Chapter 1 Introduction 1.1 Stars A star is a sphere of gas and plasma that holds its shape through hydrostatic and thermal equilibrium. Hydrostatic equilibrium in a star is achieved by a balance between the force of gravity and the pressure gradient force. The force of gravity pushes the stellar material towards the center of the star, while the gas pressure pushes the material outwards into space. The combination of the pressure, density, temperature and chemical composition enforces that stars are gaseous throughout. When a star is in thermal equilibrium, the tem- perature of the gas is constant over time for a given radius. The temperature is maintained by energy production inside the star. Many energy sources are available, e.g. gravitational, chemical and thermonuclear energy, but only thermonuclear energy can account for the stellar luminosities and lifetimes. In a thermonuclear reaction (‘burning’), energy is pro- duced by the fusing of two nuclei into a more massive nucleus. Energy losses at the surfaces of stars is what we as observers on Earth perceive as starlight. 1.2 Stellar evolution of low- and intermediate-mass stars The equilibrium structure of a star slowly (and sometimes rapidly) changes in time as the energy production in the star changes. The long-term evolution of the star is driven by successive phases of nuclear burning. Initially stars mainly consist of hydrogen, which is fused into helium in the stellar core. This phase is known as the main-sequence phase. It 10 −2.8 lasts for about 90% of the stellar lifetime, which is approximately 10 (M/M⊙) yr, where 1 M is the mass of the star and M⊙ the mass of the Sun . When hydrogen is exhausted in the core, the star increases in size and becomes a giant. Core burning ceases, however, 1This is called the nuclear evolution timescale. 1 Chapter 1 : Introduction hydrogen burning continues in a shell around the inert core. Since the core is no longer supported by enough thermal pressure, the core contracts. This in turn leads to a dramatic expansion of the stellar envelope to giant dimensions. For low- and intermediate-mass stars (M . 8M⊙) the stellar radius increases by a factor of about 10-100 compared to the main- sequence radius. When the density and the temperature in the core become sufficiently high, core helium burning is ignited and carbon and oxygen are formed. For a low mass star of M . 2M⊙, helium ignition occurs under degenerate conditions, while helium is ignited non-degenerately for more massive stars. When the core runs out of fuel once again, fusion continues in a shell around the carbon-oxygen core. At this stage there are two burning shells embedded in the star, a hydrogen burning shell and a helium burning shell. The envelope has expanded even more to roughly 100-500 solar radii (R⊙). For stars of M . 6.5M⊙ this is the end of the line; the density and temperature in the core will not reach values that are sufficiently high to ignite carbon. In more massive stars of 6.5M⊙. M . 8M⊙, carbon will ignite which leads to an oxygen-neon core. For all low- and intermediate-mass stars, stellar evolution ends when the envelope is dispersed into the interstellar medium by stellar winds. The remaining core continues to contract as it cools down, until it is supported by electron degeneracy pressure; a white dwarf is born. 1.3 Binary evolution Most stars are not isolated and single stars, like our Sun, but they are members of binary systems [or even multiple stellar systems, e.g. Duchêne & Kraus, 2013]. If a star is in a close binary system, its evolution will be modified by binary interactions. For low- and intermediate-mass stars this occurs if the initial orbital period is less than about 10 years. Examples of binary interactions are mass transfer, mergers and tidal interaction. 1.3.1 Roche lobe geometry A useful geometry for isolated, circularized binary systems, is the co-rotating frame of the binary. The potential in this frame is called the Roche potential (see Fig. 1.1 top panel). Close to a star the potential field is dominated by the gravitational potential field of that star. The surfaces of equal potential (see Fig. 1.1 bottom panel) are centred on that star and approximately circular. At larger distances the surfaces of equal potential are distorted in tear-drop shapes. The figure of eight that passes through L1 are the Roche lobes of each star. L1 is the first Lagrangian point which is a saddle point of the potential field in which the forces cancel out. If a star overflows its Roche lobe, matter can move freely through L1 to the companion. 2 1.3 Binary evolution Figure 1.1: The Roche potential of a close binary in a binary star with a mass ratio of two in the co-rotating frame. On the top the Roche potential is shown in 3D, where as on the bottom a contour plot is shown of equipotential surfaces. L1, L2 and L3 are the Lagrangian points where forces cancel out. Courtesy of Marc van der Sluys. 3 Chapter 1 : Introduction The Roche lobe geometry naturally distinguishes between three types of binary stars: Detached binaries • These are binaries in which the outer shells of both stars lie within their respective Roche lobes. The stars only influence each other through tidal interactions or through stellar winds. Semidetached binaries • In a semidetached binary, one of the star fills its Roche lobe. Mass is transferred from the envelope of the Roche-lobe filling star through L1 towards the detached companion star (see Fig. 1.1). The mass transfer significantly alters the evolution of the two stars. In this thesis we will study how mass transfer affects binaries and their stellar components. Contact binaries • Contact binaries are binaries in which both stars fill or overfill their Roche lobes. Both stellar components are gravitationally distorted and surrounded by a common photosphere through which the stars are in physical contact. 1.3.2 Mass transfer When one of the stars overflows its Roche lobe, it tends to lose most of its envelope. The evolution of the star is significantly shortened or even stopped prematurely. In the latter case, nuclear burning ceases after the mass transfer phase. Consequently, the inert core contracts and cools down to form a white dwarf2. On the other hand, the evolution of a star is shortened e.g. for a star that loses its hydrogen-rich envelope but nuclear burning continues in the helium-rich layers of the star. The companion star can accrete none, a fraction, or all of the mass that is transferred to it. The response of a non-degenerate star to accretion is to re-adjust its structure. This can cause the stellar core to grow in mass adding unprocessed material (a process called ‘rejuvenation’). On the other hand, accretion onto white dwarfs is a complicated process due to possible nuclear burning of the accreted matter (see Sect. 1.3.3). If the mass transfer phase proceeds in a stable manner [Webbink, 1985; Hjellming & Webbink, 1987; Pols & Marinus, 1994; Soberman et al., 1997], the donor star will stay within its Roche lobe, approximately. The donor has to readjust its structure to recover hydrostatic and thermal equilibrium. The orbit is affected by the re-arrangement (and possible loss) of mass and angular momentum, and it widens in general. When mass transfer becomes unstable, the donor star will overflow its Roche lobe further upon mass loss. Subsequently the mass transfer rate increases even more leading to a runaway situation. A common 2This is strictly only true for the low- and intermediate-mass binaries that this thesis focuses on. More massive stars can evolve into a neutron star or black hole. 4 1.3 Binary evolution envelope develops around both stars (see Sect. 1.3.4). The binary may evolve to a more stable configuration or merge into a single, rapidly rotating star. Mass transfer can become unstable through a dynamical or tidal instability. The dy- namical stability of mass transfer depends on the response to mass loss of the donor star and the Roche lobe of the donor star in the first place. When the Roche lobe of the donor star shrinks faster than the radius of the donor star shrinks, a dynamical instability oc- curs. Or vice versa, when the Roche lobe increases more slowly than the donor star, mass transfer is dynamically unstable. In the second place the response of the companion star is important. If the accretor star swells up while adjusting to its new equilibrium, it may fill its Roche lobe leading to the formation of a contact binary. Apart from the dynamical instability, a tidal instability [Darwin, 1879] can take place in compact systems with extreme mass ratios. Tidal forces act to synchronize the rotation of the stars with the orbit, but a stable orbit is not always possible. When there is insufficient orbital angular momentum that can be transferred to the most massive star, the star cannot stay in synchronous rotation. Tidal forces will cause the star to spin up by extracting angular momentum from the orbit, but in turn the binary becomes more compact and spins up. So that now the star needs even more angular momentum to stay in synchronous rotation. The result is a runaway process of orbital decay. Stable mass transfer can proceed on many timescales depending on the driving mech- anism of the mass transfer. The donor star itself can drive Roche lobe overflow on the timescale that it is evolving; due to its nuclear evolution or due to the thermal read- justment of the star to the new mass.