterβ. . . 66

4.8 Same as Fig. 4.5 but for the evolution of the masses. . . 67

4.9 Schematic overview of an Algol system undergoing systemic mass loss due to a hotspot on the surface of the gainer. The ticks and numbers indicate the different phases (0.0: primary eclipse). . . 69

4.10 Evolution of the mass surrounding the system. . . 70

4.11 Density and velocity profiles of the outflowing material. . . 71

4.12 Distance distribution for observed Algols. . . 73

4.13 Temperature profile and cooling time-scale of the material surrounding the star as a func- tion of distance to the star . . . 76

4.14 Top: Emissivity profiles and relative ionisation for the simulation C_ld_0.71_inter. Bot- tom:SiIVand FeIIfraction for the high-temperature hotspot simulations . . . 77

4.15 Top:Synthetic SEDs of the dust-free CLOUDYmodels in the UV-optical regime.Bottom: Same as top panel but for the different models A, B and C. . . 78

4.16 Synthetic SEDs of dust-free models in the UV regime. . . 79

4.17 Same as Fig. 4.15 but for the IR region, including the SKIRTmodel C_SK_ld. . . 79

4.18 Strömgren photometry (m1₀;c1₀) diagram for our models and for comparison normal main-sequence stars from the Long-Term Photometry of Variables project. . . 79

4.19 [SiIV] 1394 and 1403 doublet for three different configurations. . . 82

4.20 SKIRTintensity map at 12 µm (top), 25 µm (middle) and 60 µm. . . 83

4.21 Top panel: WISEF_W4/F_W1 against 2MASS J/Ks flux ratios for Algols. Bottom panel: Same as top panel but forF_W3/F_W1with SNR andχ²relative toW3. . . 88

4.22 WISE band-4 images for the genuine Algol CZ Vel (left) and the Be star SX Aur (right) . . 89

A.1 Nuclear network of the BINSTARcode. . . 98

A.2 Discretisation of the physical quantities inside the two stars. . . 99

A.3 Structure matrix for the binary system. Figure from the BINSTARmanual; Lionel Siess. . . 100

A.4 Procedural scheme of the BINSTARcode. . . 101

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A.5 Detailed version of the procedural diagrame. Figure from the BINSTARmanual; Lionel

Siess. . . 102

B.1 Magnetic pressure and tension in an accretion disc. . . 110

B.2 Disc-locking torque efficiency. . . 111

C.1 Geometry of the hotspot emission. . . 116

C.2 Representation of the effective surface of the hotspot over a full orbital period. See text for description. . . 117

C.3 Top: Continuum in the UV band for W Ser observed with IUE. Black: SWP47439 ob- servation made on 1993-04-07 (20:02:16) at phaseΦ =0.84; red: SWP47457 observation made on 1993-04-10 (21:40:17) at phaseΦ=0.06.Bottom:Difference of the two spectra. . 118

C.4 HST/GHRS spectra of the [SiIV] 1393.76 and 1402.77 Å lines of W Ser at two distinct phases (black: z0lu5108t observation made on 1991-07-12 (05:32:25) at phaseΦ = 0.00, primary eclipse; red: z0lu0308t observation made on 1991-07-19 (03:29:13) at phaseΦ= 0.5, secondary eclipse). . . 119

List of Tables

1.1 Systems presenting the largest angular separation. . . 20

2.1 Summary of the mass-transfer rates. . . 37

2.2 Summary of the angular-momentum transfer . . . 38

3.1 Observational prototypes for the different classes. . . 59

4.1 Parameters for the three models; Model A: mass ratio reversal; Model B: intermediate case; Model C: end of non-conservative mass transfer. . . 72

4.2 Parameters of the simulations performed with the CLOUDYand SKIRTcodes. . . 75

4.3 Magnitudes in Strömgren (uvby) bands and corresponding colour indices. m₁ = (v− b)−(b−^y);c₁= (u−^v)−(v−^b) . . . 80

4.4 Magnitudes in SDSS bands and corresponding colour indices. . . 80

4.5 Magnitudes in 2MASS and WISE bands assuming the models are located 300 pc away from the sun.F_J/F_Ks,F_W4/F_W1andF_W3/F_W1are the flux ratios. . . 81

4.6 2MASS and WISE magnitudes for the 13 systems deviating the most from theF_W4/F_W1 black-body law. . . 87

4.7 Strömgrenm_1,0andc_1,0for our sample of W Ser Be stars. . . 91

C.1 Chemical composition of the outflowing material for the three models computed. . . 119

Preface

Stars are similar to humans. They prefer to gather in couple, surely because it is dark and cold out there in space.

S

^TARS usually form in large brotherhoods, and binary stars are frequent objects of our universe.

Depending on the type of star, up to 80% of the objects are evolving with a companion. Contrarily to the common thought, a single star like our star, the Sun, is more the exception.

Binary stars are important objects for all fields in astrophysics and physics in general. First, they allow us to probe the physics and properties of single star. Thus, the most fundamental parameter of the evolution of a star, such as its mass, is mostly and only precisely measured thanks to gravitational interactions with its companion. Moreover, binary stars are progenitors of several interesting objects that play a role for various astrophysical domains. For example, Type Ia supernovae, the light curves of which help to constrain the expansion rate of the universe, orγ-ray bursts that are used to obtain neutron-star spin rate.

Although single star evolution is now fairly understood, the evolution of binary stars, and more pre- cisely interacting binaries, is far from benefiting of the same status. For instance, many kinds of binaries undergo phases of evolution that are only roughly comprehended. Worse, some critical aspects, such as the stellar spin rates are ignored in stellar models because of the lack of observational constraints or physical understanding. As a result, we have no clear idea about the evolution, past or future, of some type of systems.

One may think that such fundamental questions only arise for some rare and exotic systems, where some very specific physical mechanisms are needed. Unfortunately, even the simplest interacting sys- tem we can think of, with the simplest stars in their simplest evolutionary phases, still poses a lot of problems. Some of these systems just start to reveal their secrets even though they have been observed for more than two centuries and are common in our universe. This thesis will be dedicated to this kind of objects: the realm of Algol systems and its sub-categories.

Algol (βPersei), the second brightest star in the Perseus constellation and one of the most observed star, is named after the Arabic “Ra’s Al-ghul”, which translates as “head of the ogre”. This often called

“demon star” has puzzled many generations of astronomers and astrophysicists. This star has drawn the attention since the 18^th, because of its amazingly regular brightness variations. Indeed, the orbit of the two stars creates regularly repeating eclipses. Such eclipsing binaries are a real gift for astronomer because they bring strong constraints on several characteristics of the two stars like their masses. Even- tually, astronomers found out that this Algol system was composed of a young massive star (supposed to evolve quickly) and an older but less massive star (supposed to evolve much slower). However, this is in contradiction with stellar evolution theory which states that the more massive star has to be the more evolved. This problem has been called the Algol paradox and has been observed in many other binaries thereafter.

P

REFACE

Algols initially were, for me, just test-objects to constrain my models before investigating more complicated stars. However, by performing simple tests, the hidden part of the iceberg emerged. It was therefore necessary to solve these problems before continuing.

In this respect, I have co-developed and used the new state-of-the-art binary-star evolution code BINSTARin collaboration with Dr. Lionel Siess and Dr. Philip Davis. This code includes the most up-to- date physics for both stellar evolution and binary interactions. My objective is to study with this new code, the impact of mass and angular momentum transfers on the evolution of close binary stars.

In this thesis, I mainly focus on two fundamental unsolved questions:

• What happens to the gainer’s angular velocity during the mass transfer phase?

• Is mass transfer in Algols conservative?

These two questions have remained unanswered for more than 30 and 60 years respectively and blur our understanding of Algols and to a certain extent the one of interacting binaries. I will come back to these questions in Sect. 1.5, after reviewing the physics of Algols systems.

Before investigating the processes at work in binary systems, it is necessary to understand the evo- lution of single stars. I will start this thesis by introducing the basic concepts of single star structure and evolution and more specifically the low and intermediate mass stars. I will then describe the mecha- nisms involved in mass transfers between two stars and their impact on binaries. Chapter 2 is dedicated to the presentation of the binary star evolution code I am developing and using to answer these prob- lems. The following Chapters 3 and 4 are dedicated to the two problems I focused on: the critical rotation in binary stars and the systemic mass loss in Algols. I end up this thesis with a brief summary and some perspectives.

P

REFACE

DSS colored~1

1’ 19.05’ x 19.62’

N

Powered by Aladin E

2MASS colored~3

1’ 19.05’ x 19.62’

N

Powered by Aladin E

DSS colored~1

1’ 19.05’ x 19.62’

N

Powered by Aladin E

2MASS colored

1’ 19.05’ x 19.62’

N

Powered by Aladin E

FIGURE1:Optical (left) and infrared (2Mass; right) view of Algol (βPersei; top) and Sheliak (βLyræ; bottom), two prototypes of different classes of interacting binaries introduced within this thesis. Credits: Aladin outputs.

Chapter 1

I NTRODUCTION TO BINARY STAR EVOLUTION AND A ^LGOLS

...Assurons-nous bien du fait, avant que de nous inquiéter de la cause. Il est vrai que cette méthode est bien lente pour la plupart des gens qui courent naturellement à la cause, et passent par-dessus la vérité du fait ; mais enfin nous éviterons le ridicule d’avoir trouvé la cause de ce qui n’est point.

...

...De grands physiciens ont fort bien trouvé pourquoi les lieux souterrains sont chauds en hiver, et froids en été. De plus grands physiciens ont trouvé depuis peu que cela n’était pas.

Fontenelle, Histoire des Oracles, Chapitre IV, pp.20 et 23

Contents

1.1 A brief introduction to stellar evolution . . . . 2

1.1.1 Stellar evolution seen through Hertzsprung-Russell and Kippenhahn Diagrams 2 1.1.2 The birth of stars: from Pre-Main Sequence to Zero Age Main Sequence stars . . 4

1.1.3 Main Sequence stars . . . 5

1.1.4 Ascending the Red Giant branch . . . 6

1.1.5 The helium core flash . . . 6

1.1.6 Horizontal Branch . . . 6

1.1.7 Asymptotic Giant Branch and latter stages . . . 7

1.1.8 Evolution of the stellar radius . . . 7

1.2 Binarity . . . . 7

1.2.1 Classification of binary stars . . . 8

1.2.2 The importance of the initial periods and stellar masses . . . 9

1.2.3 The two-body system . . . 9

1.2.4 Mass and angular-momentum transfer between two stars . . . 11

1.2.5 Stellar winds . . . 11

1.2.6 Mass loss via Roche lobe overflow . . . 13

1.2.7 Mass accretion due to Roche lobe overflow . . . 13

1.2.8 The effects of mass transfer and mass loss on the orbital parameters . . . 14

1.3 Algols among interacting binaries . . . . 14

1.3.1 First limitation of our understanding of Algols: non-conservative evolution . . . 15

1.3.2 Second limitation of our understanding of Algols: the spin up of the gainer star 18 1.3.3 Accretion discs in Algols . . . 19

1.4 Sub-types of Algol systems . . . . 20

1.4.1 βLyræ . . . 20

1.4.2 W Ser systems . . . 21

1.4.3 The B[e] stars case . . . 22

1.4.4 Contact systems — W UMa type star . . . 22

1.4.5 Symbiotic Algols . . . 23

1.5 Tackling the “critical rotation” and “systemic mass loss” problems . . . . 24

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U

^Pto 50% of all the observed stars evolve with one (or several) companions forming a binary or multiple system (Duquennoy and Mayor,1991;Fischer and Marcy,1992;Lada,2006). Given the gargantuan number of stars (and binary systems) accessible to our telescopes, the first step of the work of an astronomer is to classify the objects. However, given the exceptional diversity of single stars, it is clear that binary stars can also offer a large variety of configurations, and therefore types of systems.

Depending on the initial period and masses, the spectral type of each star, the evolutionary status of the binary, we can classify these objects into different categories. More interestingly, some systems will show specific physical features/processes that will lead to a completely new class of binary. One thesis manuscript can not cover all binary systems and I will restrain myself to the small portion of low- and intermediate-mass binary systems that are Algol systems. I will also only consider binaries at birth and will not consider capture binaries that can form during stellar encounter. This implies that the binary systems I am treating have evolved from a stage where the two stars were on the main sequence stars.

But before investigating the evolution of binary stars, I will review some concepts of the structure and evolution of single stars.

1.1 A brief introduction to stellar evolution

T

^HEevolution of a single star is primarily governed by its initial mass, and to a lower extent by its chemical composition. It is then natural to categorize stars with respect to their mass.

Stellar objects with masses below 0.08 M_⊙ do not ignite hydrogen and are referred to as brown dwarfs for the most massive ones or planets (below 0.015 M_⊙, i.e. 16 Jupiter masses). The difference in the naming comes from the fact that the more massive brown dwarfs ignite deuterium. The realm of stars really begins with the red dwarfs whose mass ranges between approximately 0.08 and 0.4 M_⊙. These stars slowly burn hydrogen into helium in their core. Low-mass stars are objects with masses in the range 0.4 to 2-2.5 M_⊙. As we will see later, they have the particularity to evolve through the helium flash. From this upper limit and up to≈^{8 M}⊙is the category of intermediate-mass stars. Over 8 M_⊙, we enter the domain of massive stars. This thesis will only consider binary systems with the two components in the regime of low- and intermediate-mass stars. The evolution of such single stars, and by extension the evolution of the two components of very wide binary star (with no or negligible interactions) have been deeply studied within the past 50 years and then modelled thanks to increasing computational power. There is still a lack of comprehension of some properties or physical mechanisms.

However, their overall evolutions have been modelled already with accuracy. In this chapter I briefly recap the global evolutionary sketch of these stars. This chapter is based on the review ofHarpaz(1994) andCarroll and Ostlie(1996).

1.1.1 Stellar evolution seen through Hertzsprung-Russell and Kippenhahn Dia- grams

Before entering the details of stellar structure and evolution, it is necessary to introduce two interest- ing ways to ‘see’ the evolution of stars: the Hertzsprung-Russell and the Kippenhahn diagrams. Since they are complementary, these diagrams are a good way to follow the evolution of single, and by ex- tension, binary stars. Hertzsprung-Russell diagrams give indications of the surface properties of a star, the temperature and luminosity and also provide information about the evolutionary stage of a star.

Kippenhahn diagrams, on the other hand, allow to inspect the evolution of the internal structure.

Figure 1.1 shows the position of nearby stars in the Hertzsprung-Russell diagram and Fig. 1.2 illus- trates the evolution of stars with different initial masses. What is interesting to note is that in Fig. 1.1, stars populate specific regions of the diagram while Fig. 1.2 does not seem to show such effect, indicat- ing that stars spend more time in some evolutionary states than others.

1

http://dsar.u-strasbg.f r/vi z-b in/ Cat? V/70 A

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BRIEF INTRODUCTION TO STELLAR EVOLUTION

F^IGURE1.1:

Hertzsprung Russell diagram for 22 000 stars observed with the Hip- parcos¹satellite (van Leeuwen,2007) and 1 000 low luminosity stars from the Gliese² catalogue of nearby stars (Gliese and Jahreiss, 1995). The colour of each dot is representa- tive of the temperature of the star. Labelled pink lines denote the different categories of stars. The white box is the domain of Fig. 1.2.

FIGURE1.2:Stellar evolution seen through a Hertzsprung-Russell diagram for different masses (1 M_⊙- 8 M_⊙), from the pre-main sequence phase up to the blue loop. The labels correspond to the Zero Age Main Sequence (see Sect. 1.1.2) mass of each star. Dashed-cyan line: pre-main sequence phase; solid black line: main se- quence up to the establishment of a hydro- gen burning shell; solid red line: ascent on the red giant branch; solid blue line: core helium burning phase. Models computed by Lionel Siess withSTAREVOL.

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FIGURE1.3: Kippenhahn diagrams corresponding to the evolution of a 1 M_⊙star (left) and a 4 M_⊙star (right).

In Hatched regions represents the convective zones. The hydrogen burning zone is delimited by the dashed-green line and the nuclear energy production peak by a dotted-green line. The helium burning region uses the same convention but in blue. From left to right, the three panels use different time labels.

Figure 1.3 shows the Kippenhahn diagrams for two selected stars (1 M_⊙and 4 M_⊙) corresponding to two evolutionary tracks presented in Fig. 1.2. These diagrams are presented as a function of the mass (instead of the radius) to have a Lagrangian point of view. As a consequence, the core may appear much larger than the envelope which can also help us to better see the details of its evolution. For example, for the 1 M_⊙star the convective envelope (hatched regions) that forms during the first stages of stellar evolution (left box) appears thin because it only represents a small fraction of the total mass of the star (≈2.5%) although it accounts for a large portion of the star is radius. Once again, this diagram will be better explained when I will develop the various phases of the evolution of a star.

1.1.2 The birth of stars: from Pre-Main Sequence to Zero Age Main Sequence stars

Stars form from the collapse of extended molecular clouds mainly composed of hydrogen (70%), helium (28%) plus some other heavier elements called metals. The cloud composition may vary depending on, for example, the stars’ generation (primordial stars or stars forming from the ashes of other stars), the region of formation, ... These clouds, subject to gravitational instabilities, collapse and fragment, leading to the formation of dense cores. It is already worth mentioning that due to the cloud fragmentation process, stars do not form alone but rather in large brotherhoods. Indeed, massive clouds can lead to the formation of hundreds to thousands of smaller cores, each one of them possibly turning into a star.

The energy released by the gravitational contraction of the proto-stellar cores heats the matter, which in turn ionises the gas and increases the opacity causing the envelope of the proto-star to become con- vective. The pace of evolution slows down and is limited by the rate at which the star can thermally adjust to the contraction. This is the Kelvin-Helmholtz timescale.

The star now contracts as a pre-main sequence star, following a quasi-vertical line in the Hertzsprung- Russell diagram called the Hayashi line. This line represents the boundary between which stellar mod- els are allowed. To the right of the Hayashi line, there is no mechanism that can efficiently transport the luminosity outwards at these low temperatures. To the left, convection and/or radiation are responsible for the energy transport.

As the temperature increases, nuclear reactions ignite in the core. The first one to activate is the deuterium burning, although for low- and intermediate-mass stars, its nuclear energy production re- mains inefficient to oppose the contraction and the core temperature keeps increasing. The star finally arrives on the Zero-Age Main-Sequence line (ZAMS) when the central temperature reaches 10⁷K for

1.1. A

BRIEF INTRODUCTION TO STELLAR EVOLUTION

0.4 8

Core H burning

Shell H burning 1.85

2.2

He Flash

Core He Burning

H & He Shell Burning

CO White dwarf Inert He core

Inert CO core

Low- and intermediate-mass stars

Radiative core Convective envelope

Convective core radiative envelope

Main Sequence

Red Giant

AGB

Remnant

Mass

Time

1.25

FIGURE1.4:Schematic evolution of low- and intermediate mass stars in the mass range 0.4 to 8 M_⊙.

hydrogen-fusion to start. The thermal pressure from the core burning regions eventually balances the inward gravitational pull preventing any further contraction.

The physical processes at work during star formation are very rich and interesting for the study of binary stars. There are many analogies between the two types of systems, such as the formation of discs or bipolar outflows among others. In Sect. 1.4, it is shown that some observed binary stars are sometimes even confused with young stellar objects.

1.1.3 Main Sequence stars

After hydrogen ignites in the core, the star remains in thermal and hydrostatic equilibrium. The stellar luminosity, initially provided by the contraction (gravitational energy), now comes from nuclear reac- tions. During this phase, the star slowly evolves along the so-called Main Sequence (MS) on a nuclear time-scale which strongly depends on the initial mass. A rough approximation of the Main Sequence duration is given by:

τ_MS≈¹⁰¹⁰ M_∗

M_{⊙ −}2.5

yr, (1.1)

with M_∗ the stellar mass in solar masses. For the sun, this translates to a main sequence lifetime of

∼ ¹¹×^{109yr, and}∼ ⁹×¹⁰⁷ yr for a 5 M_⊙ star. Because the main sequence lifetime is substantially longer than the subsequent evolution (∼ 70 to 90% of the lifetime of the star depending on its mass), most of the stars we observed are in this stage. This explains why the main-sequence line is highly populated.

The hydrogen in the core fuses into helium following two main cycles: the PP chain and the CNO cycle. The PP chain consists on building one⁴₂He by fusing ¹₁H atoms together. On the other hand, the CNO cycle needs carbon as catalyst. The PP chains remain the main channel for low mass stars (< _1.2M⊙) due to the lower temperature required for this cycle to be efficient. On the contrary, the CNO cycle is dominant in heavier stars. At its present stage, the sun burns its hydrogen through both