Algols as limits on binary evolution scenarios

Evolutionary scenarios must account for Algol binaries surviving their first phase of mass transfer. The outcome of this phase is dependent upon the rapidity of the initial mass transfer, which can be estimated by calculating the radial reponse of potential progenitors to mass loss. Limits on the donor's evolutionary state, and its companion mass, can be placed on systems which would transfer mass on a thermal or dynamical timescale. Slower mass transfer rates are necessary for the successful transition to an Algol. Considering 1.5 and 5.0 M models, the former succeed in case A and Br systems, while the latter can do so only in case A systems. To evolve into an Algol binary, all systems seem to require initial mass ratios near one.     

Algols: Wherefrom, whereto, and what in between?

Four different aspects related to the evolution of Algols are discussed: the occurrence of a contact phase during the mass transfer, the evolution of short period systems evolving through case A mass transfer, the influence of the mass transfer on the surface abundances of both components, and the problem of the initial parameters of Algol systems. For the latter, a search is made for conservative case B systems. UZ Cyg seems to be a good candidate for such evolution. Finally, some remarks are given on the initial values of the low mass Algol S Cancri.     

Algols: Wherefrom,whereto, and what in between?

Four different aspects related to the evolution of Algols are discussed: the occurrence of a contact phase during the mass transfer, the evolution of short period systems evolving through case A mass transfer, the influence of the mass transfer on the surface abundances of both components, and the problem of the initial parameters of Algol systems. For the latter, a search is made for conservative case B systems. UZ Cyg seems to be a good candidate for such evolution. Finally, some remarks are given on the initial values of the low mass Algol S Cancri.     

Who is who in Algol-land ? - Part II -

In part I (De Greve and Packet) we have investigated the occurrence of reversed phases of mass-transfer during Case A evolution in close binaries. If the initial period of a system is shorter than 1–2 days (Early Case A) the reversed phase starts before core hydrogen exhaustion of the gainer (part I). This type of evolution is characterized by at least two phases of slow mass-transfer.We have computed the evolution of four Early Case A systems with initial masses of the loser equal to 3 Mo and 5 Mo. These four systems start mass-exchange when Xc of the primary has decreased to 0.525 (75% of its initial value). They all experience two phases of slow mass-transfer.We find that both phases have about the same duration for all systems. The mass ratios are clearly distinct, being closer to unity during the first phase. In the Hertzsprung-Russell, mass-radius and mass-luminosity diagrams both components remain close to the main-sequence band during slow mass-transfer. Evolution as an Algol is ended when both components overflow their outer critical surface after a second reversal of the mass-transfer.Observed Algol systems evolving in Early Case A are scarce. A search thruogh the catalogue by Giuricin et al. gives us the following candidates: X Tri, SX Aur and V Pup. Based on their mass ratios, SX Aur can tentatively be assigned to the first phase of slow mass transfer and X Tri to the second phase. For V Pup (which is more massive) this choice can not be made with certainty.     

Who is who in Algol-land ? - Part II -

In part I (De Greve and Packet) we have investigated the occurrence of reversed phases of mass-transfer during Case A evolution in close binaries. If the initial period of a system is shorter than 1–2 days (Early Case A) the reversed phase starts before core hydrogen exhaustion of the gainer (part I). This type of evolution is characterized by at least two phases of slow mass-transfer. We have computed the evolution of four Early Case A systems with initial masses of the loser equal to 3 Mo and 5 Mo. These four systems start mass-exchange when Xc of the primary has decreased to 0.525 (75% of its initial value). They all experience two phases of slow mass-transfer. We find that both phases have about the same duration for all systems. The mass ratios are clearly distinct, being closer to unity during the first phase. In the Hertzsprung-Russell, mass-radius and mass-luminosity diagrams both components remain close to the main-sequence band during slow mass-transfer. Evolution as an Algol is ended when both components overflow their outer critical surface after a second reversal of the mass-transfer. Observed Algol systems evolving in Early Case A are scarce. A search thruogh the catalogue by Giuricin et al. gives us the following candidates: X Tri, SX Aur and V Pup. Based on their mass ratios, SX Aur can tentatively be assigned to the first phase of slow mass transfer and X Tri to the second phase. For V Pup (which is more massive) this choice can not be made with certainty.     

A gentle process for the formation of Algols

This work is concerned with binary systems that we call ‘moderately close’. These are systems in which the primary (by which we mean the initially more massive star) fills its Roche lobe when it is on the giant branch with a deep convective envelope but before helium ignition (late case B). We find that if the mass ratio q(= M ₁/M ₂) < q _crit = 0.7 when the primary fills its Roche lobe positive feedback will lead to a rapid hydrodynamic phase of mass transfer which will probably lead to common envelope evolution and thence to either coalescence or possibly to a close binary in a planetary nebula. Although most Algols have probably filled their Roche lobes before evolving off the main-sequence we find that some could not have and are therefore ‘moderately close’. Since rapid overflow is unlikely to lead to an Algol-like system there must be some way of avoiding it. The most likely possibility is that the primary can lose sufficient mass to reduce q below q _crit before overflow begins. Ordinary mass loss rates are insufficient but evidence that enhanced mass loss does take place is provided by RS CVn systems that have inverted mass ratios but have not yet begun mass transfer. We postulate that the cause of enhanced mass loss lies in the heating of the corona by by magnetic fields maintained by an α — ω dynamo which is enhanced by tidal effects associated with corotation. In order to model the the effects of enhanced mass loss we ignore the details and adopt an empirical approach calibrating a simple formula with the RS CVn system Z Her. Using further empirical relations (deduced from detailed stellar models) that describe the evolution of red giants we have investigated the effect on a large number of systems of various initial mass ratios and periods. These are notable in that some systems can now enter a much gentler Algol-like overflow phase and others are prevented from transferring mass altogether. We have also investigated the effects of enhanced angular momentum loss induced by corotation of the wind in the strong magnetic fields and consider this in relation to observed period changes. We find that a typical ‘moderately close’ Algol-like system evolves through an RS CVn like system and then possibly a symbiotic state before becoming an Algol and then goes on through a red giant-white dwarf state which may become symbiotic before ending up as a double white dwarf system in either a close or wide orbit depending on how much mass is lost before the secondary fills its Roche lobe.     

The relation of Algols and W Serpentis stars

Evidence on the issues of whether the W Serpentis stars are a coherent class, and how they may interface with the Algol systems, is reviewed, with emphasis on the idea that they are semi-detached systems in the latter part of the rapid phase of mass transfer, with optically and geometrically thick disks of transferred gas around the (now) more massive star. We are interested in what will be seen when the gas clears away, and mainly examine the idea that it will be an Algol-type system. More particularly, consideration is given to centrifugally limited accretion as a mechanism to build up a substantial disk, and the presumed evolutionary sequence is from a W Ser to a rapidly rotating Algol to a normal Algol system. Systems such as V367 Cyg and RW Tau fit into this scheme only with difficulty. Because it is extremely difficult to measure the rotation of some W Ser (mass) primaries, it is natural to look at the rotation statistics of Algols to test this idea. The badly behaved light curves and spectroscopy of some Algols (eg. U Cep, RZ Sct) may be attributable to the double contact condition, and the ramifications of this possibility are discussed. If so, the rotation statistics of Algols should show two spikes, corresponding to the two special conditions into which a system should be driven by tidal braking and centrifugally limited spinup. Present rotation statistics do show these spikes. Algols should flip between these states fairly quickly, depending on the mass transfer rate. Thus, to the extent that the meager statistics can be accepted as meaningful, the new (fourth) morphological type of close binary (double contact) has attained demonstrable reality. The rotation statistics are presented in terms of a particular rotation parameter, R, which is zero for synchronism and unity for the centrifugal limit. Future work should develop rotation statistics to see if the rotational lobe-filling (R = 1) spike persists. It should also look into whether W Ser primaries are on the hydrogen burning main sequence, or in general what they are. We also need more light curves of W Ser type systems, high resolution line profiles for the (mass) primaries (with particular attention to the W Ser-Algol transition cases), and spectroscopy of low inclination W Serpentis systems, such as KX And.     

The relation of Algols and W Serpentis stars

Evidence on the issues of whether the W Serpentis stars are a coherent class, and how they may interface with the Algol systems, is reviewed, with emphasis on the idea that they are semi-detached systems in the latter part of the rapid phase of mass transfer, with optically and geometrically thick disks of transferred gas around the (now) more massive star. We are interested in what will be seen when the gas clears away, and mainly examine the idea that it will be an Algol-type system. More particularly, consideration is given to centrifugally limited accretion as a mechanism to build up a substantial disk, and the presumed evolutionary sequence is from a W Ser to a rapidly rotating Algol to a normal Algol system. Systems such as V367 Cyg and RW Tau fit into this scheme only with difficulty. Because it is extremely difficult to measure the rotation of some W Ser (mass) primaries, it is natural to look at the rotation statistics of Algols to test this idea. The badly behaved light curves and spectroscopy of some Algols (eg. U Cep, RZ Sct) may be attributable to the double contact condition, and the ramifications of this possibility are discussed. If so, the rotation statistics of Algols should show two spikes, corresponding to the two special conditions into which a system should be driven by tidal braking and centrifugally limited spinup. Present rotation statistics do show these spikes. Algols should flip between these states fairly quickly, depending on the mass transfer rate. Thus, to the extent that the meager statistics can be accepted as meaningful, the new (fourth) morphological type of close binary (double contact) has attained demonstrable reality. The rotation statistics are presented in terms of a particular rotation parameter, R, which is zero for synchronism and unity for the centrifugal limit. Future work should develop rotation statistics to see if the rotational lobe-filling (R = 1) spike persists. It should also look into whether W Ser primaries are on the hydrogen burning main sequence, or in general what they are. We also need more light curves of W Ser type systems, high resolution line profiles for the (mass) primaries (with particular attention to the W Ser-Algol transition cases), and spectroscopy of low inclination W Serpentis systems, such as KX And.     

Semidetached systems: Evolutionary viewpoints and observational constraints

The present knowledge on the evolution of semidetached systems is reviewed. Characteristics of observed systems are discussed and general properties tested by the behaviour of theoretical models. New models of mass accreting companion stars are computed. The accretion phase is divided into a fast and slow phase with an accretion rate depending on the initial mass of the mass losing star and on the initial mass ratio, assuming the systems are undergoing a case B of mass transfer. The results are compared with observed systems with masses of the gainers located within the theoretical range. Up to now no computations exist for the evolution of medium mass close binaries including overshooting of the convective core. However some of the influences of extended convective mixing on the interaction of close binaries are investigated. A larger probability for the occurrence of case A of mass exchange and a larger remnant mass at the end of the process are the most important results. Finally the investigation into the origin of individual systems (in mass, mass ratio and period) is discussed, showing that progress both in observations and in theoretical models result in a more detailed and more restricted determination of the initial parameters of the individual systems.Research associate, NFWO, Belgium.     

A gentle process for the formation of Algols

This work is concerned with binary systems that we call moderately close. These are systems in which the primary (by which we mean the initially more massive star) fills its Roche lobe when it is on the giant branch with a deep convective envelope but before helium ignition (late case B). We find that if the mass ratio q(= M ₁/M ₂) < q _crit = 0.7 when the primary fills its Roche lobe positive feedback will lead to a rapid hydrodynamic phase of mass transfer which will probably lead to common envelope evolution and thence to either coalescence or possibly to a close binary in a planetary nebula. Although most Algols have probably filled their Roche lobes before evolving off the main-sequence we find that some could not have and are therefore moderately close. Since rapid overflow is unlikely to lead to an Algol-like system there must be some way of avoiding it. The most likely possibility is that the primary can lose sufficient mass to reduce q below q _crit before overflow begins. Ordinary mass loss rates are insufficient but evidence that enhanced mass loss does take place is provided by RS CVn systems that have inverted mass ratios but have not yet begun mass transfer. We postulate that the cause of enhanced mass loss lies in the heating of the corona by by magnetic fields maintained by an — dynamo which is enhanced by tidal effects associated with corotation. In order to model the the effects of enhanced mass loss we ignore the details and adopt an empirical approach calibrating a simple formula with the RS CVn system Z Her. Using further empirical relations (deduced from detailed stellar models) that describe the evolution of red giants we have investigated the effect on a large number of systems of various initial mass ratios and periods. These are notable in that some systems can now enter a much gentler Algol-like overflow phase and others are prevented from transferring mass altogether. We have also investigated the effects of enhanced angular momentum loss induced by corotation of the wind in the strong magnetic fields and consider this in relation to observed period changes. We find that a typical moderately close Algol-like system evolves through an RS CVn like system and then possibly a symbiotic state before becoming an Algol and then goes on through a red giant-white dwarf state which may become symbiotic before ending up as a double white dwarf system in either a close or wide orbit depending on how much mass is lost before the secondary fills its Roche lobe.     

High signal-to-noise ratio — The spectroscopic key to Algol systems

The usefulness of high signal-to-noise-ratio spectra for both radial-velocity and abundance studies of Algol systems is emphasised. It is shown that division by a hot star is a worthwhile step in pursuit of this objective. A preliminary analysis of high signalto-noise-ratio, red and near-infrared, Reticon observations of R CMa shows that its primary has solar CNO abundances within the 0.3 dex observational error. The low-mass (0.17 m_⊙) secondary of this Algol system must have lost a large fraction of its original mass. Some of this material would have been extensively processed during the secondary's main-sequence lifetime and would therefore have had a highly non-solar CNO-abundance distribution. The lack of serious contamination of the primary's abundances is consistent with most, but not all, plausible mass-transfer scenarios.     

Reverse Algols

An Algol is a binary system having a semidetached configuration where the less massive component is in contact with the critical equipotential surface. A reverse Algol is a binary system having a semidetached configuration where the more massive component is in contact with the critical equipotential surface. In 1985, Leung suggested 5 reverse Algol systems at the Beijing Colloquium. Two more such systems have been discovered recently. The spectral types of these systems range from early B to mid G. There is also a wide spread in mass ratio among these systems. There appear to be two types of reverse Algols, hot and cool systems. The hot systems have their more massive components as the hotter stars and the cool systems their more massive components as the cooler stars. The mass-radius relation of the reverse Algols is very similar to that of the contact and near-contact systems. It is believed that reverse Algols represent the pre-mass-reversal semidetached phase of close binary evolution. Since selection effects apply to both the regular Algols and reversed Algols in a similar manner, the evolutionary time scale between them would be simply the ratio of the number of confirmed systems of these two types of Algols.     

Evolution into contact of the low-mass close binary systems

We investigated the effect of mass accretion on the secondary components in close binomy systems (M _total ≤ 2.5 M _⊙ M _2,0 ≤ 0.75 M _⊙) exchanging mass in the case A. The evolution of the low-mass close binary systems (M _total ≤ 2.5 M _⊙) exchanging the mass in the case A depends on the three main factors:

-the initial mass ratio (q ₀ = M _2,0/M _1,0), which determines the rate of mass transfer between components;

-the inital mass of the secondary component (M _2,0) and

-the effectiveness of the heating of the photosphere of the secondary component, by infalling matter.

The second factor allows to divide all systems into two essentially different groups:

1. systems in which the secondary component is a star with a radiative envelope, or with a thin convection zone in the uppermost layers;
2. and systems in which secondary component has a thick convective envelope or is fully convective.

The systems from the first group evolve into contact in a characteristic time scale 10⁵ – 10⁷ years, and reach contact after transfering of 0.03 – 0.3 M _⊙. The mass exchange proceeds only in a thermal time scale. For the systems from the group b the effectiveness of the heating of the stellar surface is the most important. In the case when the entropy of the newly accreted matter is the same as the surface entropy of the secondary, a convective star should shrink upon accretion. Then contact binaries are not formed. In the case when the entropy of the infalling matter is greater then that on the surface, the reaction of the secondary is different. The radius of the secondary component grows rapidly in response to accretion, and the systems reaches contact after the 10³ – 3 10⁶ years, and after transfer of 0.002 – 0.2. M _⊙. The reaction of the secondary is determined by the formation of the temperature inversion layer below the stellar surface. Full references in: Sarna, M.J. and Fedorova, A.V. (1988) “Evolutionary status of W UMa-type Binaries — Evolution into contact”, Astron. Astrophys., in press.     

Who is who in Algol-land ?- Part I -

We computed the evolution through case A mass transfer for 8 systems with mass of the primary equal to 3 and 5 M₀, mass ratios 0.7 and 0.9, and different periods. To this we added similar results from Packet (1988) for M_i = 9 M₀, q_i = 0.6, P_i = 1.62 d.During the mass transfer two competing mechanisms in the gainer decide on the evolution of the system: the rejuvenation of this star as the increasing convective core mixes fresh hydrogen into the inner regions, and the acceleration of nuclear burning, responding to the increasing mass.In all the cases the net result is a faster decrease of the central hydrogen content compared to the mass losing star. The secondary fills its own critical Roche lobe and reversed mass transfer starts.From our results and those of Nakamura and Nakamura (1984), we find that reversed mass transfer occurs after core hydrogen burning of the secondary (case A₁B₂) approximately for periods larger than 1 d (M_1i = 3 M₀) to 2 d (M_1i = 13.4 M₀). For smaller periods this happens before the gainer ends its core hydrogen burning (case A₁A₂).     

The effects of magnetic fields on period changes,mass transfer and evolution of algol binaries

Variations in the magnetic pressure and flux blocking by starspots during the magnetic cycle of the cool semidetached component of an Algol binary may cause cyclic changes in the quadrupole moment and moment of inertia of the star which can cause alternate period changes. Since several different processes and timescales are involved, the orbital period changes may not correlate strongly with the indicators of magnetic activity. The structural changes in the semidetached component can also modulate the mass transfer rate. Sub-Keplerian velocities, supersonic turbulence, and high temperature regions in circumstellar material around the accreting star may all be a consequence of magnetic fields embedded in the flow. Models for the evolution of Algols which include the effects of angular momentum loss (AML) through a magnetized wind may have underestimated the AML rate by basing it on results from main sequence stars. Evolved stars appear to have higher AML rates, and there may be additional AML in a wind from the accretion disk.     

The effects of magnetic fields on period changes, mass transfer and evolution of algol binaries

Variations in the magnetic pressure and flux blocking by starspots during the magnetic cycle of the cool semidetached component of an Algol binary may cause cyclic changes in the quadrupole moment and moment of inertia of the star which can cause alternate period changes. Since several different processes and timescales are involved, the orbital period changes may not correlate strongly with the indicators of magnetic activity. The structural changes in the semidetached component can also modulate the mass transfer rate. Sub-Keplerian velocities, supersonic turbulence, and high temperature regions in circumstellar material around the accreting star may all be a consequence of magnetic fields embedded in the flow. Models for the evolution of Algols which include the effects of angular momentum loss (AML) through a magnetized wind may have underestimated the AML rate by basing it on results from main sequence stars. Evolved stars appear to have higher AML rates, and there may be additional AML in a wind from the accretion disk.     

Two centuries of study of Algol systems

The periodicity of the light variation of Algol, discovered just over 200 years ago, may be regarded as the beginning of the study of eclipsing binary systems, especially those of the Algol type. Such studies, however, gained no real momentum until Vogel, 100 years ago, demonstrated by spectroscopy that the binary hypothesis of Algol's light changes is, in its essentials, correct. Three elements were needed to give us our modern notions of evolution by mass-transfer, namely: (i) results of combined analysis of light-curves and velocity-curves, (ii) evidence of circumstellar matter within binary systems and (iii) the notion that at least one component of an Algol system was near the limit of dynamical stability. All three entered the literature within about a decade, approximately halfway through the second century of eclipsing-binary studies; but it is the computational and instrumental developments of the last 25 years that have made real progress possible. We still lack commensurate theoretical developments, and the whole question of the contribution of Algol systems to the development of the Galaxy has barely been considered.     

The evolution of moderately close and moderately wide binaries

We discuss evolutionary processes in binaries where the primary becomes a red giant with a deep convective envelope before it fills its Roche lobe. Such binaries (late Case B or late Case C, if they evolve conservatively) ought to suffer drastic mass transfer, on a hydrodynamic timescale. In some circumstances this may lead to a common envelope, spiral-in, and finally either a very short-period binary or coalescence. But there appear to be other circumstances in which the outcome is an ordinary Algol, or a wide binary with a white dwarf companion as in Barium stars and some symbiotics. We try to demonstrate that stellar-wind mass loss, enhanced one or two orders of magnitude by tidal interaction with a companion, can vitally affect the approach to RLOF, and indeed may prevent RLOF in binaries with periods over 1000 d. Such mass loss is probably accompanied by angular momentum loss, by magnetic braking combined with tidal friction. The result is that it will not be easy to predict definitively the outcome of evolution in a given zero-age binary.     

The evolution of moderately close and moderately wide binaries

We discuss evolutionary processes in binaries where the primary becomes a red giant with a deep convective envelope before it fills its Roche lobe. Such binaries (late Case B or late Case C, if they evolve conservatively) ought to suffer drastic mass transfer, on a hydrodynamic timescale. In some circumstances this may lead to a common envelope, spiral-in, and finally either a very short-period binary or coalescence. But there appear to be other circumstances in which the outcome is an ordinary Algol, or a wide binary with a white dwarf companion as in Barium stars and some symbiotics. We try to demonstrate that stellar-wind mass loss, enhanced one or two orders of magnitude by tidal interaction with a companion, can vitally affect the approach to RLOF, and indeed may prevent RLOF in binaries with periods over 1000 d. Such mass loss is probably accompanied by angular momentum loss, by magnetic braking combined with tidal friction. The result is that it will not be easy to predict definitively the outcome of evolution in a given zero-age binary.