arXiv:astro-ph/9708095v2 9 Dec 1997 rpittpstuigL using typeset Preprint 2021 30, July version Draft atrcs,a ffiin antceeg rnpr sre- is transport energy magnetic efficient the massive an In a (Paczy´nski 1997). case, a system or binary either latter 1993) close be a (Woosley al. can in supernova” et which member Ib star Sahu type massive 1997a,b; a “failed grav- the Vietri of – “hypernovae” collapse 1995; the itational (2) and 1997) al. Waxman al. 1997; et Paczy´nski et M´esz´aros, 1989; Narayan Lipunov & 1992; al. Rees 1992; et 1992; Eichler radia- 1991, gravitational 1984; of 1986, black al. loss and et energy (Blinnikov star the tion neutron to (1) or due fireballs: binaries star the hole neutron of double re- sources of energy mechanisms mergers the proposed for Two attractive M´esz´aros,main Vietri & 1997). 1992; Rees Waxman 1978; 1997a,b; Rees & Cavallo (e.g. fafwhnrd,rlaigeeg fteodro 10 of order the of factor energy Lorentz releasing hundreds, bulk few a a popular rel- with of a currently blastwave – The “fireball” theoreti- expanding impulsive so-called GRBs. the ativistic the of is re-consider GRBs origin for to the model authors of models of places cal stim- number which have distance, 1997), a cosmological at al. ulated burst the et of identifi- (Metzger after- source 1997; the optical the 970508 and the GRB al. with 1997) of et associated glow al. Sahu line et absorption 1997; Guarnieri of 1997; wave-cation al. al. et optical/radio/X-ray et Paradijs at Costa van 970508 (e.g. and lengths 970228 GRB h eetdtcin ftetasetcutrat of counterparts transient the of detections recent The 1 2 3 ejn srnmclOsraoy hns cdm fScie of Academy Chinese Observatory, Astronomical Beijing eateto hsc,teCieeUiest fHn Kong, Hong of University Chinese the Physics, of Department eateto hsc,Uiest fAioa usn Z85 AZ Tucson, Arizona, of University Physics, of Department asv -a iaysse ossigo eto tradaty a and star neutron a of of flow accretion-induced mass consisting significant the system a to because binary GRB X-ray of massive source a energy the attributing of eas ftennnfriyo h tla atrsronigth surrounding matter amou stellar ( fraction moderate the small a of a with nonuniformity fireball the neutr “dirty” of the a because before scenario, AICNS this the In when to companion. phase lead eventually spiral-in may the which during companion, primarily and overflow Roche-lobe the bu e a ihnavlm oredshift to volume t a that within estimate day we expa per slow galaxies, relatively 2 for a about model with non-evolutionary star a companion the Assuming of matter ejecting the eto trwl nvtbyclas noabakhl fisms exceed mass its if hole black a into mass a collapse of inevitably collapse will the of star neutron scenario two neutron hypernova of a (2)the merger and (1)the binary include indicat hole as models distances popular cosmological currently at placed The are events the if (GRBs) eesn oa idn rvttoa nryof energy gravitational binding total a releasing xlnto o h rgno Rsadteeoedsre ob fu be stella to of deserves headings: result therefore Subject a and as GRBs GRBs. scenario, of of AICNS origin study the the that for appears explanation It rate. GRB H OLPEO ETO TR NHG-ASBNRE STEEN THE AS BINARIES HIGH-MASS IN STARS NEUTRON OF COLLAPSE THE h nrysuc a eandt etegetmseyi unders in mystery great the be to remained has source energy The A 1. oQin Bo T E tl mltajv 04/03/99 v. emulateapj style X INTRODUCTION ∼ am-as uss—sas iais ls tr:nurn—s — neutron stars: — close binaries: stars: — bursts gamma-rays: 1 , 0 2 . in-igWu Xiang-Ping , % fteeeg ssffiin ocet h bevdGB.I add In GRBs. observed the create to sufficient is energy the of 1%) ∼ O H AM-A BURSTS GAMMA-RAY THE FOR 10 − 1 igCugChu Ming-Chung , 3 rf eso uy3,2021 30, July version Draft –10 51 − 4 z ABSTRACT M erg cs ejn 000 China 100080, Beijing nces, o nΩ an for 1 = 721 ⊙ htn .. ogKn,China Kong, Hong N.T., Shatin, ∼ yr 1 10 − 54 1 o 97 a ta.19) fanurnsa collapses release star very will neutron a star in a energy neutron If binding disrupted gravitational Nussi- the 1992). its & hole, catastrophically Dar, black al. suggested a (Goodman, et into once GRBs Dar was of 1987; source latter nov possible The 1990 a al. et col- as therein). (Canal accretion-induced stars references evolu- neutron the into and stellar to dwarfs of white similar of quite extrapolation lapse is neutron natural which of a tion, collapse be accretion-induced should of stars scenario a Such ftenurnsa oece h aiu value maximum the exceed to mass star gravitating neutron to the the companion lead binary eventually of massive X-ray may the star high-mass by neutron a the transferred in mass appear the can where case likely most urdt xld h tla neoe eesn nenergy an releasing envelope, stellar of the explode to quired aini iaysse?We h aso neutron a of mass the com- When to its up example, system? grows for star binary from, a star in neutron panion a onto flow mass l eto tr ihattlms of dou- mass of total binary ex- a a The with of stars hole? merger neutron black the ble a be into can collapse circumstance treme star neutron the does limit the than less mass a having stable, M relatively is holes. black formation or the stars to neutron lead massive models of both processes, physical ent a etaserdot h eto trthrough star neutron the onto transferred be may r,w xlr eieprclytepossibility the semi-empirically explore we erg, max ti omnyblee hta sltdnurnstar neutron isolated an that believed commonly is It ∼ 2 iZiFang Li-Zhi , 0 10 nvre ossetwt h reported the with consistent universe, 1 = ≈ 54 3 r.Atog h xlsosrsl rmdiffer- from result explosions the Although erg. M xlso nietecmain and companion, the inside explosion e olpeo eto tr(IN)in (AICNS) star neutron a of collapse db ubro eetobservations. recent of number a by ed te netgtdi h theoretical the in investigated rther ⊙ v ebri ls iay Since binary. close a in member ive ebrhaeo h IN vnsis events AICNS the of birthrate he so aemyata h afterglow. the as act may rate nsion to emn sntrlyexpected naturally is beaming of nt tr ranurnsa n black a and star neutron a or stars vlto,mypoieanatural a provide may evolution, r eOBcmain hshappens This companion. O/B pe nsa egswt h oeo the of core the with merges star on htwudhpe fteei stable a is there if happen would What . adn ftegmarybursts gamma-ray the of tanding tpugsit h neoeo the of envelope the into plunges it M 3 max n igYoHu Jing-Yao and h limit the s eas ftentms deposition, mass net the of because as supergiants tars: RYSOURCE ERGY to,tebl of bulk the ition, M max 1 M > ≈ max 3 M ⊙ hl the while , , M max . 2 short time, leading to an explosion with energy of ∼ 1054 good agreement with the observed GRB intensity distri- erg, namely, the “fireball”. Are the AICNS in high-mass bution, which shows a standard candle peak luminosity of binaries able to act as the energy sources for the GRBs ? ∼ 1051 erg/s. The major difference between the hypernova model and It is estimated that there are Nx ∼ 50 massive X-ray bi- the AICNS model is the formation of black holes through naries in the Galaxy (Meurs & van den Heuvel 1989; Bhat- the collapse of neutron stars. According to the hyper- tacharya & van den Heuvel 1991) and a significant fraction nova mechanism, the hot and rapidly spinning neutron of them are the neutron star-O/B star systems. Because star cools off by neutrino emission to become a stellar the AICNS event rate is closely relevant to the lifetime black hole (Woosley 1993; Paczy´nski 1997), whereas in the of the O/B stars, which turns out to be t ≈ 5 × 106 yr AICNS scenario the black hole forms because the mass of for a typical 25M⊙ companion, we can then estimate the ˙ −5 −1 neutron star increases to the point of dynamical instability GRB birthrate roughly by NGalaxy ∼ Nx/t ≈ 1×10 LG −1 10 (Mmax). The similarity between the merging model and yr , where LG ≈ 3.6 × 10 L⊙ is the bolometric luminos- the AICNS model is that the collapse of a neutron star is ity of the Galaxy. This is comparable to the birthrates of caused by the external infalling matter. In a sense, the double neutron star binaries and black hole-neutron star AICNS as the origin of GRB is somewhat a combination binaries in the Galaxy (Narayan et al. 1991). Assuming of the merging model and the hypernova model, but seems a non-evolutionary scenario for galaxies and adopting the to be more natural according to our knowledge of stellar Schechter luminosity function with φ∗ = 1.56 × 10−2h3 −3 ∗ 9 −2 evolution. At least, the AICNS is a possible scenario that Mpc , α = −1.1 and L = 7.1 × 10 h L⊙ (Fukugita shouldn’t be overlooked in the study of the energy source & Turner 1991 and references therein), we find the total for GRBs. Since the emission mechanism of the GRBs re- luminosity of the universe within redshift z = 1 for a cos- 18 −2 mains the same as that in the fireball model, we will discuss mological model of Ω0 =1tobe Ltotal =2.5×10 h L⊙, the GRB rate and other properties of the AICNS model in where h is the Hubble constant in unit of 100 km/s/Mpc. this letter. As in other proposed models for GRBs, only a Finally, the expected GRB event rate within a volume to semi-empirical approach is applicable to such an analysis −1 z = 1 is N˙ GRB = N˙ GalaxyLtotal ∼ 700 yr , i.e., about at the present stage. two events per day. Such a rate, though rather uncertain, is consistent with that recorded by the current detectors 2. THE AICNS MODEL (e.g., Meegan et al. 1996). We confine ourselves to high-mass X-ray binaries con- 3. FURTHER REMARKS sisting of a neutron stars and a type O or B star compan- ion in order to ensure that the material transferred by the At least ∼ M⊙ mass of its companion star should be ac- companion to the neutron star enables the neutron star creted onto the neutron star during the spiral-in phase in to reach the point of dynamical instability (Mmax). Al- order to trigger the AICNS. This includes the final merger though a neutron star can capture a significant fraction of the neutron star with the core of the massive companion of the stellar wind from its companion with a mass trans- star if the AICNS does not take place before it reaches the −6 −10 −1 fer rate M˙ = 10 –10 M⊙ yr on the stellar evolution core. It appears that an average net mass accretion rate of −3 −4 −1 time scale, giving rise to the observed X-ray luminosity, 10 –10 M⊙ yr is required for the neutron star pro- 3 4 such a mass accretion rate is insufficient to disrupt the vided that the spiral-in takes about 10 –10 years (Meurs neutron star within the lifetime of the companion (∼ 106 & van den Heuvel 1989). A simple computation based on yr). A dramatic mass transfer occurs once the compan- the powder approximation (Lipunov 1992) shows that such ion expands into a giant and thereby reaches its Roche a mass accretion rate is indeed possible for a neutron star ∼ lobe. In particular, the mass of the neutron star MN may with mass M M⊙ moving with a velocity v through ˙ 2 3 rapidly grow up to Mmax while it plunges into the envelope the medium of mass density ρ: M ∼ π(2GM⊙) ρ/v ∼ −3 4 −3 −3 of its companion. Eventually, the AICNS may take place 5 × 10 (v/10 km/s) (ρ/10 ρ⊙), where the average before or after the neutron star is engulfed by its com- medium density is estimated using a giant star with mass panion, depending on when the condition MN >Mmax is 30M⊙ and radius 30R⊙, the velocity v corresponds ap- reached. Yet, the AICNS will not take place if the accreted proximately to the orbital velocity of the neutron star dur- −3 mass of a neutron star during the spiral-in to the center ing the spiral-in, and ρ⊙ = 1.4 g cm is the mean mass of its companion does not meet MN >Mmax, which then density of the Sun. Apparently, our required mass accre- −8 −1 results in the formation of a massive neutron star with tion rate exceeds the Eddington limit of 1 × 10 M⊙yr 1.4M⊙ Schwarzschild radius. Taking Mmax = models the neutron star may have an accretion rate of −3 −1 2.7M⊙ and RN = 13.5 km (Kippenhahn & Weigert 1990), M˙ ≥ 10 M⊙yr . Chevalier (1993) showed that a strong we obtain E ≈ 1 × 1054 erg. This naturally provides the accretion is possible for neutron star spiral-in through the energy needed for the explosion and hence for the genera- massive envelope because of neutrino emission, which can tion of the fireball (see, for example, Paczy´nski 1997). If a bring an initial 1.4M⊙ neutron star to a massive object of 51 small fraction of this energy, say ∼ 10 erg, is converted > 2M⊙ so that a black hole may eventually form. into gamma-ray emission, the AICNS scenario will be in Although these estimates are encouraging, the evolu- 3 tion of high-mass X-ray binaries is complicated and not gas envelope of the companion star, where matter ejec- well understood. Terman, Taam, & Hernquist (1995) have tion following the explosion is non-spherical if the AICNS demonstrated that for a wide range of orbital periods and does not occur at the center of the companion. Conse- companion masses, the spiral-in is rapid and the common quently, in contrast to the hypernova model, here a non- envelope can be ejected by the interaction of the neutron spherical expansion appears to be a natural result, which star with its red supergiant companion, resulting in a neu- may eventually accelerate a small fraction of matter to a tron star-helium core binary, not a black hole. However, very large Lorentz factor, creating the GRBs. Since the for a sufficiently short orbital period of P < Pcrit, where bulk of the ejecting matter in the companion star moves Pcrit is the critical orbital period of the progenitor binary slowly, the afterglow may show up for a relatively long time ranging from 0.2 yr to 2 yr for companion masses 12M⊙- after the observation of the GRB. It appears that the two 24M⊙, Terman et al. (1995) showed that the system would arguments raised explicitly by Vietri (1997b) can be easily eventually merge to form a red supergiant with a neutron understood in the framework of the AICNS scenario: (1) star core, namely, a massive Thorne-Zytkow Object (TZO) A nonuniform external medium surrounding the explosion (Thorne & Zytkow 1977). is needed to explain the existence of a delay between the Whether AICNS will eventually occur in a TZO is un- optical luminosity maximum and the GRB; and (2) the clear. The evolution of massive TZOs was addressed by energy source powering the GRB should be the same as Podsiadlowski, Cannon, & Rees (1995), who found that that of the afterglow. stellar-mass black holes are likely to form as one of the three endpoints of TZOs. A similar conclusion was reached 4. CONCLUSIONS by Fryer, Benz, & Herant (1996), who argued, based on In a high-mass X-ray binary system, a significant mass a numerical study of rapid neutron star accretion, that accretion onto the neutron star may take place in the later TZOs may lead to the super-Eddington accretion onto evolutionary phase of the O/B companion star. If the mass neutron stars and the formation of black holes. Podsi- of a neutron star exceeds the limit Mmax ≈ 3M⊙, the neu- adlowski et al. (1995) also estimated a TZO birthrate of tron star will inevitably collapse into a black hole. Such ≥ −4 −1 10 yr in the Galaxy, which is not significantly dif- an AICNS scenario can be regarded as the natural energy ferent from that required for GRBs if we notice the fact source for GRB, releasing a total binding gravitational en- that a number of TZOs may survive during the spiral-in ergy of ∼ 1054 erg. Because the explosion is non-spherical phase and will not give rise to AICNS (Bhattacharya & van inside the companion star, a moderate amount of beaming den Heuvel 1991). However, Podsiadlowski et al. (1995) is naturally expected and a small fraction (∼ 0.1%) of the pointed out that the rapid accretion model of Chevalier energy will be sufficient to account for the GRB. In par- (1993) assumes spherical symmetry, which is unlikely, and ticular, the bulk of the ejecting matter of the companion a more realistic calculation might rule out AICNS in TZO. star may give rise to the afterglow. It is estimated that Taking these arguments as a whole, we feel that much the AICNS event rate within redshift z = 1 is about 2 per work will be needed to understand the evolutionary sce- day, in accord with the currently observed rate of GRBs. nario of high-mass X-ray binaries and to improve our naive As compared with other popular models for the energy model of AICNS proposed in the present letter. sources of GRBs, namely, the merger of double neutron The fate of a neutron star as a result of collapse is the stars or a neutron star and a black hole binary and the formation of a stellar black hole. The binary system may hypernovae, the AICNS in a massive binary appears to still survive if the AICNS occurs before it merges with the be more reasonable according to the stellar evolutionary core of its companion and if the newly born black hole scenario, and accounts naturally for a number of observed and the core (probably a newly born neutron star) remain features of GRBs. It is pointed out that the AICNS model, gravitationally bound. It is also possible that an isolated though very schematic at the present stage, may deserve black hole is left if the explosion expels all the substance to be considered seriously in the theoretical study of the from the companion. A birthrate of ∼ 10−5 yr−1 in the 5 origin of the GRBs. In particular, one needs to under- Galaxy for the AICNS would result in about 10 stellar stand the detailed mechanism of how a significant amount black holes, including the black hole-neutron star bina- of matter is accreted onto the surface of a neutron star. ries. This number is comparable to the estimate of the population of double neutron star and black hole-neutron star binaries in the Galaxy by Narayan et al. (1991). We thank an anonymous referee for valuable comments As in the hypernova model (Paczy´nski 1997), the and suggestions. This work was supported by the National AICNS in a massive binary will lead to a “dirty” fireball Science Foundation of China, the RGC Earmarked Grant since the explosion is most likely to take place inside the CUHK4189/97P and a CUHK direct grant 702/1.

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