arXiv:astro-ph/9904105v1 8 Apr 1999 a asdfiieyblw0 star below this definitely that mass shows a secondary, has the ef- observed of The the temperature d. with fective together 9.84 (1998), of Kuulkers Casares, & by period Charles, found a information X–2 has spectroscopic Cygnus which precise binary rather 1999), X–ray Ritter, low–mass on & work the (King recent CE by of relief whether evolution sharp the into question thrown open is binary. question given an progenitor. This any giant general in red occurs in ra- evolution dwarf’s the is than white it smaller accreting However, far the is of separation dius variables, binary cataclysmic the as required which such com- probably in binaries binary of is formation the evolution the CE not, for if coalesce. separation; may en- common smaller ponents the a unbind from If with to emerge enough will velope drastically. binary is the energy orbit envelope, orbital binary the of of the release drag resulting shrink frictional the a can The at envelope mass system. envelope this the an binary component of entire expel formation accreting the to the engulfing avoid or the to accept rate is, to high That sufficiently either unable evo- be rates. may (CE) such common–envelope at of acute possibility lution particularly the & is ac- of Kafka problem of limit because this 1973; context Eddington systems, Sunyaev, the binary its & In creting than (Shakura higher that 1979). history far M´esz´aros, object Begelman, long rates compact 1976; a a at has to mass happens fed what is of question The re 150L order httehlu oei o–eeeae e Kippenhahn see non–degenerate; ‘massive’ en- is and stellar core convective, helium the than the that rather that means radiative ‘early’ is has across velope star expanding gap: mass–losing evolu- is Hertzsprung the B and the that Case hydrogen–burning, means massive core B’ early finished ‘Case of that Here is product one a tion. viable is only the X–2 that Cygnus show and explanations ble rpittpstuigL using typeset Preprint 2018 13, August version Draft 1 2 3 nttt o hoeia hsc,Uiest fCaliforn of University Physics, Theoretical for Institute srnm ru,Uiest fLietr ecse E 7R LE1 Leicester Leicester, of University Group, Astronomy IA nvriyo ooao ole,C 00-40 U.S. 80309-0440, CO Boulder, Colorado, of University JILA, rnfr aso hra iecl oanurnsa rbakh black wh or in star neutron binary a any values to lo reach timescale in mass thermal may avoided which a probably from on mas mass radius is the transfers maximum evolution all the almost common–envelope estimate which We that in disc. dom (1999), radiation–pressure accretion Begelman are the & cases Blandford such by in proposed flows commo accretion undergoing the without that rates transfer mass super–Eddington ujc headings: radiative Subject are envelopes state. their this that in provided gap, Hertzsprung the ⊙ eetwr nCgu – togysget htneutron–sta that suggests strongly X–2 Cygnus on work Recent ig&Rte 19)cnie eea possi- several consider (1999) Ritter & King . AITVL–RVNOTLW N VIAC FCOMMON–ENVE OF AVOIDANCE AND OUTFLOWS RADIATIVELY–DRIVEN A 1. T E tl mltajv 04/03/99 v. emulateapj style X INTRODUCTION ujc edns crto,aceindss—bnre:coe—X- — close binaries: — discs accretion accretion, headings: Subject ∼ . 10 7M − ⊙ 3 n e uioiyof luminosity a yet and nrwR King R. Andrew M ⊙ yr VLTO NCOEBINARIES CLOSE IN EVOLUTION − 1 hscnlso rbbyapisas odnr xadn across expanding donors to also applies probably conclusion This . rf eso uut1,2018 13, August version Draft aa at abr,C 30-00 U.S.A. 93106-4030, CA Barbara, Santa at ia 1 , 2 ABSTRACT ,U.K. H, A. n icelC Begelman C. Mitchell and 1 iecl ( timescale egr,16.I ynsX2a ntal oemassive more initially an X–2 Cygnus ( In 1967. Weigert, & tri vdnl bet jc setal l ftematter the of all neutron essentially the eject that Thus to is ( able mass. picture for evidently much this available is so of star energy ejected feature means orbital have inescapable little to period an mechanism too orbital cannot CE far long evolution the was X–2’s CE there Cyg that as periods. occurred, orbital bi- have pulsar short millisecond with dwarf several white naries in large the found for X– masses explanation Cyg natural companion of a as properties well observed as present 2, the to fit satisfying eeae yifl ont radius to super– luminosity down highly the infall mat- medium, by a of electron–scattering generated at fate an ac- dissipative object of the spherically–symmetric, cretion compact to In a rate. as Eddington onto views dumped two ter essentially are There rates igo ii taradius a at limit dington in uheplincnocrwtottesse going system condi- the what envelope. without under common occur determine a to can into is expulsion such paper this tions of aim The y – srte ls otecnnclvleo 1 of value canonical the to close rather is X–2 Cyg adcno vroeteavcino htn nad If inward. photons out- of diffusion advection the photon overcome which cannot also below ward is This radius”, “trapping 1979). the (Begelman, radius Schwarzschild the is astase aefo h opno tri u case), our in star companion the M from rate transfer mass where M ∼ > ˙ Edd 2 2 i − ≃ ∼ > = M 3M ˙ 3 2. 10 L tr . S3 a ea xml fasystem a of example an be may SS433 . 5M Edd –neoeeouin esgethere suggest We evolution. n–envelope l,ee huhtems rnfrrate transfer mass the though even ole, ntdvrin fte‘DO’picture ‘ADIOS’ the of versions inated ⊙ ∼ − XUSO YRDAINPRESSURE RADIATION BY EXPULSION stems nalrt tlrerdu ie the (i.e. radius large at rate infall mass the is rbakhl iaissriehighly survive binaries hole black or r 6 rnfre oi thgl super–Eddington highly at it to transferred ) 10 M ⊙ /c eodr rnfre aso thermal a on mass transferred secondary ) ⊙ 6 2 r otenurnsa.Ti dagvsa gives idea This star. neutron the to yr) steEdntnaceinrt,and rate, accretion Eddington the is yr seple rmlrerdiin radii large from expelled is s R si ieyt cu,adshow and occur, to likely is ss − 1 ex 1 , c ansqec donor main–sequence a ich 3 ned h eto trms in mass star neutron the Indeed, . ∼ M M ˙ ˙ Edd tr as stars rays: R R LOPE S , ilrahteEd- the reach will . 4M R (1) ⊙ S . 2 the compact object is a black hole, the radiation generated where m1 = M1/M⊙ is the mass of the compact accretor in excess of the Eddington limit can thus be swept into (black hole or neutron star). the black hole, and lost. If the compact object is a neu- CE evolution will be avoided if Rex is smaller than the tron star, however, radiation pressure building up near the accretor’s Roche lobe radius R1. If the accretor is the less star’s surface must resist inflow in excess of M˙ Edd, caus- massive star (as will generally hold in cases of interest) we ing the stalled envelope to grow outward. This situation can use standard formulae to write would lead to the formation of a common envelope. 1/3 2/3 The outcome may be very different if the accretion flow r1 =1.9m1 Pd , (4) has even a small amount of angular momentum. Shakura & Sunyaev (1973) suggested that super–Eddington flow in where r1 = R1/R⊙ and Pd is the orbital period measured an accretion disk would lead to the formation of a strong in days. Combining with equation (2) gives wind perpendicular to the disk surface, which could carry away most of the mass. Such a model (an “Adiabatic −3 1/3 2/3 −1 M˙ < 10 m P M⊙ yr . (5) Inflow-Outflow Solution,”, or ADIOS) was elaborated by tr ∼ 1 d Blandford & Begelman (1999: hereafter BB99), who con- sidered radiatively inefficient accretion flows in general. This form of the limit can be compared directly with ob- BB99 recalled that viscous transfer of angular momentum servation if we have estimates of the transfer rate, orbital also entails the transfer of energy outward. If the disk period and the accretor mass. For more systematic study were unable to radiate efficiently (as would be the case at it is useful to replace the dependence on the accretor’s Roche lobe by that on its companion’s. Thus, since the R < Rtr), the energy deposited in the material well away from the inner boundary would unbind it, leading to the mass transfer rate is specified by properties of the com- creation of powerful wind. BB99 described a family of panion star, which is assumed to fill its Roche lobe radius self-similar models in which the mass inflow rate decreases R2, we eliminate R1 from the condition Rex ∼< R1 by using inward as M˙ ∝ rn with 0
∼ 0.8 ∼ 3 r2 m2 , l2 m2. (10) Inserting in (9) and (8) we find
˙ ∼ × −8 2.8 Mtr 3 10 m2 , (11) so comparing with (7) we require
0.18 m2 ∼< 53m1 (12) and thus (from 11)
˙ ∼ × −3 0.51 −1 Mtr, max 2 10 m1 M⊙ yr . (13) Hence we expect CE evolution to be avoided in thermal– timescale mass transfer from a main–sequence star, or from a Hertzsprung gap star, provided that it has a radia- tive envelope. This is in agreement with the assumption of no CE evolution in Cyg X–2 made by King & Ritter (1999), where the initial donor mass was about 3.5M⊙.
4. CONCLUSIONS We have derived a general criterion for the avoidance of common–envelope evolution in a binary in which the ac- cretor is a neutron star or a black hole. This shows that thermal–timescale mass transfer from a main–sequence star is unlikely to lead to CE evolution, as is mass transfer from a Hertzsprung gap star, provided that the envelope is radiative. The first possibility allows the early massive Case B evolution inferred by King & Ritter (1999) for the progenitor of Cyg X–2. SS433 may be an example of the second possibility, with a fairly massive donor star. We will discuss this possibility in detail in a future paper. The considerations of this paper suggest that common– envelope evolution with a neutron–star or black–hole ac- cretor generally requires an evolved donor with a deep convective envelope. This represents a slight restriction on some of the routes invoked in the possible formation of Thorne–Zytkow˙ objects.
This research was carried out at the Institute for Theoret- ical Physics and supported in part by the National Science Foundation under Grant No. PHY94–07194. ARK grate- fully acknowledges support by the UK Particle Physics and Astronomy Research Council through a Senior Fellow- ship. MCB acknowledges support from NSF grant AST95– 29170 and a Guggenheim Fellowship. 4
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