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P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 Binary Stars Steven N. Shore Indiana University, South Bend I. Historical Introduction II. Some Preliminaries III. Classification of Close Binary Systems IV. Evolutionary Processes for Stars in Binary Systems V. Mass Transfer and Mass Loss in Binaries VI. X-RaySourcesandCataclysmics VII. Formation of Binary Systems VIII. Concluding Remarks GLOSSARY Red giant Stage of helium core burning; subsequent to the subgiant stage. Accretion disk Structure formed when the material ac- Subgiant Stage of hydrogen shell burning, when the deep creting onto a star has excess angular momentum, form- envelope initiates nuclear processing around an inert ing a circulating disk of material supported by internal helium core produced by main sequence hydrogen core pressure and heated by turbulent stresses. fusion. This is the transition stage in the expansion of Lagrangian points Stable points in the orbit of a third the envelope from the main sequence to the red giant body in a binary system; the inner Langrangian point, phase. L1, lies along the line of centers and marks the Roche Units Solar mass (M⊙), 2 × 1033 g; solar radius (R⊙), limit for a tidally distorted star. 7 × 1010 cm. Main sequence Phase of hydrogen core burning; first stable stage of nuclear processing and longest epoch in the evolution of a star. BINARY STARS are gravitationally bound stars, formed Mass function Method by which the mass of an unseen simultaneously or by capture, that orbit a common cen- companion in a spectroscopic binary can be estimated ter of mass and evolve at the same time. These stars are using the radial velocity of the visible star and the or- formed with similar initial conditions, although often quite bital period of the binary. different masses. Visual binaries are both sufficiently sep- Orbital parameters Inclination, i , of the orbital plane arated in space and sufficiently near that their angular mo- to the line of sight; P, the period of revolution; e, the tion can be directly observed. Spectroscopic binaries are eccentricity of the orbit; q, the mass ratio. unresolved systems for which motion is detected using 7 P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 78 Binary Stars radial velocity variations of spectral lines from the com- sult of the work at Bamberg under Argelander, large-scale ◦ ponent stars. If the orbital plane is inclined at nearly 90 searches for variable stars began to produce very large to the line of sight, the components will display mutual samples of stars with β Persei-like behavior. By the mid- eclipses. Depending on the orbital period and mass, the 1920s, much of the theory of geometric eclipses had been stars may share a common envelope (contact), be in a state developed. Russell and Shapley, in particular, included of unidirectional mass transfer between the components the effects of reflection (scattering) and ellipsoidal (tidal) (semidetached), or evolve without mass transfer but with distortions. mutual gravitational perturbation (detached). In semide- Most theoretical work on binary stars is the product of tached systems, depending on the rate of mass transfer and the past 70 years. Methods for the analysis of eclipses, the nature of the accreting object, a hot accretion disk will based on light curve fitting by spheroids, were developed be formed. If the companion star is gravitationally col- by Russell and Merrill in the first two decades of this cen- lapsed, being a neutron star or black hole, X-ray emission tury. Atmospheric eclipses were first discussed by Kopal will result. Accretion onto white dwarf or neutron stars in the 1930s. The study of mass transfer in binary sys- results in flash nuclear reactions that can trigger the nova tems was initiated largely by Struve in the mid-1930s, and event. the applications of orbital dynamics to the study of mass transfer began in the 1940s with Kuiper’s study of β Lyrae. Using large-scale computer models, stellar evolution in bi- I. HISTORICAL INTRODUCTION nary star systems was first studied in detail in the 1960s by Paczynski and collaborators in Warsaw, Plavec and At the close of the eighteenth century, William Herschel colleagues in Prague. Hydrodynamic modeling has only argued that the frequency of close visual pairs was larger in recently been possible using realistic physics and remains any area of the sky than would be expected by chance. On a most interesting area of study. Much recent work on bi- this basis, it was suggested that binary stars—that is, phys- nary star evolution and hydrodynamics has been spurred ically gravitationally bound stellar systems—must exist. by the study of binary X-ray sources. Following the dis- Prior to the discovery of Neptune, this was the most dra- covery of binarity for several classical novas, by Walker matic available demonstration of the universality of New- in the 1950s, the connection between low-mass X-ray bi- ton’s theory of gravitation. Herschel, Boole, and others naries and cataclysmics has been central to the study of extended this study to the demonstration that clustering is evolution of stars undergoing mass exchange. a general phenomenon of gravitational systems. The discovery of the wobble in the proper motion of Sirius led Bessel, in the 1840s, to argue for the presence of a low- II. SOME PRELIMINARIES mass, then unseen companion; it was discovered about 20 years later by Clarke. Routine observations of visual The broadest separation between types of binary stars is on binary star orbits were being made by the end of the cen- the basis of observing method. For widely separated sys- tury. For very low mass stars, the method is still employed tems, which are also close to us, the stars appear physically in the search for planets through proper motion perturba- distinct on the sky. If the orbital periods are short enough tions, much like the method by which Neptune was dis- (that is, less than millennia), it is possible to determine the covered, although velocity variations have now supplanted plane of the projected orbit by observing directly the mo- this search strategy. tion of the stars. For those systems in which the luminosity About the same time as Herschel’s original work, ratios (and possibly mass ratios) are large, it is possible Goodricke and Piggott observed the photomeric variations to obtain orbital characteristics for the two members by in the star β Persei, also known as Algol. The variations, observing periodic wobbling in the proper motion of the he argued, were due to the system being an unresolved, visible member. Such methods are frequently employed in short-period binary system, with one star considerably the search for planetary-like companions to high proper brighter than the other but otherwise about the same phys- motion stars (that is, stars with large transverse velocities ical size. They postulated that the light variations were to the line of sight, such as Barnard’s star). For systems of consistent with eclipses, and that were we able to resolve low proper motion and possibly long period, speckle in- the system, we would see two stars orbiting a common cen- terferometry, intensity, and Michelson interferometry, as ter of mass with about a three-day period. The dramatic well as lunar occultations, can be useful in separating com- confirmation of this picture came with the discovery, by ponents and at least determining luminosity ratios. Such Hartmann and Vogel at the end of the last century, of ra- methods, extended to the near infrared, have been recently dial velocity variations in this system consistent with the employed in the search for brown dwarf stars, objects of eclipse phenomenology. By mid-century, in part as a re- Jupiter-sized mass. P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 Binary Stars 79 When the system is unresolved, even at separations that marks the major axis of each ellipse, determines the of several milliarcseconds, it is necessary to employ shapes of the velocity variation curve with orbital phase. spectroscopic methods to determine the composition and motion of the constituent stars. These are the spectroscopic binaries, by far the largest group so far studied. Two meth- B. Eclipsing Binary Light Curves ods of analysis, which are happily sometimes complemen- The orbital plane of eclipsing stars lies perpendicular to tary, can be used—observation of radial velocity variations the plane of the sky. Depending on the relative sizes of the of the components and eclipse phenomena. stars, the orbital inclination over which eclipses can occur is considerable, but in general only a small fraction of the A. Spectroscopic Binary Velocity Curves known binary systems will be seen to undergo eclipses. The variation in light serves two purposes. It permits a Consider two stars in a circular orbit about the center of determination of the relative radii of the stars, since the mass. Regardless of the perturbations, we can say that the duration of ingress and the duration of eclipse depend on separation of the two stars of mass M1 and M2 is a = the difference in the sizes of the stars. That is, if t1 is r1 + r2 in terms of separation of the stars from the cen- the total time between first and last contact, and t2 is the ter of mass. The individual radii are the distances of the duration of totality, assuming that the eclipse is annular or components from the center of mass: total, then, r1/r2 = M2/M1 (1) t1 rg + rs = (5) The velocity ratio is given by V2/V1 = M1/M2 for a circu- t2 rg − rs lar orbit, where V is the orbital velocity. By Kepler’s law, 2 3 where r s is the smaller and rg is the greater radius, respec- G M = ω a (2) tively. The diminution in light from the system depends where ω is the orbital frequency, given by 2π/P where P on the relative surface brightness of the stars, which in is the period, and M is the total mass of the system. Now, turn depends on the surface (effective) temperature, T eff. assume that the inclination of the plane of the orbit to the Eclipses will not be total if the two stars are not precisely observer is i , that the maximum observed radial velocity in the line of sight, unless they differ considerably in ra- for one star is given by K , and that we observe only one dius, so that the mark of totality is that the light does not of the stars. Then, vary during the minimum in brightness. / 3 3 3 2 K P/2πG = M sin i M = f (M) (3) 2 The function f (M) is called the mass function and depends C. Distortions in Photometric only on observable parameters, the maximum radial ve- and Velocity Curves locity of one of the stars, and the period of the orbit. If M1 Several effects have been noted that distort the light curve is the mass of the visible star, f (M) serves to delimit the and can be used to determine more physical information mass of the unseen companion. If both stars are visible, about the constituent stars. then, K1/K2 = M2/M1 (4) 1. Reflection Effect: External Illumination independent of the inclination. Thus, if both stars can be observed, both the mass ratio and the individual masses Light from one component of a close binary can be scat- can be specified to within an uncertainty in the orbital in- tered from the photosphere and outer atmosphere of the clination using f (M). The mass function permits a direct other, producing a single sinusoidal variation in the system determination of stellar masses, independent of the dis- brightness outside of eclipse. This reflection effect is use- tance to the stars. This means that we can obtain one of ful in checking properties of the atmospheres of the stars. the most important physical parameters for understanding If the illuminating star is significantly higher temperature, stellar evolution merely by a kinematic study of the stars. it can also produce a local heating, which alters the atmo- If the orbit is eccentric, departures from simple sinu- spheric conditions of the illuminated star. Such an effect soidal radial velocity variations with time are seen. The is especially well seen in X-ray sources, particularly HZ eccentricity of the orbit also introduces another symmetry- Her = Her X-1, which varies from an F-star to an A-star breaking factor into the velocity variations, because the an- spectrum as one moves from the unilluminated side to the gle between the observer and the line of apsides, the line substellar point facing the X-ray source. P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 80 Binary Stars 2. Photospheric Nonuniformities: Starspots 5. Limb Darkening A similar phenomenon has been noted in the RS CVn stars, Stellar surfaces are not solid, and they have a continuous where it is caused by the presence of large-scale, active variation in surface brightness as one nears the limb. This magnetic regions, called starsports, on the stellar surfaces. effect, called limb darkening, is produced by the temper- Unlike reflection, these dark regions migrate with time ature gradient of the outer stellar atmosphere compared through the light curve as the active regions move with the with the photospheres. The effect of limb darkening on differential rotation of the stellar envelope, analogously light curves is to produce a departure from the behavior to the motion of sunspots. Chemically peculiar magnetic of simple, uniform spheres most notable in the softening stars also show departures from simple eclipse profiles, of the points of contact during eclipse. It is one of the best because of locally cooler photospheric patches, but these ways available for measuring the temperature gradients of appear to be stable in placement on the stellar surface. stellar atmospheres. 3. Circumstellar Material 6. Apsidal Motion: Orbital Precession The presence of disks or other circumstellar matter also The additional effect of the tidal distortion is that the stars distorts the light curves and can alter the radial velocity are no longer simple point sources, but produce a perturba- variations as well. In Algol systems, this is especially im- tion on the mutual gravitational attraction. The departure portant. The timing of eclipses indicates a circular orbit, of the gravitational potential from that of two point masses while the radial velocity variations are more like that of produces apsidal motion, the slow precession of the line a highly eccentric one. The explanation lies in the fact connecting the two stars. This rate depends on the de- that here is considerable optical depth in the matter in the gree of distortion of the two stars, which in turn provides orbit, which results in the atomic lines producing a dis- a measure of the degree of central concentration of the tortion in the radial velocity variations. Many of the W stars. Such information is an important input for stellar Serpentis stars show this effect. It is most noticeable in evolutionary models. One system that has been especially eclipsing systems because these present the largest path well studied is α Virginis (Spica). An additional source length through material in the orbital plane. In some cases, of apsidal motion is the emission of angular momentum atmospheric eclipses can also distort the lines because of from the system, and the presence of a third body. stellar winds and convection cells intercepted by the line of sight. These motions, however, are generally small com- 7. Third Light pared with the radial velocity and so alter the photometry (light-curve instabilities during eclipse are well marked Either because of circumstellar material in the orbital in the ζ Aur stars) but do not seriously affect the radial plane, which is not eclipsed but which scatters light from velocity determinations. the binary components, or because of the presence of a faint third body in the system that is unresolved, some additional light may be present at a constant level in the 4. Ellipsoidal Distortions: Tidal Interaction eclipsing binary light curve. Frequently, high-resolution spectroscopy is able to reveal the lines of the companion If the stars are close enough together, their mutual gravita- star, as in Algol, but often it remains a problem to figure tional influences raise tides in the envelopes, distorting the out the source for the nonphotospheric contributions to the photospheres and producing a double sinusoidal continu- light curve. This is simply added as an offset in the deter- ous light variation outside of eclipse. Many of these sys- minations of eclipse properties in most methods of light- tems also suffer from reflection-effect distortion, so there curve analysis. Such emission may also arise from shocks are many equivalent periods in these systems, depending in accretion disks and from intrinsic disk self-luminosity. on whether or not they eclipse. Departures from symmetric minima should accompany expansion of the stars within their tidal surfaces. As the photosphere comes closer to the tidal-limiting radius, the III. CLASSIFICATION OF CLOSE Roche limit, the star becomes progressively more distorted BINARY SYSTEMS from a symmetric ellipsoid and the photometric variations become more like sinc curves. An additional feature is There are several distinctive classes of binary stars, dis- that as the stars become larger relative to the Roche limit tinguished nominally by their prototypes, usually the first they subtend a greater solid angle and display increasing observed or best known example of the phenomenology. reflection effect from the companion. In several cases, however, overlaps in the properties of the P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 Binary Stars 81 various systems make the prototypical separation confus- companion and possibly from the system. This actually ing and less useful. Two main features distinguish classes occurs before the photosphere reaches RRL in the absence of stars: the masses of the components and the separations. of magnetic fields or other constraints on the flow. Several Alternatively, the period of the binary and the evolution- analytic approximations have been derived for the radius ary status of the components are useful, and we shall use of the equivalent sphere whose volume equals that of the these alternately as needed. appropriate lobe. In general, the Roche radius depends on The broad distinction among various binaries is whether the mass of the components and q through RRL = f (q)a, the stars are physically separated by sufficient distance that where f (q) is provided by functional approximate fits to the photospheres are distinct, in which case they are called the exact calculations. Two compact, though restricted, detached, or have been significantly tidally distorted and approximations are may be in the process of mass transfer in some form. This latter class divides into those that have only one star f (q) = 0.2 + 0.38 log q (0.5 ≤ q ≤ 20) transferring mass, the semidetached, and those with both ( ) 1/3 (7) stars immersed in a common envelope of gas that is mu- q f (q) = 0.462 (0 ≤ q ≤ 0.5) tually exchanged, the contact systems. This classification, 1 + q first developed by Kuiper, has proven to be a most general taxonomic tool for distinguishing the various physical Binary systems are theoretically distinguished by the processes that occur at different stages in the evolution of sizes of the components relative to their respective Roche close binaries. It is most important to note that a binary, lobes, although a system in its lifetime may pass through depending on its initial period, mass, and mass ratio may several or none of these, depending on the separation of pass through any or all of these stages at some time in its the stars and their masses. Stars that are in mutual contact life. This is due to the expansion of stellar envelopes as with, or overflowing, their critical equipotential surfaces stars evolve. are called common envelope or contact systems. When only one star’s radius equals its Roche radius, the system is called semidetached. Finally, if both stars are sep- A. The Roche Surface arate, however much they may be distorted, the binary is The key element in binary star evolution is the role of the detached. Geometrical methods for treating light curves Roche limit, which was first introduced in the three-body have been developed based on this idea, each treating the problem. It is known in the celestial mechanics literature as shape of the star and the distribution of temperature over a zero-velocity surface, but we will treat it as the bounding the surface more or less phenomenologically (by scaling equipotential for a self-gravitating star: model atmospheres to the local conditions on tidal ellip- soids or Roche surfaces and piecing together the surface). G M1 G M2 1 2 2 (r) = − − − r ω (6) The tidal distortion is also important for the internal struc- r1 r2 2 ture of the stars and must be handled in a more detailed where ri = |r − xi | for masses located at positions x1 = way than the axisymmetric case, but similar problems arise M2a/M and x2 = M1a/M for a circular orbit with the nonetheless. stellar separation a. This is the potential in the corotating The Roche surface is the star’s response to the tide raised frame with frequency ω. There are five equilibrium points by its companion. There are two sorts of tides. One is the where the gradient of vanishes, three of which are along equilibrium tidal surface that is instantaneously in hydro- the line of centers. Two are peripheral to the masses and static equilibrium everywhere in the star. The baroclinicity lie as the critical points along equipotentials that envelope of the surfaces, as in the rotationally distorted case, induces both stars. These are saddle points for which particle tra- slow circulation that ultimately redistributes angular mo- jectories are unconditionally unstable. Two other points, mentum as well as energy. This produces circularization L4 and L5, lie diametrically opposite each other perpen- by loss of orbital angular momentum through viscosity and dicular to the line of centers. These are quasi-equilibrium is most efficient for stars with deep convective envelopes points for which local orbits are possible because of the because the turbulence acts like an effective viscosity. The Coriolis acceleration. The Roche lobe is the equipotential other is a dynamical tide that acts like a nonradial pulsa- that passes through L1, called the inner Lagrangian point, tion of the envelope and produces faster internal flows, that lies between the masses along the line of centers. Mass internal mixing, and redistribution of angular momentum. loss is inevitable for the star that is contacting its Roche In the Earth–Moon system, the Moon rotates with the lobe. As a star’s radius approaches the Roche surface, the same period as its orbit—that is, synchronously—while body becomes more distorted and eventually, when it con- the Earth rotates more rapidly. Any point on Earth must tacts L1, the inner Lagrangian point, it loses mass to the then experience a periodic tidal acceleration since, in the P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 82 Binary Stars rotating frame, any locale on the planet is carried through RRL until contact is broken by expansion of the system and the alternating extrema of the perturbing force. This slowly thereafter the more evolved star continues as if it were a alters the lunar orbit. The solid Earth is not distorted suffi- single star. In the event of mass loss from the gainer, the ciently to dissipate its rotational energy, hence the rotation process of mass transfer may be reinitiated at some later only slowly approaches the lunar orbital period through stage, but this is unlikely. Dropping these assumptions of tidal friction. The physical mechanism must be something constant binary mass and total angular momentum makes like this. Stars are fluid and fluids yield to shear. Hence, the the scenario more realistic but leads to a dizzying range of induced tidal distortion produces flows because the grav- phenomenological models, each marked by the adoption itational potential develops along equipotential surfaces. of specific mechanisms for breaking constancy of one or These flows transport momentum in the rotating frame, both of these quantities. leading toward solid body rotation and synchronism depending on the internal viscosity, the precise nature of 1. Common Envelope Evolution which is currently not known. Since the Roche surface represents the limit of a set of bounding equipotentials, it is a surface along which flows B. Evolutionary Stages of Stars can occur but that a star can maintain as an equilibrium in Close Binaries shape. A particularly important state is encountered by On reaching the Roche surface, the stellar envelope is pre- the binary if the radius of the outer layers of both stars sumed to become unbound, and mass loss or transfer is ini- exceeds RRL , since matter does not have to catastrophi- tiated on a hydrodynamic timescale. The star is generically cally flow toward either one from the other component. referred to as the loser or donor, terms usually applied in Instead, if both stars are in contact with L1, a low-speed the case of mass transfer between the binary components. circulation can, in principle, be established because of The companion is called the gainer, which implies some the pressure reaction from the companion’s outer layers. amount of accretion. The alternative—to call one star the The resulting optically thick common envelope should, primary and the other the secondary—is based on the rel- for contact systems, behave as if the layer sits on top of a ative contributions to the combined spectroscopic and/or very strange equipotential surface, one where the surface photometric properties and does not capture the physical gravity depends on both colatitude and colongitude. The nature of the interaction. For detached systems on the main outer bounding surface through which some mass is cer- sequence, these terms also describe the respective masses tainly lost from the binary passes through either L2 and but that correspondence breaks down once the stars begin L3, but this is small compared with the flow that must their ascent of the H–R diagram. pass through L1 to maintain thermal balance. This is the The taxonomic distinctions for the different evolution- observed situation in the W UMa stars. Marked by contin- ary cases are based on the stage at which the nomenclature uous light variations, these stars appear to be surrounded applies. Case A occurs before the terminal main sequence, by a common atmosphere, but they have otherwise stable when the loser is still undergoing core hydrogen burn- cores that place them on the main sequence. Observa- ing. This is a slow nuclear stage, and not very sensitive tionally, although the stars have different masses (q ≈ 0.5 to the stellar mass. For mass transfer to occur requires and luminosities up to a factor of 10), their envelopes very small orbital separation because of the small stellar have nearly uniform temperature requiring very efficient radii and the time scale for stellar expansion is very slow. heat transport between the components while leaving the Case B occurs after hydrogen core exhaustion and dur- stellar interior otherwise unaffected. The coolest W UMa ing a relatively rapid stage of radial expansion, either in stars must have common convective envelopes, where the the traverse across the Hertzsprung gap (hydrogen shell temperature gradient adjusts to the large variation in the burning) or on first ascent of the giant branch but before surface gravity due to the angular gradients in the equipo- helium core ignition. Case C is a late stage, when the tential. How this happens has been a controversial question star has developed a helium core and is on or near the gi- for decades and remains an important unsolved problem ant branch or asymptotic giant branch (helium shell burn- in stellar hydrodynamics. The current consensus is that ing). Two mass-transfer cases are distinguished, as well. the envelopes are never precisely in thermal equilibrium In conservative mass transfer, the process can be studied and that the mass transfer fluctuates between the com- in a straightforward way because we neglect any net mass ponents. One way to picture this is that the mass-transfer or angular momentum losses. The Roche surface would rate exceeds the thermal time-scale for the entire envelope recede into the loser were it not for the increase in the which drives thermal oscillations that periodically overfill separation between the components that results from the the Roche lobe of the gainer, or rather the star that is the change in the mass ratio. The loser maintains contact with accreter at that moment. P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 Binary Stars 83 Main sequence contact systems are only one example of 2. RS Canes Venaticorum Stars evolutionary stages where common envelopes occur. Any and Active Binaries circumstellar matter that completely engulfs the compan- Close binaries with periods less than 2 weeks induce syn- ion and is optically thick is, in effect, a common envelope. chronous rotation via tidal coupling on time scales of order Cataclysmic binaries are extremely close systems with 8 9 10 —10 yrs. For main sequence stars, this generally re- periods of less than 1 day and at least one degenerate sults in slow rotation compared with that observed in sin- component. Their origin is linked in current hypotheses gle stars; for evolved stars, the opposite holds. The RS CVn to a relatively late stage in the evolution of one of the and related stars show rapid rotation of a cool evolved star more massive components, since there are no main se- that displays enhanced dynamo activity. These stars are quence progenitors with these characteristics. There are marked by exceptionally strong chromospheres and coro- two obvious ways to form a white dwarf. One is to invoke nas, sometimes having ultraviolet (UV) and X-ray fluxes magic and drive the envelope off during planetary neb- 3 greater than 10 times that observed in normal G–K giants ula formation in the post-AGB phase. The other occurs (cool giants). The photometric behavior of these systems in a common envelope. If one star engulfs the other as is marked by the appearance of a dark wave (large active it evolves, and this can happen for virtually any system regions) which migrates through the light curve toward a with orbital periods of less than a few weeks on the main decreasing phase, suggestive of differential rotation. The sequence, the lower mass companion will find itself orbit- active stars have deep convective envelopes. Several sub- ing within a dense circumstellar environment produced by giant systems, notably V471 Tau, have white dwarf com- the more massive star. Differential motion leads to heating, panions, although most systems consist of detached sub- 3 −1 −5/2 which scales as v a ∼ a , and transfer of angular orb giant or giant primaries and main sequence secondaries. momentum between the lower mass component and the With the exception of HR 5110, most of these systems are engulfing envelope. Consequently, if the heating is suf- detached. Other representative members of this class are ficient, the more massive star is stripped of its envelope AR Lac, Z Her, and WW Dra. Typically, the mass ratios with the resulting loss of binding energy, and the com- are very near unity, although this may be a selection effect. panion spirals inward. The result is a white dwarf with An analog class, the FK Com stars, shows many of a much less evolved companion in a very short period the RS CVn characteristics, especially enhanced chromo- system. spheric and coronal activity and rapid rotation, but it appears to be a class of single stars. The FK Com stars are argued to have resulted from the common envelope phase of C. Some Prototype Subclasses an evolved system leading to accretion of the companion. of Binary Systems Both of these subclasses are especially notable as radio sources, often displaying long-time-duration (days to In this section, we summarize some general properties of 7 weeks) flares with energy releases of some 10 times that important subclasses of close binary stars. Several of these of the largest solar flares. The dMe stars are the low-mass have been discussed previously as well, in order to place analogs of these systems, although not all of these are bina- them in a more physical context. ries. It appears that the binarity is most critical in producing more rapid than normal rotation, which is responsible 1. W Ursa Majoris Systems for the enhanced dynamo activity. These are main sequence contact binaries. They are typically low mass, of order 1 − 2M⊙, with orbital periods 3. z Aurigae Stars and Atmospheric Eclipses from about 2 hr to 1 day. The envelopes are distinguished as being in either radiative or convective equilibrium. The These systems consist of hot, main sequence stars, typi- chief observational characteristics are that they show con- cally spectral type B, and highly evolved giants or super- tinuously variable light curves and line profile variations giants with low surface temperatures (G or K giants). For indicative of uniform temperature and surface brightness several eclipsing systems, notably ζ Aur, 31 Cyg, and 32 over both stars, although the mass ratio ranges from 0.1 to Cyg, eclipses of the hot star can be observed through the 1. Surface temperatures range from about 5500 to 8000 K. giant atmosphere. The B star thus acts like a probe through The lower mass systems are called W type, the higher mass the atmosphere of the giant during eclipse, almost like a systems are A type; the W-type envelopes are convective. CAT scan. Observations of photometric and spectroscopic Typical of this class are W UMa, TX Cnc, and DK Cyg. fluctuations during eclipse provide a unique opportunity There may be massive analogs of this class, although the for studying turbulence in the envelopes of evolved stars. light curves are more difficult to interpret. The systems are long period, although for several, notably P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 84 Binary Stars 22 Vul, there is evidence for some interaction between the neutron star companions. They display outbursts of the stars due to accretion of the giant wind by the main se- nova type when flash nuclear reactions release sufficient quence star in the form of an accretion wake. The most energy to expel the outer accreted layers off the surface extreme example of this subclass is ε Aur, a 27-yr-period of the collapsed star, or show unstable disks that appear binary with an unseen supergiant or hypergiant evolved to account for the dwarf novas. These systems will be dis- cool star accompanied by an early-type companion. cussed later at greater length. Among the best examples of this class are U Gem, SS Cyg, and OY Car for the 4. Algol Binaries dwarf novae; GK Per and DQ Her for the classical novae; and AM Her and CW 1103 + 254 for the magnetic white These are the classic semidetached systems. They are dwarf accreters. The low-mass X-ray binaries share many marked by evidence for gas streams, distortions of the of the same characteristics without the extreme photomet- eclipse profiles due to instabilities in the circumstellar ric variability (for example, Cyg X-2 and Sco X-1). material on the time scale of several orbits, and sometimes enhanced radio and X-ray flaring activity of the more evolved star. For several systems, notably U Cep, IV. EVOLUTIONARY PROCESSES the stream ejected from the giant hits the outer envelope FOR STARS IN BINARY SYSTEMS of the accreting star and spins it up to very high velocity. For others, the stream circulates to form an accretion Normally, stars evolve from the main sequence, during disk about the companion, which is heated both by turbu- which time their energy generation is via core hydrogen lent viscosity and the impact of the stream in its periph- fusion, to red giants, when the star is burning helium in its ery. These systems typically show inverted mass ratios, core, at roughly constant mass. While stellar winds carry in that the more evolved star has the lower mass. They off some material during the main sequence stages of mas- have masses ranging from about 1M⊙ each to greater than sive stars, most stars do not undergo serious alteration of 5M⊙ for the constituent stars. Among the best examples their masses until the postgiant stages of their lives. This of these systems are SX Cas, W Ser, and β Lyr. is only achieved when the escape velocity has been reduced to such an extent that the star can impart sufficient 5. Symbiotic Stars momentum to the outer atmosphere for a flow to be ini- These systems are so named because of the observation tiated. Envelope expansion reduces the surface gravity of of strong emission lines from highly ionized species and the star, so that the radiative acceleration due to the high cool absorption lines of neutral atoms and molecules in luminosity of stars in the postgiant stage, or the extreme the same spectrum. They consist of a highly evolved cool heating affected by envelope convection in the outer stel- giant or supergiant and either a main sequence, subdwarf, lar atmosphere, provides the critical momentum input. In or collapsed companion. Several of the systems, notably a binary system, however, the star is no longer necessarily R Aqr, show pulsating primary stars with periods of hun- free to expand to any arbitrary radius. The presence of a dreds of days. The orbital periods are typically quite long, companion fixes the maximum radius at which matter can of order one year; the mass ratios have not generally in- remain bound to a star. verted except in those systems where a white dwarf is Should the primary (that is, more massive) star in a established as a member. The ionizing source appears to binary have a radius that exceeds this value, it will develop be an accretion disk about the companion star, fed by a a cusp along the line of centers at the inner Lagrangian stellar wind and perhaps gas streams in the system. Radio point, L1. Nuclear processes continue in the stellar interior, and optical jets have been observed emanating from sev- driving the increase in the envelope radius, so that even eral systems, especially CH Cyg and R Aqr. Many of the though the mass of the star is decreasing, the center of phenomena observed in these systems are similar to those mass of the system shifts toward the companion star and observed in recurrent novae like RSOph TCrB and V3890 the continued expansion of the primary causes the mass Sgr, which have red giant companions. These systems also transfer to be maintained. Inexorably, the mass ratio will display unstable light curves, presumably attributable to continue to increase until the star is so sufficiently stripped instabilities in the accretion disks. The most extreme ex- of matter that it becomes smaller than the instantaneous amples of this class, having the longest periods and the Roche lobe. At this point, the mass transfer stops. most evolved red components, are the VV Cep stars. The evolution of the system is determined by the fraction of the lost mass that is accreted by the second star 6. Cataclysmic Variables and the fraction of both mass and angular momentum of These systems typically consist of low-mass main se- the system that is lost through the outer contact surface. quence stars of less than 1M⊙, and either white dwarf or The loss of mass from one of the stars alters its surface P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 Binary Stars 85 composition as successive layers are peeled off. It is gener- The formation of a stream is assured if the mass loss rate ally assumed that the star will appear as nitrogen enhanced, is low and the star losing mass is in contact with the Roche because the outer layers of the CNO-burning shell will be surface. In this case, the L1 point in the binary acts to exposed to view if enough of the envelope is removed. funnel the mass into a narrow cone, which then transports The OBN and WN stars are assumed to be the result of both angular momentum and mass from the loser to the such processing. In addition, the alteration of the mass of gainer. the star will produce a change in the behavior of turbu- The atmosphere of the mass losing star has a finite pres- lent convection in the envelope, although the details are sure, even though at the L1 point the gravitational accel- presently very uncertain. The enhancement of turbulent eration vanishes; thus, the mass loss becomes supersonic mixing should be responsible for exposing the effects of interior to the throat formed by the equipotentials, and nuclear processing of even deeper layers to view, but this a stream of matter is created between the stars. The fact has yet to be fully explored. that the center of mass is not the same as the center of The behavior of the mass loser with time is significantly force (that is, L1) means that the stream has an excess sensitive to whether the envelope is convective or radiative, angular momentum when it is in the vicinity of the sec- that is, to whether the primary mode of energy transport is ondary or mass gaining star. It thus forms an accretion disk by mass motions or photons. In turn, these are sensitive to around the companion. However, if the ejection velocity the temperature gradient. If the envelope is convective, the is great enough, the size of the companion large enough reduction in mass causes the envelope to expand. If radia- compared with the separation of the stars, and the mass tive, the envelope will contract on mass being removed. ratio small enough, the stream will impact the photosphere Consequently, the mass transfer is unstable if the envelope of the gainer. Instead of the formation of a stable disk, the is convective, and the star will continue to dump mass onto stream is deflected by the stellar surface, after producing the companion until it becomes so reduced in mass that an impacting shock, with the consequence that the outer its envelope turns radiative. The instability, first described layers of the gainer are sped up to nearly the local orbital by Bath, may be responsible for the extreme mass-transfer speed, also called the Keplerian velocity: events seen in symbiotic stars and may also be implicated 1/2 νK = (G M2/R2) (9) in some nova phenomena. Some mass (the fraction is not well known) will also be lost through the outer Lagrangian point, L3, on the rear V. MASS TRANSFER AND MASS side of the loser from the gainer along the line of centers. LOSS IN BINARIES The mass of the system as a whole is therefore reduced. This means that the matter can also carry away angular Mass transfer between components in a binary system momentum from the system. If the reduced mass of the takes place in two ways, by the formation of a stream or a system is given by wind. Either can give rise to an accretion disk, depending µ = M1M2/M (10) on the angular momentum of the accreting material. In the ζ Aur systems and in most WR binaries, the accretion is where M is the total mass, then the angular momentum of windlike. This also occurs in some high-mass X-rays bi- the binary is naries (HMXRB), notably Cir X-1. In these, the accretion 2 2/3 −1/3 −4/3 radius is given by the gravitational capture radius for the J = µa ω = G M1M2 M ω (11) wind, which varies as: where / 2 1 1 1 R ∼ M ν (8) wind = + µ M1 M2 where M is the mass of the accreting star and νwind is the is the reduced mass. The change in the angular momentum wind velocity at the gainer. The formation of an accretion of the system then produces a period change wake has been observed in several systems, notably the ζ ( ) ( ) Aur systems. The wake is accompanied by a shock. Should δM1 1 M1 δM2 1 M2 4 δP FJ = 1 − + 1 − + the star have a wind of its own, however, the material from M 1 3 M M2 3 M 3 P the primary loser will be accelerated out of the system (12) along an accretion cone, with little actually falling onto the lower mass component. Such wind–wind interaction for a fraction FJ of angular momentum lost from the sys- is observed in Wolf–Rayet systems, notably V444 Cyg, tem and an amount of δM of mass lost. Notice that the and is responsible for strong X-ray emission. period evolution is very sensitive to both the amount of P1: ZBU Revised Pages Encyclopedia of Physical Science and Technology EN002E-52 May 25, 2001 13:43 86 Binary Stars angular momentum lost and to the fraction of the mass gent spectrum of the material is not that of a blackbody, lost from M1, which is lost from the binary system. nor even very similar to a star. In general, it will appear to The loss of angular momentum from the system is one be a power law distribution with frequency, looking non- of the currently unknown physical properties of various thermal but in fact reflecting the run of temperature and models. It is the most critical problem currently facing pressure in the disk. those studying the long-term behavior of the mass transfer in binaries, since it is the controlling factor in the A. Accretion Disks Processes orbital evolution. Two classes of models have been pro- posed, those in which much of the angular momentum of If only one star is in contact with RRL , then secular mass transfer happens. That will now occupy our attention. the stream is stored in the accretion disk or in the spun- Mass loss must occur whenever a star comes into con- up stellar envelope of the gainer and those in which the tact with its Roche surface as a stream directed toward the J is carried out of the system entirely. Magnetic fields companion. The net gravitational acceleration vanishes at can also act to transport angular momentum, and the degree of spin–orbit coupling between the components also L1. Gas in the envelope of a star whose radius equals RRL therefore generates a pressure-driven acceleration that at affects the overall system evolution. As a result, much of the detailed behavior of mass exchanging or semidetached L1 reaches the sound speed. The result is a highly supersonic flow that launches toward the companion with the systems is not yet fully understood. sound speed from the L1 point and is deflected by the Coriolis acceleration. The stream orbits the companion and collides with itself, again supersonically, forming an VI. X-RAYSOURCESANDCATACLYSMICS oblique shock that eventually deflects it into an orbit. Ul- timately, a disk is formed, the structure of which we now The presence of a collapsed component in the system alters treat. much of the observable behavior of binaries. In particular, Mass lost through the L1 point generally carries angular the signature of mass accretion onto a white dwarf, neutron momentum, so it so cannot fall directly onto the gainer. star, or black hole is X-ray emission. With the discovery Even if it were coming from the precise center of mass, of binary X-ray sources in the late 1960s, following the the Coriolis acceleration in the corotating frame causes launch of UHURU, the first all-sky X-ray survey satel- the stream to deviate from radial infall. The condition for lite, the field has rapidly grown. Early observations were disk formation is that the angular momentum is sufficient interpreted as accretion onto white dwarf stars, but the to send material into orbit around the gainer. If the angular physical details of the accretion processes onto specific momentum is too small, the stream may directly impact the compact objects have been refined so that it is now possi- gainer. The result is local shock heating and a deflection of ble to distinguish many of the marks of a specific gainer the stream by the gainer’s atmosphere. If a disk does form, by the observable behavior. this interaction point is moved out, but it is still present. X-ray emission results from accretion onto a collapsed The reason is that the stream, which is flowing superson- star because of the depth of its gravitational potential well. ically, cannot adjust its structure on the slower sonic time As the infalling matter traverses the accretion disk, it heats scale. As a result, it slams into the circulating material up because of collisions with rapidly revolving matter and and forms a standing shock. Since it is an oblique impact, radiates most of its energy away. If the disk is optically this region refracts the shock and produces a contact, slip, thick, this radiation will appear at the surface of the ac- discontinuity at the boundary. cretion disk as a local blackbody emitter at a temperature Assuming hydrostatic equilibrium, the disk’s vertical characteristic of the local heating rate for the matter in the structure is governed by the tidal component of the disk. Since the material is slowly drifting inward, because acceleration: of loss of angular momentum through viscosity-like inter- actions within the disk, the heating can be likened to that 2 1 d P G M z v K resulting from a turbulent medium that is capable of ra- = − = − z (13) 2 2 p dz r r r diating away kinetic energy gained from infall. The mass distribution is not radially uniform, and the vertical extent The simplest estimate of the disk thickness comes from of the disk is determined by pressure equilibrium in the z 2 assuming that it is vertically isothermal, so P = pc , with s direction, so that the surface area and temperature vary as cs being the sound speed. The density therefore displays functions of distance from the central star. As a result, the a gaussian vertical profile with a scale height: flux merging from the surface and seen by a distant observer is an integrated one, summing up different regions cs z0 = r (14) of the disk which have different temperatures. The emer- vK