Binary stars, their role as determining the specific properties of stars, cluster history and in novae creation By Emilio GARCIA 13/03/2007 Uppsala University Course:1FA223 - Report code:63061 I Introduction A binary star is a star system where two stars orbit around their common barycenter. This special configuration allows certain precise measurements of their properties that are very useful as understanding the physics of stars. Especially those deduced characteristics can be included in general models to analyze a large population of various types of stars [7]. Moreover, binary are subject to a singular phenomenon. Usually, during the evolution of a normal single star, it can only lose matter under the effect of the stellar wind which gradually empties their envelope. Reversely, a star from a binary system can also acquire mass, coming from its companion. The mass of a star conditions its internal equilibrium conditions and the processes that take place in. Hence, mass transfers affect their evolution and allows extremely complex ones, depending on the gain and loss of each of the components (Part 4.1 of [1]). These interactions may end to specific creations, like novae stars. They result from the rapid fusion reaction of the very dense and hot accreted hydrogen, from one of the binary components above the surface of its companion. This material is then powerfully expelled around by the energy resulting. Hat new radiation is the light we visually observe and call as a nova star. (Part 11.5 page 220 of [10]) In this essay, we will discuss the way to observe binary systems, their role in determining the stars properties and finally the gravitational interactions ending with the formation of novae II Role in determining the properties of stars Measuring the orbits of a binary star system in terms of size, speeds, and periods is very useful. Indeed quantities calculated from are very precise, so that they can be used to calibrate instruments or provide references for astrophysics models. a) Methods of observation There are three techniques by which binary stars can be observed (page 7,9,10 of [5])[3]: - By a simple visual observation through a telescope. (about 5 to 10% of our visible stars). - By photometric measurement of changes in brightness due to eclipsing phases. - By spectroscopic measurement of the periodic changes in their spectrum. The components of binary stars orbiting in the same plane along our line of sight will eclipse and transit each other. We then call them as eclipsing binaries. By detecting their changes in brightness and spectrum during eclipse and transit phases, further analyses ends to derive physical quantities. [7] b) Measurements and deductions Masses of visual binaries can be well-determined through their observable orbits which respect Kepler s laws.[7](page 18 of [5]) Indeed ones can deduce the relation a 2 =((a 1 +a 2 ).m 1 )/ (m 1 +m 2 ). Where a 1 & a 2 are the orbital radii of the stars around the center of mass and m 1 and m 2 are respectively the two stars masses.(page 18 of [5])
Measurements of the space observatory designed for astrometry (like Hippareos and Gaia parallaxes of the European Space Agency 1997, 2013) are introduced in a suitable model taking orbital motion into account. It permits to evaluate the parallax and deduce the mass with a fractional error three times the parallax one. Finally, mass can be combined to the radius and we obtain the surface gravity, from which can be deduced the photosphere pressure and then a series of star s characteristics. [7] The scale of an eclipsing binary system may be obtained without distance consideration, and allows precise analyses of its physical proprieties. For exemplar, surface gravities may be precisely deduced from the radial velocity measurements, yielded through the orbital-motion Doppler shifts in absolute units of km/s (page 10 of [5]. The masses are then given from this radial velocities while the total duration of the eclipse is combined with the relative orbital velocities to give the radii times the sine of the angle of inclination. Radii is hence easily deductible since the angle is almost 90 for eclipsing systems. The measurements are available for both stars. Indeed, even if during the eclipse phase we only see the light of the larger star, combining spectroscopy performed during the eclipse with recordings at other phases gives the spectrum of the smaller star alone. On the other hand, eclipsing binaries are often less suitable for testing spectroscopic pressure criteria because one is faced with composite spectra. [7] Otherwise, those quantities combined with the light measured also lead to determine an empirical mass-luminosity relation for main-sequence stars (L~M ⁴). The deduced relation can then be applied to similar -no multiple- stars and estimate these star masses. (page 24 of [5]) Normally, typical formal errors are 5% with a range of 1-11% for dwarfs, and double for evolved stars. [7] But, for short orbital dimensions compared to the size of the stars, we have to take into account the possibility of mass exchange or simply often tidal interaction distorting atmospheres which induce anomalous line strengths. A small separations of the binary components usually goes with an anomalous spectrum, which can lead to radial velocity errors. Otherwise, wide binaries have small radial velocity variations, and their individual spectral lines are difficult (or impossible) to separate. Therefore the measurements we told about before, and coming from orbital analysis, are correspondingly difficult to perform and may come with increased uncertainties. [7] Finally, binary star population still represent a valuable opportunity to obtain the physical characteristics of stars, and testing ground for spectroscopic methods of determining surface gravity. All these informations can then be applied to other stars models. III Matter transfer between the binary components Gravitational interactions can distort the outer stellar atmospheres of two close binary stars. It can ends to mass exchanges between, which profoundly affect their evolution and may make them evolve to stages that are impossible to attain for single stars This evolution by mass transfer is made via the physical principle of Roche-lobe overflow. a) Roche lobe The Roche lobe designates the region around a given star in a binary system, where gravity manages to bind its orbiting material. The region in delimited by critical gravitational equipotential. [8] The precise shape of the Roche lobe can be obtained by the relation on the right, expressed as a function of the two body mass ratio (q = m 1 / m 2 ), their orbital separation (A), and where r1 is the radius of the Roche lobe around mass M1.[6] r 1 A = 2 3 0,49.q 2 0,6 q 3 +ln(1+q 1 3 )
Close to each star they are almost spherical shaped and concentric with the nearer star, but a critical equipotential intersects itself at the 1 rst Lagrangian point, forming two lobes in a figure of eight, with one of the two stars at the center of each lobe.[8] Figure 1: (on the right) Adapted from [9]: Show a numerical draw of equipotential curves in the orbital plane for a binary star system. The unstable equilibrium position L1,L2 and L3 are figured. b) configuration of binary stars and mass transfer We directly understand that the distance between the pair and their respective mass will determine the shape and size of their lobe. Reversely, the size of the star does not influence this limit. Regarding the way binary stars fill their Roche lobes permit to classify in 3 principal types: - The detached binaries, for which no star fills its lobe, so that there is no transfer of matter. These stars essentially do not affect each other and evolve separately. Most binary systems belong to this class.(page 16 of [5]) - Semi-detached binaries, where one of the two components fills its lobe and transfers part of the envelope to its companion. Their evolution is led by the mass transfer. For example, with Algol (Perseus). (page 16 of [5]) - The contact binaries whose both fill their respective lobes. The upper stellar atmospheres surround both stars as a common envelope whose internal frictions brakes their orbital motion. The stars may eventually collide, resulting in a spectacular phenomenon like a supernova or Neutron star collisions.(page 16 of [5]) Notice that a couple of binary stars can evolve from one group to another, since this description only reflects a particular stage of its evolution at the given time of observation. Their evolution depends on the initial masses of the two stars and their separation. We will then focus on binary stars sufficiently close to have a lobe limit reachable in certain conditions of star evolution. When the more-massive star of a pair evolves into a red giant, the outer envelope extends beyond its Roche lobe. The material which exceeds the Roche lobe can "fall off" into the Roche lobe of the less-massive companion via the first Lagrangian point.[8](part 4.1 & 4.2 of [1]) Otherwise, it is also possible for some matter to leave the system in the form of stellar wind or through other Lagrange points. This amount would be effectively lost to both components so that it will not be detailed in this document.(part 4.1 & 4.2 of [1]) c) Relativistic binary evolution and cluster influence The constant progress of observational techniques and technologies over the last decade led to regular and significant discoveries concerning relativistic binary, and their behavior as an isolated system or member of clusters. Actual researches are aimed at using relativistic binary population as a tracer to analyze the dynamical evolution of globular clusters. (part1&7 of [1]) Globular clusters contain an old and dense population of stars, many of which are relativistic objects. This density leads to many close dynamical interactions between stars. (Abstract of [1]) Relativistic binary contains two degenerate or collapsed stellar masses with a close orbital period. During the process by which stars become a relativistic binary, the system is composed of a normal star and a single degenerate or collapse stellar object. In the Galactic field (that is to say in relative isolation from any dense stellar clusters) most of isolated
relativistic binary systems arise from the evolution of primordial binary stars to ultra-compact orbit configurations. However, the final properties of relativistic binaries in globular clusters result from the combined effects of stellar evolution, interaction between the gravitational dynamics of N-body systems, mass transfers, and gravitational field of the galaxy. (part 4&7 of [1]) Notice that new binary systems can be created while some of them can also be turned into multiple systems, by inserting compact stellar objects into their relativistic orbits, under the effect of the gravitational dynamics in the core of a globular clusters. Moreover, it can also drive wide binary systems toward short orbital periods. Reversely, as systems get a larger and larger velocity, it may eventually be ejected from the cluster. (part 5&7 of [1]) Globular clusters with an abundance of 10 4-10 ⁶ stars were formed early in the history of the Milky Way (Abstract & 2 of [1]). The gravitational potential of this environment and the one of the globular cluster determine the threshold for ejection.(part 7 of [1]) The environment will logically change as orbiting the Milky Way. Now consider that relativistic binaries are over-represented in Galactic globular clusters, compared to the Galactic field (part 1&2 of [1]). The nature and abundance of the cluster s population (especially relativistic binaries) could inform us about the orbital history of the globular cluster. (Part 5& 7 of [1]) IV Binary evolution: The creation of a nova star Etymologically, the term nova designates a new star (stella nova). This name comes from the ancient astronomers who have been detecting them only during their phase of high luminosity, so that appearing as new to them. We will explain how, in reality, the novae stars correspond to a brief stage, intervening at the end of the existence of certain stars which are initially faint illuminating, and during which the luminosity increases suddenly. a Stage evolution by mass transfer Evolution of potential novae begins with a system of two main sequence stars. Let s consider a couple with a white dwarf and a second star that reaches the red giant stage. The white dwarf, is a small but very dense stellar core remnant, mostly composed of electron-degenerate matter without fusion processes. The small brightness emitted comes from the stored thermal energy.(part 11.6 page 223 of [10]) If the relative orbit between the stars is sufficiently tight, the outer layers of the red giant are sufficiently close to the white dwarf to be attracted. Accretion onto the white dwarf may result in a very spectacular phenomenon called a nova.[8](part 4.1 & 4.2 of [1]) When the mass transfer occurs, part of the hydrogen and helium from the red giant upper layers comes to form a disc of matter around the white dwarf. The internal friction forces applied on the gas of this accretion disk will gradually make matter falls on the dwarf and creates a layer of hydrogen, which becomes more and more dense and hot. (Part 3, 4.1&4.2 of [1])(Part 11.5 page 220 of [10]) Figure 2: Illustration above of white dwarf and the Roche lobe overflow of the main sequence companion. From [2]
b The fusion of hydrogen The temperature in the white dwarf will gradually reach about tens million kelvin where nuclear burning is initiated via the CNO cycle. At this step, a powerful thermonuclear explosion occurs on the surface, converting rapidly hydrogen in a series of heavier elements. The thermonuclear runaway here occurring ejects about 10 ⁵-10 ⁴ M of matter with a high velocities of 10²-10³ km/s [4]. The released energy, depending on the amount of hydrogen accumulated, blows the remaining gas outward and create the quick but bright outburst of light observed. [4](Part 11.6 page 223 of [10]) This phenomenon do not overly affect the white dwarf and the accumulation of hydrogen falling from its companion may end to a new explosion, after a period varying between a century and tens of thousands years. RS Ophiuchi is a good example of recurrent nova. V Conclusion We established to role of binary star system as references to supply precise physical relations and how to use it to determine the proprieties of stellar populations. We studied the ways that physical parameters are derived from different type of measurements on stars. Moreover, we analysed the uncertainties that physical models resulting will have to deal with. Then, we studied the mass transfers between two stars, and the conditions where it can occur. Analyses of this specific situation were used to introduce the possibility of studying evolution of globular clusters through the relativistic binary in. We then had a discussion about on a special cataclysm case: The novae creation. This phenomenon has been explained with respect to the physical rules developed before. Finally, ones could look further at how stable orbit shapes would change around an evolving binary star system. Then, how would evolve a third object, initially in equilibrium, like a planet? VI References [1] Relativistic Binaries in Globular Clusters Matthew J. Benacquista and Jonathan M. B. Downing - Living Rev. Relativity (December 2013) [2] CHANDRA X-ray Observatory, NASA's flagship mission for X-ray astronomy Illustration retrieved by 2017/03/12 Direct link : http://chandra.harvard.edu/edu/formal/snr/images/dwarf.jpg [3] Cornell University Chatterjee & Haynes Binary Stars courses astro2201, for spring 2017 retrieved by 2017/03/12 - http://astrosun2.astro.cornell.edu/academics/courses/ astro201/binstar.htm [4] "On the progenitors of galactic novae" Part 1 - by Darnley, Ribeiro, Bode, Hounsell and Williams - 2012/01/25 - in The American Astronomical Society [5] Caltech University, course George Djorgovski Kepler s Laws, Binaries & Stellar Masses 2004, retrieved by 2017/03/13 http://www.astro.caltech.edu/~george/ay20/ay20- Lec4x.pdf [6] Page 1, equation (2) - Eggleton, P.P. (1 May 1983). "Approximations to the radii of Roche lobes". The Astrophysical Journal. 268: 368 [7] Chap page 342 & chap 377 D. GRAY The Observation and Analysis of Stellar Photospheres Oxford Press 3rd Edition [8] Part 1 & 2 - Modelling of W UMa-type variable stars - P.L. Skelton; D.P. Smits Dpt of Mathematical Sciences - S. Afr. j. sci. vol.105 n.3-4 Pretoria Mar./Apr. 2009 [9] Chap 6 - Fig 6.11 - General Relativity With Applications to Astrophysics by Straumann, Norbert 2004 [10] An Introduction to the Theory of Stellar Structure and Evolution 2 nd Edition - Oxford Press - Dina Prialnik